Applied Science, Faculty of
Engineering, School of (Okanagan)
DSpace
UBCO
Loi, Wei Sen
Doctor of Philosophy - PhD
University of British Columbia
The objective of this thesis is to explore the integration of light simulation techniques from computational nanophotonics, computer graphics, and daylighting to model the visual appearance and optical behavior of nanoengineered structures in real-world settings. This thesis is inspired by the desire to produce high-fidelity predictions of the optical properties of nanostructured materials across multiple size scales, invoking both wave optics and geometric optics where appropriate. Bridging different descriptions of light behavior requires careful consideration of scaling strategies, synergizing computation techniques from different research areas, and finding a right balance between computational efficiency and accuracy. First, an efficient multi-scale computation visualization approach is developed by combining electrodynamic simulations with physically-based rendering to produce photorealistic predictions of the appearance of thin metallic films and multilayers. Next, this computation approach is extended by augmenting its wavelength and spectral resolution in order to accurately describe the iridescence of patterned plasmonic nanostructures. One of the interesting aspects of this work is that has enabled, for the first time, exploration of the influence of both microscopic and nanoscopic roughness on the visual appearance of nanostructured media. Finally, the elements of the aforementioned multi-scale computation approach are integrated with climate-based daylight modeling to investigate the daylighting and glare control performance of window coatings and daylight redirecting structures consisting of semi-transparent thin metallic films. This thesis presents a robust computational strategy to enable modelling of the visual appearance and optical properties of nanostructured materials under application-specific settings. The modelling introduced by this work believes might accelerate the development and deployment cycles of nanomaterials in real-world applications.
MULTISCALE COMPUTATIONALVISUALIZATION ANDMODELLING OF OPTICALNANOMATERIALS AND THEIRAPPLICATIONbyWei Sen LoiB.Sc. Mathematics, Universiti Teknologi Malaysia, 2009M.Sc. Engineering Mathematics, Universiti Teknologi Malaysia, 2011A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE COLLEGE OF GRADUATE STUDIES(Electrical Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Okanagan)October 2021© Wei Sen Loi, 2021The undersigned certify that they have read, and recommend to theCollege of Graduate Studies for acceptance, a thesis entitled:MULTISCALE COMPUTATIONAL VISUALIZATION AND MOD-ELLING OF OPTICAL NANOMATERIALS AND THEIR APPLI-CATIONsubmitted by Wei Sen Loi in partial fulfilment of the requirements of thedegree of Doctor of PhilosophyDr. Kenneth J. Chau, School of EngineeringSupervisor, ProfessorDr. Jonathan F. Holzman, School of EngineeringSupervisory Committee Member, ProfessorDr. Lorne Whitehead, Department of Physics & Astronomy, UBC VancouverSupervisory Committee Member, ProfessorDr. Tao Lu, Faculty of Electrical and Computer Engineering, University of VictoriaExternal Examiner, ProfessorDr. Joshua Brinkerhoff, School of EngineeringUniversity Examiner, ProfessoriiAbstractThe objective of this thesis is to explore the integration of light sim-ulation techniques from computational nanophotonics, computer graphics,and daylighting to model the visual appearance and optical behavior of na-noengineered structures in real-world settings. This thesis is inspired bythe desire to produce high-fidelity predictions of the optical properties ofnanostructured materials across multiple size scales, invoking both waveoptics and geometric optics where appropriate. Bridging different descrip-tions of light behavior requires careful consideration of scaling strategies,synergizing computation techniques from different research areas, and find-ing a right balance between computational efficiency and accuracy. First,an efficient multi-scale computation visualization approach is developed bycombining electrodynamic simulations with physically-based rendering toproduce photorealistic predictions of the appearance of thin metallic filmsand multilayers. Next, this computation approach is extended by augment-ing its wavelength and spectral resolution in order to accurately describe theiridescence of patterned plasmonic nanostructures. One of the interestingaspects of this work is that has enabled, for the first time, exploration ofthe influence of both microscopic and nanoscopic roughness on the visualappearance of nanostructured media. Finally, the elements of the aforemen-tioned multi-scale computation approach are integrated with climate-baseddaylight modeling to investigate the daylighting and glare control perfor-mance of window coatings and daylight redirecting structures consisting ofsemi-transparent thin metallic films. This thesis presents a robust compu-tational strategy to enable modelling of the visual appearance and opticalproperties of nanostructured materials under application-specific settings.The modelling introduced by this work believes might accelerate the devel-opment and deployment cycles of nanomaterials in real-world applications.iiLay SummaryIt can be difficult to predict the visual appearance and optical proper-ties of nanostructured materials under real-world application settings be-cause it requires accurate modelling of light behavior at size scales rangingfrom the subwavelength (tens of nanometers) to life scales (meters). Thisthesis presents the novel integration of light simulation approaches fromcomputational nanophotonics, computer graphics, and daylighting to en-able multi-scale simulation of the appearance, behavior, and performanceof nanoengineered optical materials, including thin metallic films, metallicmultilayers, hole arrays, and plasmonic nanostructures. Where possible, theresults from computational approach are computed to experimental resultsand other works in the literature. Key results from this thesis include thefirst physically-accurate computational visualization of plasmonic structuralcoloration, better understanding of the roles of nano- and micro-scale rough-ness on the visual appearance of nanostructures, and a proposal for a newdaylight redirecting structure based on semi-transparent thin metallic films.iiiPrefaceThis work has been done under the supervision of Dr. Kenneth Chau atthe School of Engineering at The University of British Columbia.Portions of my thesis have been presented and published in the followingpeer-reviewed conferences:1. Wei Sen. Loi and Kenneth J. Chau, “Visualization of Ultra-thin Semi-transparent Metallic Films by Wave Simulations and Ray-tracing Ren-dering”, ACM SIGGRAPH 2019, Posters-51, 2019, 1-2.2. Wei Sen. Loi and Kenneth J. Chau, “Visualization of Angle-dependentPlasmonic Structural Coloration by FDTD-simulated BSDF and Ray-tracing Rendering”, ACM SIGGRAPH 2020, Posters-59, 2020, 1-2.3. Wei Sen. Loi and Kenneth J. Chau, “Multi-scale ComputationalVisualization of Angle-dependent and Roughness-sensitive PlasmonicStructural Coloration”, ACM SIGGRAPH 2021, Posters-46, 2021, 1-2.Portions of this thesis have been refined and extended into publication-ready manuscripts that are ready for submission:1. Wei Sen. Loi and Kenneth J. Chau, “Multi-scale Computational Vi-sualization of Semi-transparent Metallic Thin Films with Roughness”,to be submitted.2. Wei Sen. Loi and Kenneth J. Chau, “Plasmonic Structural Coloration:Wave-optical Multi-scale Rendering of Polarization Independent Metal-lic nanostructures”, to be submitted.3. Wei Sen. Loi and Kenneth J. Chau, “Multi-scale Models of PlasmonicStructural Colors with Nanoscale Surface Roughness”, to be submit-ted.4. Wei Sen. Loi and Kenneth J. Chau, “Multi-scale Modelling of Day-lighting Enhancements by Metallic Nano Films and Multilayers”, tobe submitted.ivTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . xxvAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . .xxviiiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xxixChapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . 11.1 Wave vs Particle Behavior . . . . . . . . . . . . . . . . . . . . 31.2 Maxwell’s Equations . . . . . . . . . . . . . . . . . . . . . . . 41.3 Drude Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.4 Surface Plasmons . . . . . . . . . . . . . . . . . . . . . . . . . 81.5 Fresnel Equations . . . . . . . . . . . . . . . . . . . . . . . . . 111.6 Radiometry vs Photometry . . . . . . . . . . . . . . . . . . . 161.7 Discrete Method to Solve Maxwell’s Equations . . . . . . . . 171.8 Physically Based Rendering . . . . . . . . . . . . . . . . . . . 191.9 Physically-Based Rendering Materials . . . . . . . . . . . . . 251.10 Microfacet Theory . . . . . . . . . . . . . . . . . . . . . . . . 261.11 Multi-scale Modeling and Simulations . . . . . . . . . . . . . 31vTABLE OF CONTENTS1.12 Nanofabrication and Nanomaterials . . . . . . . . . . . . . . . 321.13 Structural Coloration . . . . . . . . . . . . . . . . . . . . . . . 331.13.1 Plasmonic Metallic Nanostructures . . . . . . . . . . . 341.14 Climate-based Daylighting and Glare Control . . . . . . . . . 361.15 Previous Works . . . . . . . . . . . . . . . . . . . . . . . . . . 401.16 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . 42Chapter 2: Visualization of Semi-transparent Metallic ThinFilms . . . . . . . . . . . . . . . . . . . . . . . . . . . 432.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432.2 Our Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . 442.2.1 FDTD Simulation Domain . . . . . . . . . . . . . . . 452.2.2 Rendering Setup . . . . . . . . . . . . . . . . . . . . . 462.3 Results and Discussions . . . . . . . . . . . . . . . . . . . . . 482.3.1 Validation of Schlick Approximation . . . . . . . . . . 482.3.2 Comparison of Rendered Image to Real Image . . . . 512.3.3 Influence of Lighting Conditions . . . . . . . . . . . . 512.3.4 Influence of Nanoscale Roughness . . . . . . . . . . . . 542.3.5 Influence of Microscale Roughness . . . . . . . . . . . 562.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58Chapter 3: Plasmonic Structural Coloration . . . . . . . . . . 593.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593.2 Our Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.2.1 Plasmonic Structural Colors . . . . . . . . . . . . . . . 603.2.2 Electrodynamic Simulations . . . . . . . . . . . . . . . 623.3 Plasmonic BSDF Model . . . . . . . . . . . . . . . . . . . . . 633.3.1 Rendering Setup . . . . . . . . . . . . . . . . . . . . . 653.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . 663.4.1 Preliminary Results . . . . . . . . . . . . . . . . . . . 663.4.2 Nanohole Array . . . . . . . . . . . . . . . . . . . . . . 683.4.3 Nanodisk Array . . . . . . . . . . . . . . . . . . . . . . 713.4.4 Nanohole-nanodisk Arrays . . . . . . . . . . . . . . . . 733.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74Chapter 4: Influence of Nanoscale Roughness on PlasmonicStructural Coloration . . . . . . . . . . . . . . . . . 754.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 754.2 Our Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . 764.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . 77viTABLE OF CONTENTS4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86Chapter 5: Daylight and Glare Control by Nanomaterials . . 875.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 875.2 Our Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . 885.2.1 Thin Metallic Films for Window Structures . . . . . . 885.2.2 Finite-Difference Time-Domain (FDTD) Simulations . 905.2.3 Climate-based Daylight Modeling . . . . . . . . . . . . 925.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . 965.3.1 Preliminary Results . . . . . . . . . . . . . . . . . . . 965.3.2 Daylight Performance Analysis . . . . . . . . . . . . . 995.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116Chapter 6: Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 117Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141Appendix A: FDTD Iterative Field Updating Equation . . . . . . . 141Appendix B: Monte Carlo Integration . . . . . . . . . . . . . . . . 144Appendix C: Computational Settings . . . . . . . . . . . . . . . . . 149Appendix D: Plasmonic Metallic Nanostructures Supplement In-formation . . . . . . . . . . . . . . . . . . . . . . . . . 151Appendix E: BSDF Extraction Scripts . . . . . . . . . . . . . . . . 158Appendix F: CBDM Supplement Information . . . . . . . . . . . . 160Appendix G: Virtual Classical Car Showroom . . . . . . . . . . . . 167viiList of TablesTable 1.1 Plasma frequency and collision rates for Ag, Au, andAl. The data is measured by [1]. . . . . . . . . . . . . 11Table 1.2 Delta E color difference indicator. . . . . . . . . . . . . 17Table 1.3 List of selected commercially available, open source,and research-based rendering engines. . . . . . . . . . 24Table 1.4 Normal distribution function, D(mˆ), and masking/shad-ing function, G(vˆ, mˆ), in microfacet theory. . . . . . . 30Table 1.5 DGP Glare Indicator. . . . . . . . . . . . . . . . . . . 39Table 2.1 Surface roughness parameters. . . . . . . . . . . . . . . 46Table 2.2 Statistical data for the resulting errors between Schlickapproximation and Fresnel reflectance . . . . . . . . . 49Table 2.3 Surface roughness parameters (Adapted from [2]) . . . 56Table 4.1 Average and Maximum ∆E00 comparison for the rougharray (in-plane roughness). . . . . . . . . . . . . . . . . 80Table 5.1 Thickness parameters for single layer Ag thin film andmultilayer Ag | TiO2 thin films. . . . . . . . . . . . . . 89Table 5.2 CBDM simulation parameters. . . . . . . . . . . . . . 94Table 5.3 Daylighting performance indicators . . . . . . . . . . . 95Table C.1 Specifications of the computer workstation used for theelectrodynamic simulations and PBR. . . . . . . . . . 149Table C.2 FDTD simulation parameters used to model structuresdescribes in Chapters 2, 3, and 4. . . . . . . . . . . . . 150Table C.3 NVIDIA IRAY settings used to model structures de-scribes in Chapter 2, 3, and 4. . . . . . . . . . . . . . . 150Table D.1 Material, thickness period and diameter combinationsfor generating silver nanohole arrays with the fixedratio D : P = 1 : 2 in FDTD simulations. . . . . . . . . 151viiiLIST OF TABLESTable D.2 Period and diameter combinations for Silver tandemnanodisk arrays in FDTD simulations. . . . . . . . . . 154Table D.3 Pillar height, diameter and period combinations forgenerating aluminum nanohole and nanodisk arraysin FDTD simulations. . . . . . . . . . . . . . . . . . . 154Table F.1 List of Radiance material parameters applied into eachlayer of the shoebox room model. . . . . . . . . . . . . 160Table F.2 Daylighting and glare performance metrics at workplane and lighting levels for Ag and Ag | TiO2 thinfilms coated window pane. . . . . . . . . . . . . . . . . 162Table F.3 Daylighting and glare performance metrics at workplane and lighting levels for Ag and Ag | TiO2 thinfilms coated flat slats. . . . . . . . . . . . . . . . . . . 163Table F.4 Daylighting and glare performance metrics at workplane and lighting levels for Ag and Ag | TiO2 thinfilms coated wing-flap slats. . . . . . . . . . . . . . . . 164ixList of FiguresFigure 1.1 Hierarchy of visible light modelling approaches acrossvarious size scales. . . . . . . . . . . . . . . . . . . . . 3Figure 1.2 A single interface between two distinct media. Undercertain conditions, the interface can support surface-bound electromagnetic waves that obey Maxwell’s equa-tions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Figure 1.3 Oblique incident with (a) E perpendicular to the planeof incidence (TE) and (b) E parallel to the plane ofincidence (TM). . . . . . . . . . . . . . . . . . . . . . 12Figure 1.4 Cross-sectional areas (highlighted in yellow circle) ofthe incident, reflected, and transmitted light beams,compared to the cross-sectional area of the beam onthe interface. . . . . . . . . . . . . . . . . . . . . . . . 15Figure 1.5 Illustration of (a) scattered spectral radiance, (b) in-coming spectral radiance and (c) BSDF relating direc-tional and intensity of incoming and scattered spec-tral radiance over a point, xo. In the figure, the openarrowhead describes the direction of spectra radianceand the closed arrowhead describes the directionalvector for ωˆi and ωˆo. . . . . . . . . . . . . . . . . . . . 21Figure 1.6 (a) Monte Carlo integration to approximate the amountof light arriving at point P . (b) Recursive procedureto determine the amount of light arriving at point P . 23Figure 1.7 The scattering distribution patterns for reflectionsand transmission from a surface for increasing sur-face roughness. Rougher surface tends to have a wider(spread out) scattering distribution pattern. . . . . . 25xLIST OF FIGURESFigure 1.8 Geometric effects of microscale roughness: (a) thegreen dashed arrows indicate an area that is shad-owed (occluded from the light) by another microge-ometry, (b) the grey dashed arrows indicate an areathat is masked (occluded from view) by another mi-crogeometry, (c) the light inter-reflects between themicroscale structures. . . . . . . . . . . . . . . . . . . 27Figure 1.9 NDFs fit to measured chrome from the MERL database.Left: The specular peak over θm for chrome (black),GGX (red; αg = 0.006), Beckmann (green; αg =0.013), and Blinn-Phong (blue dashes; = 12000). Ren-dered highlights are shown on the right for chrome,GGX, and Beckmann. (Figure courtesy of [3]). . . . . 29Figure 1.10 Shimmering blue shade from a specimen sample ofMorpho butterfly wings. Credit: Vincent Loi. . . . . 34Figure 1.11 Plasmon hybridization due to disk-hole coupling. (a)Energy diagram showing the hybridization of the cou-pled plasmonic modes of the disks and holes of thestructure into a low energy mode (bonding) and ahigh energy mode (antibonding). (b) Reflectance spec-tra for the same parameters of nanodisk-nanodisk butfor varying pillar height, h. The two modes are seenas dips in the spectra. (Image courtesy [4]) . . . . . . 35Figure 1.12 Daylighting and glare windows solutions. Micron scale:3M [5] and SerraGlaze daylight redirecting films [6]and dynamic daylight control system (DDCS) [7]. Cen-timeter scale: Oksolar blinds [8, 9], fish louver, RetroLuxblind [10, 11] and laser cut panel. Meter scale: Lightshelves. . . . . . . . . . . . . . . . . . . . . . . . . . . 40Figure 2.1 Schematic diagram of (a) thin metallic film modelwith the hierarchy scale of roughness from microscaleroughness using microfacet model to (b) nanoscaleroughness using FDTD simulation. . . . . . . . . . . 45Figure 2.2 Rendering setup to generate appearance of thin metal-lic film in (a) interior room and (b) studio room. . . . 47xiLIST OF FIGURESFigure 2.3 Comparison of Fresnel reflectance (left column) andSchlick approximation (right column) over visible spec-trum wavelength with incident angles from 0° to 90°for the single-layer and multilayer metallic thin filmwith the corresponding percentage of error (right col-umn). Color bars on the right shows the angular RGBcolors of Fresnel reflectance (F) and Schlick approxi-mation (S). . . . . . . . . . . . . . . . . . . . . . . . . 50Figure 2.4 Visual comparison between (a) lab-fabricated and (b)rendered 20-nm-thick silver film coated glass substrateusing Schlick approximation. . . . . . . . . . . . . . . 51Figure 2.5 Computationally rendered images of a 25-nm-thicksilver film on a glass slide with a white backgroundwith varying studio lights having color temperature(a) 5000K (b) 5500K (c) 6500K (d) 7500K. . . . . . . 53Figure 2.6 Rendered appearance of (a) single layer silver film and(b) multilayer Ag | TiO2 films. . . . . . . . . . . . . . 55Figure 2.7 Rendered images of single layer film 25-nm-thick sil-ver film and multilayer thin film Ag | TiO2 – 23 nm| 38 nm coated on anti-glare, ground, frosted andetched glass on (a) a square glass substrate placedon the white paper bearing a dark blue UBC logo,and (b) pieces of a 3D chess set (Rendering time: 3-4minutes for each image). . . . . . . . . . . . . . . . . 57Figure 3.1 Schematic diagrams of metallic nanostructures (top)and 2D-cross section view of FDTD unit cell simu-lations (bottom) for (a) silver nanohole arrays, (b)silver nanodisk arrays, and (c) aluminum nanohole-nanodisk arrays. . . . . . . . . . . . . . . . . . . . . . 61Figure 3.2 Illustration of (a) near-field and far-field zones of in-teractions and (b) geometrical angles used for a singleBRDF measurement for the incoming direction ωˆi,and outgoing scattered light direction, ωˆo. . . . . . . 64Figure 3.3 Schematic diagrams of three-dimensional renderingsetups for generating the appearance of metallic nanos-tructures under influence of (a) HDRI lighting and (b)studio lighting. . . . . . . . . . . . . . . . . . . . . . . 65xiiLIST OF FIGURESFigure 3.4 Comparison of experimental (adapted with permis-sion from [12]) and FDTD-simulated (a) reflectanceand (b) transmittance spectra at normal incidence forsilver tandem nanodisk array with a periodicity of 340nm and diameter of 140 nm. . . . . . . . . . . . . . . 66Figure 3.5 Reflectance over visible spectrum of 20-nm-thick alu-minum nanohole-nanodisk arrays with a periodicityof 200 nm, a diameter of 80 nm, and separation dis-tance of 80 nm at normal incidence (a) measured byreflectance spectroscopy and (b) modeled FDTD sim-ulations (Adapted with permission from [4, 13]) . . . 67Figure 3.6 Rendered appearance for the (a) reflection and (b)transmission color of 20-nm-thick nanohole array withthe period from 150 nm to 200 nm and diameter from75 nm to 100 nm, respectively on the spherical sub-strate (top row) and body of the pedal car (bottomrow). . . . . . . . . . . . . . . . . . . . . . . . . . . . 69Figure 3.7 Rendered images of the reflection color on the spheri-cal substrate coated with 20-nm-thick silver (top row)and aluminum (bottom row) nanohole array with di-ameter from 75 nm to 95 nm and period from 150 nmto 190 nm, respectively. . . . . . . . . . . . . . . . . . 70Figure 3.8 Rendered images for both (a) reflection and (b) trans-mission colors for silver-alumina-silver tandem nan-odisk arrays coated on spherical substrate (top row)and the body of pedal car (bottom row) with the di-ameter, D from 90 nm to 220 nm with the associatedperiod, P from 270 nm to 450 nm. . . . . . . . . . . . 72Figure 3.9 Rendered reflection colors of 20-nm-thick aluminumnanohole and nanodisk arrays with the period of 200nm coated on the spherical substrate (top row) andbody of the pedal car (bottom row) with varying sep-aration distance, d between hole and disk from 30 nmto 80 nm. . . . . . . . . . . . . . . . . . . . . . . . . . 73Figure 3.10 Rendered reflection color of 20-nm-thick aluminumnanohole-nanodisk arrays, a separation distance of80 nm and period of 200 nm with a varying diam-eter ranging from 80 nm to 110 nm coated on thespherical substrate (top row) and body of the pedalcar (bottom row). . . . . . . . . . . . . . . . . . . . . 74xiiiLIST OF FIGURESFigure 4.1 (a) Schematic diagram and (b) cross-section view ofa unit cell FDTD simulation (bottom) of 20-nm-thicksilver nanohole array coated on the glass substrate. . 77Figure 4.2 Spectral reflectance and transmittance of 20-nm-thicksilver nanohole array with 5 distinct surface rough-ness profiles (randomly generated using the same pa-rameters σRMS = 2 nm and Lc = 15 nm) as shownin top insets. . . . . . . . . . . . . . . . . . . . . . . . 78Figure 4.3 Rendered images of the visual appearance in reflectance(middle left column) and transmittance (middle rightcolumn) of a smooth spherical glass substrate coatedwith silver nanohole arrays that are either smooth orrough. The rough arrays in 1, 2 and 3 are randomlygenerated with silver nanohole arrays using the simi-lar roughness parameters σRMS = 2 nm and Lc = 15nm but different seed numbers 101, 102, and 103 for1, 2, and 3, respectively. The color difference betweenthe rough and smooth arrays is quantified by the colordifference parameter, ∆E00 which is calculated for re-flectance (far right column) and transmittance (farleft column). . . . . . . . . . . . . . . . . . . . . . . . 79Figure 4.4 Spectral reflectance and transmittance of 20-nm-thicksilver nanohole array with various in-plane roughness. 81Figure 4.5 Comparative rendered appearance of smooth and roughnanohole arrays coated on an opaque sphere whenviewed in reflectance (middle left column) and trans-mittance (middle right column). The rough nanoholearrays have parameters of identical out-of-plane rough-ness, σRMS = 2 nm but varying the in-plane rough-ness, Lc from 25 nm to 75 nm. The color differ-ence, ∆E00, between the rough and smooth arraysare shown in the false color images in reflectance (farleft column) and transmittance (far right column). . . 82Figure 4.6 Spectral reflectance (top), transmittance (middle), andabsorbance (bottom) of 20-nm-thick silver nanoholearray with for various out-of-plane roughness param-eters. The surface topology is shown in the top inset. 84xivLIST OF FIGURESFigure 4.7 Comparative rendered appearance of smooth and roughnanohole arrays coated on an opaque sphere whenviewed in reflectance (middle left column) and trans-mittance (middle right column). The rough nanoholearrays have parameters of identical in-plane rough-ness, Lc = 100 nm but varying the out-of-plane rough-ness scale, σRMS from 1 nm to 5 nm. The color dif-ference, ∆E00, between the rough and smooth arraysare shown in the false color images in reflectance (farleft column) and transmittance (far right column). . . 85Figure 5.1 Schematic side view diagram of coated daylight-redirectingwindow structures to be examined including (a) di-rect coating on the inner glass pane, (b) coating ontop of flat slats and (c) coating on top of wing-flapslats. . . . . . . . . . . . . . . . . . . . . . . . . . . . 90Figure 5.2 Cross-sectional view of the two-dimensional FDTDunit-cell used to model the reflectance and transmit-tance of a multilayer Ag | TiO2 thin metallic film ona glass substrate. . . . . . . . . . . . . . . . . . . . . 92Figure 5.3 Schematic drawings of (a) shoebox indoor space withsingle south-facing window embedded with the fol-lowing window structures: window coating, flat slatsand wing-flap slats; (b) sensor grid for daylightingmeasurements in the simulation environment; and (c)sensor grids for glare measurements in the simulationenvironment, including view orientation (inset). . . . 94Figure 5.4 FDTD-simulated normal-incidence reflectance and trans-mittance spectra of (a) single-layer silver thin films(Ag) and (b) multilayer titanium dioxide coated onsilver thin films (Ag | TiO2). (c) TMM-simulated an-gular Fresnel reflectance spectra over the visible forbare window glass (SiO2) (left column), single-layer20-nm thick Ag film (middle column) and multilayerAg | TiO2 – 18 nm (right column) coated on glasssubstrate. . . . . . . . . . . . . . . . . . . . . . . . . 97xvLIST OF FIGURESFigure 5.5 (a) RADIANCE rendered images of shoebox roomwith south-facing window equipped with Ag-coated(20 nm thick) wing-flap slats at May 15, 1.30pm us-ing CIE Perez Sky condition [14] and (b) the corre-sponding false-color image of luminance distributionin the room. . . . . . . . . . . . . . . . . . . . . . . . 98Figure 5.6 Daylight performance metrics in the room when thewindow is (a) coated with Ag films of various thick-nesses and (b) multilayer Ag | TiO2 thin films of var-ious TiO2 film thicknesses. Average illumination dis-tributions (over the year) at the work plane (0.9mabove ground) and ceiling level (2.7m above groundwhen the window is (c) coated with Ag films of var-ious thicknesses and (d) multilayer Ag | TiO2 thinfilms of various TiO2 film thicknesses. . . . . . . . . . 100Figure 5.7 Rendered images and corresponding false-color im-ages of daylight distribution for control, window panecoated with Ag (50 nm) and Ag | TiO2 (23 | 57 nm)in the summer solstice (Jun 21st), fall equinox (Sep21st), and winter solstice (Dec 21st).The sun and skyconditions are derived from the Summerland weatherdata. . . . . . . . . . . . . . . . . . . . . . . . . . . . 101Figure 5.8 Annual glare charts for (a) control (bare window) andfor a window coated with (b) Ag – 20 nm, (c) Ag –50 nm, (d) Ag | TiO2 – 23 | 18 nm and (e) Ag | TiO2– 23 | 57 nm. . . . . . . . . . . . . . . . . . . . . . . . 103Figure 5.9 Rendered image of the occupant’s viewpoint with thesouth-facing coated window pane and the correspond-ing false-color luminance distribution on March 12,12.30pm for (a) Ag – 20 nm, (b) Ag – 50 nm, (c) Ag| TiO2 – 23 | 18 nm and (d) Ag | TiO2 – 23 | 57 nm. 104Figure 5.10 Daylight performance metrics of flat slats coated by(a) single layer Ag thin films and (b) multilayer Ag| TiO2 thin films on south-facing window. Averageillumination distributions at work plane (0.9m aboveground) and ceiling (2.7m above ground) for (c) singlelayer Ag thin films and (d) multilayer Ag | TiO2 thinfilms coated on flat slats. . . . . . . . . . . . . . . . 105xviLIST OF FIGURESFigure 5.11 Rendered images and corresponding false-color im-ages of daylight distribution for control, flat slats coatedwith Ag (50nm), and flat slats coated with Ag | TiO2(23|57nm) on the summer solstice (Jun 21st), fall equinox(Sep 21st) and winter solstice (Dec 21st). The sunand sky conditions are derived from the Summerlandweather data. . . . . . . . . . . . . . . . . . . . . . . 106Figure 5.12 Annual glare charts for (a) control (bare window) anda window equipped with flat slat that are coated with(b) Ag – 20 nm, (c) Ag – 50 nm, (d) Ag | TiO2 – 23| 18 nm and (e) Ag | TiO2 – 23 | 57 nm. . . . . . . . 108Figure 5.13 (a) Rendered image from the occupant’s viewpointwith the south-facing window equipped with Ag |TiO2 – 23 | 18 nm coated flat slats on April 29, 9 amand (b) the corresponding false-color image of day-light luminance distribution at the viewing position. . 109Figure 5.14 Daylight performance metrics of wing-flap slats coatedby (a) single layer Ag thin films of various thicknessesand (b) multilayer Ag | TiO2 thin films of variousTiO2 film thicknesses. The average illumination dis-tributions at work plane (0.9m above ground) andceiling (2.7m above ground) for (c) single layer Agthin films and (d) multilayer Ag | TiO2 thin filmscoated on wing-flap slats. . . . . . . . . . . . . . . . . 110Figure 5.15 Rendered images and corresponding false-color im-ages of daylight distribution for control, wing-flapslats coated with Ag (50 nm) and Ag | TiO2 (23| 57nm) in the summer solstice (June 21st), fall equinox(Sept 21st), and winter solstice (Dec 21st). The sunand sky conditions are derived from the Summerlandweather data. . . . . . . . . . . . . . . . . . . . . . . 112Figure 5.16 Annual glare charts for (a) control (bare window) anda window equipped with wing-flap slats coated with(b) Ag – 20 nm, (c) Ag – 50 nm, (d) Ag | TiO2 – 23| 18 nm and (e) Ag | TiO2 – 23 | 57 nm. . . . . . . . 114Figure 5.17 (a) Rendered image from the occupant’s viewpointwith south-facing window equipped with Ag | TiO2 –23 | 57 nm coated wing-flap slats on March 3, 12.30pmand (b) the corresponding false-color image of lumi-nance daylight distribution. . . . . . . . . . . . . . . . 115xviiLIST OF FIGURESFigure 6.1 Screenshot of a webXR application built by VincentLoi to showcase plasmonic structural coloration onvarious substrates. The bodies of classic car are coatedwith silver nanohole array with a diameter of 70 nmand a period of 140 nm with varying nanoscale rough-ness scale. The users can virtually walk through theshowroom and examine various examples of struc-tural coloration. (Link to access the virtual showroom).119Figure A.1 One-dimensional FDTD computation structures forleap-frog time stepping forward scheme. . . . . . . . . 143Figure B.1 (a) Area below the integration of function, f(x) forthe integration limits [a, b], (b) Area of rectangle dueto estimator value, X, (c) The estimate average areaunder the curve using 4 random number points. . . . 146Figure D.1 Extended rendered appearance for the reflection colorof 20-nm-thick silver nanohole array with the period(at fixed ratio D : P = 1 : 2) varying from 140 nm to360 nm coated on the body of the pedal car. . . . . . 152Figure D.2 Extended rendered appearance for the transmissioncolor of 20-nm-thick silver nanohole array with theperiod (at fixed ratio D : P = 1 : 2) varying from 140nm to 360 nm coated on the body of the pedal car. . 153Figure D.3 FDTD-simulated (a) Reflection and (b) Transmissionspectra of silver tandem nanodisk with varying diam-eter and period based on the period and diametercombinations at Table D.2. . . . . . . . . . . . . . . . 155Figure D.4 FDTD-simulated bidirectional reflectance distributionof silver tandem disk array at P = 300 nm and D =110 nm for the incident angle from 0° to 89° with 2°increment. . . . . . . . . . . . . . . . . . . . . . . . . 156Figure D.5 FDTD-simulated bidirectional transmittance distri-bution for silver tandem disk array at P = 300 nmand D = 110 nm for the incident angle from 0° to 89°with 2° increment. . . . . . . . . . . . . . . . . . . . . 157Figure F.1 Detail of dimensions and measurements (in milime-ters) of the shoebox room. . . . . . . . . . . . . . . . 161xviiiLIST OF FIGURESFigure F.2 Rendered images and the corresponding false-colorimage of daylight distribution for control (bare win-dow),window pane, flat slats, and wing-flap slats coatedwith Ag (50 nm) in the summer solstice (Jun 21st),fall equinox (Sep 21st), and winter solstice (Dec 21st).The amount of daylight including sun and sky con-ditions in the room is derived from the Summerlandweather data. . . . . . . . . . . . . . . . . . . . . . . 165Figure F.3 Rendered images and the corresponding false-colorimage of daylight distribution for control (bare win-dow),window pane, flat slats, and wing-flap slats coatedwith Ag | TiO2 (23 | 57 nm) in the summer solstice(Jun 21st), fall equinox (Sep 21st), and winter solstice(Dec 21st). The amount of daylight including sunand sky conditions in the room is derived from theSummerland weather data. . . . . . . . . . . . . . . . 166Figure G.1 Plasmonic structural coloration preview of aluminumnanohole-nanodisk arrays developed by Vincent Loi.The bodies of classic car are coated with nanohole-nanodisk array with a diameter of 80 nm, a periodof 200 nm and varying separation distance. (Link toaccess the virtual showroom) . . . . . . . . . . . . . . 167xixList of Symbolsαb Beckmann’s Microfacet surface roughness parameterαg GGX-Smith’s Microfacet surface roughness parameterαp Blinn-Phong’s Microfacet surface roughness parameterαt GTR’s Microfacet surface roughness parameterE¯v,avg Relative average illuminancex¯, y¯, z¯ Standard color match matching functions∆E00 Delta E (CIE 2000)δ Sampling resolutiond Dielectric permittivitym Metal permittivityo Free-space electric permittivityr Relative electric permittivityηo Free space impedanceΓ Characteristic frequencynˆ Macrosurface normal vectorωˆi Inward light directionωˆo Outward light directionhˆr Normalized half reflection vectorhˆt Normalized half transmission vectormˆ Microsurface normal vectorxxLIST OF SYMBOLSvˆ Arbitrary projection from macrosurfaceλ Wavelength|E|2 Electric field intensityax x-vector componentsay y-vector componentsaz z-vector componentsB(r, t) Magnetic flux density vectorD(r, t) Electric displacement vectorE(r, t) Electric field strength vectorH(r, t) Magnetic field strength vectorJ(r, t) Electric current density vectorM(r, t) Magnetic current density vectorR Real numberr Position vectorA Absorbancen Macrosurface normalµo Free-space magnetic permeabilityµr Relative magnetic permeabilityΩ Hemisphere of scatted lightω Frequencyωo Natural resonant frequency of electronω2p Plasmon frequencyωs,i Solid angle of the i-th glare sourceφ Azimuthal anglexxiLIST OF SYMBOLSρe Electric charge density vectorρm Magnetic energy charge density vectorσ Electric conductivityσRMS In-plane roughnessτ Collision ratesθi Incidence angleθr Reflected angleθt Transmitted anglec Speed of light in vacuumD Diameterd ThicknessD(mˆ, hˆr) Microfacet normal distribution function (BRDF)D(mˆ, hˆt) Microfacet normal distribution function (BTDF)Ev Vertical illuminanceEv,c Average illuminance for controlEv,lvl Average illuminance for the targeted lighting levelF Fresnel ReflectanceF0 Fresnel reflectance at normal incidencefr Bidirectional reflectance distribution function (BRDF)ft Bidirectional transmittance distribution function (BTDF)findex Indexing offset functionG(ωˆi, ωˆo, mˆ, hˆr) Masking-shadowing function (BRDF)G(ωˆi, ωˆo, mˆ, hˆt) Masking-shadowing function (BTDF)iφ Index of the scattering data (azimuthal)xxiiLIST OF SYMBOLSiθi Index of the scattering data (incoming)iθo Index of the scattering data (outgoing)ID65(λ) Spectral power distribution of a standard D65 illuminantK Scaling factorkx, ky, kz Wave number on x,y,z-componentLc Out-of-plane roughnessLe Emitted spectral radianceLi Incoming spectral radianceLo Outgoing spectral radianceLs,i Luminance of the i-th glare sourcem Microsurface normalme Mass of an electronN Number of atoms per volumen Refractive indexnφ Equal spaced steps size of azimuthal anglenθ Equal spaced steps size of incidence angleP Macroscopic polarizationP PeriodicityP Spectral power intensityPi Position index of i-th glare sourceq ChargeR Reflectancer Reflection coefficientS(λ) Spectral responsexxiiiLIST OF SYMBOLST Transmittancet Timet Transmission coefficientv Speed of light in mediumX,Y, Z Tristimulus responsexxivList of Abbreviations2D Two-dimensional. xii, 35, 61, 913D Three-dimensional. xii, 35, 57, 58, 65, 74, 118Ag Silver. viii, ix, xii, xv–xvii, xix, 10, 39, 48, 51,54–57, 60, 75, 88–90, 92, 96, 97, 99–115, 151,162–166Al Aluminum. viii, 10, 11, 39, 60ASE Annual sun exposure. 37, 95, 104, 110, 162–164Au Gold. 10, 39, 60BFAST Broadband fixed angle source technique. 62BRDF Bidirectional reflectance distribution func-tion. xii, 25, 27, 28, 41, 46, 63–65, 74BSDF Bidirectional scattering distribution function.x, 14, 20, 21, 25, 26, 31, 41, 42, 59, 63, 64,118BTDF Bidirectional transmittance distribution func-tion. 25, 27, 28, 46, 63, 65, 74CBDM Climate-based daylight modeling. viii, 37, 39,88, 91–94, 99, 116, 117CDF Cumulative distribution function. 145CFL Courant Friedrich Lewy conditions. 18, 19CIE International Commission on Illumination.xvi, 16, 17, 63, 67, 94, 98CPU Central processing unit. 22, 24, 63, 119Cu Copper. 39CVD Chemical vapor deposition. 32DDCS Dynamic daylight control system. xi, 40xxvList of AbbreviationsDGP Daylight glare probability. viii, 38, 39, 88, 92,95, 96, 109FDTD Finite-difference time domain. xi–xv, xviii,17–19, 41, 44–46, 61–63, 66, 67, 74, 76, 77,92, 118–120, 141–143, 155FTO Fluorine-doped tin oxide. 39GI Global illumination. 23, 24GPLv2 GNU general public license version 2. 24GPU Graphic processing unit. 22, 24, 63, 119, 120GTR Generalized Trowbridge-Reitz. 30HDR High dynamic range. 23, 46, 65, 76HDRI High dynamic range imaging. xii, 65ITO Indium tin oxide. 39LSPR Localized surface plasmon resonance. 33, 35MDL Material definition language. 46, 47, 64MERL Mitsubishi Electric Research Laboratories.xi, 29MIM Metal-insulator-metal. 60MLT Metropolis light transport. 21, 22NDF Surface normal distribution function. 26, 28,29, 56NIR Near infra-red. 39PBR Physically-based rendering. 19, 22, 25, 28,30–32, 40–44, 46, 47, 59, 60, 63–65, 74, 88,91–93, 118, 119PDF Probability density function. 145PLR Pupillary light reflex. 37PML Perfectly matched layer. 18, 62, 76, 91PMMA Polymethyl methacrylate. 60, 62, 70, 73RGB Red, green, and blue. xii, 16, 20, 28, 31, 48,50–52, 63, 64, 93xxviList of AbbreviationsRMS Root mean square. 46, 54sDA Spatial daylight autonomy. 37, 95, 99, 104,162–164sDG Spatial disturbing glare. 38SIGGRAPH Special Interest Group on Computer Graphicsand Interactive Techniques. 119SiO2 Silicon dioxide (Glass). xv, 97SP Surface plasmon. 8, 32, 33, 70, 86SVBRDF Spatial-varying bidirectional reflectance dis-tribution function. 41TE Transverse electric. 9, 13, 91TiO2 Titanium dioxide. ix, xii, xv–xvii, xix, 44, 48,49, 54–57, 88, 90, 92, 96, 97, 99–116, 162–164,166TM Transverse magnetic. 9, 13, 91TMM Transfer matrix method. xv, 48, 96, 97UV ultra-violet. 60VR/AR/XR Virtual Reality/Augmented Reality/Ex-tended Reality. 119webXR Web-based XR. xviii, 119xxviiAcknowledgementsI offer my sincere gratitude to the faculty, staff, and fellow students atUBC Okanagan, who have inspired and support me throughout the journeyof study. I want to express my gratitude to my supervisor, Dr. KennethChau, for his unconditional support and guidance. Thank you for enlighten-ing me with critical thinking skills, which have help me think about researchproblems from all angles. Without his unconditionally support, this workwould not have made it past the finish line. I would like to express mysincere gratitude to Dr. Jonathan Holzman and Dr. Lorne Whitehead fortheir valuable feedback and suggestions to elevate the research. I wouldlike to thank all my friends and research colleagues, especially MohammedAl Shakhs, Iman Aghanejad, Connor Badowich, Nibirh Jawab, Ali Malek,Ahmed Sabry, Cael Warner, and Marek Splawinski. Special thanks to JanJordan, NVIDIA Senior Software Product Manager, for assistance in con-verting BSDF material into .mbsdf material databases.Lastly, I would like to thanks to my parents, whose have supported methroughout my years of education, both morally and financially.xxviiiDedicationThis dissertation is dedicated to the memory of my mother, Foo Jook Lan(1946-2019). Although she was my inspiration, mental support to pursuemy doctoral degree, she was unable to see my graduation. This is for you.Thank you for everything you did for us. We love you. You will always inmy memory.xxixChapter 1IntroductionNanophotonics - the study of light interaction at nanometer scales andthe development of technologies to control the flow of light using nanofab-ricated structures – is of importance in optics, optical engineering, elec-trodynamics, and nanotechnology. Advancements in nanofabrication andmanufacturing capabilities in the past decades have stimulated tremendousadvancements in a new generation of optical devices which rely on lightinteraction in highly ordered systems, such as photonic band gap materi-als, plasmonic systems, and metamaterials [15–17]. Given the complexityof light behavior in these structures, computational nanophotonics has be-come essential for describing, analyzing, and predicting light-matter interac-tions and enabling device design without going into costly fabrication cycles[18]. In a growing number of settings, analysis of nanophotonic phenom-ena requires that we account for intricate interactions of processes occurringover extended ranges of space and time, which may arise from materialeffects (quantum, electronic, thermal, mechanical), environmental factors,and measurement artifacts [19–22]. There are few current approaches toovercome these challenges, and many of these make simplifying assumptionsthat can lead to poor predictions or even mismatch between model and data.In this thesis, the integration of electrodynamic simulations, physically-based rendering, and climate-based daylight modelling is explored to pro-duce physically accurate simulations of the visual appearance of engineerednanoscale structures and their potential application in coloration and day-lighting control. The central questions of this thesis were inspired by adesire to understand how nanofabricated materials would look and behaveunder real-world conditions and at human scales. Although this is currentlynot possible to achieve in real-world settings because nearly all fabricatednanophotonic devices are limited to centimeter-scale prototypes, it is po-tentially possible to leverage advancements in computational nanophotonicsand the graphics community to enable modelling of nanoscale materials ap-plied on large, macroscopic scales and observed by human eyes or cameras[23]. It should be noted that the synthesis of wave optical modelling andrendering is not new and there has been interest in this endeavor as early1Chapter 1. Introductionas the 1980s to explain the beautiful iridescence colors found in the naturalworld [24, 25]. Part of the challenge of developing seamless descriptions oflight across multiple size scales is that the behavior of light at large scales(several meters or more) is governed by ray optics whereas the behavior oflight at wavelength scales (100s of nanometers or less) is governed by waveoptics, as illustrated in Figure 1.1. Bridging this divide requires carefulconsideration of scaling strategies, synthesizing computational techniquesfrom different fields, and striking the right balance between computationalefficiency and accuracy.In the beginning of this thesis, a multi-scale computational visualizationapproach that leverages electrodynamic simulations and physically-basedrendering is developed to model the visual appearance of thin metallic filmsand plasmonic metallic nanostructures. Using our hierarchical approach, weare able to study, for the first time, the influence of nanoscale and microscaleroughness on the appearance of various structures coated by thin metallicfilms and nanostructures. In addition, we show that that their appearancecan be affected by factors that extend beyond the film structure, such as theproperties of the underlying substrate, environmental lighting conditions,light source, and detector. Next, we combine elements of our multi-scaleapproach with climate-based daylight modeling to investigate the daylightand glare performance of windows coated with semi-transparent metallicthin films. We propose a unique design for a coated micro-louvre whichachieves gains in daylighting performance due to the angular-selective op-tical properties of a semi-transparent metallic coating. Overall, this the-sis is an important contribution to both the nanophotonics and computergraphics communities because it offers the first step towards generic com-putational modelling of the visual appearance and optical performance ofnanostructured materials under real-world application settings. Continueddevelopment of the work presented in this thesis could potentially reducethe monetary and time costs of developing and deploying nanostructuredmaterials for real-world applications.21.1. Wave vs Particle BehaviorFigure 1.1: Hierarchy of visible light modelling approaches across varioussize scales.1.1 Wave vs Particle BehaviorA central theme of this thesis concerns the duality of light as a particleand as a wave and the necessity to use disparate modelling approaches tocapture these behaviors. Historically, the scientific community has waveredon its understanding of light as a particle or a wave. In the 1730s, Sir IsaacNewton presented the first particle picture of light as discrete corpusclestravelling in straight-line trajectories [26]. It was later shown by ThomasYoung in 1801 that light travelling through double slits could diffract aroundobstacles and form interference patterns – zones of constructive and destruc-tive interference due to the coherent superposition of waves originating fromthe slits [27]. Subsequently, Albert Einstein presented the idea of a lightphoton – a discrete packet of energy – through his famous photoelectric ex-periments [28]. It is now accepted that light can behave as either a particleor a wave, depending on the type of experiment and critically, the size scaleover which light interacts with materials.The transition point between when light behaves as a particle or a waveremains debated and has sometimes been a source of confusion in the liter-ature. For example, a widely cited 1998 experiment by Thomas Ebbesen’sgroup published in Nature demonstrated what was then claimed to be ex-31.2. Maxwell’s Equationstraordinary light transmission through a nanohole array [29]. The measuredlight transmission through the hole array was 130% greater when comparedto a model of the expected light transmission through the hole array basedthe amount of light falling on the area of the holes (a particle-like picture)[30]. Subsequent electrodynamic simulations demonstrated that the hole-array transmission could not solely be attributed to light falling through thearea of the holes, but that a significant portion of transmission derived fromthe coupling of incident light into surface plasmons, which then shuttledlight through the nanoholes [31]. This example illustrates the importanceof selecting the appropriate modelling approach when describing light in-teraction with materials, which can be particle-like, wave-like, or perhapsboth.1.2 Maxwell’s EquationsComputational nanophotonics is rooted in electrodynamic simulationswhich solve Maxwell’s equations. Maxwell’s equations are a set of fundamen-tal mathematical relations which describe the interaction between electricand magnetic fields and their sources. These equations were first introducedby the Scottish mathematician and physicist, James Clerk Maxwell in 1862[32] in order to summarize empirical observations of electrical and magneticeffects observed by Michael Faraday and others. Maxwell’s equations aregiven by∇×H(r, t) = ∂D(r, t)∂t+ J(r, t) (1.1a)∇×E(r, t) = −∂B(r, t)∂t(1.1b)∇.D(r, t) = ρe (1.1c)∇.B(r, t) = 0 (1.1d)where E(r, t) is the electric field vector, D(r, t) is the electric displacementvector, H(r, t) is the magnetic field vector, B(r, t) is the magnetic flux den-sity vector, J(r, t) is the electric current density vector, ρe is the electriccharge density, r = xax + yay + zaz is the position vector, t is the timevariable.Maxwell’s equations consist of four equations and six independent vari-ables and cannot be fully solved without further constraints. To modelelectromagnetic effects in materials, we rely on constitutive relations to link41.2. Maxwell’s Equationsthe electric displacement vector, D(r, t), and magnetic flux density vector,B(r, t), to the electric field, E (r, t), and magnetic field, H (r, t), respectively.The simplest and most widely used constitutive relation is to assume linearrelationsD(r, t) = r0E(r, t) (1.2)andB(r, t) = µrµ0H(r, t) (1.3)where r is the relative electric permittivity, 0 is the free-space electricpermittivity, µr is the relative magnetic permeability, and µ0 is the free-space magnetic permeability. The relative permittivity and permeabilitypresented in Equations (1.2) and (1.3) describe, respectively, the electric andmagnetic response of a material that is uniform, isotropic, and independentof frequency. Throughout this thesis, we assume that materials are uniformand isotropic, but, when we treat metallic media, we will assume frequencydependence (to be described in the next section). As our investigations arerestricted to the infrared and visible frequency range, we will assume thatall materials are non-magnetic, meaning that we set µr equal to 1. We willalso invoke an additional constitutive relation known as Ohm’s law whichfurther constrains Maxwell’s equations such that current density, J(r, t), isrelated to the electric field, E(r, t), byJ(r, t) = σE(r, t) (1.4)where σ is the electric conductivity. Although not immediately apparent,Maxwell’s equations fully describe the wave nature of electromagnetic waves.This can be shown by first assuming a source free region where ρe = 0 andJ = 0, which reduces Maxwell’s equations to∇×H(r, t) = r0∂E(r, t)∂t(1.5a)∇×E(r, t) = −µrµ0∂H(r, t)∂t(1.5b)∇.D(r, t) = 0 (1.5c)∇.B(r, t) = 0 (1.5d)Taking the curl in Equation (1.5b) and assuming a non-magnetic medium(µr = 1) yields∇×∇×E(r, t) = −µ0 ∂∂t[∇×H(r, t)] (1.6)51.3. Drude ModelBy using Equation(1.5a), Equation (1.6) becomes∇×∇×E(r, t) = −µ0r0∂2E(r, t)∂t2(1.7)Note that the left-hand side of Equation (1.7) can be simplified using thefollowing vector calculus identity (valid only if the electric field is continuousand differentiable)∇×∇×E(r, t) = ∇ (∇ ·E(r, t))−∇2E(r, t) (1.8)and by assuming a source-free region, such that Equation (1.7) simplifies to∇2E(r, t)− µ0r0∂2E(r, t)∂t2= 0. (1.9)Assuming the speed of light in free space isc = 1√µ00(1.10)yields a wave equation that describes the spatio-temporal evolution of theelectric field∇2E(r, t)− rc2∂2E(r, t)∂t2= 0, (1.11)commonly known as the Helmholtz wave equation. A similar process can beapplied to Equation (1.5a) to obtain a wave equation for the magnetic field∇2H(r, t)− rc2∂2H(r, t)∂t2= 0. (1.12)Hence, Maxwell’s equations model light as a vector wave consisting ofcoupled electric and magnetic fields travelling at the speed of light dividedby √r.1.3 Drude ModelThe frequency dependence of the electric response of certain materialscan be described through an elegant material model proposed by Paul Drudein 1900 [33, 34]. The model considers a plasma consisting of a gas of mobileelectrons with free number density N moving against a fixed background ofposition ion cores under the influence of an applied electric field. The mo-tion of the electrons is damped via collisions occurring with a characteristic61.3. Drude Modelfrequency, Γ = 1/τ , where τ is the relaxation time of the free-electron gas.The Newtonian displacement of an electron is given byme∂2r∂t2+meγ∂r∂t+meω20r = −qE (1.13)where me is mass of an electron, ωo is the natural resonance frequency ofthe electron, q is the charge of the electron and r is the displacement ofthe electron. By assuming that both the displacement and driving field aretime-harmonic at a frequency ω, we can isolate the frequency-dependentdisplacement of a single electron in response to an electric field asr(ω) = − qmeEω20 − ω2 − iωΓ(1.14)The collective response of the electron gas contributes toward a macro-scopic polarization, P = −Nqr(ω), can now be expressed asP = Nq2meEω20 − ω2 − iωΓ. (1.15)The polarization can be related to the displacement vector byD = 0rE = 0E + P. (1.16)Substituting Equation (1.16) and replacing Γ = 1/τ into the Equation (1.15)yieldsD = 0[1 +ω2pω20 − ω2 − iω(1/τ)]E (1.17)where ω2p = Nq20meis the plasma frequency. The Drude model then gives arelative, frequency-dependent electric permittivity expressed asr = 1 +ω2pω20 − ω2 − iω(1/τ). (1.18)In the case of a metal in which the electrons are free and not bound to anucleus, there is no natural resonance frequency. As a result, the relativeelectric permittivity simplifies tor = 1−ω2pω2 + iω(1/τ) . (1.19)71.4. Surface PlasmonsSplitting Equation (1.19) into distinctive real and imaginary parts yieldsr = 1−ω2pω2 + 1τ2+ iω2pτω(1 + ω2τ2) . (1.20)A key insight from the Drude model is that in the presence of dispersion(frequency dependence of the permittivity), the real part of the electricpermittivity can take on positive and negative values. This can be clearlyshown by assuming a negligible damping force, 1/τ ≈ 0, such that theelectric permittivity can be further simplified intor = 1−ω2pω2(1.21)which is negative (metal-like) for frequencies less than the plasma frequency,ω < ωp, and positive (dielectric-like) for frequencies greater than the plasmafrequency, ω > ωp.1.4 Surface PlasmonsFigure 1.2: A single interface between two distinct media. Under certainconditions, the interface can support surface-bound electromagnetic wavesthat obey Maxwell’s equations.Surface plasmons (SPs) are electromagnetic waves coupled to collectivefree-electron oscillations at an interface [29]. By solving Maxwell’s equations81.4. Surface Plasmonsusing the planar interface configuration in Figure 1.2, we can demonstratea few salient features of surface plasmons and necessary conditions for theirexistence. Medium 1 occupies the half-space z > 0 and has a relative electricpermittivity 1. Medium 2 occupies the half-space z < 0 and has a relativeelectric permittivity 2. The plane of incidence is defined by the planecreated from the wave vector of the incident plane wave and the normalto the interface. There are two unique polarization states which can beconsidered: one in which the incident electric field is perpendicular to theplane of incidence (also known as transverse electric, TE) and the other inwhich the incident electric field is parallel to the plane of incidence (alsoknown as transverse magnetic, TM). Assuming a transverse magnetic (TM)plane wave at the interface, the magnetic fields in the two regions H1 andH2 areH1 = (H1yay) ei(k1,xx+k1,zz−ωt) (1.22a)H2 = (H2yay) ei(k2,xx+k2,zz−ωt) (1.22b)where kj = kj,xx+ kj,zz is the wavevector. The corresponding electric fieldsin the two regions E1 and E2 areE1 =1ω1[−k1,zax − k1,xaz] ei(k1,xx+k1,zz−ωt) (1.23a)E2 =1ω2[−k2,zax − k2,xaz] ei(k2,xx+k2,zz−ωt). (1.23b)To fulfill continuity of the tangential component of the electric field atz = 0, the wavevector is conserved at the interface: k1,x = k2,x = kx.Equating the x-component of Equation (1.23a) and (1.23b) yieldsk1,z1= k2,z2→ k1,zk2,z= 12. (1.24)In order for the field solutions to be bound to the interface, the normalwavevector components are required to be imaginary and have opposite signto describe field decay away from the interface. Comparing Equation (1.24),it is clear that the dielectric constants of both materials must have oppositesigns (1 = −2), implying that surface plasmons only exist at the interfacebetween a dielectric (positive real part of permittivity) and a metal (negativereal part of permittivity). Applying a similar treatment while assuming TEpolarization shows that TE-polarized surface plasmons would require an91.4. Surface Plasmonsinterface between materials of opposing sign of the magnetic permeability.Due to the absence of materials with negative real part permeability, TE-polarized surface plasmons cannot exist [35].Further analysis of the surface plasmon electromagnetic solution yieldsthe dispersion relation governing their existence. From Equation (1.24), wehavek21,x + k21,z =ω2c21 (1.25a)k22,x + k22,z =ω2c22. (1.25b)Dividing Equation (1.25a) by Equation (1.25b) and simplifying the expres-sion yieldsk21,zk22,z=ω2c2 1 − k2xω2c2 2 − k2x. (1.26)Substituting Equation (1.24) into the expression above and simplifyingagain, we have the dispersion relationkspp ≡ kx = ωc√121 + 2. (1.27)Note that the dispersion relation applies only to surface plasmons on in-finite planar interfaces. Surface plasmons can exist on discrete particles andarrays, but their dispersion relations are more complicated and not easilysolved by analytical approaches. The coupling of incident light into surfaceplasmons can lead to sharp frequency- or angular-dependent optical proper-ties and is sometimes referred to as a surface plasmon resonance [36]. Noblemetals such as gold (Au), silver (Ag), and aluminum (Al) are commonlyused to sustain surface plasmons since their collision rates are several ordersof magnitude smaller than the plasma frequency, as summarized in Table1.1.101.5. Fresnel EquationsMetal Plasma frequency,ωp (Hz) Collision rate,τ−1(s−1)Silver 2.186× 1015 5.139× 1012Gold 2.15× 1015 17.14× 1012Aluminum 2.911× 1015 31.12× 1012Table 1.1: Plasma frequency and collision rates for Ag, Au, and Al. Thedata is measured by [1].1.5 Fresnel EquationsWhen a beam of light with a well-defined direction strikes a dielectricsurface, a portion of incident light is reflected and another portion is re-fracted into the medium. The reflected light has a direction defined by lawof reflectionθr = θiwhere the angle of reflected light, θr, is equal to the angle of incident light,θi. The refracted light has a direction defined by Snell’s lawn1 sin θi = n2 sin θtwhere n1 and n2 are the refractive indexes for medium 1 and medium 2,respectively, and θt is the angle of transmitted light. Both the law of reflec-tion and Snell’s law were originally discovered from empirical observations,but can be readily derived from Maxwell’s equations by considering planewave solutions at a planar interface.Fresnel equations relate the amplitude of the reflected and refractedplane waves from a planar interface to the amplitude of an incident planewave. We will consider two semi-infinite half-spaces, medium 1 occupyingthe region (z < 0) and medium 2 occupying the region (z > 0), and theplanar interface between the regions at z = 0. A plane wave is incident atan oblique angle from medium 1 and is both reflected from and refractedacross the interface as illustrated in Figure 1.3. In general, any wave can bebroken down into a linear combination TE and TM polarization. We beginby first considering TE polarization.111.5. Fresnel Equations(a) (b)Figure 1.3: Oblique incident with (a) E perpendicular to the plane of inci-dence (TE) and (b) E parallel to the plane of incidence (TM).Assuming TE polarization, the incident electric field and magnetic fieldin medium 1 are respectively defined byEis = Eioeiki(x sin θi+z cos θi)ay (1.28a)His =Eioη1(− cos θiax + sin θiaz) eiki(x sin θi+z cos θi), (1.28b)the reflected electric field and magnetic field in medium 1 are respectivelydefined byErs = Eroeikr(x sin θr−z cos θr)ay (1.29a)Hrs =Eroη1(cos θrax + sin θraz) eikr(x sin θr+z cos θr), (1.29b)and the transmitted field and magnetic field in medium 2 are respectivelydefined byEts = Etoeikt(x sin θt+z cos θt)ay (1.30a)Hts =Etoη2(− cos θtax + sin θtaz) eikt(x sin θt+z cos θt) (1.30b)where η1 and η2 are the relative impedances for medium 1 and medium 2,respectively. In order to conserve energy, the tangential components of the121.5. Fresnel Equationselectric and magnetic fields must be continuous at z = 0, resulting inEio + Ero = Eto (1.31a)Eioη1(− cos θi) + Eroη1(cos θr) =Etoη2(− cos θt) (1.31b)1η1(Eio − Ero) cos θi = Eioη2cos θt. (1.31c)Next, replacing the right-hand side of Equation (1.31c) with Eto fromEquation (1.31a) and yields(η2 cos θi − η1 cos θt)Eio = (η2 cos θi + η1 cos θt)Ero. (1.32)Note that the relative impedance for medium 1 and medium 2 are η1 = ηoη1and η2 = ηoη2 where ηo is the free-space impedance. So, Equation (1.32)becomes(ηoη2cos θi − ηoη1cos θt)Eio =(ηoη2cos θi +ηoη1cos θt)Ero (1.33a)(n1 cos θi − n2 cos θt)Eio = (n1 cos θi + n2 cos θt)Ero. (1.33b)The Fresnel reflectivity coefficient for TE polarization can be expressedasrTE =EroEio= n1 cos θi − n2 cos θtn1 cos θi + n2 cos θt(1.34)and the Fresnel transmissivity coefficient for TE polarization can be ex-pressed astTE =2n1 cos θin1 cos θi + n2 cos θt. (1.35)A similar approach can be applied for the transverse magnetic case,which yields the Fresnel reflectivity coefficient for TM polarizationrTM =EroEio= n1 cos θt − n2 cos θin1 cos θt + n2 cos θi(1.36)and the Fresnel transmissivity coefficient for TM polarizationtTM =2n1 cos θin1 cos θt + n2 cos θi. (1.37)The reflectance and transmittance describe the ratio of power that isreflected or transmitted from an interface. This is used, for example, in131.5. Fresnel Equationsthe bidirectional scattering distribution function (BSDF) of an object whichinvokes reflectance and transmittance as the function of directions of in-cidence, reflection, and transmission from the interface of an object. Thereflectance and transmittance can be described byR = PrPi; T = PtPi(1.38)where Pr is the reflected power, Pt is the transmitted power, and Pi is theincident power. For media with no absorption, continuity of energy givesPi = Pr + Pt → 1 = R+ T. (1.39)Equation (1.39) can be re-expressed in terms of the product of irradiance(intensity received by a surface per unit area) and area of the beam asIiAi = IrAr + ItAt (1.40)where Ii, Ir and It are the intensities of the incident, reflected, and transmit-ted beams, respectively, while Ai, Ar and At are the cross-sectional areas ofthe incident, reflected, and transmitted beams, as illustrated in Figure 1.4.By relating the cross-sectional area, A, on the interface to the cross-sectionalareas of the beams, Equation (1.40) becomesIi cos θi = Ir cos θr + It cos θt. (1.41)Given that the intensity is related to the field by I = 12n0cE2, Equation(1.41) can be written as12n10cE2io cos θi =12n10cE2ro cos θr +12n20cE2to cos θt (1.42a)→ n1E2io cos θi = n1E2ro cos θr + n2E2to cos θi. (1.42b)By dividing Equation (1.42b) with the terms on the left-hand side, theexpression reduces to1 = E2ro cos θrE2io cos θi+ n2E2to cos θtn1E2io cos θi. (1.43)Since θi = θr, the expression above can be simplified to1 =(EroEio)2+ n2 cos θtn1 cos θi(EtoEio)2. (1.44)141.5. Fresnel EquationsFinally, reflectance and transmittance can be related to the reflectivityand transmissivity coefficients byR =(EroEio)2= r2 (1.45)T = n2 cos θtn1 cos θi(EtoEio)2= n2 cos θtn1 cos θit2. (1.46)In situations where we consider daylight or other unpolarized light sources,the reflectance and transmittance are approximated by averaging of re-flectance and transmittance from both transverse electric and transversemagnetic polarizations byR = 12 (RTE +RTM ) =12(r2TE + r2TM)(1.47)T = 12 (TTE + TTM ) =12n2 cos θtn1 cos θi(t2TE + t2TM). (1.48)Figure 1.4: Cross-sectional areas (highlighted in yellow circle) of the inci-dent, reflected, and transmitted light beams, compared to the cross-sectionalarea of the beam on the interface.151.6. Radiometry vs Photometry1.6 Radiometry vs PhotometryLight intensity measurements can be made in terms of radiometric orphotometric quantities [37]. Radiometry describes measurements of opticalradiation in the infrared, visible and ultraviolet, in terms of its power distri-bution over space. Photometry describes measurements of visible radiationas perceived by the human eye. Human color perception varies from personto person. In computational nanophotonics, light quantities are expressedin radiometric measurements such as spectral power distributions [38]. Incomputer graphics, light quantities are expressed in terms of human eyeperception and presented based on. Color measurements are a systematicalapproach of quantifying the colors perceived by humans as numerical values.Colour measurements depend on the illumination, spectral characteristics ofthe object, and spectral sensitivity of the human eye [39]. Colorimetry is amethod to correlate colour perceived by human eyes in terms of a tristimuluscolour system. For example, the CIE 1931 XYZ color space defines perceivedcolours in terms of X (red), Y (green), and Z (blue). The conversion of spec-tral response into XYZ color space uses CIE 1931 XYZ color transformationsystem integration with a D65 illuminant light source expressed asM = KN∫λS(λ)ID65(λ)M¯(λ)dλ (1.49)whereN =∫λID65(λ)y¯(λ)dλ. (1.50)In the above equations, M = X,Y, Z is the tristimulus response, x¯, y¯, z¯ arethe standard color matching functions, M¯ . S(λ) is the spectral reflectanceor transmittance, ID65(λ) is the spectral power distribution of a standardD65 illuminant, and K is the scalar factor either 0 or 100 [40].There is a common misconception that photometric representations oflight based on RGB values are less accurate or inferior compared to radio-metric representations based on spectral distributions [41]. In reality, theyare distinct approaches which have value depending on application. For ex-ample, physically-based rendering employs a fundamental rendering equa-tion (to be discussed further) which uses radiometric quantities, but oftenconverts radiometric quantities into photometric quantities for producing afinal rendered image based on human eye perception. The conversion fromradiometric quantities to photometric quantities is possible by taking radio-metric quantities weighted by a typical human eye responses described by aluminosity function, V (λ) [42].161.7. Discrete Method to Solve Maxwell’s EquationsDelta E,∆E00 Rating< 1 Imperceptible difference1− 2 Perceptible difference after close observation2− 10 Perceptible difference at a glance10− 49 Colors that are more similar than opposite100 Color that are exactly oppositeTable 1.2: Delta E color difference indicator.The perceived color from the eye is subjected to human response andthe difference between two colors can be quantified by Delta E, ∆E, a well-established metric to describe the distance between two colors based on anumber rating. For instance, the CIE Delta E 2000 standard, ∆E00 evaluatescolor difference according to the ranges presented in Table 1.2.1.7 Discrete Method to Solve Maxwell’sEquationsElectromagnetic wave interactions in configurations which can be fullydescribed by analytical solutions to Maxwell’s equations are generally lim-ited to those with a high degree of symmetry. Mie theory, for example, isset of analytical solutions which describe the scattering of an incident planewave by a spherical particle of arbitrary dimensions [43]. Another exampleis analytical solutions for the electromagnetic modes in highly symmetricsemi-infinite waveguides, such as a slot waveguide. For most configura-tions, particularly those lacking symmetry or those of finite extent, it isnecessary to use numerical solutions to Maxwell’s equations to model lightinteractions. Numerical methods are based on defining a region of space interms of a discrete grid, implementing adequate boundary conditions, andthen computing for the electric and magnetic fields over the grid, either inthe time or frequency domains. Frequency-domain techniques, such as thefinite-element-method, are widely used to model the steady-state responseof materials at single frequencies. Time-domain techniques, such as thefinite-difference time-domain (FDTD) method, are used to model the tran-sient response of materials over a spectral range. In this thesis, the FDTDmethod is chosen due to its ease of implementation and ability to modelbroadband behaviour in a single simulation [44].The FDTD method was originally proposed by Yee [45] to solve the171.7. Discrete Method to Solve Maxwell’s EquationsMaxwell’s equations in the time-domain by applying central-difference ap-proximations to discretize the spatial and temporal partial derivatives inMaxwell’s equations. The FDTD method is implemented over a Yee grid(in either one-, two-, or three-dimensions): a staggered grid in which elec-tric and magnetic field quantities are offset from each other by half of thenormal grid spacing in both space and time. The field update equationsare formulated by substituting finite difference approximations for the timederivatives appearing in Maxwell’s equations and then solving for updatedfield values based on field values at a previous time steps [46]. Please re-fer to Appendix A for the details of derivation of iterative field updatingequations.To prevent the wave reflections from the edges of the computational do-main, absorbing boundary conditions are typically placed around the sim-ulation space. A common implementation is the perfectly matched layer(PML), which is based on matching the impedance of a boundary region tothat of the simulation domain [47, 48]. When examining a periodic system,such as an array, periodic boundary conditions are used. Periodic bound-ary conditions naturally duplicate the electric and magnetic fields at oneside of the simulation domain and inject them at another side. The advan-tage of periodic boundary conditions is that they enable computation of theresponse of an infinite system by simulating just a single unit cell of thesystem.The spatial and temporal grid resolutions are required to be sufficientlyfine to ensure accuracy, limit numerical dispersion, and maintain stabilityof the FDTD method. The general rule of thumb to achieve low numericaldispersion and high accuracy is to keep the spatial grid size to less than1/10λ or less than the shortest wavelength in the simulation domain, givenby [46, 49]min(∆x,∆y,∆z) ≤ λmin10nmax (1.51)where nmax is the maximum refractive index value in the computation do-main, and ∆x, ∆y, ∆z are the spatial grid resolutions in the x, y and zdirections, respectively. The temporal grid resolution is linked to the spatialgrid resolution and must fulfill the Courant Friedrich Lewy (CFL) conditionto maintain stability of the FDTD method. In three dimensions, the CFLcondition is defined by [46]∆t ≤ 1v√1(∆x)2 +1(∆y)2 +1(∆z)2(1.52)181.8. Physically Based Renderingwhere v is the speed of the light in medium and ∆t is the temporal gridresolution.One of the main advantage of the FDTD method is that it is versatileand intuitive. The user can specify the arbitrary material distributions inthe simulation domain and, because it is a time-domain technique, com-puted electric and magnetic fields can be visualized by animated moviesof their spatio-temporal evolution, which can lead to enhanced physical in-sights [50]. In addition, the FDTD method can be used with a broadbandsource to investigate the response of a model over a wide range of frequen-cies in a single stimulation. This capability can be useful, for example,when simulating a configuration with an unknown resonant response [50].The disadvantage of the FDTD method is computational intensiveness. TheFDTD method requires the sub-wavelength spatial discretization and finetemporal resolution to maintain the CFL condition, resulting in long com-putation times, large memory usage during the simulation, and large outputfiles. The computational challenges scale up quickly as the dimensions ofthe simulation increase. When implementing the three-dimensional FDTDmethod on a single computer, it becomes infeasible to deploy simulationdomains greater than 1000 × 1000 × 1000 pixels. Furthermore, when sim-ulating configurations with dimensions that encompass many wavelengths,the FDTD method can provide excessive details on overall light behaviorwhich could otherwise be simulated using ray-optical approaches, such asphysically-based rendering.1.8 Physically Based RenderingPhysically based rendering (PBR) is a photometric computation imag-ing technique that models the photorealistic appearance of objects by track-ing physically plausible point-to-point transport of light in an environmentfrom source to a camera. PBR has evolved from early geometric represen-tations and visibility algorithms of computation imaging (ray casting) inthe 1960s–1970s which were developed within the constraints of low com-putational power [51]. PBR began to take off in popularity in the 1980safter Whitted’s seminal paper introduced the concept of a recursive ray-tracing technique for simulating reflection, refraction, and shadows causedby objects [52]. The rendered images from his approach demonstrated thepotential to create computational images that were photorealistic – emulat-ing the real-life appearance of the object that would be seen by the humaneye.191.8. Physically Based RenderingThe rendered appearance of objects using ray-tracing techniques in the1980s was far from perfect, particularly with respect to their inability tomodel diffuse reflections due to roughness. The next major advancementfrom Cook and Torrance, who introduced microfacet reflection models todescribe diffuse appearances of objects with roughness [24]. Kajiya nextintroduced a path-tracing technique along with the rendering equations tomodel light transport by using just a handful of recursive rays to form pixelsof an image, tracing their paths between different surfaces in an environmentuntil they reached the light source or any predefined termination condition[53]. The general rendering equation introduced along with path tracing isbased on computing the scattered spectral radiance, Lo(xo, ωˆo, λ) (Figure1.5(a)) from each surface interaction by [53, 54]Lo(xo, ωˆo, λ) = Le(xo, ωˆo, λ) +∫Ωf(ωˆi, ωˆo, λ)Li(xo, ωˆi, λ)(ωˆi.nˆ)dωˆi (1.53)where ωˆo is the outward light direction at the point xo, ωˆi is the inwardlight direction at point xo, nˆ is the surface normal vector, λ is the vari-able describing the spectral distribution of light into either three (RGB) ormore (spectral) channels, Le(xo, ωˆo, λ) is the emitted spectral radiance fromthe point, f(ωˆi, ωˆo, λ) is the bidirectional scattering distribution function(BSDF) that relates incoming radiance along a direction i to outgoing ra-diance along with a direction o of a surface (Figure 1.5(c)), Li(xo, ωˆi, λ) isthe incoming spectral radiance along ωˆi, ωˆi.nˆ is the weakening factor de-scribing the cosine Lambert rule (Figure 1.5(b)), and Ω is the hemispherecentered around nˆ containing all possible values for ωˆi. Depending on thetype of object, the emitted spectral radiance, Le is generally omitted fornon-self-illuminant and non-florescent objects.The light paths which terminate at the camera generally undergo mul-tiple interactions with different surfaces in a scene after emerging from thelight source. The algorithm tracks the transfer of radiant energy from thelight source to the terminal camera position by applying Equation (1.53) re-cursively to describe point-to-point energy transport between multiple sur-faces from the source to the camera.201.8. Physically Based Rendering(a) (b) (c)Figure 1.5: Illustration of (a) scattered spectral radiance, (b) incoming spec-tral radiance and (c) BSDF relating directional and intensity of incomingand scattered spectral radiance over a point, xo. In the figure, the openarrowhead describes the direction of spectra radiance and the closed arrow-head describes the directional vector for ωˆi and ωˆo.Analytical computation of the integral expression in Equation (1.53) isgenerally not possible because light is treated as discrete particles (geometryoptics). Kajiya demonstrated that Monte Carlo integration could be used tofind an approximate numerical solution to the rendering equation integral.Monte Carlo integration uses random sampling to approximate the solutionof integrals. The principle of the Monte Carlo integration is illustratedin Figure 1.6(a), where the amount of light arriving at the hemisphere iscalculated by casting random sample rays to the scene from point, P , tosample the rays and approximate the amount of light reaching point P .For a more detailed discussion about Monte Carlo integration, please referto Appendix B. If a ray cast from P intersects with another object, MonteCarlo integration is applied again to approximate the light returned to pointP by this object. Figure 1.6(b) illustrates the recursive process of applyingMonte Carlo integration to trace the path of a ray sampled at the lightsource. This method is simple and robust because the value of the integralis evaluated for arbitrary points in the domain without solving the entireintegral. It is interesting to note that the original demonstration of path-tracing was viewed as computationally expensive and nearly infeasible, as arendering time of 9 hours was required to produce an image of two spheresat a resolution of 256 × 256 pixels [53].Bidirectional path tracing and metropolis light transport (MLT) are newtechniques introduced to improve the original path tracing approach. Bidi-211.8. Physically Based Renderingrectional path tracing is a two-pass rendering approach that first begins withboth normal path tracing from a camera and backward path tracing fromthe light source and then meeting in the middle to find the most importantpaths between the source and camera [55, 56]. The MLT technique uses theMonte Carlo method to describe light transport, finding the most mean-ingful path between the camera point and light source. Once it has foundthis path, it will use small perturbations of the interaction point to findother meaningful paths [57]. With continued improvements in optimizingpath tracing algorithms, increased computational power, and greater paral-lel processing, it is now possible to realize the ideal of real-time ray tracing inwhich photorealistic scenes can be computed on the fly [58] . PBR is a lightsimulation technique based on geometric optics that can model the visualappearance of objects by tracking ray propagation in a virtual environment.Assumptions of modern PBR rendering engines [59] include:a. Linearity: The combined effect of two inputs to an optical system isidentical to total of the effects of each of input individually.b. Energy conservation: Outputs from a scattering event cannot exceedthe inputs.c. No polarization: Unpolarized light is assumed throughout the ray-tracing computation.d. No fluorescence: Behaviour at one wavelength is independent of be-haviour at other wavelengths.e. Steady state: Light in the virtual environment is presumed to havereached equilibrium and the radiance distribution remains constant overtime.These assumptions result in the inability for PBR to describe wave interac-tions at sub-wavelength scales, such as diffraction and interference. However,this limitation has been alleviated by recent efforts to modify PBR to handlewave interactions. These efforts will be described in Section 1.15.Table 1.3 summarizes some of the commercially available, open-source,and research-based rendering engines, which are optimized for renderingmodes in CPU or GPU or both (hybrid). The rendering modes will influencethe time required to generate images that are production ready (low noise).GPU rendering modes can yield production-ready renders in no time, butthe limited VRAM (video memory) restricts the complexity of the scene. Inaddition, the quality of renderers depends on the algorithm used to recreate221.8. Physically Based Renderingnatural lighting, also known as global illumination (GI). In general, there areseveral GI algorithms such as radiosity, ray tracing, path tracing, metropolislight transport, ambient occlusion, photon mapping, and HDR image-basedlight to recreate physically plausible lighting environment.(a) (b)Figure 1.6: (a) Monte Carlo integration to approximate the amount of lightarriving at point P . (b) Recursive procedure to determine the amount oflight arriving at point P .231.8. Physically Based RenderingRenderer Developer RenderingModeGI LicenseArnold Autodesk GPU/CPU Physically-based uni-directionalpath tracerProprietaryCoronaRenderCorona CPU Intel Embreeray tracingkernelsProprietaryCycle Blender CPU/GPU Physically-based pathtracingGPLv2Cycles 4D Insydium GPU/CPU Path tracing GPLv2Iray Nvidia CPU/GPU Path tracing ProprietaryKeyshot Luxion CPU Real-time raytracingProprietaryLuxCoreRenderGrimaldi,J.P et al.CPU/GPU Path Tracing GPLv2Maxwell Next Limit GPU Path tracingphotorealisticProprietaryMitsuba 2 Jakob,W CPU/GPU Varying(research-based ren-derer)Free OpenSourceOctane OTOY GPU Path tracing ProprietaryRadiance Ward, G CPU Ray tracing Free OpenSourceRenderMan Pixar Hybrid Monte Carlopath tracingProprietaryVray Chaos Hybrid Path tracing ProprietaryTable 1.3: List of selected commercially available, open source, and research-based rendering engines.241.9. Physically-Based Rendering Materials1.9 Physically-Based Rendering MaterialsGenerating physically plausible rendered images not only depends onthe ray-tracing algorithm, but also requires representation of the proper-ties of the material, including its surface finishing, color, glossiness and re-flectivity/transmissivity. The PBR material model is the representation ofmaterials in PBR and is described by the bidirectional scattering distribu-tion function (BSDF), which generally consist of a bidirectional reflectancedistribution function (BRDF) and a bidirectional transmittance distributionfunction (BTDF) describing the direction and strength of light scattered pat-terns for a given incoming light direction. For instance, Figure 1.7 illustratesthe reflection and transmission patterns of a material for various degrees ofsurface roughness. The scattering patterns generally become wider as rough-ness increases, causing the reflection and transmission from the surface tochange from specular highlights to blurry highlights. Further discussion ofthe surface roughness of materials will be covered in the next section.Figure 1.7: The scattering distribution patterns for reflections and trans-mission from a surface for increasing surface roughness. Rougher surfacetends to have a wider (spread out) scattering distribution pattern.The rendered appearance of an opaque object can be determined solelyfrom the BRDF. The rendered appearance of translucent and transparentobjects is determined from both the BRDF and BTDF. The PBR materialmodels can be mathematically derived or created from empirical measure-ments. Mathematically-derived material models incorporate descriptions of251.10. Microfacet Theorya wide range of light interactions, including Fresnel reflectance of the ma-terial, microgeometry of the roughness, albedo, anisotropy, metallicity, andother physical properties [54, 59–61]. For some translucent materials, suchas wine, milk, human skin, gemstones, and some translucent plastics, ma-terial models are adapted to mimic light scattering at the subsurface of theobject, in which light will penetrate through the surface and be reflectedmultiple times at irregular angles inside the material before exiting the ma-terial at a different angle [62–66]. Empirically-measured material modelsuse photogrammetry techniques to capture the radiant intensity scatteringpattern of a real-world material to generate an empirical BSDF [67–69].The acquisition of a measured BSDF uses an opto-mechanical device con-sisting of gonio-photometers/reflectometers and image-based devices thatautomates the collection of scattered light intensity [68–70]. The acquiredmeasurements are encoded into a binary BSDF material database and readdirectly by the rendering software.1.10 Microfacet TheoryMicrofacet theory is a mathematical approach to describe light reflec-tion from a rough surface. Fundamentally, it decomposes a surface intoa collection of microfacets, which individually reflect incident light. Eachvisible surface normal point contains many microfacet surface normals thatbounce reflected light in different directions. The orientations of the individ-ual microfacets are randomly distributed, and it is described by a statisticaldistribution known as the normal distribution function (NDF) [61, 71, 72].Occluded shadowing and masking effects due to the height of microfacetsand viewing angle are also important considerations in microfacet theory[73].As shown in Figure 1.8, shadowing describes the occlusion of the light bymicrofacet surface details and masking describes how some microfacets canhide other surface details from the camera.If there is a correlation between the microgeometry height and the sur-face normal, then shadowing and masking can effectively change the normaldistributions. For instance, imagine a surface where the raised parts havebeen smoothed by weathering and the lower parts remain rough. At glanc-ing angles, the lower part will tend to be shadowed or masked, resulting aneffectively smoother surface. The occluded light due to microfacet detailsdoes not disappear, and there is a possibility that light is reflected onto themicrogeometry and undergoes multiple bounces before reaching the cam-era. Each bounce of light reflected in the microgeometry is modified by the261.10. Microfacet TheoryFresnel reflectance. Interreflections within the microgeometry tend to besubtle in most dielectric materials but in metallic materials, the multiplebounces can yield a visibly diffuse reflection and greater color saturationdue to multiple surface interactions.(a) (b) (c)Figure 1.8: Geometric effects of microscale roughness: (a) the green dashedarrows indicate an area that is shadowed (occluded from the light) by an-other microgeometry, (b) the grey dashed arrows indicate an area that ismasked (occluded from view) by another microgeometry, (c) the light inter-reflects between the microscale structures.Microfacet theory can be extended to model diffuse transmission througha rough surface. Microfacet theory describing light reflection from and re-fraction through a rough surface is expressed asf(ωˆi, ωˆo, nˆ, mˆ) = fr(ωˆi, ωˆo, nˆ, mˆ, hˆr) + ft(ωˆi, ωˆo, nˆ, mˆ, hˆt) (1.54)where fr(ωˆi, ωˆo, nˆ, mˆ, hˆr) is the bidirectional reflectance distribution function(BRDF) for reflection from the microfacets and ft(ωˆi, ωˆo, nˆ, mˆ, hˆt) is thebidirectional transmittance distribution function (BTDF) for transmissionthrough the microfacets. The BRDF is given by [2]fr(ωˆi, ωˆo, nˆ, mˆ, hˆr) =F (ωˆi, mˆ)G(ωˆi, ωˆo, mˆ, hˆr)D(mˆ, hˆr)4|ωˆi · nˆ||ωˆo · nˆ| (1.55)with the normalized half reflection angle vector,hˆr =sgn(ωˆi · ωˆo)(ωˆi + ωˆo)‖(ωˆi · ωˆo)(ωˆi + ωˆo)‖ (1.56)271.10. Microfacet Theoryand the BTDF is given byft(ωˆi, ωˆo, nˆ, mˆ, hˆt) =n2o(1− F (ωˆi, mˆ))G(ωˆi, ωˆo, mˆ, hˆt)D(mˆ, hˆt)(n2i (ωˆi · hˆt) + n2o(ωˆi · hˆt))2 (1.57)with the normalized half transmission angle vector,hˆt = − (niωˆi + noωˆo)‖niωˆi + noωˆo‖ (1.58)where nˆ is the macrosurface normal vector, mˆ is the microfacets with normalvector, F (ωˆi, mˆ) is the Fresnel reflectance of the microsurface, D(mˆ, hˆr) andD(mˆ, hˆt) are the microfacet normal distribution functions (NDFs) describ-ing the statistical distribution of surface normal mˆ over the microsurfacefor the BRDF and BTDF respectively, G(ωˆi, ωˆo, mˆ, hˆr) and G(ωˆi, ωˆo, mˆ, hˆt)are the masking-shadowing functions describing the relative orientation ofthe microfacets visible in both directions ωˆi and ωˆo with a fractional value0 ≤ G ≤ 1 for the BRDF and BTDF respectively, and ni and no are therespective refractive indexes on the incident and transmitted side [2, 24].The Fresnel reflectance, F (ωˆi, mˆ), corresponding to the microfacets iscomputed either as a function of wavelength or RGB values and largely dic-tates the color appearance of a rough surface. Various analytic expressionsfor F have been reported in the past. The most widely used model is theunpolarized Fresnel reflectance, introduced by Cook and Torrance [24]. Be-cause of the visual effect of polarization is limitation in most of the PBRsystem, the light is assumption is unpolarized to interact with the envi-ronment that resulting the Fresnel reflectance used in the PBR system isaverage value of TE and TM polarization Fresnel reflectance [59].Direct calculation of the Fresnel reflectance for the microfacets is com-putationally expensive and requires refractive index values over the visiblespectrum. When computational efficiency is important, various approxima-tions are introduced to approximate the Fresnel reflectance including Schlickapproximation [74], artist-friendly metallic Fresnel approximation [75] andLaza´nyi reparameterization [76]. Among these approximations, the Schlickapproximation of the Fresnel reflectance is widely used for various materialtypes (metallic and dielectric) and given by [74]F (ωˆi, mˆ) ≈ F0 + (1− F0)(1− (nˆ · ωˆi))5 (1.59)where F0 is the spectral reflectance at normal incidence. This formula has281.10. Microfacet Theorybeen shown to be accurate in describing the reflectance from bulk materialssuch as metal, glass, and various plastics [54].Various microfacet NDFs, D(mˆ), and masking/shading functions havebeen introduced in the computer graphics literature. Table 1.4 summarizessome of the most popular NDFs with the associated masking/shading func-tions, where vˆ is an arbitrary projection from the macrosurface, vˆ = 〈θv, φv〉are angular coordinates in the spherical coordinate system, and αb, αp, αgand αt are the microfacet roughness parameters for Beckmann, Blinn-Phong,GGX-Smith, and GTR NDFs. Figure 1.9 shows simulations of the specularand diffuse reflections from a MERL chrome material using the GGX, Beck-mann, and Blinn-Phong NDFs compared to measurements. Both Beckmannand Blinn-Phong NDFs exhibit good match in regard to the specular reflec-tions (at the degree of macrosurface normal, θm < 2.5o) but not the diffusereflections (at the degree of macrosurface normal, θm ≥ 2.5o). The GGXNDF better matches the specular reflections (at the degree of macrosurfacenormal, θm < 2.5o) and the diffuse reflections. Due to the strong tail onGGX NDF, the rendered appearance of chrome using GGX better matchesthe measured chrome appearance.Figure 1.9: NDFs fit to measured chrome from the MERL database. Left:The specular peak over θm for chrome (black), GGX (red; αg = 0.006),Beckmann (green; αg = 0.013), and Blinn-Phong (blue dashes; = 12000).Rendered highlights are shown on the right for chrome, GGX, and Beck-mann. (Figure courtesy of [3]).291.10. Microfacet TheoryName Normal distributionfunction,D(mˆ)Masking/shading func-tion, G(vˆ, mˆ)Beckmann[77]D(mˆ) =χ+(nˆ·mˆ)piα2b(nˆ·mˆ)e[(nˆ·mˆ)2−1α2b(nˆ·mˆ)2] G(vˆ, mˆ) = χ2 + ( vˆ,mˆvˆ,nˆ ) ·21+erf(a)+ 1a√pie−a2; a =1αb tan θv or simplified andcomputation efficient ver-sion [2]:G(vˆ, mˆ) ≈ χ2 +(vˆ,mˆvˆ,nˆ){3.535a+2.181a21+2.276a+2.577a2 ; a < 1.61 ; a ≥ 1.6Blinn-Phong[78]D(mˆ) = χ+(nˆ ·mˆ) αp+22pi (nˆ ·mˆ)αpG(vˆ, mˆ) = χ2 +(vˆ,mˆvˆ,nˆ)·21+√1+α2g tan2 θmGGX-Smith[2]D(mˆ) =χ+(nˆ·mˆ)α2gpi(1+χ+(nˆ·mˆ)(α2g−1))2GTR[3]D(mˆ) = k(α,γ)pi[1+(nˆ·mˆ)2(α2t−1)]γwherek(α, γ) =(γ−1)(α2−1)(1−α2)(1−γ) , γ 6= 1,&γ 6= 1(α2−1)ln (α2) , γ = 1,&γ 6= 11 , γ = 1Table 1.4: Normal distribution function, D(mˆ), and masking/shading func-tion, G(vˆ, mˆ), in microfacet theory.Surface irregularities on materials tend to exist over a wide range of sizescales, for example, from a few nanometers to a few hundred microns. Theeffects of surface irregularities become difficult for the PBR algorithm tomodel when the size scale is less than the wavelength of light (i.e., nano-geometry). At these size scales, interference and diffraction can occur whichis better described using a wave-optical model. There have been several pub-301.11. Multi-scale Modeling and Simulationslished adaptions of BSDF models that enable PBR to accurately describethe effects of interference and diffraction due to nano-geometry, which hasbeen applied to render the appearance of metals with scratches [79–81],iridescence of soap bubbles [82], and the multiple colors observed from acompact disk [83, 84]. In contrast to these other works, the approach de-scribed in this thesis has the advantage of generality, but at the cost ofhigher computational cost.1.11 Multi-scale Modeling and SimulationsRecent advancements in nanofabrication and manufacturing have stim-ulated the development of new optical devices with improved performance,efficiency, and functionality due to features which are engineered on wave-length or sub-wavelength scales. For instance, photo-emissive quantum dotparticles in display technologies have been shown to improve the displaybrightness and allow for a wider color gamut as opposed to traditional RGBcolor filters [85]. Prototyping these devices requires an iterative process thatbegins with electrodynamic simulations to model light interactions with thenanomaterial and capture its spectral responses, usually in the form of itsfar-field transmission and reflection. Once simulated data reaches agree-ment with a targeted performance metric, the physical parameters are usedto fabricate lab-scale prototypes, which are typically built on centimeterscale wafers. The optical response of the prototype is characterized and,if further optimization is required, the process is repeated until fabricatedprototypes meet performance requirement.Despite remarkable advancements in computation, it is still not possi-ble to predict the optical behavior of nano-engineered materials under real-world application settings. To date, there are no physically accurate simu-lations that can be applied to model the optical behavior of nanomaterialsby incorporating multi-scale effects ranging from subwavelength scale to themacroscale. The goal of this thesis is to explore this possibility for the mod-elling of nanoscale optical materials. Multi-scale modeling and simulationapproaches generally combine existing and emerging approaches to bridgethe wide range of temporal and spatial scales [86]. Multi-scale modeling isa multi-dimensional process that can invoke a large number of variables andparameters at every scale to be modelled. The classification of multi-scalemodeling approaches is based on the priority of the scale model and the in-fluence of spatial and temporal scale parameters and generally fall into twocategories: hierarchical and on-the-fly concurrent methods [87]. Hierarchi-311.12. Nanofabrication and Nanomaterialscal multi-scale methods compute parameters on one scale using precomputedparameters on a different scale. On-the-fly concurrent methods computesscale parameters concurrently based on parameters computed at a differentscale.Physically accurate descriptions of large-scale nanostructures require amulti-scale approach that is best achieved by treating light as both discreteparticles and electromagnetic waves depending on the size scale. PBR andelectrodynamic simulations have proven to be powerful, but both have sizescale limitations. On the one hand, PBR fails to render the effects of diffrac-tion, interference, and subwavelength interactions occurring at wavelengthscales but is efficient and physically accurate in describing large-scale lighttransport. On the other hand, electrodynamic simulations are limited tosimulation domains of just a few microns due to the required spatial dis-cretization mentioned earlier, but provides essential descriptions of waveoptical effects occurring at subwavelength scales. Even though electrody-namic simulation and PBR are built with different assumptions about lightbehavior (waves versus particles), are based on different physical laws (waveoptics versus geometric optics), both models are physically accurate at theirrespective scale level. The central question to be explored in this thesis iswhether it is possible to exploit the advantages of both models to enablenew computational approaches to study optical materials with nanoscalegeometries.1.12 Nanofabrication and NanomaterialsPerhaps the most pervasive nanomaterial in modern society is thin films,which have found applications as low-e window coatings, transparent con-ductors, heat insulators and as coating to enhance corrosion and scratchresistance [88]. Thin films are simple to manufacture and can be applied toa wide range of materials. There are many thin film fabrication techniquesranging from physical methods, such as evaporation, sputtering, and pulselaser deposition, to chemical methods, such as chemical vapor depositions(CVD) and plasma enhanced CVD.In recent years, there has been renewed interest in metallic thin films,particularly those composed of noble metals, due to their ability to sustainand support SPs. Selective absorption of light due to SP resonances onmetal films can lead to pronounced changes in their visual appearance. Inmore complex multilayer structures and patterned metallic films, complexinterference channels can exist for SPs, such as localized surface plasmon321.13. Structural Colorationresonance (LSPR), resonant coupling effects with adjacent nanostructures,and plasmon hybridization [4, 12, 89–91]. There have been intensive researchefforts to develop plasmonic metamaterials, engineered materials designedto exploit surface plasmon effect to realize new materials with optical prop-erties not found in naturally occurring materials. Development of thesematerials relies on an iterative process of design, fabrication, and character-ization, which is costly both in terms of time and resources. The multi-scalecomputational approach proposed in this thesis promises to accelerate thedevelopment of plasmonic systems which rely on SP effects occurring atsubwavelength size scales.1.13 Structural ColorationA promising application of nanostructured materials which will be ex-plored in this thesis is for coloration. Color generation mechanisms aregenerally divided into two physical mechanisms: pigmentary and structuralcoloration. Pigmentary coloration relies on a pigment or dye chemical, typi-cally based on metal oxides or organic compounds, which absorb and reflectcertain wavelengths of incoming light to achieve desired coloration. Struc-tural coloration relies solely on structures that are fine enough to cause lightinterference to produce a desire coloration. Nature has arguably perfectedstructural coloration, with beautiful displays of iridescence observed in in-sects and birds, including in the Morpho butterfly wing [92], blue jay feathers[93], Coleoptera [94] and Chrysochroa beetles [95]. These natural examplesof iridescence result from light interference with organic materials tightlypacked at microscopic scales [96]. For instance, the Morpho butterfly wingsconsist of a multilayer of cuticles and air in the wings, which selectivelyreflects the shorter wavelengths of light (predominantly blue) and producesmagnificent shimmering blue shades on the wings, as shown in Figure 1.10[36].Recent efforts to develop artificial structural solution have used engi-neered nanomaterials, often using designs that are inspired by those foundin Nature. Unlike traditional dye/pigment coloration which fades over timedue to UV degradation, the advantages of artificial coloration include colorpermanence so long as the structure remains intact and color tunability.Examples of structural coloration have been created using dielectric [23, 97–101]- and metallic-based nanostructures[4, 12, 89–91, 102–107], metamate-rials [108, 109], and metasurface [110–117]. Artificial structural colorationdesigns that exploit plasmonic effects occurring at sub-diffractive size scales331.13. Structural Coloration(less than the wavelength of light) have attracted significant research inter-est, potentially opening the door to coloration technologies with ultra-highresolution and arbitrarily tunable optical properties across the visible fre-quency range. In particular, this thesis will apply multi-scale computation toexplore the potential application of plasmonic nanostructures for colorationand study the influence of micro- and nano-scale roughness on the resultingperceived color.Figure 1.10: Shimmering blue shade from a specimen sample of Morphobutterfly wings. Credit: Vincent Loi.1.13.1 Plasmonic Metallic NanostructuresPlasmonic metallic nanostructures have a long history in coloration dat-ing back to ancient Roman glass making techniques in which noble metallicnanoparticles such as gold, silver, and copper were mixed with glass to stun-ning dichroic properties, such as those visible in the Lycurgus cup [118]. Dueto metallic nanoparticles that are suspended in the glass, the Lycurgus cupchanges color from jade-green to ruby-red when a white light source illumi-nates the inside of the glass. The color changes result from the resonanceresponse associated with light coupling into the surface plasmon modes ofthe metallic nanoparticles.In recent years, numerous plasmonic metallic nanostructures have beenproposed for coloration and can be grouped into two types of implemen-tation: 1) free-standing metallic nanoparticles or nanoparticle aggregates341.13. Structural Coloration[102, 119] and 2) chip-based two- or three-dimensional nano-array patterns[120, 121]. A colloidal metallic nanoparticle solution is an example of a free-standing metallic nanoparticle implementation which derives its color fromthe excitation of localized surface plasmon resonance (LSPR) [122].Figure 1.11: Plasmon hybridization due to disk-hole coupling. (a) Energydiagram showing the hybridization of the coupled plasmonic modes of thedisks and holes of the structure into a low energy mode (bonding) and a highenergy mode (antibonding). (b) Reflectance spectra for the same parametersof nanodisk-nanodisk but for varying pillar height, h. The two modes areseen as dips in the spectra. (Image courtesy [4])The resonant wavelength is dependent on the size, shape, and type ofmetal of the nanoparticles as well as the dielectric constant of the surround-ing materials. On the other hand, the coloration mechanisms in complex 2Dand 3D nano-arrays rely not only on resonant plasmon interactions but alsoeffects which are coupled and hybridized with other plasmonic interactionsfrom adjacent structures. For instance, the coloration mechanism of the well-studied aluminum nanohole-nanodisk arrays relies on plasmon hybridization[4, 123–125], in which the plasmon dipole excited in the nanohole hybridizeswith the dipole states in the vertically displaced nanodisk, as illustratedin Figure 1.11 (a). The energy of plasmon hybridization becomes greatestin the “antibonding” (in-phase) mode – both nanodisk and nanohole have351.14. Climate-based Daylighting and Glare Controlsimilar signs of charge distribution, which causes the dip valley in Figure1.11(b) and the opposite for the “bonding” (out-of-plane) mode. Increasingseparation distance between hole and disk arrays reduces the strength ofplasmon hybridization and become less effective, resulting in less vibrantcolor arising from this structure [4]. The strength of plasmonic interactionsin array implementations are sensitive to the size of particles, periodicity,and material choice. These variables provide parametric control over thedesired coloration over a wide color gamut.1.14 Climate-based Daylighting and GlareControlThe multi-scale modelling approaches developed in this thesis are alsoused to explore the potential application nanostructured materials on win-dows for enhanced daylight control. Windows serve multiple proposes, allow-ing natural daylight to illuminate indoor spaces and enabling visual contactwith the outdoor environment. Adequate daylight penetration into indoorspace reduces electrical light loads and provides passive heating in coldermonths; this helps to reduce the energy expenses to maintain indoor cli-mate. However, glare near windows can be caused by direct sunlight andskylight diffused by the atmosphere under clear sky conditions. Discomfortglare describes user discomfort when there are bright sources of light whoseluminance is greater than the eye can adapt to; it can be immediately no-ticeable or over a long period of exposure. Detailed daylighting modeling ofa building is necessary, as daylighting and glare experienced in indoor spacesdepend on a multitude of factors, including the location of the site, windoworientation, room setup, and human subjective responses [126–131].Daylighting and glare experiences are location-dependent because thelatitude of a location dictates the solar altitude and hours of sunlight ina year. A higher latitude region, like Canada, tends to have lower win-ter sun, which yields great daylight penetration to illuminate deeper indoorspace, but with an increased likelihood of glare. South-facing windows re-ceive the most direct sunlight throughout a day, while north-facing windowspredominantly receive skylight and about half of the illuminance of south-facing windows. West- and east-facing windows receive portions of directsunlight in the day. Room setup can contribute to glare near windows, asit determines the position of occupants and their vision field. Daylight re-flecting from objects and certain surfaces in an occupied space can becomesecondary light sources causing glare. Lastly, the glare experience is per-361.14. Climate-based Daylighting and Glare Controlsonal, depending on occupants’ ages, gender, and eye adaptability to highluminance [132, 133].Climate-based daylight modeling (CBDM) uses a local weather datafileto model the variability of sun and sky conditions to predict the luminousquality in an indoor space [14, 134–137]. CBDM uses a validated physically-based daylighting simulation tools, such as open-source code RADIANCE orDAYSIM, and allows users to define custom materials, incorporate them intofull-scale mock-ups, and model illuminance distributions while accountingfor artificial light sources, local climate, and daily and seasonal changes innatural (solar) light distributions.The indoor space light performance is accessed based on the averageilluminance, relative average illuminance, average illuminance distribution,spatial daylight autonomy, and annual sun exposure. Average illuminance isthe average value (in lux) of the daylight available in an indoor space overa year. Relative average illuminance is the percentage of change of averageilluminance between the test structure and control case at the designatedlighting level and evaluated byE¯v,avg =Ev,c − Ev,lvlEv,c× 100% (1.60)where Ev,c is the average illuminance for the control (bare window in thiscase) and Ev,lvl is the average illuminance for the lighting level (work plane orceiling levels in this case). E¯v,avg can be a positive or negative percentage toindicate the increment or decrement of average illuminance at the targetedlighting level relatively to the control. Average illuminance distributionsdescribe the average distribution map of illuminance (in lux) of daylightavailable over a year in an indoor space at an occupant’s work plane, withan imaginary horizontal plane positioned at nominal working height. Thespatial daylight autonomy (sDA300|50%) describes the percentage of spacereceiving at least 300 lux at a minimum of 50% of occupied hours [134].Annual sun exposure (ASE1000|250) is the percentage of space receiving aminimum 1000lux of direct sunlight for at least 250 occupied hours.The adaption of the human eye to light intensity is non-linear, with astatic contrast ratio of around 100:1 to a dynamic contrast ratio of around1,000,000:1 in different lighting levels [138]. These adaptions arise from thepupillary light reflex (PLR), which adjusts the opening of the pupil to allowvision to adapt to different lighting levels and color appearances[139].This adaption response varies from person to person, but has been shownto be dependent on age and gender. For example, the elderly are less sus-371.14. Climate-based Daylighting and Glare Controlceptible to glare as they have less visual contrast sensitivity due to senilepupillary miosis (decreased pupil size due to aging) and lens absorption dueto greater light scattering within the aged eye and retinal cell loss due todegeneration [140, 141]. Over-bright environments or luminaries with higherluminance than the eye can adapt to can cause discomfort glare. The glareexperience can occur immediately or over a period of time [142].Estimating the level of glare experience is based on characterization andassessment of the human subject response and physically factors such asthe size, position, and luminance of glare sources in the field of vision rel-ative to the background luminance [142]. Even the human eye can detectglare instantly, the quantification of glare experience is more challengingand must be done by experimental measurement or picture evaluation [134].Daylight glare probability (DGP), one of the most common glare experienceassessment metrics, describes the likelihood of an occupant experiencingdiscomfort from glare at a particular position and orientation. The DGP isevaluated by [134]DGP = 5.87× 10−5Ev + 9.18× 10−2 log[1 +∑iL2s,iωs,iE1.87v P2i]+ 0.16 (1.61)where Ev is the vertical eye illuminance, Ls,i is luminance of the i-th glaresource, ωs,i is solid angle of the i-th glare source and Pi is the position indexof the i-th glare source.[143]. The constants in Equation 1.61 are empiri-cally derived from 349 case studies conducted in Copenhagen, Denmark andFrieiburg, Germany [143]. The value of DGP is bounded between 0 to 1, andthe level of glare experience is summarized in Table 1.5. Among these glareindicators, a good working position needs to keep the amount of intolera-ble glare (the worst glare) and other glare indicators at a minimum duringthe occupied hours. For overall glare performance, spatial disturbing glare(sDG) is introduced to describe the percentage of views across the regularlyoccupied floor area that experience Disturbing or Intolerable Glare (DGP> 0.38) for at least 5% of occupied hours.381.14. Climate-based Daylighting and Glare ControlGlare Indicator RangeImperceptible glare DGP < 0.34Perceptible glare 0.34 < DGP≤ 0.38Disturbing glare 0.38 <DGP≤ 0.45Intolerable glare DGP> 0.45Table 1.5: DGP Glare Indicator.There are many products (both commercially available and under de-velopment) which attempt to address glare while optimizing for daylight-ing. These solutions generally consist of horizontally aligned structures,which can be categorized according to their size from micron-scale (films) tocentimeter-scale (blinds) to meter-scale (shelves), as summarized in Figure1.12. These solutions are generally based on a series of reflective horizontalslats that are static and optimized to regulate the amount of daylight pen-etrating indoor space. There has been recent research on next-generationnanostructured materials with spectrally selective and photothermal prop-erties design to enhance daylighting and thermal regularity [144]. Spectrallyselective films have been engineered to reflect the heat from the sun (pre-dominantly in the near-infrared region) by coating glass with transparentconductors such as indium tin oxide (ITO) and fluorine-doped tin oxide(FTO) and metallic thin films (Ag, Cu, Au, Al) [145, 146]. There has beenexciting research on the application of metallic nanoparticles with SP reso-nance shifted to the NIR region to provide additional heating for the indoorspace during colder months [144, 147, 148]. One of the goals of this thesisis to incorporate electrodynamic simulations approach into CBDM, open-ing up the possibility for daylight researchers to study the application ofadvanced nanomaterials to provide better daylighting and glare control inindoor spaces.391.15. Previous WorksFigure 1.12: Daylighting and glare windows solutions. Micron scale: 3M [5]and SerraGlaze daylight redirecting films [6] and dynamic daylight controlsystem (DDCS) [7]. Centimeter scale: Oksolar blinds [8, 9], fish louver,RetroLux blind [10, 11] and laser cut panel. Meter scale: Light shelves.1.15 Previous WorksThe computer graphics community has made tremendous progress indeveloping PBR approaches to produce physically accurate simulation of thevisual appearance of materials. There have been numerous developments toextend the ability of PBR so that it can describe wave optical effects thatcan become prominent when light interacts with objects that have featuresizes comparable to the wavelength of light.To date, efforts have relied on combining ray tracing with analytical ex-pressions or approximate models that encapsulate wave optical effects from aparticular structure into efficient prescriptions that describe the structure’seffect on the spectral reflection and transmission of an incoming light ray.For instance, Smits and Meyers used a thin-film interference model to renderthe iridescent colors in perfectly smooth thin films of varying thickness [25].Wolff and Kurlander incorporated a coherence matrix into the Torrance-Sparrrow reflectance model that enabled modeling of the polarization stateof light upon reflection [149]. Jos Stam introduced a new diffraction modeldue to surface roughness and render the iridescence of wave nature of light401.15. Previous Worksin compact disk [83]. Gondek et al. used a wavelength-dependent bidi-rectional reflectance function to model the iridescent colors of pearls, thinfilms, and paints [150]. Hirayama et al. rendered the appearance of smoothmulti-layered thin films composed of dielectric and conducting materials byrecursive scattering solutions of a multilayer configuration [151, 152].Sun employed rendering and a model based on stacked multilayer thinfilms to describe the iridescent colors found in the Morpho butterfly wingand ground beetle [153].In subsequent work, the authors derived a genericexpression describing the reflectance, transmittance, and absorption fromsingle layer thin-film interference to render film-coated thin objects [154].Wu et al. developed a full spectrum rendering model for multilayer films withmicro-scale roughness to demonstrate the visual effects in a diverse rangeof film structures [155]. Tom et al. introduced a new wave-BSDF basedon Wigner distribution function to simulate the interference and diffractionwave effects due to micro-geometry on the surface of material [156]. Belcourand Barla developed an extended microfacet model to describe the irides-cent effect of thin films on top of rough base layers [157]. Holzschuch andPacanowski introduced a two-scale roughness microfacet reflectance modelthat separately treated features much larger than the wavelength and thosecomparable to the wavelength using a diffraction model [72]. Sebastian etal. developed a new diffraction model with spatial-varying bidirectionalreflectance distribution function (SVBRDF) to describe the iridescence mi-croscopic scratches on the surfaces including door handle, metal spoon, andcompact disk [79]. Ling-Qi et al. modeled the iridescence metal due toscratches, brushed and bumpy surface imperfections using a wave opticsreflection integral over the coherence area to approximate the phase-delaygrating representation and apply the spatial detail of micro-geometry of sur-face [80]. Joe¨l et al. introduced transfer matrix method on the BSDF thateffective in managing the forward and backward light transport occurring inthe layered materials, and used the approach to render the roughness inter-ferences and arbitrary scattering volumes of layered materials [158]. Thesecontributions have extended the scope of materials that can be describedby PBR through a potpourri of methods that are computationally efficient,but they are application-specific and not readily generalizable.There have been just a few previous attempts to integrate electrody-namic simulations with PBR approaches. Okada et al. created a physicallyaccurate description of the iridescence of Morpho butterfly wings by us-ing modified FDTD methods to extract a far-field BRDF, which was thenused by a PBR algorithm to render the appearance of the butterfly wing ina virtual scene [159]. Auzinger et al. used electrodynamic simulations to411.16. Thesis Outlinecorrelate the coloration and structure of dielectric nanostructures createdby additive manufacturing [23]. The process was based on parameterizingthe dielectric nanostructures and mapping those parameters onto a range ofachievable structural colors for both normal and wide-angle viewing direc-tions. This thesis works extended the capability of PBR by incorporating ofwave optical modeling and physically based rendering to model the visualappearance and behaviour of engineered nanoscale structures such as thinmetallic films and plasmonic metallic nanostructures with multitude of in-fluences including surface roughness, lighting environments, and substrategeometry.1.16 Thesis OutlineThis thesis presents a comprehensive and systematic study of multi-scale light modeling to study the visual appearance and optical propertiesof nanostructures with metallic constituents, including thin metallic films,and patterned metallic nano arrays. Chapter 1 provides a background onthe topics pertinent to the thesis work, including wave-particle duality, basicconcepts in electromagnetics, electrodynamic simulations, physically-basedrendering, plasmonics, structural coloration, and climate-based modelling.Chapter 2 demonstrates the application of multi-scale modeling of light torender the visual appearance of thin metallic films of arbitrary composi-tion, thickness, and roughness (at both micro- and nano-scales) when theyare coated on flat and rounded substrates. Chapter 3 demonstrates a newtechnique to extract the far-field BSDF of periodic metallic nanostructuresusing electrodynamic simulations to create physically-based material mod-els. These material models are then used to render the appearance of peri-odic metallic nanostructures with varying diameter, periodicity, and mate-rial composition coated various macroscopic substrates. Chapter 4 analyzesthe effects of nanoscale roughness on structural color achieved using plas-monic nanostructures consisting of nanohole array. We also analyze theeffect of nanoscale roughness on the resulting coloration, revealing for thefirst time the ability for roughness to nullify the plasmon resonance. Chap-ter 5 shows the integration of electrodynamic simulations with climate-baseddaylighting modeling to examine the effect of thin semi-transparent metallicfilms applied on windows to improve daylighting while reducing the glare.The conclusions of this research and future research directions are presentedin Chapter 6.42Chapter 2Visualization ofSemi-transparent MetallicThin Films2.1 IntroductionSemi-transparent metallic films are widely used in decorative coatings,anti-reflection layers, and low-emissivity coatings for windows and haveemerging applications in new optical systems such as those relying on plas-monic effects. The visual appearance of devices that deploy thin metallicfilms can be an important design consideration, but in general, it is diffi-cult to model and accurately predict the appearance of metallic films witha high degree of realism, particularly those that are thin enough to yieldsemi-transparency. When the thickness of a metallic film is sufficiently thinto permit light penetration (typically tens of nanometers), its color, luster,and transparency are sensitive to the deposition conditions, thickness, andnanoscale roughness of the film. In addition, the appearance of the film isaffected by factors that extend beyond the film structure, such as the prop-erties of the underlying substrate, environmental lighting conditions, lightsource, and detector.The purpose of this chapter is to explore the integration of two compu-tation approaches – physically based rendering (PBR) which models lightas a discrete particle and electrodynamic simulation which models light asan electromagnetic wave – to enable physically accurate predictions of thevisual appearance of thin metallic films of arbitrary composition and thick-ness in complex environments and under realistic conditions. Modeling allthese effects with accuracy requires multi-scale computational approachesthat can simultaneously describe light behavior at size scales ranging fromseveral nanometers to several meters.Thin metallic films are an ideal configuration to explore rendering ap-proaches that leverage electrodynamic simulations because they are struc-432.2. Our Approachturally simple yet have a visual appearance that is strongly affected byoptical effects occurring at subwavelength spatial scales. The nanoscaletopology of a thin metallic film is highly dependent on the method and con-ditions of deposition, the type of metal and substrate, and the substratesurface roughness. For example, Volmer-Weber type film growth (commonfor high-mobility metals) is characterized by the formation of discrete is-lands, which grow and coalesce to form a continuous film. Light scatteringfrom nanoscale roughness can result in the near-field scattering [160], fieldlocalization [161], coupling to plasmonic modes [162], and enhanced absorp-tion [163–165]. These factors, and others, can cause the visual appearanceof a thin metallic film to depart from that predicted by simplistic modelsbased on, for instance, reflectance calculations assuming a perfectly smoothfilm. In this chapter, we used single layer silver metallic film deposited onglass substrate and titanium dioxide (TiO2) coated on a silver metallic filmand investigate the effects of nano- and micro-scale surface roughness affectsthe appearance of thin films. In addition, we investigated the appearance ofthin metallic films under the influence of lighting environments and shapesof substrates.2.2 Our ApproachThe multiscale surface roughness is due to microscale surface imper-fections of substrates and nanoscale surface imperfections of thin metallicfilms as shown in Figure 2.1. Microfacet theory is selected to describe mi-croscale surface roughness. The nanoscale surface roughness is assumed itis fine (subwavelength-scale) enough such that normal PBR algorithms areunable to interpret their effects. To capture the effects of nanoscale rough-ness, FDTD simulations is used to model wave interaction with thin metallicfilms featuring nanoscale roughness.Direct computing the Fresnel reflectance of rough thin metallic films overall the possible angles is computational intensity process and requires thetremendous amount of simulations over those incident angles. As forma-tion of surface roughness is a random distribution, it requires multiple setsof surface roughness profiles to describe the effects of nanoscale roughnessoverall. By harnessing the Schlick approximation, the number of FDTDsimulations are reduced to only normal incident angle with various sets ofsurface roughness profiles.442.2. Our ApproachFigure 2.1: Schematic diagram of (a) thin metallic film model with the hier-archy scale of roughness from microscale roughness using microfacet modelto (b) nanoscale roughness using FDTD simulation.2.2.1 FDTD Simulation DomainThe FDTD simulation configuration is shown in Figure 2.1(b), consistingof a three-dimensional domain with a spatial resolution of 0.25 nm. Thevolumetric simulation domain encapsulates the substrate, thin film(s), andair region with x-y plane aligned with the plane of the substrate. We usedBloch (periodic) boundary conditions for the x and y boundaries of thesimulation domain. Perfectly matched layers are set for the z boundaries tominimize reflections from the edges. The illumination source is a polarizedcontinuous wave plane wave that is injected 780 nm above the substratesurface at normal incidence with a wavelength that varies over the visiblespectrum (380 nm to 780 nm). The time-averaged intensity reflected andtransmitted through the structure are captured 1000 nm above and belowthe substrate surface.The metallic films are modelled with nanoscale roughness. The surfacetopology of the films is described by a surface correlation function [166]given by〈h(r)h(r + δ)〉 = σ2e(δLc)2(2.1)where h(r) is surface height at position r, 〈. . . 〉 is assembly average, δ issampling resolution of the surface in the x and y directions, σ is the average452.2. Our Approachroot mean square (RMS) of surface height variability in the z direction, andLc is the correlation length of the surface height variability in the plane ofthe film (x and y directions). Randomized surface topologies are generatedusing the parameters in Table 2.1. For each value σ, transmittance andreflectance values are averaged over 20 simulations (10 randomly generatedsurface profiles simulated for orthogonal incident polarizations). About 4-5minutes are required for each simulation, which are run on a Desktop com-puter with Intel i7-8700K CPU (3.7 Ghz, 6 cores, 12 threads) and 32GBDDR4 2667Mhz RAM. The computer specifications and simulation param-eters are listed in Table C.1 and C.2.Variables ValuesRMS amplitude, σ 1-15 nmSampling resolution of thesurface, δ4 nmCorrection length of roughness, Lcx direction 2 nmy direction 2 nmTable 2.1: Surface roughness parameters.2.2.2 Rendering SetupWe used the NVIDIA IRAY physically based rendering engine to renderthe appearance of thin metallic film using the FDTD-derived BRDF andBTDF of the films due to the render engine natively supports PBR ma-terials created by MDL. The appearance of thin metallic film is renderedwith controlled indoor room and studio room rendering setups as shown inFigure 2.2. The indoor room configuration (Figure 2.2(a)) has overhead ar-tificial lighting and daylight from an adjacent window modelled from a 360HDR image capture of physical space on the UBCO campus. These interiorlights create the mixed direct and diffuse lights to illuminate the samplesin the scene and cast the environment shadow on the samples. The studioroom configuration (Figure 2.2(b)) has three rectangular lights with stan-dard adjustable color temperatures and a diffuse white canvas background.The studio room is surrounded by black background where there are notambient reflections from the background to cast environment shadows onthe film. These rectangular lights create user-controllable uniform diffuselighting to illuminate the samples as a function of intensity and color tem-462.2. Our Approachperature. Both configurations use cameras to capture overhead or obliqueimages of a 15 cm × 15 cm coated glass substrate placed on top of a 20 cm× 20 cm printed white paper.Physically based material models for the metallic-coated substrates isdefined by Material definition language (MDL) with incorporating bothmicroscale roughness of the substrate through the GGX-Smith microfacetmodel and nanoscale roughness of the film through Schlick’s approximatedFresnel reflectance. RGB reflectance of FDTD-simulated film are calculatedby using the CIE 1931 XYZ color transformation systems with D65 stan-dard illuminant [167]. The Schlick’s approximated Fresnel reflectance iscalculated by using color matched RGB reflectance and Equation1.59.Rendering was performed on a workstation computer (specifications inTable C.1). The rendering time required to produce an image is highly de-pendent on the complexity of the virtual environment including the lightingsetup, number of polygons in the scenes, textures of PBR material, andrendering settings (number of ray bounces, noise threshold and resolutions).An average of 2-3 minutes are required to render an interior room image and1 minute is required to render a studio room image. The rendering settingsare listed in Table C.3.(a) (b)Figure 2.2: Rendering setup to generate appearance of thin metallic film in(a) interior room and (b) studio room.472.3. Results and Discussions2.3 Results and Discussions2.3.1 Validation of Schlick ApproximationWe compared the angular spectral Fresnel reflectance computed usingthe Schlick approximation to analytical values calculated using the transfermatrix method (TMM). We examined single-layer silver films (Ag) and mul-tilayer titanium dioxide coated on silver thin films (Ag | TiO2) of variousthicknesses and assume that the films are perfectly smooth and planar. Re-flectance values are calculated for incident angles from 0 to 90 degrees andfor wavelengths across the visible spectrum (380 nm-780 nm). As shown inFigure 2.3, there is generally good agreement between the Schlick approxi-mation and analytical values for shallow angles of incidence.For the single-layer silver films, the Schlick approximation has betteragreement for thicker films than for thinner films. In the case of the thinnest20 nm silver film, the error of the Schlick approximation can reach as highas 23% for large incidence angles and shorter wavelengths (400 nm-450 nm).The Schlick approximation applied to multilayered films generally exhibitslarger reflectance errors, which is not surprising given that the Schlick ap-proximation does not account for reflections between the layers.Despite this shortcoming, the Schlick approximation is fairly accuratein modelling the reflectance of the multilayer films for shallow angles ofincidence. As seen in Table 2.2, the overall errors (calculated by averagingthe entire individual errors over wavelengths and incident angles) are about2% for the thinnest silver layer and 7% for the thinnest multilayer structure.Generally, the overall errors diminish as the film thickness increases. Figure2.3 also compares the resulting angular RGB colors of the films derivedfrom TMM and the Schlick approximation of their reflectance. There is agood color match between the two methods for smaller angles of incidenceand both techniques predict color shifts from a base color to white as theincidence angle approaches 90 degrees. These results suggest that the Schlickapproximation provides a good approximation of the Fresnel reflectance ofthin films. It can be prone to errors at larger angles of incidence but providesconsiderable computational efficiencies.482.3. Results and DiscussionsThin Film Thickness(nm)Max. Error(%) Overall (%)StandarddeviationSingleLayer (Ag) 20 23.6157 2.0714 3.499335 15.9829 1.037 1.939750 9.8752 0.5252 1.0447Multilayer 18 45.8415 6.9215 10.3575Ag(23 nm)| TiO2 38 42.1933 4.3129 5.673557 75.319 3.0881 5.2976Table 2.2: Statistical data for the resulting errors between Schlick approxi-mation and Fresnel reflectance492.3. Results and DiscussionsFigure 2.3: Comparison of Fresnel reflectance (left column) and Schlick ap-proximation (right column) over visible spectrum wavelength with incidentangles from 0° to 90° for the single-layer and multilayer metallic thin filmwith the corresponding percentage of error (right column). Color bars on theright shows the angular RGB colors of Fresnel reflectance (F) and Schlickapproximation (S). 502.3. Results and Discussions2.3.2 Comparison of Rendered Image to Real ImageWe next visually compared the appearance of a rendered thin metallicfilm with a photographed lab-fabricated thin film. The lab-fabricated 20-nm-thick silver film is prepared by magneton sputter deposition (AngstromEngineering Nexdep) of a 99.99% pure Ag target onto a 100-micron thickplanar glass substrate. We use the iPhone X back camera to photograph thelab-fabricated film in an indoor room located on the UBCO campus. Weused the same indoor room setup as shown in Figure 2.2(a) to render theappearance of the coated glass slide. Figure 2.4 shows images of the lab-fabricated (a) and rendered (b) silver-coated substrate taken as an obliqueangle of incidence facing the windows of the indoor room. Both the real andrendered images capture the glossy semi-transparent and reflective finish ofthe silver films. The color base of the films is a bluish-gray, consistent withthe RGB color derived from the spectral Fresnel reflectance in Figure 2.3.(a) (b)Figure 2.4: Visual comparison between (a) lab-fabricated and (b) rendered20-nm-thick silver film coated glass substrate using Schlick approximation.2.3.3 Influence of Lighting ConditionsWe examined the effect of the color temperature of the light source onthe perceived colors of a glass substrate coated by a thin silver film. Us-ing the studio room configuration, Figure 2.5 depicts rendered images of a25-nm thick silver film coated onto a 100-micron thick glass slide when thecolor temperature of the studio lights varies from 5000K, 5500K, 6500K and7500K (warmer to cooler light). The images capture the coated glass slide,512.3. Results and Discussionswhite paper background, and diffuse white background which is about 7.16cm away from the bottom of the paper background. The white paper back-ground has a printed UBC logo in dark blue ink (HEX: 002145), which isvisible through the coated slides due to the semi-transparency of the silverfilm. The studio lighting setup provides highly diffuse environment, as evi-dent by the even distribution of light across the image and the appearanceof slight shadowing underneath the paper background. The observation po-sition of the coated slides at normal incidence and black background resultsin no environment shadows and glossy reflection cast on the films.Changes in the lighting color temperature are most evident from thewhite paper background, which has a large and uniform reflectance spec-trum. The white paper appears in a more yellowish-white color under in-fluence of warmer color temperature light sources. The observed color ofthe slides is largely due to light that has transmitted through the slide andreflected from the white paper background and the color appearance of thefilm is close to the RGB transmittance (R: 125, G: 148, B: 175). However,the color temperature slightly affects the perceived color of the films asthe film has a grey-brownish base color under warmer light sources (5000Kand 5500K) and a grey-bluish color under cooler light sources (6500K and7500K). The film is also slightly more transparent when viewed under coolerlight sources, which is due to the slightly higher transmissivity of the thinsilver film at lower (bluish) wavelengths.522.3. Results and Discussions(a) (b)(c) (d)Figure 2.5: Computationally rendered images of a 25-nm-thick silver filmon a glass slide with a white background with varying studio lights havingcolor temperature (a) 5000K (b) 5500K (c) 6500K (d) 7500K.532.3. Results and Discussions2.3.4 Influence of Nanoscale RoughnessFabricated film often suffers from size inhomogeneities and roughnessissues which can lead to deviations from its performance from those expectedfrom simulations. We chosen single layer Ag films coated on glass substrateand multilayer Ag | TiO2 films to investigate the nanoscale surface roughnesseffects on the appearance of films. The variables we explored here are thenanoscale roughness using RMS roughness as the roughness parameter forthe top and bottom surfaces of the Ag layer in the single-layer configurationand both Ag and TiO2 films in the multi-layer configuration. We varied thethickness of Ag film in the single-layer configuration and TiO2 film in themulti-layer configuration and investigate the change of the appearance of thefilms. We used rendering setup from Figure 2.2(a) to render the appearanceof films.As shown in Figure 2.6(a), increasing the thickness of the Ag film changesits appearance from semi-transparent to opaque. Increasing the RMS rough-ness of the Ag films causes its color to shift from grey-bluish to slightlygrey-brownish. The increased roughness creates “void” regions on the filmwhich not only alter the spectral response of the film, but also increase thetransparency of thicker Ag films (noticed from the appearance of the UBClogo underneath the substrate).As shown in Figure 2.6(b), increasing the thickness of the TiO2 filmwith lower RMS roughness changes the color of the film from grey bluish togrey-brownish color, without affecting its transparency. Increasing the RMSroughness causes just a slight change in appearance and, unlike the case forthe Ag layer, reduces the transparency of the film.542.3. Results and Discussions(a)(b)Figure 2.6: Rendered appearance of (a) single layer silver film and (b) mul-tilayer Ag | TiO2 films.552.3. Results and Discussions2.3.5 Influence of Microscale RoughnessMicrofacet theory enables us to model the effect of microscale roughnesson the underlying substrate. In this work, we assumed the nanoscale rough-ness does not affect diffuse scattering from the surface (which is attributed tomicroscale roughness) and that nanoscale roughness only affects the Fresnelreflectance and the intrinsic color appearance of the films [168]. The ap-pearance of the films coated on the underlying textured glasses is modeledby the microfacet GGX-smith model and the roughness parameters listed inTable 2.3.In general, the surface appearance of the glass substrate is describedby the αg in GGX NDF. The smooth surface (smaller αg) will tend tohave glossy, specular reflection finishes on the surface appearance. As αgincrease, the surface appearance of glass will tend to have matte, diffusereflection finishes and loss the details of reflection highlights on the surface.Glass Microscale roughness, αg Nanoscale roughness, σAnti-glare 0.0275 nmGround 0.394Frosted 0.454Etched 0.553Table 2.3: Surface roughness parameters (Adapted from [2])Figure 2.7(a) illustrates rendered images of a single layer Ag 25 nm filmand multilayer Ag | TiO2 film coated on various flat square glass substrateswith varying degrees of microscale roughness. Both types of film coatingsretain their intrinsic color appearance but it is clear that the surface appear-ance can change considerably due to the roughness of the underlying glasssubstrate.562.3. Results and Discussions(a)(b)Figure 2.7: Rendered images of single layer film 25-nm-thick silver filmand multilayer thin film Ag | TiO2 – 23 nm | 38 nm coated on anti-glare,ground, frosted and etched glass on (a) a square glass substrate placed onthe white paper bearing a dark blue UBC logo, and (b) pieces of a 3D chessset (Rendering time: 3-4 minutes for each image).572.4. SummaryFigure 2.7(b) shows rendered images of complex 3D glass objects (chesssets) coated thin films in which the glass objects have varying degrees ofmicroscale roughness. Specular, glossy finishes are visible with anti-glareglass, which contrast with the matte, diffuse finishes of etched glass. Notethe loss of reflection highlights (mirror-like environment shadows) as high-lighted in red circles, which is due to the microgeometry on the rough glasssubstrate. Light occulated by the microgeometry of surface does not disap-pear. Rather, it is reflected and has a high probability of impinging ontoother microgeometry features, undergoing multiple reflections and attenu-ated by Fresnel reflectance at each reflection site before reaching the cameraas diffuse reflections.2.4 SummaryThis work demonstrated the feasibility of rendering the physical ap-pearance of semi-transparent metallic films and multilayers by combiningmulti-scale electromagnetic simulations with ray-tracing-based rendering ap-proach. Electromagnetic simulations enabled modelling of light interactionwith nano-roughness while ray-tracing-based rendering enables modelling ofmicro-roughness and creates photo-realistic images of coated objects. Weshowed that the Schlick approximation can be used to describe the Fresnelreflectance of thin metallic films and multilayers, particularly at low angles ofincidence. Caution must be used when invoking the Schlick approximationfor very thin films and for very steep angles of incidence. A material modelbased on microfacet GGX model has been applied to study the appearanceof thin films and multilayers coated on arbitrary 3D objects composed ofetched glass, frosted glass, and ground glass. The photorealistic images gen-erated using our approach were qualitatively consistent with real images ofa fabricated thin film sample.58Chapter 3Plasmonic StructuralColoration3.1 IntroductionPlasmonic structures have a resonant spectral response due to the cou-pling of visible light into surface plasmons - electromagnetic waves confinedto the interfaces of metallic structures. The confinement of light within plas-mons results in sharp spectral features present in light that is reflected fromor transmitted through the structure. Plasmonic responses are generally de-pendent on angle and polarization and can be controllably manipulated bychanging the geometric parameters and composition of the nanostructure.As a result, plasmonic structural colors are highly tunable over a wide colorspace and can produce iridescence not readily achieved by pigments anddyes. While the spectral response of a plasmonic structure can be modeledthrough electrodynamic simulations, there is no simulation method availableto model the overall visual appearance of objects colored by the applicationof a plasmonic coloration layer. This requires multi-scale techniques thataccount not only for the plasmonic response occurring at nanometer scales,but also for effects occurring at larger scales such as the external lightingconditions, shape, size, and opacity of the underlying object, surface finish,and presence of micro-scale roughness.In this chapter, we shown that the visual appearance of arbitrary objectscolor-coated by plasmonic structures can be physically simulated by incorpo-rating electrodynamic simulations of plasmonic effects with physically-basedrendering (PBR) algorithms. We used electrodynamic simulation to modelthe resonant interaction of visible light with metallic nanostructures andcreate approximate descriptions of their far-field response in reflection andtransmission through spectral- and angular-dependent far-field bidirectionalscattering distribution functions (BSDF). We developed a physically basedmaterial database of prototypical plasmonic structures including periodicnanohole, nanodisk, and nanohole-nanodisk arrays as a function of their593.2. Our Approachgeometrical parameters, composition, size, configuration, and periodicity.The material models are applied to macroscopic three-dimensional objectsand the visual appearance of the plasmonic colored objects are modeled us-ing PBR algorithms for various environments, lighting setups, and camerapositions.3.2 Our Approach3.2.1 Plasmonic Structural ColorsPlasmonic structural coloration relies on the ability of nanostructurescomposed of noble metals (Au, Ag, Al) to support plasmons, electromag-netic modes confined to the surface of metals. The presence of plasmonscan result in strong field enhancements, causing enhanced absorption andscattering at distinct frequencies near the intrinsic bulk plasma resonancefrequency of the metal (in the UV and visible spectral range). The plasmonresonance frequency can be tuned by changing the nanoscale geometry of thestructure and through the choice of material (both the metal and surround-ing dielectric). Structures designed for coloration are typically implementedas periodic arrays. In this study, we will focus on three types of well-studiedarrays composed of nanoholes, nanodisks, and hybrid nanohole-nanodisks.The specific details of the arrays are given below and have been selected tomatch the parameters of published experimental studies.a. Nanohole array: 20-nm-thick silver thin film coated on a 1000-nm-thick glass substrate with periodic nanoholes arranged in a square arraywith individual hole diameter, D and periodicity, P at ratio D : P = 1 : 2along with the lateral directions (x- and y-axis), as shown in Figure 3.1(a)and mimicking the study in [89]. (Details in Appendix D, Table D.1)b. Nanodisk array: Periodic nanodisks on a 1000-nm-thick glass substratecomposed of silver-alumina-silver layers (metal-insulator-metal,MIM) andarranged in a square array. The respective thicknesses of the silver andalumina layers are 30 nm and 20 nm. Nanodisks have an identical di-ameter of D and periodicity of P along with the lateral directions (x-and y-axis), as shown in Figure 3.1(b) and mimicking the study in [12].(Details in Appendix D, Table D.2)c. Nanohole-nanodisk array: Textured surface consisting of period cylin-drical nanopillars on an acrylic, polymethyl methacrylate (PMMA) sub-strate. The nanopillars are arranged in a square array and each cylin-603.2. Our Approachdrical nanopillar has a diameter, D, periodicity, P along with the lateraldirections (x- and y-axis), and height distance, d of 10 nm. A 20-nm-thick aluminum layer coats the textured surface, covering the top surfaceof the nanopillars and the bottom surface of the substrate, but not thesidewalls of the nanopillars, as shown in Figure 3.1(c) and mimicking thestudy in [4]. (Details in Appendix D, Table D.3)There are a variety of well-studied resonance effects that can occur in pe-riodic metallic arrays, including extraordinary optical transmission throughnanohole arrays [89, 169], metal-insulator-metal resonances in nanodisk ar-rays [12], and plasmon hybridization in nanohole-nanodisk arrays [4, 90].The strength of these various mechanisms is sensitive to the size, periodic-ity, and material choice of the array. It is through these properties that wewill tune the plasmonic structure to achieve the desired coloration in thevisible frequency range.(a) (b) (c)Figure 3.1: Schematic diagrams of metallic nanostructures (top) and 2D-cross section view of FDTD unit cell simulations (bottom) for (a) silvernanohole arrays, (b) silver nanodisk arrays, and (c) aluminum nanohole-nanodisk arrays.613.2. Our Approach3.2.2 Electrodynamic SimulationsWe used ANSYS Lumerical FDTD software to model visible light inter-action with the periodic metallic nanoarrays by solving Maxwell’s equationsover a discrete three-dimensional grid with a size resolution of 0.25 nm.This mesh resolution was chosen based on convergence tests conducted atmultiple coarser mesh resolutions. The simulation volume is defined by theperiod of nano array, P for the width and length dimensions alongside by1000 nm (height) encompassing a unit cell of the periodic arrays and portionsof the underlying substrate and free-space region, as shown in Figure 3.1.The unit-cell is illuminated from the free-space region with a broadbandplane electromagnetic wave emerging from a source plane 300 nm abovethe substrate surface. We used the broadband fixed angle source technique(BFAST) to interrogate the response of the structure over the visible fre-quency range (wavelength λ from 380 to 780 nm). The electromagnetic waveis injected at an angle of incidence, θi, 0° to 75° in 5° increments. The 5° stepwas selected to provide sufficient accuracy while minimizing computationaltime. Periodic boundaries are applied at each of the lateral boundaries ofthe simulation volume along the x and y directions to describe the mutualinteraction of the unit cell elements.Perfectly matched layers (PMLs) are applied at each of the verticalboundaries of the simulation volume along the z-direction to minimize spu-rious reflections from the top and bottom faces of the simulation volume.Voxels in the simulation domain are assigned refractive index values over thevisible frequency range based on measured values for silver, aluminum, glass[170] and PMMA [171]. All structures studied in this work are azimuthallysymmetric. For a given angle of incidence, the time-averaged intensity of theelectromagnetic wave reflected from and transmitted through the nanostruc-ture are captured using monitors placed 400 nm above and 300 nm belowthe substrate surface, respectively. FDTD simulations are conducted on aworkstation computer with specification listed in Table C.1 and simulationsetting listed in Table C.2. Simulation time increases with increasing in-cidence angle of the source. For example, about 4 minutes is required tosimulate at normal incidence and about 1 day is required to simulate at 75°.Computing the full bidirectional scattering distribution requires 4-5 days.623.3. Plasmonic BSDF Model3.3 Plasmonic BSDF ModelOur far-field bidirectional scattering distribution function (BSDF) mate-rial model for plasmonic structures consists of both BRDF and BTDF thatdescribe scattered light from objects coated by metallic nanostructures. Inthis work, we used standard far-field projection over a 1-meter distance togenerate the far-field BSDF with the captured reflected and transmittedelectric fields from the FDTD simulations. The far-field BSDF is the prod-uct of integrating the incoming and scattered (reflected and transmitted)light that covers the hemisphere dome, Ω as shown in Figure 3.2(a) with thefollowing expression [46]:f(ωˆi, ωˆo, λ) =∫∫Ωd |Eo,λ|2 duxduycos θo∫∫Ωd |Ei,λ|2 duxduycos θo, (3.1)where ux and uy are the unit coordinate vectors in the far-field, |Ei,λ|2and |Eo,λ|2 are the intensity of the electric field at far-field at wavelengthλ for incoming and outgoing directions, respectively, and θo is the anglebetween the normal line (z-axis) and projection. We assumed the intensityof the electric field at wavelength λ on the illuminating substrate is fullyreceived from the source so that the intensity is equal to 1. Due to theHelmholtz reciprocity principle equating the scattering of incoming and itsreverse encounter light, we only computed the scattering distribution forincident angles from 0° to 75° with a 5° step.The far-field BSDF of metallic nanostructures are computed in ANSYSLumerical FDTD with the programming scripts in Appendix E and con-verted into a spectral BSDF material data file. We selected the commer-cially available NVIDIA IRAY as the PBR system to render the appearanceof metallic nanostructures in virtual space. The PBR system is highly op-timized for fast and real-time ray tracing using either computer processingunit (CPU) or graphic processing unit (GPU) rendering. Like most modernPBR systems, NVIDIA IRAY uses RGB material models due to its com-putational efficiency and memory usage. We converted the spectra BSDFmaterial datafile to RGB BSDF material datafile using CIE 1931 XYZ colortransformation system integrals with D65 illuminant light source from Equa-tion (1.49).633.3. Plasmonic BSDF Model(a) (b)Figure 3.2: Illustration of (a) near-field and far-field zones of interactionsand (b) geometrical angles used for a single BRDF measurement for theincoming direction ωˆi, and outgoing scattered light direction, ωˆo.The selected PBR system uses material definition language (MDL), ashading language to determine physically based material. We convertedthe color-matched RGB BSDF data into a .mbsdf binary material data filefor creating the physically-based material for the metallic nanostructures.The purpose of binary material data file due to computational efficiencyin computing the light quantities in PBR. The binary material data filestores the scattering distributions in the order defined by an indexing offsetfunction, findex (iθi , iθo , iφ) asfindex (iθi , iθo , iφ) = iθi × nφ × nθ + iθonφ + iφ (3.2)where iθi , iθo ,iφ are the index of the scattering data for the associated incom-ing incident angle, θi, outgoing scattered angle, θo and azimuthal angle,φas illustrated in Figure 3.2(b), nθ is the number of steps used for an equalspaced angular resolutions of incident angles, θi and θo, and nφ is the num-ber of steps used for an equal spaced angular resolution of azimuthal angle,φ. Images in Figure D.4 and D.5 in Appendix D demonstrate the indexedscattered distribution with the associated incident angles.643.3. Plasmonic BSDF Model3.3.1 Rendering SetupWe modelled the appearance of objects in both transmission and reflec-tion mode based, respectively, on the BRDF and BTDF. This allows us tohave full control in generating structural colors of the structures in BxDFmode (the general mode, neither BRDF or BTDF). The rendering setup isa 3D virtual space consisting of 3D objects, cameras, and lights. We cre-ated two virtual spaces: a high-dynamic-range image (HDRI) environmentcreated from a 360 HDR image of an indoor room with artificial light anddaylight at the UBCO library (the PBR system extracts each pixel valuein the HDR image to generate realistic 360° dome lighting) and a studioenvironment consisting of three rectangular diffuse light sources and a whitematte diffuse canvas (Figure 3.3).(a) (b)Figure 3.3: Schematic diagrams of three-dimensional rendering setups forgenerating the appearance of metallic nanostructures under influence of (a)HDRI lighting and (b) studio lighting.The PBR system extracts each pixel value in the HDR image to gen-erate realistic 360° dome lighting that mimics the lighting of the imagedenvironment. Rectangular lights in Figure 3.3(b) creates a mixed diffuselight environment to illuminate the pedal car which is placed on top ofthe white matte diffuse canvas. In the HDRI environment, we imaged theplasmonic coatings on a smooth, opaque spherical substrate. In the studio653.4. Results and Discussionenvironment, we image the plasmonic coatings on the body of a pedal car.The wheels, front grill, and bumper of the pedal car are smooth chrome, thetires are black rubber, and the cushion and steering wheel are black leather.Camera 1 and 2 in Figure 3.3 depict their relative positions and direction ofview. All rendered images are produced using a workstation computer withspecifications listed in Table C.1. The image in Figure 3.3(a) took about20 seconds to render. The image in Figure 3.3(b) took about 44 seconds torender.3.4 Results and Discussion3.4.1 Preliminary ResultsPrior to rendering the appearance of the arrays, we compared our elec-trodynamic simulated spectral response with those available from publishedworks [4, 12]. Figure 3.4 shows a spectral response comparison betweenFDTD-simulated reflectance and transmittance with experimental data forsilver tandem nanodisk arrays for normal incidence excitation.(a) (b)Figure 3.4: Comparison of experimental (adapted with permission from [12])and FDTD-simulated (a) reflectance and (b) transmittance spectra at nor-mal incidence for silver tandem nanodisk array with a periodicity of 340 nmand diameter of 140 nm.Although there is not exact match with experimentally measured data,both the simulated and measured spectral responses have similar peak and663.4. Results and Discussiondip features in reflectance and transmittance, respectively. The reflectancepeak and transmittance dip in the FDTD results are blue-shift comparedto experimental data by about 38 nm. The FDTD results are, on aver-age, 28% lower in reflectance and 14% higher in transmittance comparedto experimental values. This is attributed to the FDTD simulated spectralresponse modelling idealized metallic nanostructures which do not accountfor surface imperfection, micro-and nano-scale roughness inherent to fabri-cation. We suspected that surface roughness weakens resonant interactionsand causes the red-shift on the resonant wavelength and broadening of thespectra responses.(a) (b)Figure 3.5: Reflectance over visible spectrum of 20-nm-thick aluminumnanohole-nanodisk arrays with a periodicity of 200 nm, a diameter of 80nm, and separation distance of 80 nm at normal incidence (a) measured byreflectance spectroscopy and (b) modeled FDTD simulations (Adapted withpermission from [4, 13])Figure 3.5 shows the normal-incidence spectral reflectance of 20-nm-thickaluminum nanohole-nanodisk arrays obtained from experimental measure-ments and FDTD simulations. The colors under the curves in Figure 3.5represent the reflected color of the array derived either from the color mea-sured from an image obtained from a bright field microscope in reflectionmode or by color-matching the FDTD simulated spectral responses usingCIE XYZ color system and a standard D65 illuminant. The simulated spec-tral reflectance has a resonance dip that is slightly blue-shift compared to673.4. Results and Discussionexperimental reflectance and about 26-27% higher. The simulated color isdarker and slightly more greenish than the experimentally observed color.The color difference, a well-establish metric to quantify the difference be-tween two colors, is ∆E00 = 24.8852, indicating that the simulated andmeasured colors are more similar than opposite.3.4.2 Nanohole ArrayFigure 3.6 shows the rendered reflection and transmission colors of thesilver nanohole arrays on the spherical substrate and the body of the pedalcar using the periodicity and diameter parameters in the Table D.1. Due todifferences in environment lighting conditions, we noticed a slight color dif-ference of the same nanohole arrays when coated on the spherical substratesand pedal cars. There are reflection highlights on the spherical substrateswhich show the room lights and dark colored carpets of the environmentand shadowing effects on the lower part of the sphere. On the other hand,the body of the pedal car has less reflection highlights since the rendered en-vironment lighting is predominantly diffuse. Both reflection (Figure 3.6(a))and transmission (Figure 3.6(b)) colors change with increasing periodicityand diameter of the nanoarray. As the periodicity increases from 150 nmto 200 nm, the reflection color shifts from purple to turquoise in reflectioncolor and the transmission color shifts from light blueish purple to pinkishpurple. (Please refer to Figure D.1 and D.2 in Appendix D for an extendedstudy of the effect of array periodicity) Iridescence (color change dependenton viewing angle) is observed in both reflection and transmission, and evi-denced by color changes at various positions on both the sphere and pedalcar.683.4. Results and Discussion(a)(b)Figure 3.6: Rendered appearance for the (a) reflection and (b) transmissioncolor of 20-nm-thick nanohole array with the period from 150 nm to 200 nmand diameter from 75 nm to 100 nm, respectively on the spherical substrate(top row) and body of the pedal car (bottom row).Next, using parameters listed in Table D.1, we compared the reflectedcolor of identical nanohole arrays made from 20-nm-thick silver and alu-minum films to investigate the effect of the film material. By side-by-sidecolor comparison between aluminum and silver nanohole arrays in Figure 3.7,we noticed that, unlike the silver array, the color of the aluminum nanohole693.4. Results and Discussionarray does not significantly change as the period and diameter increase. Itis well known that aluminum has higher Ohmic losses at visible frequenciesthan silver and therefore, cannot support SP propagation as well as silver.This result also supports the conclusion that the color observed from thesilver nanohole arrays can be attributed to SP effects. We have also investi-gated the effect of replacing the underlying glass substrate with a differentmaterial (PMMA) and observed no color change, confirming that the coloris predominantly derived from the array itself.Figure 3.7: Rendered images of the reflection color on the spherical sub-strate coated with 20-nm-thick silver (top row) and aluminum (bottom row)nanohole array with diameter from 75 nm to 95 nm and period from 150nm to 190 nm, respectively.703.4. Results and Discussion3.4.3 Nanodisk ArrayThe silver tandem nanodisk arrays are another interesting coloration sys-tem capable of generating highly saturated and bright colors [4, 105, 113,172, 173]. The saturated and bright color are attributed sharp resonancesarising from the metal-insulator-metal sandwiched nanodisks [12]. (Pleaserefer to Figure D.3 for the details about the reflection and transmissionspectra of silver tandem nanodisk arrays) We used periodicity and diameterparameters in Table D.2 to render the reflection and transmission color ofsilver tandem nanodisk arrays coated on spherical substrates and the bodyof a pedal car. As shown in Figure 3.8 we observed bright and saturatedcolors for both reflection and transmission. In addition, there are massivecolor changes over relatively small changes in the diameter and periodicity.In reflection, we observed blue, green, and brown colors and in transmis-sion, we observe bright yellowish green, pinkish purple, blue, turquoise, andlime green colors. Compared to the nanohole array, the silver nanodisk ar-ray demonstrates much stronger iridescence, evidenced by profound colorchanges over the surface of the sphere and the body of the pedal car.713.4. Results and Discussion(a)(b)Figure 3.8: Rendered images for both (a) reflection and (b) transmissioncolors for silver-alumina-silver tandem nanodisk arrays coated on sphericalsubstrate (top row) and the body of pedal car (bottom row) with the diam-eter, D from 90 nm to 220 nm with the associated period, P from 270 nmto 450 nm.723.4. Results and Discussion3.4.4 Nanohole-nanodisk ArraysNanohole-nanodisk arrays are a special hybrid structure that combinesresonances of nanohole and nanodisk arrays. It is an opaque structure andonly displays colors in reflection. One advantage of the nanohole-nanodiskarray is that the separation distance between the two arrays provides ameans to tailor color without altering the period and diameter. Figure 3.9shows the reflection colors of a 20-nm-thick and 80-nm-diameter aluminumnanohole-nanodisk array in which the separation distance between two ar-rays is varied by PMMA pillars. There is an angular color dependencehighlighted by colored halos on the spherical substrate and color differenceson the front body and front-facing part of the back-wheel cover of the pedalcar. Increasing separation distance between hole and disk arrays reducesthe strength of plasmon hybridization between the elevated nanodisk andnanohole (i.e. reduces the coupling effect of bonding (out-of-phase) and an-tibonding (in-phase) modes), resulting in less vibrant colors [4]. When theseparation distance increases beyond 50 nm, the color change of aluminumnanohole-nanodisk arrays becomes less pronounced.Figure 3.9: Rendered reflection colors of 20-nm-thick aluminum nanoholeand nanodisk arrays with the period of 200 nm coated on the sphericalsubstrate (top row) and body of the pedal car (bottom row) with varyingseparation distance, d between hole and disk from 30 nm to 80 nm.We next highlighted the color tunability of the nanohole-nanodisk array.Fixing the separation distance between the arrays at 80 nm and the periodat 200 nm, we vary only the diameter of the nanodisk and nanodisk arraysfrom 80 nm to 110 nm to recover the bluish color previously observed formuch smaller separation distances. As shown in Figure 3.10, the color ofthe arrays change from brownish purple to blue as the diameter increases733.5. SummaryFigure 3.10: Rendered reflection color of 20-nm-thick aluminum nanohole-nanodisk arrays, a separation distance of 80 nm and period of 200 nm witha varying diameter ranging from 80 nm to 110 nm coated on the sphericalsubstrate (top row) and body of the pedal car (bottom row).from 80 nm to 110 nm. Increasing the diameter causes the holes and disksbecome closer, which augments nearest-neighbor coupling and recovers theresonant interactions necessary to produce the bluish color.3.5 SummaryIn this work, we demonstrated a multi-scale approach using FDTD simu-lations and modern PBR systems to render coloration by metallic nanostruc-tures such as nanohole, nanodisk and nanohole-nanodisk arrays coated ontoarbitrary 3D objects. We used spectral and angular BRDF and BTDF toaccurately describe the iridescence of these plasmonic structures, expandingupon the work in the previous chapter. We had shown that plasmonic ar-rays can achieve vibrant and iridescent colors, which are tunable by varyingthe geometric parameters of the arrays and the material choice. We believethat this work will improve the ability to design and optimize plasmonicstructural colors. The future work should examine ways to speed up thecomputation time to generate the rendered images. There should also befurther experimental comparisons to validate the accuracy of the renderedimages.74Chapter 4Influence of NanoscaleRoughness on PlasmonicStructural Coloration4.1 IntroductionStructural coloration can be achieved through plasmonic nanostructurestailored on size scales below the wavelength of light. The perceived colors ofthese structures are highly sensitive to surface geometry and are generallyangular- and frequency-dependent [4, 36, 114]. Fabricated plasmonic nanos-tructures exhibit roughness which can lead to deviations in its performancecompared to those predicted from simulations [174, 175]. Roughness can oc-cur at micro- and nano-scales, perturbing surface plasmon resonances and,in turn, affecting both the far- and near-field electromagnetic field patternsassociated with the plasmonic structure [161, 176, 177]. Despite considerableprogress in the development of coloration technology using plasmonic struc-tures [175], there is still limited understanding on the impacts of multi-scalesurface roughness on the resulting color produced from plasmonic structuresand it is not yet possible to predict how the roughness of a plasmonic struc-ture will in turn affect its visual appearance. This endeavor is important,as the development of plasmonic coloration technology is still confined tophysical fabrication and prototyping cycles that are lengthy and costly.In this chapter, we applied multi-scale computational methods developedin the previous chapter to investigate the variance of structural color arisingfrom metallic plasmonic nano-structures due to nano-scale roughness. Thewell-studied nanohole array configuration is used in a thin metallic (Ag)film (Figure 4.1(a)) as the sample plasmonic structures to achieve visible-frequency coloration. The randomized nano-scale roughness is introducedonto the top and bottom surfaces of the Ag film using the surface correlationfunctions from Equation (2.1).754.2. Our Approach4.2 Our ApproachANSYS Lumerical FDTD software is used to model the time-averagedelectromagnetic wave amplitudes that are transmitted and reflected fromthe nanohole arrays. The configuration is shown in Figure 4.1. A singlevolumetric domain is defined in the FDTD simulations with dimensions of200 nm × 200 nm × 1000 nm (Figure 4.1 (b)). The simulation volumeencompasses a unit cell of the nano-hole array, a portion of the underlyingsubstrate, and a portion of a free-space region above the array. The silverfilm is 20 nm thick and coated on a 1000 nm thick glass substrate. Thenanohole pattern consists of individual holes of diameter, d = 70 nm andperiodicity on both lateral directions, P = 140 nm. The electromagneticresponse of the silver material is described by refractive index data from[170].The nanohole arrays are illuminated by a broadband plane electromag-netic wave injected at 360 nm above the substrate for incident angles, θvarying from 0° to 75° in steps of 5°. The incident electromagnetic wave en-compasses frequencies in the visible spectrum. The reflected and transmittedelectric field amplitudes are captured by monitors positioned, respectively,400 nm above and 300 nm below the substrate. The time-averaged reflectedand transmitted electric field amplitudes are converted into reflectance, R,and transmittance, T , values through far-field transformation [46]. The ab-sorbance can be derived from A = 1− T −R. The periodicity of the nanos-tructure is modelled by periodic boundary conditions along the x- and y-directions. Perfectly matched layers (PMLs) are used along the z-direction,which absorb impinging electromagnetic waves with minimal reflection. Tomodel randomized nano-scale roughness, the top and bottom surfaces of thesilver nanohole array are generated by using a surface correlation functiongiven by Equation (2.1), which includes in-plane and out-of-plane roughnessparameters. Different surface profiles with identical roughness parametersare created using a random number generator.The visual appearance of the nanohole arrays is modelled by incorpo-rating the FDTD-calculated reflectance and transmittance values into aphysically-based rendering scheme. The process to obtain the physically-based material model is similar to the approach discussed in the previouschapter. The environmental lighting conditions are generated from 360°HDR images of an indoor environment (UBC Okanagan Library during asunny day) consisting of both natural sunlight and artificial warm lighting.The effects of surface roughness on the visual appearance of the nanoholearrays are quantified by the FDTD-simulated transmittance and reflectance764.3. Results and Discussionspectra and the color difference, Delta E (∆E00), between silver nanoholearrays that are smooth and rough.Figure 4.1: (a) Schematic diagram and (b) cross-section view of a unit cellFDTD simulation (bottom) of 20-nm-thick silver nanohole array coated onthe glass substrate.4.3 Results and DiscussionFigure 4.2 demonstrates the effect of slight roughness (roughness param-eters σRMS = 2 nm and Lc = 15 nm) on the normal-incidence transmittance,reflectance, and absorbance spectra of the silver nanohole arrays. Comparedto the smooth surface profile, the slightly rough surface profiles have ∼20%reduced reflectance across the visible spectrum and ∼30% increase in trans-mittance for wavelengths greater than 500 nm. This result is consistentwith many reports in the literature of enhanced transmission through roughmetallic films, which have increased the conversion of incident light into sur-face plasmons. Compared to the smooth array, slight roughness does notappreciably affect the absorbance. Apart from a slight red-shift in the re-flectance dip (from 505 nm to 520 nm), slight roughness characterized byσRMS = 2 nm and Lc = 15 nm does not affect the shape of the spectra(although later examples will show that this is not always true).Figure 4.3 shows the visual appearance of a spherical opaque substrate inthe rendering environment when the substrate is coated with silver nanoholearrays that are either smooth or slightly rough. All nanohole arrays exhibita purple color in reflectance and a khaki color in transmittance. Iridescenceis visible from a slight color difference between the center and edge of thesphere. There is a very slight color difference between the rough and smootharrays, with an average ∆E00 value of 1.555. Slight roughness does notappreciably affect the visual appearance of the nanohole array.774.3. Results and DiscussionFigure 4.2: Spectral reflectance and transmittance of 20-nm-thick silvernanohole array with 5 distinct surface roughness profiles (randomly gen-erated using the same parameters σRMS = 2 nm and Lc = 15 nm) as shownin top insets.784.3. Results and DiscussionFigure 4.3: Rendered images of the visual appearance in reflectance (middleleft column) and transmittance (middle right column) of a smooth sphericalglass substrate coated with silver nanohole arrays that are either smooth orrough. The rough arrays in 1, 2 and 3 are randomly generated with silvernanohole arrays using the similar roughness parameters σRMS = 2 nm andLc = 15 nm but different seed numbers 101, 102, and 103 for 1, 2, and 3,respectively. The color difference between the rough and smooth arrays isquantified by the color difference parameter, ∆E00 which is calculated forreflectance (far right column) and transmittance (far left column).Figure 4.4 shows the effect of in-plane roughness on the normal-incidencetransmittance, reflectance, and absorbance spectra of the silver nanoholearrays as the correlation length, Lc increases from 10 nm to 75 nm. Theout-of-plane roughness parameter is kept constant at σRMS = 2 nm andcan be considered negligible. Compared to the smooth surface profile, thepresence of in-plane roughness generally decreases the reflectance, increasesthe transmittance, and has minimal effect on the absorbance. The overall794.3. Results and Discussionshapes of the reflectance, transmittance, and absorbance spectra are similar.There is red-shifting of the spectral location of the reflectance dip as the in-plane roughness increases, which could be attributed to an effective increasein the separation distance between adjacent holes. Due to the stochasticnature of the randomly generated surface profiles, it is not surprising that thespectral responses of the arrays are also subject to some degree of variability.For instance, the spectral transmittance and absorbance for the case of Lc =75 nm possess a different shape than the other cases, which could arise fromwave interference mechanisms unique to that configuration.Figure 4.5 shows the rendered visual appearance of a spherical opaquesubstrate when the substrate is coated with silver nanohole arrays withvarying degrees of in-plane roughness. All nanohole arrays exhibit a similarpurple color in reflectance and a khaki color (purple spot on the top-off-center of sphere) in transmittance. There is a very slight color differencebetween rough and smooth arrays with an average ∆E00 value of 1.63887,which describes perceptible difference after close observation. This is ex-cept for roughness characterized by Lc = 25 nm which has an average andmaximum ∆E00 value of 3.2405 and 8.5949 shown in Table 4.1.In-planeroughness, Lc(nm)Avg. ∆E00(R)Avg. ∆E00(T)Max.∆E00 (R)Max.∆E00 (T)25 0.5471 3.2405 1.8897 8.594950 0.7636 2.7668 2.7086 7.38475 1.256 1.2592 3.8711 4.5965Table 4.1: Average and Maximum ∆E00 comparison for the rough array(in-plane roughness).804.3. Results and DiscussionFigure 4.4: Spectral reflectance and transmittance of 20-nm-thick silvernanohole array with various in-plane roughness.814.3. Results and DiscussionFigure 4.5: Comparative rendered appearance of smooth and rough nanoholearrays coated on an opaque sphere when viewed in reflectance (middle leftcolumn) and transmittance (middle right column). The rough nanoholearrays have parameters of identical out-of-plane roughness, σRMS = 2 nmbut varying the in-plane roughness, Lc from 25 nm to 75 nm. The colordifference, ∆E00, between the rough and smooth arrays are shown in thefalse color images in reflectance (far left column) and transmittance (farright column).Interestingly, in-plane roughness has a minimal, but perceptible effecton the visible color of nanohole arrays. For the case where Lc = 25 nm, thesphere has a slightly blueish spot on the top-off-center of the sphere in trans-mittance, which is not evident for the other rough arrays. In reflectance, thecolor difference is between the smooth and rough arrays are mostly presentat high incidence angles (the circular ring in false color ∆E00 images). Thecolor difference between smooth and rough arrays can be attributed to shad-824.3. Results and Discussionowing effects introduced by the rough surface which are magnified at highglancing angles.Figure 4.6 highlights the effect of out-of-plane roughness on the normal-incidence transmittance, reflectance, and absorbance spectra of the silvernanohole arrays as the parameter σRMS varies from 1 nm (smoothest) to9 nm (roughest). The in-plane roughness parameter is kept constant atLc = 50 nm. Variation of the out-of-plane roughness parameter can havea dramatic effect on the overall shape and amplitude of the transmittance,reflectance, and absorbance spectra of the nanohole array. Increasing σRMSfrom 1 nm to 3 nm causes the reflectance to decrease and the transmittanceto increase without shifting the positions of the spectral dips, consistent withthe known effect that roughness enhances surface plasmon coupling. Inter-estingly, as σRMS increases from 5 nm to 7 nm, the dips in the reflectanceand transmittance spectra and the peak in the absorbance spectra are redshifted to larger wavelengths and broadened. The roughness of this magni-tude is sufficient to perturb the electromagnetic resonance of the nanoholearray, with a shift to lower frequencies consistent with the augmented opticalpath length between adjacent cells. When σRMS increases to 9 nm, there isa double resonance evident by the two dips in the reflectance, transmittance,and absorbance spectra. To our knowledge, the two-dip feature observed inthe nanoarray array induced by the roughness has yet to be studied.Figure 4.7 shows the visual appearance of a spherical opaque substratein the rendering environment coated with silver nanohole arrays as σRMSvaries from 1 nm (smoothest) to 5 nm (roughest). All nanohole arraysexhibit similar purple color hue in reflectance and khaki color hue in trans-mittance. The rough arrays exhibit less color saturation in reflectance anddifference in its angular colors in transmittance compared to the smootharray. These color differences in both reflectance and transmittance arehighlighted in the color difference map. The color difference becomes moresignificant with increasing out-of-plane roughness, with a maximum ∆E00value of 18.7267 and 10.53722 for reflectance and transmittance color whenthe out-of-plane roughness parameter reaches 5 nm. Increasing the out-of-plane roughness perturbs the propagation of surface plasmons in the regionsbetween holes. It is also hypothesized that the sharp points on the surface(with low radius of curvature) are sites where surface plasmons can becomelocalized and cease to propagate across the surface, destroying or signifi-cantly changing the resonance condition of the overall array. Increasing theout-of-plane roughness has a more pronounced effect than increasing thein-plane roughness, as a larger in-plane roughness effectively smooths thesurface (increasing the radius of curvature of rough points).834.3. Results and DiscussionFigure 4.6: Spectral reflectance (top), transmittance (middle), and ab-sorbance (bottom) of 20-nm-thick silver nanohole array with for variousout-of-plane roughness parameters. The surface topology is shown in thetop inset.844.3. Results and DiscussionFigure 4.7: Comparative rendered appearance of smooth and rough nanoholearrays coated on an opaque sphere when viewed in reflectance (middle leftcolumn) and transmittance (middle right column). The rough nanoholearrays have parameters of identical in-plane roughness, Lc = 100 nm butvarying the out-of-plane roughness scale, σRMS from 1 nm to 5 nm. Thecolor difference, ∆E00, between the rough and smooth arrays are shown inthe false color images in reflectance (far left column) and transmittance (farright column).854.4. Summary4.4 SummaryWe used computational methods to examine the influence of nano-scalesurface roughness on the visual appearance of silver nanohole arrays coatedonto opaque spherical substrates. We studied nanohole arrays created inthin films having roughness mathematically defined using both out-of-planeand in-plane roughness parameters, enabling systematic study of the influ-ence of surface roughness along orthogonal directions. The results shownthat out-of-plane roughness has a much greater effect the perceived struc-tural colors of nanohole arrays that in-plane roughness. Nanohole arrayshad structural resonance which depend on the propagation and interfer-ence of surface plasmons emerging from adjacent subwavelength sized holes.Surface roughness was a critical parameter for these arrays because it af-fects the propagation of surface plasmons to neighboring holes. In-planeroughness did not significantly perturb SP propagation, but slight increasesin out-of-plane roughness (from 2 nm to 9 nm) had been shown to causessignificant changes in their reflectance, transmittance, and absorbance spec-tra and can potentially introduce new resonances. The color variance ofnanohole arrays compared to smooth arrays was computed as a functionof both in-plane and out-of-plane roughness. This work provides a physi-cally accurate computational approach to investigate the effect of nanoscaleroughness on nano-structured materials.86Chapter 5Daylight and Glare Controlby Nanomaterials5.1 IntroductionThe emergence of digital fabrication and additive manufacturing has en-abled geometrically complex transparent materials that can potentially beapplied at scale to enhance daylighting in buildings, decrease reliance on arti-ficial lighting, and open new design opportunities [178, 179]. Nanophotonicthin film coatings hold promise for lighting and daylighting applicationsdue to their ability to achieve tailored spectral and angular characteristics[145, 180, 181], which could help to regulate amount of daylight alongsideheat admitted into indoor spaces for daylighting and indoor climate control.So far, there have been no studies of the potential impact that nanophotoniccoatings on the lighting and daylighting conditions in buildings. Part of thischallenge is that computational methods to model lighting and daylightingon building scales do not incorporate wave modelling necessary to accuratelydescribe the optical properties of nanophotonic devices.In this chapter, we integrated electrodynamic simulations and daylightsimulations (DAYSIM, RADIANCE) to model, quantify, and evaluate theapplication of nanophotonic thin film coatings to enhance daylighting inbuildings. We focused on nanostructured coatings with angular-selectiveproperties that could improve the quality of indoor illumination by redi-recting or diffusing direct sunlight (reducing glare) while maintaining hightransparency to preserve views.875.2. Our Approach5.2 Our ApproachSilver (Ag) thin films and titanium dioxide (TiO2) coated on Ag filmswith varying thickness are selected as the candidate materials to study forpotential applications in daylight control. Ag and TiO2 films are widely usedin low-e window coatings, where Ag film serves as a high infrared reflectancelayer and TiO2 serves as anti-reflective layer to increase visible light trans-mittance [182]. Both materials are well-characterized, can be manufacturedat large scales, and have angular responses can be tuned over a wide rangeby changing the thickness of the film over a small range. For instance, Agthin films that are only tens of nanometers in thickness can change semi-transparent to fully opaque with an addition of just a few nanometers ofthickness. The large-scale daylighting and glare performance of these struc-tures is evaluated based on window structures applied on a window in thecontrol test room.Wave optics is used to model the spectra response of thin metallic film tocreate PBR material for CBDM. CBDM is instrumental to explore how envi-ronmental variables, including time of day, seasonal variations, sun position,indoor lighting, occupant positioning, and room dimensions can affect theselection, optimization, and performance of a nanophotonic thin film coat-ing. Finally, the performance of these structures is evaluated based on theilluminance distribution map, daylight autonomy, and daylight glare prob-ability (DGP) generated in time-series spanning days, months, and years.5.2.1 Thin Metallic Films for Window StructuresWe purposed to study the influence of semi-transparent thin metallic filmon daylighting and glare control by coated the film on window structuresincluding the glass pane, traditional flat slats and wing-flap slats. The detailsof thin metallic film structures used in this study are summarized in theTable 5.1 below:885.2. Our ApproachConfiguration Material 1 Thickness(nm) Material 2Thickness(nm)Single layer Ag20- -253035404550Multilayer Ag 23 TiO21824384657Table 5.1: Thickness parameters for single layer Ag thin film and multilayerAg | TiO2 thin films.The window structures studied in this work include:a. Window Coating: A single or multi-layer metallic thin film with vary-ing thickness described in Table 5.1 coating the inner layer of a windowglass pane as shown in Figure 5.1(a). This configuration reassemblesconventional window glass with low-e coating.b. Flat Slats: The flat slats are made from thin glass and the top facingslat is coated by single or multi-layer metallic film with varying thicknessdescribed in Table 5.1. Each of the slats has identical 50 mm width andis aligned vertically with equal spacing of 25mm from adjacent slats tocover the entire window as shown in Figure 5.1(b).c. Wing-flap Slats: The asymmetrical “V” shape slats inspired from thewing-flaps of aircraft but applied here as a daylight redirecting structure.Each wing-flap slat consists of two slats arranged side-by-side in whichthe front slat (shorter section) is 13.92 mm wide and tilted upward at 15°and the back slat (longer section) is 32.08mm wide and tilted upward at10°. The tilting angle of both sections are to mimic the concave shapealike for optimizing the redirecting light upward. Wing-flap slats arevertically aligned with equal spacing of 25mm between adjacent slats asshown in Figure 5.1(c).895.2. Our Approach(a) (b) (c)Figure 5.1: Schematic side view diagram of coated daylight-redirecting win-dow structures to be examined including (a) direct coating on the inner glasspane, (b) coating on top of flat slats and (c) coating on top of wing-flap slats.Slat aperture describes the regular spacing between adjacent slats. Itis an important parameter because it affects daylight redirection and glarereduction, in addition to outward views. A smaller slat aperture is effec-tive in re-directing low-angle sun present during winter months, but is noteffective in re-directing high-angle sun present during summer months. Inaddition,a smaller slat aperture results in greater blockage of outward views.Since the goal is to achieve good overall performance throughout the year,the slat aperture value is optimized based on the solar altitude during thespring or fall equinox, which is the average solar altitude throughout theyear. Assuming a flat slat of width w, we select the maximum slat apertureso that all direct sunlight at a solar angle d will reflect and bounce upwards.The slat apertures in Figure 5.1(b) and 5.1(c) are optimized bys = w tan d (5.1)As a result, the 25 mm aperture and 50 mm width are chosen.5.2.2 Finite-Difference Time-Domain (FDTD) SimulationsThe spectra response of materials simulated using software such as RA-DIANCE are usually based on empirical spectral measurements on the real-world materials. In this work, we used electrodynamic simulations to modelthe spectral reflectance and transmittance of single silver (Ag) thin filmcoated on a glass substrate and multilayer titanium dioxide (TiO2) and Ag905.2. Our Approachfilms coated on a glass substrate. Based on the simulated spectra responses,we will define a PBR material model to be used in CBDM.The commercially available ANSYS Lumerical FDTD software is usedto model the time-averaged electromagnetic wave amplitudes that are trans-mitted and reflected from the thin films under plane-wave continuous-waveillumination at normal incidence. The computation process is identical withthe approach discussed in Section 2.2.1. In this study, we assumed that thethin metallic films are smooth as illustrated in Figure 5.2.A 4µm ×4µm glass substrate is coated on its top side by silver thinfilm and followed by titanium dioxide thin film, using the film thicknessparameters described in Table 5.1. Due to symmetry, the simulations areconducted over a 2D simulation region with dimension of 300 nm × 300 nm.The horizontal boundaries are defined by Bloch boundary conditions alongthe lateral directions (x- and y-axis). Perfectly matched layers (PMLs) areused along the vertical direction (z-axis), which absorb both reflected andtransmitted waves with minimal reflection. We used measured refractiveindex data for silver thin film [170] and titanium dioxide thin film [183] inthe simulations.The thin metallic films and substrate are illuminated by a plane-wavesource at normal incidence, 780 nm above the surface for incident wave-lengths from 380 nm to 780 nm with 5 nm steps. The reflected and trans-mitted light are captured 1000 nm above and 1000 nm below the substratesurface. Due to natural light being unpolarized light (50:50 mixed TE andTM polarization), the reflectance and transmittance spectra of the metallicfilms averaged are over both polarizations.915.2. Our ApproachFigure 5.2: Cross-sectional view of the two-dimensional FDTD unit-cell usedto model the reflectance and transmittance of a multilayer Ag | TiO2 thinmetallic film on a glass substrate.5.2.3 Climate-based Daylight ModelingModelling the daylighting in an indoor space is complex and highly dy-namic as the luminous quality varies over the course of the day and yeardue to cloud conditions, location of test side, room orientation, presence ofadjacent buildings, position and orientation of fac¸ade, and local climate. Weuse ClimateStudio application in conjunction with material models definedthrough the DGP simulations to perform CBDM and analyze the daylightingperformance and glare reduction.In this study, we created an indoor shoebox room with dimension 3.9m (wide) × 2.8 m (height) × 8.5 m (depth) consisting of a south-facingwindow that is 1 meter above the ground with an opening 3 m (wide) ×1.5 m (height) as shown in Figure 5.3 For the details of room dimension,please refer to Figure F.1. Given the location of the test site (in the northernhemisphere), a south-facing window is selected as it receives the most directdaylight during occupied hours (opposite for north facing windows in south-ern hemisphere). Thus, a south facing window orientation will be a goodcase study for examining window solutions that can achieve daylighting andglare reduction.Each layer in the room model is defined by the associated PBR mate-rials available in ClimateStudio library. Since ClimateStudio uses RADI-ANCE materials in the CBDM, we used BRTD function in the RADIANCE925.2. Our Approachmaterial library to describe the PBR models of thin metallic films. TheBRTD function allows us to have full control over defining the reflectanceand transmittance of the material while accounting for absorbance [184].Like PBR rendering, RADIANCE uses the Schlick approximation to de-scribe the angular Fresnel reflectance properties of a material [185]. Hence,the reflectance and transmittance of the BRTD function are described fromthe normal-incident RGB FDTD-simulated reflectance and transmittance atwavelengths 700 nm, 520 nm, and 430 nm, in conjunction with the Schlickapproximation [186].Summerland, BC weather data is selected for CBDM due to its closeproximity to our test location, UBC Okanagan. The local weather datawill be used to derive the sun and sky conditions to feed into the CBDMsimulations. The climate pattern at Summerland, BC is dry warm-summerhumid continental, which is predominately clear sky in summer months,mixed clear sky and overcast in spring and fall months, and predominatelyovercast sky in winter months. The lighting levels are determined by twohorizontal planes at 0.9 m and 2.7 m above the floor, which respectivelyrepresent the lighting levels at the work plane and ceiling. Each lightinglevel has sensor points which are 500 mm equally spaced in both lateraldirections as shown in Figure 5.3 (b). The occupied hours are assumed from8:00 am to 6:00 pm. Detailed CBDM simulation parameters are summarizedin Table 5.2.935.2. Our ApproachFigure 5.3: Schematic drawings of (a) shoebox indoor space with singlesouth-facing window embedded with the following window structures: win-dow coating, flat slats and wing-flap slats; (b) sensor grid for daylightingmeasurements in the simulation environment; and (c) sensor grids for glaremeasurements in the simulation environment, including view orientation (in-set).No Parameters Details1 Location UBC Okanagan (49.939 N, 119.394 W)2 Weather Data Summerland, BC (Source: ([187]))3 Sky Condition CIE Perez Sky (derived from weatherdata) [14]4 Lighting level (a) Work plane (0.9m above the floor)(b) Ceiling (2.7m)5 Target illumi-nance300 lux6 Occupied hours 8.00am to 6.00pmTable 5.2: CBDM simulation parameters.The daylighting quality in the indoor space is evaluated based on bothwork plane and ceiling lighting levels. The work plane lighting level is cred-945.2. Our Approachited based on providing adequate light at the level for the occupants withoutproducing glare. The ceiling lighting level is credited based on the inten-sity of daylit area at the ceiling and the size of region that achieves betterdaylight redirecting and diffuse light penetration into the indoor space. Arectangular array of sensor points is defined on each light level to record theamount of daylight falling onto the points. The luminous quantities in thesensor points will be later used to calculate daylighting performance met-rics including spatial daylight autonomy (sDA300|50%), annual sun exposure(ASE1000|250), average illuminance, Ev,lvl, relative average illuminance andaverage illuminance distribution summarized in Table 5.3.Indicator DescriptionssDA300|50% The percentage of space receiving at least 300 luxat minimum of 50% occupied hours.ASE1000|250 The percentage of space receiving at least 1000lux of direct sunlight at minimum of 250 occupiedhours.Ev,lvl Average illuminance of daylight falls from all thesensor points at the lighting level (work plane orceiling).E¯v,avg The percentage of change in average illuminancebetween the test structure and control case.Average illuminancedistributionThe illuminance distribution map in generated byaveraging the illuminance value each sensor pointsover the course of the year at the lighting level.Table 5.3: Daylighting performance indicatorsDGP evaluates the luminous quantities in each sensor point at 8 equal-angled orientation disks, which are 1.2 m above the floor as shown in Figure5.3 (c) and (d). These sensors mimic the eye height of an adult humansitting and looking around the surrounding. The color in each segmentof the orientation disk indicates the level of glare experienced, where redindicates intolerable glare, orange indicates disturbing glare, yellow indicatesperceptible glare and grey indicates imperceptible glare.The glare experience is highly dependent on the occupant’s working po-sitions including the eye height and orientation of viewing direction. Directview at the window as well as bright light spots in the field of view leadto severely intolerable glare experience. Hence, the glare experience is ana-955.3. Results and Discussionlyzed based on an annual glare chart at the occupant sitting position withorientation facing the monitor highlighted in Figure 5.3 (c). Annual glareis a collective of hourly DGPs over the course of a year which gives a fullpicture of glare experience at the position and the orientation.5.3 Results and Discussion5.3.1 Preliminary ResultsWe first review the FDTD-simulated reflectance and transmittance dataof the thin metallic film structures. Figure 5.4 (a) and (b) show the FDTD-simulated normal-incidence reflectance and transmittance spectra for singlelayer Ag thin films and multilayer Ag | TiO2 thin films over the visiblespectrum with varying thickness. For the Ag thin film, the average visiblereflectance of the film increased from 55.52% to 90.14% as the thicknessincreases from 20 nm to 50 nm. Over this film thickness increase, the Agfilm transitions from semi-transparent to become opaque and highly reflec-tive. The corresponding appearance change with increasing thickness ishighlighted by the rendered images of Ag films shown in Figure 5.4(a).For the Ag | TiO2 film, the average visible reflectance increases slightlyfrom 45.75% to 50.33% as the thickness of TiO2 increased from 18 nm to57 nm while the thickness of bottom Ag layer remains 23 nm. The Ag |TiO2 film generally possesses transparency bands (spectral regions of lowreflectance and high transmittance). For the thinnest multilayer film, thetransparency band is in the blue part of the visible spectrum. As the thick-ness of TiO2 increases, the transparency band shifts towards longer wave-lengths. The shifting transparency bands causes changes to the visual ap-pearance of the films, as shown in the rendered images in Figure 5.4(a). Asthe thickness of TiO2 increases, the color of the film changes from grey-blueish to grey-brownish, all while having almost similar transparency.To highlight the angular reflectivity of single and multilayer coatings,we applied the transfer matrix method (TMM) to extract the angular- andspectral-dependent reflectance. Figure 5.4 (c) illustrates the reflectance of abare glass window. In comparison, Figure 5.4 (d) and (e) illustrate the highreflectance imparted by the single and multilayer coatings at large angles ofincidence and longer wavelengths. The high reflectance of the coatings canbe exploited to achieve daylight redirecting, which will be explore in thiswork.965.3. Results and Discussion(a) (b)(c)Figure 5.4: FDTD-simulated normal-incidence reflectance and transmit-tance spectra of (a) single-layer silver thin films (Ag) and (b) multilayer ti-tanium dioxide coated on silver thin films (Ag | TiO2). (c) TMM-simulatedangular Fresnel reflectance spectra over the visible for bare window glass(SiO2) (left column), single-layer 20-nm thick Ag film (middle column) andmultilayer Ag | TiO2 – 18 nm (right column) coated on glass substrate.975.3. Results and DiscussionNext, we applied the FDTD-simulated spectral response to define RADI-ANCE materials (Table F.1) for the various window solutions. In addition,we applied generic RADIANCE materials to define all other materials inthe shoe-box room as shown in Figure 5.5(a). The daylight quantities usedthe local weather data to derive the sun and sky conditions for simulatingdaylight distributions under the influence of local climate patterns. Thefish-eye rendered image provides a glimpse of the daylight distribution inthe room with a south-facing window equipped with various window struc-tures (in the case of Figure 5.5, Ag-coated wing-flap slats) from the viewpoint of the occupant. There is noticeable noise in the rendered image dueto the artefacts of the RADIANCE ray-tracing rendering algorithm whenthe sampling rays fail to reach light sources in the scene. The noise can bereduced by increasing number of sample rays or number of ray bounces, butthis will come at the cost of increased simulation time and will have littleimpact on the accuracy of the luminous quantities in the space.The false color image in Figure 5.5(b) provides a distribution of thedaylight luminance intensity distributed near the window, wall, and floorand enables identification of potential glare sources. The pink-colored spotsin the image highlight the extreme bright areas of the room receiving morethan 2000 cd/m2, which contributes to glare from the direction of the view.(a) (b)Figure 5.5: (a) RADIANCE rendered images of shoebox room with south-facing window equipped with Ag-coated (20 nm thick) wing-flap slats at May15, 1.30pm using CIE Perez Sky condition [14] and (b) the correspondingfalse-color image of luminance distribution in the room.985.3. Results and Discussion5.3.2 Daylight Performance AnalysisCoated Window PaneFigure 5.6 shows the daylight performance metrics and average illumi-nance distribution calculated from CBDM simulations in the shoebox roomover the course of a year when the window has its inner pane coated with Agfilm and Ag | TiO2 films. The control corresponds to the room with a barewindow without any shading structures or coatings. The detailed data onthe daylighting performance metrices are available at Table F.2 in AppendixF.For the case of Ag-coated window, the amount of daylight availability inthe space at both lighting levels (work plane and ceiling) gradually reducesas the thickness of the Ag film increases. The reduced daylighting is evidentin both the daylight performance metrics shown in Figure 5.6(a) and theaverage illuminance distributions at both the work plane and ceiling shownin Figure 5.6(b). Increasing the Ag film from 20 nm to 50 nm causes thesDA300|50% to drop from 50% to 1.79%. The negative relative average illu-minance indicates the reduction of average illuminance quantities comparedto the control case, which can be attributed to the high reflectance of themetallic films. Although the Ag layer films can achieve some measure ofglare reduction, it greatly compromises the amount of daylight admittedinto the indoor space.For the case of Ag | TiO2 -coated window, the amount of daylight avail-ability in the space at both lighting levels (work plane and ceiling) is reducedby about half for all multi-layer systems studied. Interestingly, Ag | TiO2multilayers where the TiO2 layer is 38 nm and 46 nm thick has slightlyhigher sDA300|50% and average illuminance than the others. Ag | TiO2 mul-tilayer thin films generally outperform the 20-nm-thick Ag thin film in termsof daylight availability. The additional TiO2 film makes the Ag film moretransparent [188]. It can also be seen in Figure 5.6(d) that the multilayercoating does a better job of redirecting daylight onto the ceiling level thanthe single Ag layer alone.995.3. Results and Discussion(a) (b)(c) (d)Figure 5.6: Daylight performance metrics in the room when the windowis (a) coated with Ag films of various thicknesses and (b) multilayer Ag| TiO2 thin films of various TiO2 film thicknesses. Average illuminationdistributions (over the year) at the work plane (0.9m above ground) andceiling level (2.7m above ground when the window is (c) coated with Agfilms of various thicknesses and (d) multilayer Ag | TiO2 thin films of variousTiO2 film thicknesses.Figure 5.7 shows the daylight availability of Ag (50 nm) and Ag | TiO2(23 | 57 nm) coated window pane inside the room model. Overall, both filmsreduce high-intensity daylight (>2000cd/m2) admitted during the summersolstice and fall equinox as compared to the control (bare window) configu-ration.1005.3. Results and Discussion(a)(b)Figure 5.7: Rendered images and corresponding false-color images of day-light distribution for control, window pane coated with Ag (50 nm) and Ag |TiO2 (23 | 57 nm) in the summer solstice (Jun 21st), fall equinox (Sep 21st),and winter solstice (Dec 21st).The sun and sky conditions are derived fromthe Summerland weather data.1015.3. Results and DiscussionFor the case of the Ag-coated window pane, there is significant reductionin intensity, but the room has a bluish color due to the transmitted color ofthe Ag film. On the other hand, the Ag | TiO2 coated window reduces theintensity of daylight falling on the floor but still suffers bright light spots onthe windows which can potentially lead to glare. The film has slight colorbleeding issues due to the transmitted color of the coating, but the color ismore neutral than the Ag-coated window. The Ag | TiO2 coated windowproduces a bright light spot on the floor at summer solstice and fall equinoxbut the luminance if these spots is not as intense as the luminance fromthe windows. This suggests that the Ag | TiO2 layer reflects a portion ofdaylight while the remaining daylight admits and falls on the floor. Duringthe winter solstice, the room is dimmer compared to both summer solsticeand fall equinox and the luminance from the window is less intensive in theviewing direction. This is due to the lower daylight intensity from the low-angle sun in the winter months mixed with the overcast sky derived fromthe local weather data pattern.Figure 5.8 shows the annual glare charts for the case of the window coatedwith Ag and Ag | TiO2 thin films. The annual glare charts depict timeperiods over the course of a year in which an occupant of the room wouldexperience glare, classified as either imperceptible, perceptible, disturbing,and intolerable glare. The annual glare chart for the control case (barewindow) in Figure 5.8(a) indicates that most glare experiences are betweenthe fall equinox to spring equinox (mid-September to early April), when thesun is generally at a lower sky position than during the summer months.The glare experiences typically occur in the morning until afternoon, withthe worst glare around 12 pm slot. Both Ag and Ag | TiO2 window coatingsremove the glare experienced in the morning hours but there are still someintolerable glare experiences during the 12 pm - 2 pm time slot.To further the investigation, we rendered the occupant’s viewing positionon March 12, 12.30pm during the time of intolerance glare experienced by theoccupant. Figure 5.9 shows the rendered images and false-color luminancedaylight distributions for window panes coated with Ag (20 nm), Ag (50nm), Ag | TiO2 (23 | 18 nm) and Ag | TiO2 (23 | 57 nm). The highlyreflective 50 nm Ag film is the best at glare reduction, but it comes at thecost of significant illuminance reduction. For the other cases, the windowacts as a glare source (as highlighted in pink) and causes intolerable glareexperience. Apart from glare, the room suffers from color bleeding throughthe thin films, resulting in grey-bluish coloration. The color bleeding willcause the color appearance of objects to slightly differ from their appearanceunder natural daylighting.1025.3. Results and DiscussionFigure 5.8: Annual glare charts for (a) control (bare window) and for awindow coated with (b) Ag – 20 nm, (c) Ag – 50 nm, (d) Ag | TiO2 – 23 |18 nm and (e) Ag | TiO2 – 23 | 57 nm.1035.3. Results and DiscussionFigure 5.9: Rendered image of the occupant’s viewpoint with the south-facing coated window pane and the corresponding false-color luminance dis-tribution on March 12, 12.30pm for (a) Ag – 20 nm, (b) Ag – 50 nm, (c) Ag| TiO2 – 23 | 18 nm and (d) Ag | TiO2 – 23 | 57 nm.Coated flat slatsFigure 5.10 shows the daylight performance metrics and relative averageilluminance distributions for the case in which the window is equipped withcoated flat slats. (Please refer to Table F.3 in Appendix F for the averageilluminance values and other performance metrics calculated for this study).The flat slats are coated with either single-layer Ag thin films or multilayerAg | TiO2 thin films. Generally, the coated flat slats cause a 10-15% dropin the daylight availability (sDA300|50% ) compared to the control case (barewindows). ASE1000|250 for both single and multilayer coated flat slats ismaintained around 24%, which indicates that about a quarter of the workplane still experiences overlit problem and potentially causes glare. The flatslats coated with Ag and Ag | TiO2 films result ∼15% and ∼10% reductions,respectively, of the overall average illuminance compared to that of the barewindow. These reduction performance metrics suggest the flat slats are lesseffective than wing-flap slats in redirecting the daylight upward to ceiling,and less protection in reducing the overlit area in near the window, resultingin the potential of glare and overheating issue at the area.1045.3. Results and Discussion(a) (b)(c) (d)Figure 5.10: Daylight performance metrics of flat slats coated by (a) singlelayer Ag thin films and (b) multilayer Ag | TiO2 thin films on south-facingwindow. Average illumination distributions at work plane (0.9m aboveground) and ceiling (2.7m above ground) for (c) single layer Ag thin filmsand (d) multilayer Ag | TiO2 thin films coated on flat slats.1055.3. Results and Discussion(a)(b)Figure 5.11: Rendered images and corresponding false-color images of day-light distribution for control, flat slats coated with Ag (50nm), and flat slatscoated with Ag | TiO2 (23|57nm) on the summer solstice (Jun 21st), fallequinox (Sep 21st) and winter solstice (Dec 21st). The sun and sky condi-tions are derived from the Summerland weather data.1065.3. Results and DiscussionTo investigate further, we rendered the room model (Figure 5.11) wherethe window is equipped with flat slats coated with Ag (50 nm) or Ag |TiO2 films (23 | 57 nm) under the influence of varying the sun angle fromthe lowest (winter solstice) to the highest (summer solstice). Both Ag andAg | TiO2 coated flat slats still admit most of the direct sunlight into theroom and create extremely bright light spots on the floor and the windowduring the summer solstice and fall equinox. This indicates that both Agand Ag | TiO2 films coated on flat slats have poor daylight redirect abilityand do not block excessive amounts of daylight from entering the space.During the winter solstice, both Ag and Ag | TiO2 films coated on flat slatscause overall dimming of the room. The daylighting metrics and renderedimages indicate that coated single-layer and multilayer slats have minimaldaylight redirecting capability as the average illuminance distribution onboth lighting levels remain almost identical to the bare control window.Figure 5.12 shows the annual glare charts for Ag and Ag | TiO2 thinfilms coated on flat slats. The glare experience becomes more severe withthe coated flat slats compared to the bare window, with instances of glareoccurring more frequently than the bare window. For instance, Ag | TiO2 –23 | 18 nm thin films coated on flat slats has more glare experience (mainlyperceptible glare) in the 8 am – 10 am morning hours from April to Septem-ber.1075.3. Results and DiscussionFigure 5.12: Annual glare charts for (a) control (bare window) and a windowequipped with flat slat that are coated with (b) Ag – 20 nm, (c) Ag – 50nm, (d) Ag | TiO2 – 23 | 18 nm and (e) Ag | TiO2 – 23 | 57 nm.1085.3. Results and DiscussionTo investigate further, we render the occupant’s viewing position at April29, 9.00am as shown in Figure 5.13. There is a large area of glare sources(highlighted as pink pixels in Figure 5.13(b)) which encompasses the win-dow, floor and walls. These glare sources result in higher DGP values asit is logarithmically proportional to the luminance of the glare sources asdefined in Equation (1.61). Therefore, the results suggest that coating theflat slats with either Ag or Ag | TiO2 thin films does not improve daylightredirecting and does not improve glare performance.(a) (b)Figure 5.13: (a) Rendered image from the occupant’s viewpoint with thesouth-facing window equipped with Ag | TiO2 – 23 | 18 nm coated flat slatson April 29, 9 am and (b) the corresponding false-color image of daylightluminance distribution at the viewing position.Wing-flap slatsLastly, we introduce the wing-flap slat design, which has long- and shortslat sections tilted up as shown in Figure 5.1(c). The purpose of the tiltedslats is to capture glancing daylight (higher incident angles) to improvedaylight redirecting performance and ultimately reduce glare. Combinedwith the high reflectivity of thin metallic films at steep incidence angles, itis hypothesized that the coated wing-flap slats will exhibit strong daylightredirecting. Figure 5.14 shows the daylight performance metrics and averageilluminance distributions for thin metallic film coated on wing-flap slats.(Please refer to Table F.4 in Appendix F for the average illuminance values1095.3. Results and Discussionand other performance metrics calculated for this study).(a) (b)(c) (d)Figure 5.14: Daylight performance metrics of wing-flap slats coated by (a)single layer Ag thin films of various thicknesses and (b) multilayer Ag |TiO2 thin films of various TiO2 film thicknesses. The average illuminationdistributions at work plane (0.9m above ground) and ceiling (2.7m aboveground) for (c) single layer Ag thin films and (d) multilayer Ag | TiO2 thinfilms coated on wing-flap slats.The relative average illuminance at the workplane level drops by abouthalf due to the presence of the coated wing-flap slats, relative to the caseof bare window. Ag-coated wing-flap slats are the best at reducing overlitarea, as evidence by ASE1000|250 values near 0% for all thickness except for20 nm when it reaches 7.14%. Interestingly, the average illuminance, illu-1105.3. Results and Discussionminance distribution maps and relatively average illuminance all increase inthe presence of the wing-flap slats compared to the bare window. For exam-ple, the 50-nm-thick Ag-coated wing-flap slats exhibit a 41.13% increase onthe average illuminance at the ceiling level, which is evident from the illu-minance distribution at ceiling level shown in Figure 5.14(c). The wing-flapslats coated with Ag | TiO2 are not as effective at redirecting daylight as thewing-flap slats coated with Ag. The maximum relative average illuminancegain at the ceiling level is 26.63% when the wing-flap slats are coated withAg | TiO2 (23 | 57 nm).The daylighting redirecting capability of the wing-flap slats results in no-ticeable bright spots on the ceiling near the window as shown in Figure 5.15.Both Ag (50 nm) and Ag | TiO2 (23 | 57 nm) coated wing-flap slats partiallyredirects daylight upward from summer to winter solstices (correspondingto high-angle and low-angle sun, respectively). During the summer solstice,daylight levels with both types of coatings are similar. The Ag | TiO2 (23 |57 nm) coated wing-flap slats cause a cool blueish color in the space. Duringthe fall equinox, the Ag | TiO2 (23 | 57 nm) coated wing-flap slats produce abright spot on the floor, suggesting that it redirects partial daylight upwardwhile the remaining daylight falls on the floor. During the winter solstice,the daylight levels when the wing-flap slats are coated with both types offilms are dimmed, but there are weak bright light spots on the ceiling (evenunder overcast sky conditions). In addition, the luminance from the windowwhen viewed by the occupant becomes less intensive compared to summersolstice and fall equinox, suggesting less likelihood to glare from the viewingdirection. The performance metrics and rendered images indicate the wing-flap slats demonstrate the good daylighting redirecting capability over thecourse of the year, particularly when they are coated with single-layer Agfilms.1115.3. Results and Discussion(a)(b)Figure 5.15: Rendered images and corresponding false-color images of day-light distribution for control, wing-flap slats coated with Ag (50 nm) andAg | TiO2 (23| 57 nm) in the summer solstice (June 21st), fall equinox (Sept21st), and winter solstice (Dec 21st). The sun and sky conditions are derivedfrom the Summerland weather data.1125.3. Results and DiscussionThe daylighting redirecting capabilities of the wing-flap slats results indramatic reduction in glare over the course of the year. Figure 5.16 showsthe annual glare charts for both Ag and Ag | TiO2 coated wing-flap slats.In particular, the 50 nm Ag- coated wing-flap slats remove most of the glareoccurrences while reducing the worst intolerable glare experiences duringthe 12 pm-2 pm slot to minor perceptible glare experiences. This is due tothe high reflectivity of the 50-nm-thick Ag thin film, which redirect daylightaway from the work plane to the ceiling level to achieve more diffuse lightingin the indoor space.Although thicker Ag | TiO2 (57 nm) coated slats have lower daylight redi-recting capability than the Ag-coated slats, it still achieves significant glarereduction compared with thin films coated flat slats. The semi-transparencyof Ag | TiO2 means that glancing daylight is still admitted to the work planelevel. To further investigate, we render the occupant’s viewpoint at March12, 12.30pm (Figure 5.17). The rendered image shows that there are multi-ple admitted daylight shadows corresponding to intolerable glare sources atthe viewing position. Although the thicker Ag | TiO2 (57 nm) coating is notoptimal for daylight redirecting, it may be useful for fixed or adaptive angleadjusting slat system and for applications where it is important to preserveoutdoor views.1135.3. Results and DiscussionFigure 5.16: Annual glare charts for (a) control (bare window) and a windowequipped with wing-flap slats coated with (b) Ag – 20 nm, (c) Ag – 50 nm,(d) Ag | TiO2 – 23 | 18 nm and (e) Ag | TiO2 – 23 | 57 nm.1145.3. Results and Discussion(a) (b)Figure 5.17: (a) Rendered image from the occupant’s viewpoint with south-facing window equipped with Ag | TiO2 – 23 | 57 nm coated wing-flapslats on March 3, 12.30pm and (b) the corresponding false-color image ofluminance daylight distribution.Overall, we conclude from this study that daylight redirecting structuresaugmented with semi-transparent, reflective thin metallic films are a goodcandidate solution for achieving glare reduction. We have examined a varietyof configurations in which two types of thin-film coatings have been appliedto various window structures and examined their impact of their deploymenton the illuminance distribution and glare experiences in a room with a south-facing window. (Please refer to Figure F.2 and F.3 in the Appendix F for theside-by-side rendered images comparison of metallic thin film coated windowstructures.) Based on our preliminary analysis, coated wing-flap structuresappear to achieve a good balance between acceptable admittance of daylightand redirection to reduce glare.1155.4. Summary5.4 SummaryWe demonstrated the feasibility of using multiscale models incorporatingwave optical modelling and CBDM to explore the daylighting and glare nearwindows that are equipped with window coatings and simple daylight redi-recting structures (flat slats and wing-flap slats) coated with various thinfilm structures.We have studied the performance of these systems as a func-tion of film thickness. Our analysis indicated that coated wing-flap slats area promising solution, as it demonstrates good daylight redirecting capabilitywith increased average illuminance at the ceiling level compared to a barewindow. Silver coatings that incorporated an additional high-refractive in-dex TiO2 film have increased transparency and result in increased daylightavailability in the space (and better visual contact with the outdoors). Fu-ture work could build on our framework to analyze the daylighting and glareperformance of more complex daylighting structures and optical materials,including plasmonic nanomaterials, photonic crystals, and metamaterials.116Chapter 6ConclusionThis thesis has demonstrated the integration of wave optical modellingand physically based rendering to model the visual appearance and behaviorof engineered nanoscale structures such as thin metallic films and plasmonicmetallic nanostructures. We have applied a multiscale computational ap-proach to examine the performance of these structures in the context ofapplications in artificial coloration and daylighting. In Chapter 2, we intro-duced a computationally efficient multi-scale approach to generate visual ap-pearance of thin metallic films as a function of micro- and nano-scale rough-ness and for various lighting environments, film composition, and substrates.The use of Schlick’s approximation to approximate Fresnel reflectance hasbeen validated with various thin film systems, which was important to signif-icantly reduce the number of electrodynamic simulations required to gener-ate physically-based material models. In Chapter 3, we rendered the visibleiridescence of various plasmonic structures that have been proposed for ar-tificial structural coloration, including metallic nanohole-, nanodisk-, andnanohole-nanodisk-arrays. We used electrodynamic simulations to createangular- and frequency-dependent physically based material models, whichwere then incorporated into a spectral rendering engine. Through our work,it is now possible to preview the angular- and spectral-selective appearanceof engineered plasmonic structures of arbitrary complexity. In Chapter 4, weused multi-scale approach to investigate the effect of nanoscale roughness onplasmonic structural coloration. By parameterizing the surface roughnessinto in-plane and out-of-plane components, we have been able to examine theimpact of roughness variations along orthogonal directions on the variance ofthe perceived color from hole arrays. In Chapter 5, we applied wave opticalmodelling to describe the spectral response of thin metallic films, which werethen used in CBDM to investigate the daylighting and glare performanceof coated daylight-redirecting structures. A promising daylight-redirectingstructure has been identified, which leverages the angular-selective scatter-ing properties of very thin metallic films and multilayers.117Chapter 6. ConclusionOur work has developed a simulation approach to predict the visualappearance and behavior of engineered nanoscale structures materials, butsome limitations of our approach should be mentioned. In Chapters 2 and 5,we use Schlick’s approximation instead of full-FDTD simulated angular andspectral reflectance in order to reduce the computation time. As discussed,Schlick’s approximation breaks down for very thin films and steep viewingangles. In Chapter 4, our investigation of nanoscale rough surfaces used alimited number of randomly generated surfaces due to the long computa-tional times necessary to carry out 3D FDTD simulations. Throughout thethesis, we have assumed that wave interactions on the nanoscale are fullycoherent. This is a reasonable assumption, as the coherence length of in-coherent daylight is on the order of a couple microns, which is beyond thefeature scales that we have explored (typically 100s of nanometres). In ad-dition, we have assumed that multi-scale roughness occurring at the micro-and nano-scales can be treated independently and separately (micro-scaleroughness modelled by microfacet theory and nanoscale roughness modelledby wave optics). It is yet unknown if our separate treatment of roughness atthese scales is fully valid, but, given the current state of knowledge on thistopic, we feel that our approach is at the very least a very good first guess.Overall, this thesis leverages recent advancements in computational nan-ophotonics and computer graphics to enable visualization and prediction ofnanomaterial behavior at scales that were not previously possible. By aug-menting the computational ability to generate physically-accurate predic-tions of the optical properties of nanomaterials, this work can potentiallyshorten design cycles and help speed the development and application ofnanomaterials for real-world applications. Our multi-scale light modelingframework is an important first step, but considerable future work is re-quired to fully develop this concept. Important future topics include:a. Computational efficiency: Creating far-field BSDF material modelsfor nano-arrays is a data- and computationally-intensive process. Ma-chine learning and data mining algorithm applied to a library of FDTDsimulations could help to reduce the simulation times by estimating thenear-field response of nanostructures. There has been recent work demon-strating the potential feasibility of deep learning algorithms to predict thestructural color resulting from various configurations and compositions ofnanostructures. So far, the works have been limited to simple structuressuch as metallic nanoparticles, meta-grating antenna, dielectric pyramidand ring arrays [189–192].b. Rendering quality: Our work uses commercially available PBR ren-118Chapter 6. Conclusiondering engine (highly optimized to compute in CPU/GPU architectures)for fast, accurate, real-time rendering. The rendering quality can be fur-ther improved by using spectral rendering with research-based renderingengine (Mitsuba 2)[193]. In addition, there is the exciting possibility ofleveraging our PBR material models to connect with the latest immersivetechnologies in VR/AR/XR, opening up new ways to preview, interactand research nanomaterials. We have demonstrated this potential inat the SIGGRAPH 2020 (Figure G.1) and SIGGRAPH 2021 conference(Figure 6.1), in which we leveraged webXR to create a life-scale virtualshowroom experience (access by link: https://banditvr.ca/webvr/plasmonics)featuring plasmonic nanostructures coated on the body of classic cars.This capability can potentially be used to create full VR/AR/XR appli-cations using the state-of-the-art game engine such as Unreal Engine andUnity to study and examine nanostructured materials.Figure 6.1: Screenshot of a webXR application built by Vincent Loi toshowcase plasmonic structural coloration on various substrates. The bodiesof classic car are coated with silver nanohole array with a diameter of 70 nmand a period of 140 nm with varying nanoscale roughness scale. The userscan virtually walk through the showroom and examine various examples ofstructural coloration. (Link to access the virtual showroom).c. More accurate FDTD algorithm: The conventional FDTD uses stan-dard central finite difference which inherits naturally small errors due to119Chapter 6. ConclusionTaylor’s series approximation to discretize the Maxwell’s equation by in-troducing the staggered grid. These errors will be truncated throughmulti-time-step computing and cause simulation results to be less accu-rate. Alternatively, new algorithms such as non-standard (NS)-FDTDcan further reduce errors due to discretization [159].d. More complex nanostructures: Due to limitations on time and com-putational resources, we have restricted our work to a small subset ofnanostructures, particularly those with some degree of symmetry. Withfurther research and development of GPU-accelerated parallel processingoptimized FDTD algorithms, it is foreseeable that FDTD computationtimes will dramatically reduce [194, 195]. 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CRCPress, 2018. → pages 148140Appendix AFDTD Iterative FieldUpdating EquationTo formulate the field updating equation (also known as forward scheme)for FDTD method, we use Equation (1.1a) and (1.1b) as:∇×H = ∂E∂t+ σeE + J (A.1a)∇×E = ∂H∂t+ σmH + Mi (A.1b)Solving the curl equal equations for Equation (A.1a) and (A.1b) above, thiswill yield 6 equations as below:∂Ex∂t= 1x[∂Hz∂y− ∂Hy∂z− (σexEx + Jix)](A.2a)∂Ey∂t= 1y[∂Hx∂z− ∂Hz∂x−(σeyEy + Jiy)](A.2b)∂Ez∂t= 1z[∂Hy∂x− ∂Hx∂y− (σezEz + Jiz)](A.2c)∂Hx∂t= 1µx[∂Ey∂z− ∂Ez∂y− (M + σxHx)](A.2d)∂Hy∂t= 1µy[∂Ez∂x− ∂Ex∂z− (M + σyHy)](A.2e)∂Hz∂t= 1µz[∂Ex∂y− ∂Ey∂x− (M + σzHz)]. (A.2f)In this section, we only show the derivation for field updating equation for Exsince the derivation process for the others are identical.The 3-points centraldifference approximation for the spatial grid of x and y with step as:f ′(x) ≈f(x+ ∆x2)− f(x− ∆x2)∆x (A.3)141Appendix A. FDTD Iterative Field Updating Equationfor the partial derivatives in Equation (A.2a). The expression becomesEn+1x (i, j, k)− Enx (i, j, k)∆t =1x(i, j, k)Hn+ 12z (i, j, k)−Hn+12z (i, j − 1, k)∆y− 1x(i, j, k)Hn+ 12y (i, j, k)−Hn+12y (i, j − 1, k)∆z− σex(i, j, k)x(i, j, k)En+ 12x (i, j, k)− 1x(i, j, k)Jn+ 12ix (i, j, k)(A.4)Since the E field is only available at the integer time steps, so, En+12x (i, j, k)is approximated by averaging the En+1x (i, j, k) and Enx (i, j, k) asEn+ 12x (i, j, k) =En+1x (i, j, k) + Enx (i, j, k)2 . (A.5)Substitute the expression above into the Equation (A.4) and solve for En+1x (i, j, k)to obtain the forward scheme updating equation for Ex byEn+1x (i, j, k) =2x(i, j, k)− σex((i, j, k)∆t(2x(i, j, k) + σex(i, j, k)∆t)Enx (i, j, k)+2∆t[Hn+ 12z (i, j, k)−Hn+12z (i, j − 1, k)](2x(i, j, k) + σex(i, j, k)∆t) ∆t−2∆t[Hn+ 12y (i, j, k)−Hn+12y (i, j − 1, k)](2x(i, j, k) + σex(i, j, k)∆t) ∆z− 2∆t(2x(i, j, k) + σex(i, j, k)∆t)Jn+ 12ix (i, j, k)(A.6)The forward scheme equations for the other field components can be derivedusing this approach. Figure A.1 illustrates the one-dimensional FDTD com-putational scheme for the both E and H fields computation in the leap-frogmanner where the computation E fields in the current computation looprequires the computed H fields from the previous computation loop andvice-versa. The similar process for the two-, or three-dimensions FDTDcomputation scheme.142Appendix A. FDTD Iterative Field Updating EquationFigure A.1: One-dimensional FDTD computation structures for leap-frogtime stepping forward scheme.143Appendix BMonte Carlo IntegrationMonte Carlo integration is a numerical method that uses random sam-pling number to estimate the result of numerical integral. The ideology ofMonte Carlo method resembles estimation approaches in statistics, whichuses a sample of the population to estimate the likelihood outcome of thepopulation. For instance, calculating the average incomes of fresh graduatesof a country would requires the huge data survey of each respondence underthe category, summing up the numbers and average the number to find theaverage incomes. The easier way to use a sample of the population and com-pute its average incomes. This is might not yield the exact average incomesfrom the entire the population, but it provides an estimate of the value iseven this trade off over the accuracy over the speed. The accuracy of thevalue can be improved with increase sample size. Before deep dive into theMonte Carlo integration, we begin with some fundamental of statistics andprobability.Random VariablesA random variable is a variable whose value is numerical outcome ofa random phenomenon. A random variable can be classified as discreterandom variable if the possible outcomes are countable (e.g., the flip coinwhere the set of possible outcomes is X = {head, tail} ) or continuous if thepossible outcomes are taking on real value, R (e.g a person’s height, whichcan take on set of real numbers). In Monte Carlo integration, the randomvariable is continuing which use the continuous value of integral limits suchas the limits of hemisphere of integral, Ω.144Appendix B. Monte Carlo IntegrationCumulative Distribution and Density FunctionThe cumulative distribution function (CDF) of a random variable, X isthe probability of an outcome value from the variable’s distribution is lessthan or equal to a threshold of x ascdf(x) = F (x) = P (X ≤ x) (B.1)The probability density function (PDF) is the derivative of the CDF aspdf(X) = ddx[F (x)] (B.2)This important relationship between the CDF and PDF. To calculate theprobably of a random variable lies within an interval, we integrate the PDFwithin the intervalP (a ≤ X ≤ b) =∫ bapdf(x)dx (B.3)Expected Values and VarianceThe expected values of a random variable Z = f(X) over domain µ(x)is defined asE[Y ] =∫µ(x)f(x)pdf(x)dµ(x) (B.4)and variance isσ2[Y ] = E[(Y − E[Y ])2](B.5)where σ is the standard derivation. For a constant, a multiply on Y , thecorresponded expected values and variance becomeE[aY ] = aE[Y ]σ2[aY ] = a2σ2[Y ](B.6)145Appendix B. Monte Carlo IntegrationMonte Carlo EstimatorMonte Carlo integration uses random sampling of function to estimatethe result of its integral. Assume the one-dimensional integral is defined asF =∫ baf(x)dx (B.7)where a and b are the lower and upper limits of the integral function, f(x).The integral of a function, f(x) means determine the area below the func-tion’s curve as Figure B.1.(a) (b)(c)Figure B.1: (a) Area below the integration of function, f(x) for the integra-tion limits [a, b], (b) Area of rectangle due to estimator value, X, (c) Theestimate average area under the curve using 4 random number points.146Appendix B. Monte Carlo IntegrationNext select a random value, Xi ∈ [a, b] to evaluate the function, f(X1)and multiple with (b − a). Figure B.1(b) shows a rectangle are overlapwith the curved from the function, f(X1) and some areas of the curve areunderestimate and overestimate by the rectangle. By average of the estimatearea will give approximate area under the curve but less accurate. However,if the evaluate the function with a greater number of random points betweena and b used, and average the average this area, the resulting area willclose to the actual result of the integral. Figure B.1(c) shows the averageapproximate area under the curve from 4 random numbers between a andb, the approximate the area become more reassemble to the area under thecurve. We can formalize this approximation into a general formula as:〈FN 〉 = (b− a) 1NN−1∑i=1f(Xi) (B.8)where N is the number of samples used in the approximation. Equation(B.8) known as the Monte Carlo estimator. The set of uniform distributedrandom number in Xi ∈ [a, b] can be generated byxi = a+ ξi(b− a) (B.9)where ξi is the uniform distribution between 0 and 1. Hence, Equation (B.8)can be written as〈FN 〉 = (b− a) 1NN−1∑i=1f(a+ ξi(b− a)) (B.10)Since 〈FN 〉 is a random variable which sum of random numbers, we can147Appendix B. Monte Carlo Integrationprove the expected value of 〈FN 〉 is in fact F asE[〈FN 〉]= E[(b− a) 1NN−1∑i=1f(Xi)]= (b− a) 1NE[N−1∑i=1f(Xi)]= (b− a) 1NE[N−1∑i=1∫ bbf(x)pdf(x)dx]= 1NE[N−1∑i=1∫ bbf(x)dx]=∫ bbf(x)dx = F(B.11)Due to the Strong Law of Large Numbers, the Monte Carlo approximationwill convergence to the actual result whereP(limN→∞〈FN 〉)= 1 (B.12)The Monte Carlo estimator is the basic of Monte Carlo estimator for one-dimensional integral with uniform distribution random variable. For multi-dimensional Mont Carlo estimator and improving the Monte Carlo integra-tion approach, there are good reference including [57],[59] and [196].148Appendix CComputational SettingsWorkstation SpecificationsCPU Intel i7-8700K, base clock 3.7 GHz, turboboost up to 4.7 Ghz 6 cores, 12 threadsRAM Kingston 2× 16 GB DDR4 2667MhzGPU NVIDIA GeForce RTX 3090 24GB GDDR6XStoragei. Samsung PCI-E NVME 970 EVO 500 GB(OS drive)ii. Crucial SATA MX500 SSD 1 TBiii. Seagate HDD 1 TBCooling system Corsair H100i Platinum AIO liquid coolingsystemMotherboard MSI Z370 GAMING PLUS (MS-7B61)Operating system Window 10 Pro 64-bitTable C.1: Specifications of the computer workstation used for the electro-dynamic simulations and PBR.149Appendix C. Computational SettingsSimulation Parameters ValuesMesh Accuracy 8 (highest)Mesh refinement Conformal variantdt stability factor 0.99ft (fs) 0.00844181Minimum mesh step (nm) 0.25Auto shutoff (min) 1× 10−6BFAST alpha 1BFAST dt multiplier 0.5Table C.2: FDTD simulation parameters used to model structures describesin Chapters 2, 3, and 4.Rendering settings ValuesResolution i. Interior room: 2048 × 2048 pixelsii. Studio room: 1920 × 1440 pixelsMaximum number ofbounces22Rendering pass/frame 1000Noise reduction AI-denoiseRendering mode Spectral RenderingInput color space ACEScgOutput color space ACEScgTable C.3: NVIDIA IRAY settings used to model structures describes inChapter 2, 3, and 4.150Appendix DPlasmonic MetallicNanostructures SupplementInformationSample Material Thickness(nm)Period, P(nm)Diameter, D(nm)1Ag 20140 702 150 753 160 804 170 855 180 906 190 957 200 1008Al 20150 759 160 8010 170 8511 180 9012 190 9513 Ag | PMMA 20 140 7014 200 100Table D.1: Material, thickness period and diameter combinations for gen-erating silver nanohole arrays with the fixed ratio D : P = 1 : 2 in FDTDsimulations.151Appendix D. Plasmonic Metallic Nanostructures Supplement InformationFigure D.1: Extended rendered appearance for the reflection color of 20-nm-thick silver nanohole array with the period (at fixed ratio D : P = 1 : 2)varying from 140 nm to 360 nm coated on the body of the pedal car.152Appendix D. Plasmonic Metallic Nanostructures Supplement InformationFigure D.2: Extended rendered appearance for the transmission color of 20-nm-thick silver nanohole array with the period (at fixed ratio D : P = 1 : 2)varying from 140 nm to 360 nm coated on the body of the pedal car.153Appendix D. Plasmonic Metallic Nanostructures Supplement InformationSample Period, P (nm) Diameter, D (nm)1 270 902 300 1103 340 1404 380 1605 410 1906 450 220Table D.2: Period and diameter combinations for Silver tandem nanodiskarrays in FDTD simulations.Sample Pillar height, d (nm) Diameter, D (nm) Period, P (nm)1 30802002 403 504 605 706 80780908 1009 110Table D.3: Pillar height, diameter and period combinations for generatingaluminum nanohole and nanodisk arrays in FDTD simulations.154Appendix D. Plasmonic Metallic Nanostructures Supplement Information(a)(b)Figure D.3: FDTD-simulated (a) Reflection and (b) Transmission spectraof silver tandem nanodisk with varying diameter and period based on theperiod and diameter combinations at Table D.2.155Appendix D. Plasmonic Metallic Nanostructures Supplement InformationFigure D.4: FDTD-simulated bidirectional reflectance distribution of silvertandem disk array at P = 300 nm and D = 110 nm for the incident anglefrom 0° to 89° with 2° increment.156Appendix D. Plasmonic Metallic Nanostructures Supplement InformationFigure D.5: FDTD-simulated bidirectional transmittance distribution forsilver tandem disk array at P = 300 nm and D = 110 nm for the incidentangle from 0° to 89° with 2° increment.157Appendix EBSDF Extraction Scripts1 clear;23 res = 150;4 simCount = 0;5 illumination = 2; # 1-Gaussian , 2-Plane Wave Source6 index_up = 1; #n_air7 index_down = 1; #n_air (exit the PMMA)8 direction_up = 1;9 direction_down = 1;10 f_all = getdata("R","f");11 halfAngle = 5;12 thetaOut = linspace (0 ,90 ,101);13 phiOut = linspace (0 ,180 ,101);14 BRDF = matrix(length(f_all),length(thetaOut),length(phiOut));15 BTDF = matrix(length(f_all),length(thetaOut),length(phiOut));1617 radius = [70;80;95;110;55];18 period = [340;380;410;450;270];19 for(n = 1: length(radius)){20 simCount = 0;21 radius1 = radius(n);22 period1 = period(n);23 for(m = 1:17){24 simCount = simCount + 1;25 load("AgDiskR"+num2str(radius1)+"nmP"+num2str(period1)+"nm_"+num2str(simCount)); #loading simulationfile26 for(i=1: length(f_all)){27 #Getting E2 for farfield28 E2_up = farfield3d("R",i,res ,res ,illumination ,index_up ,direction_up);29 ux_up = farfieldux("R",i,res ,res ,index_up);30 uy_up = farfielduy("R",i,res ,res ,index_up);31 E2_down = farfield3d("T",i,res ,res ,illumination ,index_down ,direction_down);32 ux_down = farfieldux("T",i,res ,res ,index_down);33 uy_down = farfielduy("T",i,res ,res ,index_down);158Appendix E. BSDF Extraction Scripts343536 Ux_up = meshgridx(ux_up ,uy_up);37 Uy_up = meshgridy(ux_up ,uy_up);38 cos_theta_up = sqrt(1-Ux_upˆ2-Ux_up ˆ2);3940 ux_down = farfieldux("T",i,res ,res ,index_down);41 uy_down = farfielduy("T",i,res ,res ,index_down);42 Ux_down = meshgridx(ux_down ,uy_down);43 Uy_down = meshgridy(ux_down ,uy_down);44 cos_theta_down = sqrt(1-Ux_downˆ2-Uy_down ˆ2);4546 #using cosine theta for E2 with ux and uy.47 for(j=1: length(phiOut)){48 BRDF(i,1: length(thetaOut),j) =farfield3dintegrate(E2_up*cos_theta_up ,ux_up ,uy_up ,halfAngle ,thetaOut ,phiOut)/( farfield3dintegrate (0* E2_up+1,ux_up ,uy_up ,halfAngle ,thetaOut ,phiOut)+1e-20);49 BTDF(i,1: length(thetaOut),j) =farfield3dintegrate(E2_down*cos_theta_down ,ux_down ,uy_down ,halfAngle ,thetaOut ,phiOut)/( farfield3dintegrate(0* E2_down+1,ux_down ,uy_down ,halfAngle ,thetaOut ,phiOut)+1e-20);50 }5152 } #frequency5354 BRDF = real(BRDF);55 BTDF = real(BTDF);56 data_filename = "Raw_AgDiskBSDF_R"+num2str(radius1)+"nmP"+num2str(period1)+"nm_"+num2str(simCount);5758 matlabsave(data_filename ,BRDF ,BTDF);59 } #load Simulation file6061 } #sweeping159Appendix FCBDM SupplementInformationNo Layer Material Rvis (%) Tvis(%)1 3D Wall White Wall 83.4 02 Door Frame Wooden Frame 13.3 03 Window Frame Wooden Frame 13.3 04 Door Wooden Door 5.1 04 Glazing Azuria - Clear (Argon) 10.5 59.55 Ceiling White ceiling 85.7 06 Floor Concrete floor 28.9 07 Table Laminate brown table 17.6 08 LCD Monitor screen 7 301A 5.6 0Table F.1: List of Radiance material parameters applied into each layer ofthe shoebox room model.160Appendix F. CBDM Supplement InformationFigure F.1: Detail of dimensions and measurements (in milimeters) of theshoebox room.161Appendix F. CBDM Supplement InformationSample Work Plane CeilingsDA(%)ASE(%)Avg.Lux sDGsDA(%)Avg.LuxControl 91.96 26.79 2788.60 25.45 76.79 920.59Ag 20nm 66.96 23.21 2657.29 19.87 57.14 877.74Ag 25nm 55.36 23.21 2648.60 17.86 44.64 876.13Ag 30nm 30.36 16.96 2605.44 16.85 18.75 864.41Ag 35nm 20.54 15.18 2607.84 16.63 8.93 858.52Ag 40nm 10.71 12.50 2596.24 15.74 0.00 867.72Ag 45nm 10.71 12.50 2584.46 15.51 0.00 856.41Ag 50nm 4.46 10.71 2580.25 14.51 0.00 856.28Ag | TiO218nm 73.21 23.21 2705.47 21.09 60.71 887.59Ag | TiO224nm 66.96 23.21 2666.12 20.76 57.14 882.55Ag | TiO238nm 92.86 26.79 2733.25 24.67 70.54 899.77Ag | TiO246nm 86.61 24.11 2683.82 24.55 70.54 883.23Ag | TiO257nm 71.43 23.21 2664.02 21.21 59.82 879.51Occupancy Time: 8am-6pm with DST, sDA: sDA300|50%, ASE: ASE1000|250Table F.2: Daylighting and glare performance metrics at work plane andlighting levels for Ag and Ag | TiO2 thin films coated window pane.162Appendix F. CBDM Supplement InformationSample Work Plane CeilingsDA(%)ASE(%) Avg.Lux sDGsDA(%)Avg.LuxControl 91.96 26.79 2788.60 25.45 76.79 920.59Ag 20nm 83.04 25.00 2657.29 24.22 67.86 877.74Ag 25nm 82.14 24.11 2648.60 24.11 69.64 876.13Ag 30nm 82.14 23.21 2605.44 24.22 66.07 864.41Ag 35nm 84.82 23.21 2607.84 24.22 67.86 858.52Ag 40nm 82.14 23.21 2596.24 22.43 66.07 867.72Ag 45nm 80.36 23.21 2584.46 23.44 67.86 856.41Ag 50nm 83.04 23.21 2580.25 23.21 66.96 856.28AgTiO218nm 87.50 25.00 2705.47 24.11 67.86 887.59AgTiO224nm 83.04 25.00 2666.12 23.77 67.86 882.55AgTiO238nm 84.82 26.79 2733.25 25.11 70.54 899.77AgTiO246nm 88.39 25.00 2683.82 23.66 72.32 883.23AgTiO257nm 84.82 25.00 2664.02 23.55 68.75 879.51Occupancy Time: 8am-6pm with DST, sDA: sDA300|50%, ASE: ASE1000|250Table F.3: Daylighting and glare performance metrics at work plane andlighting levels for Ag and Ag | TiO2 thin films coated flat slats.163Appendix F. CBDM Supplement InformationSample Work Plane CeilingsDA(%)ASE(%)Avg.Lux sDGsDA(%)Avg.LuxControl 91.96 26.79 2788.60 25.45 76.79 920.59Ag 20nm 74.11 7.14 2657.29 20.09 58.93 877.74Ag 25nm 75.00 0.00 2648.60 20.42 60.71 876.13Ag 30nm 75.89 0.00 2605.44 21.21 63.39 864.41Ag 35nm 77.68 0.00 2607.84 20.65 63.39 858.52Ag 40nm 76.79 0.00 2596.24 22.54 63.39 867.72Ag 45nm 77.68 0.00 2584.46 20.98 65.18 856.41Ag 50nm 80.36 0.00 2580.25 21.99 65.18 856.28AgTiO218nm 70.54 16.96 2705.47 19.42 58.04 887.59AgTiO224nm 67.86 15.18 2666.12 18.75 56.25 882.55AgTiO238nm 71.43 23.21 2733.25 19.75 58.93 899.77AgTiO246nm 75.89 18.75 2683.82 21.32 61.61 883.23AgTiO257nm 79.46 8.93 2664.02 22.54 64.29 879.51Occupancy Time: 8am-6pm with DST, sDA: sDA300|50%, ASE: ASE1000|250Table F.4: Daylighting and glare performance metrics at work plane andlighting levels for Ag and Ag | TiO2 thin films coated wing-flap slats.164Appendix F. CBDM Supplement Information(a)(b)Figure F.2: Rendered images and the corresponding false-color image ofdaylight distribution for control (bare window),window pane, flat slats, andwing-flap slats coated with Ag (50 nm) in the summer solstice (Jun 21st), fallequinox (Sep 21st), and winter solstice (Dec 21st). The amount of daylightincluding sun and sky conditions in the room is derived from the Summer-land weather data.165Appendix F. CBDM Supplement Information(a)(b)Figure F.3: Rendered images and the corresponding false-color image ofdaylight distribution for control (bare window),window pane, flat slats, andwing-flap slats coated with Ag | TiO2 (23 | 57 nm) in the summer solstice(Jun 21st), fall equinox (Sep 21st), and winter solstice (Dec 21st). Theamount of daylight including sun and sky conditions in the room is derivedfrom the Summerland weather data.166Appendix GVirtual Classical CarShowroomFigure G.1: Plasmonic structural coloration preview of aluminum nanohole-nanodisk arrays developed by Vincent Loi. The bodies of classic car arecoated with nanohole-nanodisk array with a diameter of 80 nm, a periodof 200 nm and varying separation distance. (Link to access the virtualshowroom)167
Thesis/Dissertation
eng
Electrical Engineering
Vancouver : University of British Columbia Library
Attribution-ShareAlike 4.0 International
Graduate
Chau, Kenneth
Multiscale computational visualization and modelling of optical nanomaterials and their application
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