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A silicon photonic circuit for optical trapping and characterization of single nanoparticles Mirsadeghi, Seyed Hamed 2017

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A Silicon Photonic Circuit for Optical Trapping andCharacterization of Single NanoparticlesbySeyed Hamed MirsadeghiB. Physics, Shahid Beheshti University, 2007M.Sc. Physics, The University of British Columbia, 2010A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Physics)The University Of British Columbia(Vancouver)April 2017© Seyed Hamed Mirsadeghi, 2017AbstractIn this thesis, two slightly different silicon-on-insulator (Silicon-on-Insulator (SOI))planar photonic integrated circuits for optically trapping and characterizing singlenanoparticles are designed, fabricated, and fully characterized. These symmetric(input/output) structures are formed by etching two dimensional patterns through a220 nm thick silicon slab atop a micrometer thick layer of silicon dioxide, and areoperated in a fluidic cell at wavelengths of ≈ 1.55 µm. Each consist of two gratingcouplers, two parabolic tapered waveguides, two single mode ridge waveguides,two photonic crystal waveguides and a single photonic crystal slot (PCS) micro-cavity, designed using a Finite Difference Time Domain (FDTD) electromagneticsimulation tool. The circuits are designed to concentrate continuous wave laserlight incident on the input grating coupler to a small volume within the fluidicchannel of the microcavity in order to achieve a high electric field intensity gradi-ent capable of attracting and trapping nanoparticles from the solution via opticalgradient forces.The fabricated PCS cavities exhibit Q factors > 7500 and resonant transmis-sions as high as T = 6%, when operated in hexane and without undercutting thecavities. Due to fabrication imperfections, the cavity Q and peak transmission val-ues were not as high as simulation predicted, nevertheless, these robust, deviceswere successfully used to optically trap single sub-50 nm Au nanospheres andnanorods with < 0.5 mW of laser power. Furthermore, it was found that whilethe particles were trapped, the transmitted laser intensity varied randomly in time,providing a simple means of characterizing the Brownian motion of the particle inthe trap. The intensity variation is caused by the backaction of the dielectric objecton the cavity resonance, the magnitude of which depends on the real part of theiitrapped particle’s polarizability tensor, and its position in the cavity. By exploitingthis cavity-nanoparticle interaction, we developed a self-consistent analysis of thetransmission signal of circuits that enabled us to determine the size and anisotropyof the trapped nanoparticles without any direct imaging, with nanometer sensitiv-ity.iiiPrefaceThe initial design of the research program was primarily set by my research super-visor, Jeff F. Young. My role was primarily implementation and development ofthe experimental setups, measurements, modelling, and analysis used to implementthe research program. Three publications arising entirely from the work within thisthesis are as follows:• S. Hamed Mirsadeghi, Ellen Schelew, and Jeff F. Young. Photonic crystalslot-microcavity circuit implemented in silicon-on-insulator: High q opera-tion in solvent without undercutting. Applied Physics Letters, 102(13):131115,2013 [1]• S. H. Mirsadeghi, E. Schelew, and J. F. Young. Compact and efficient siliconnanowire to slot waveguide coupler. In 2013 13th International Conferenceon Numerical Simulation of Optoelectronic Devices (NUSOD), pages 3132,19-22 Aug. 2013 [2].• S. Hamed Mirsadeghi and Jeff F. Young. Ultrasensitive diagnostic analy-sis of Au nanoparticles optically trapped in silicon photonic circuits at sub-milliwatt powers. Nano Lett., 14(9):50045009, September 2014 [3]The simulation and modelling results in [1, 2] are presented in Chapter 2. Andthe measurements and characterization in [1] is incorporated in Chapter 3. My rolein these two publications was FDTD modelling, designing devices, creating theirlayout for fabrication, chip preparation, experimental measurement, analysis of theresults, and majority of manuscript preparation and review of them. The originaltransmission set-up was build by Ellen N. Schelew and further development of theivdata acquisition and device holding system were done by me. Ellen N. Schelewwas also the main writer of the manuscript in [2]. The chip fabrication was donein collaboration with Dr. Lukas Chrostowski and University of Washington Micro-fabrication Facility, a member of the NSF National Nanotechnology InfrastructureNetwork [4]. Much of the text of these two publications are directly included intothis thesis.The simulation, measurement and modelling results in [3] are all presented inChapter 4. My role in this publication was FDTD modelling, designing devices,creating their layout for fabrication, chip and Au solution preparation, experimen-tal measurement, and analysis of the results. I also worked with Jeff F. Young indeveloping the backaction model for optical trapping in photonic crystal slot cavi-ties, manuscript preparation, and review of it. Much of the text in this publicationis also directly included into this thesis.The simulation, measurement and modelling that are presented in Chapter 5have not been published yet. My role in this chapter was FDTD modelling, design-ing devices, creating their layout for fabrication, majority of chip and Au solutionpreparation, experimental measurement, and analysis of the results. I also workedwith Jeff F. Young in developing the more general version of backaction model foranisotropic particle trapping in photonic crystal slot cavities. Jonathan Massey-Allard also contributed in chip and Au solution preparation, Au nanorod opticaltrapping experiments, SEM/AFM imaging of the chips after trapping experiments,and preparing the manuscript for publishing the results of this chapter.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xxxiiiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxv1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Silicon Photonic Integrated Circuits . . . . . . . . . . . . . . . . 51.3 Photonic Crystal Nanostructures . . . . . . . . . . . . . . . . . . 61.4 Optical Tweezers . . . . . . . . . . . . . . . . . . . . . . . . . . 131.4.1 Optical Force . . . . . . . . . . . . . . . . . . . . . . . . 141.4.2 NanoTweezers . . . . . . . . . . . . . . . . . . . . . . . 201.5 Sensing and Backaction Effect . . . . . . . . . . . . . . . . . . . 262 Device Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.2 SC1 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32vi2.2.1 Grating Couplers and Slab Waveguides (device SC1) . . . 342.2.2 Photonic Crystal Slot Cavity (SC1 device) . . . . . . . . . 362.2.3 SC1 Device Performance Discussion . . . . . . . . . . . 382.3 SC2 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422.3.1 PC Slot Cavity Q Factor Enhancement (SC2 devices) . . . 432.3.2 Photonic Crystal Slot (PCS) Waveguide Optimization (SC2device) . . . . . . . . . . . . . . . . . . . . . . . . . . . 442.3.3 1D Nanowire to Slot Waveguide Adapter (SC2 device) . . 462.3.4 SC2 Device Performance Discussion . . . . . . . . . . . 532.3.5 1D Grating Coupler (SC2 device) . . . . . . . . . . . . . 542.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543 Device Characterization And Sensing Application . . . . . . . . . . 573.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.2 Chip Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.2.1 Chip EB312 Layout (SC1 design) . . . . . . . . . . . . . 583.2.2 Chip EB485 Layout (SC2 design) . . . . . . . . . . . . . 603.2.3 Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . 633.3 Measurement Setup . . . . . . . . . . . . . . . . . . . . . . . . . 643.3.1 Liquid Cell . . . . . . . . . . . . . . . . . . . . . . . . . 643.3.2 Transmission Setup . . . . . . . . . . . . . . . . . . . . . 663.4 Experimental Characterization . . . . . . . . . . . . . . . . . . . 683.4.1 Chip EB312 Measurements . . . . . . . . . . . . . . . . 683.4.2 Chip EB485 Characterization . . . . . . . . . . . . . . . 733.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 764 Optical Trapping And Sensing Using Photonic Crystal Slot Cavities 794.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.2 Refractive Index Sensing . . . . . . . . . . . . . . . . . . . . . . 804.3 Optical Trapping Of Au Nanospheres . . . . . . . . . . . . . . . 814.3.1 Experiment Setup . . . . . . . . . . . . . . . . . . . . . . 814.3.2 Trapping Experiment . . . . . . . . . . . . . . . . . . . . 824.3.3 Time-series Analysis . . . . . . . . . . . . . . . . . . . . 84vii4.3.4 Cavity Mode 2 and Size Sensing In Heterogeneous Solution 934.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 945 Optical Trapping of Nanorods . . . . . . . . . . . . . . . . . . . . . 1005.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1005.2 Self Consistent Model Including Anisotropic Particles . . . . . . . 1015.3 Explaining the Need to Average Histograms for Imperfect Nanospheres1055.4 Trapping Gold Nanorods . . . . . . . . . . . . . . . . . . . . . . 1085.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1116 Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . . . . 1126.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1126.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117viiiList of TablesTable 2.1 Summary of the transmission efficiency of different parts ofSC1 and SC2 designs for the Mode1 of the PCS cavity. Thesecond column shows the peak transmission efficiency of grat-ing couplers. The third column is showing the FWHM of thegrating couplers. The fourth column summarizes the transmis-sion of the reference devices in Fig. 2.6 and Fig. 2.14. Thefifth column is the coupling efficiency from the end of the inputPC(S) waveguides into the PCS cavities. . . . . . . . . . . . . 56Table 3.1 The feature sizes for SC1 devices that are used in chip EB312layout. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58Table 3.2 The feature sizes for SC2 devices that are used in chip EB485layout. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62Table 3.3 Summary of the results from simulations and transmission mea-surements on 5 different devices. All of these devices are onchip EB312. The transmission values are from input channelwaveguide to output channel waveguide. rc is the nominal ra-dius of the coupling hole at the end of W1 photonic crystalwaveguides that controls the coupling of the waveguides to thecavities. s is the nominal width of the slot waveguide. . . . . . 73Table 4.1 Summary of trapping performance of various tweezers. . . . . 99ixList of FiguresFigure 1.1 Layout of a full device designed and fabricated in this workfor optical trapping and sensing experiments. It includes thediffraction grating couplers, cavity and waveguides all pat-terned in a 220 nm silicon slab sitting on top of SiO2 substrate(in red). The gratings, which consist of a 2D lattice of holesetched in silicon, are separated by 680 microns. The input/out-put light is injected/collected at a 17◦ angle to the normal tograting plane. The vertical scale bar is different than the in-plane scale bar for better visibility. . . . . . . . . . . . . . . 2Figure 1.2 (a) Typical silicon-on-insulator (SOI) dimensions used for fab-ricating photonic integrated circuits. (b) Example fabricationprocess for creating pattern on silicon slab. Additional func-tionality may be achieved by lithographic integration of metalcontacts, ion doping, and deposition of other materials [5]. . . 4Figure 1.3 (a) Schematic of a generic SOI photonic integrated circuit con-sisting of different active and passive photonic elements suchas grating couplers, waveguides, splitters, filters, switches, etc.The minimum size of splitters, is limited by how tightly chan-nel waveguides may be bent before break down of TIR, whichis dictated by relative indices of refraction of the waveguideand surrounding cladding. . . . . . . . . . . . . . . . . . . . 7xFigure 1.4 Example structures taken from the literature (not work done aspart of this thesis); (a) Scanning Electron Microscope (Scan-ning Electron Microscope (SEM)) image of one-dimensional(1D) PC made of successive layers of AlInN (darker) and GaN(brighter) (reprinted from [6]). (b) SEM image of a two-dimensional(2D) PC made of macroporous silicon lattice (reprinted from [7]).(c) SEM micrographs of a three-dimensional (3D) photoniccrystal. Left image is the top view of a completed four-layerstructure and the right image is the cross-sectional view of thesame 3D photonic crystal. The rods are made of polycrys-talline silicon (reprinted from [8]). . . . . . . . . . . . . . . 8Figure 1.5 [(a)-(b)] Schematic of a 2D planar hexagonal lattice PC struc-ture in a SOI photonic circuit with two types of propagat-ing modes: TE (with only in-plane electric field polarization)and Transverse Magnetic (TM) (with only in-plane magneticfield polarization). (c) Example photonic band structure for the2D planar PC above the substrate in (a) (reprinted from [5]).The gray light-cones show the area above substrate light-line,where the TIR fails and leads to coupling of the PC modes tocontinuum modes and therefore to intrinsic out-of-plane diffrac-tion losses in the PC region. . . . . . . . . . . . . . . . . . . 10Figure 1.6 (a) Schematic of a line defect (also known as W1) PC waveg-uide which is created by removing a row of holes in a hexago-nal lattice of holes. (b) Example band structure of a W1 waveg-uide showing two guided TE modes (the red has even symme-try and the blue has odd symmetry) in the projected bulk PCbandgap (yellow region). . . . . . . . . . . . . . . . . . . . . 11Figure 1.7 (a) Schematic of a PC L3 cavity, consisting of a defect (threemissing holes) in a hexagonal lattice of holes in a silicon slab.(b) A sketch of the local photonic density of states at the cavitycenter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12xiFigure 1.8 (a) Schematic focused beam of laser propagating downwardthat produces optical forces on a particle that has larger re-fractive index than its surrounding. Two rays of light (R1 andR2) are showing the light refraction in the particle. Since R2is coming from the focal center of the beam, its intensity isstronger, and therefore it transfers larger momentum to the par-ticle compared to R1. Therefore, the conservation of momen-tum dictates the particle experiences a force toward the beamfocal center. This force, which is a result of laser intensity vari-ation and in the direction of light intensity gradient, is calledthe gradient force. Also, both rays exert “scattering force” inthe direction of light propagation because of momentum trans-fer from refracted or absorbed light. This force tries to pushthe particle out of the laser trap. (b) An experimental exampleof optical manipulation of multiple micron-size colloidal silicaspheres using laser tweezers (reprinted from [9]). . . . . . . . 15xiiFigure 1.9 (a) Schematic of a plasmonic nanotweezers experimental set-up, in which a pattern of micrometre-sized gold structure isilluminated under the Kretschmann configuration through aglass prism. The red arrows give the direction of the inci-dent and reflected light (reprinted from [10]). (b)-(c) SEM andatomic force microscope images of fabricated gold nanopil-lars. Scale bar is 1 µm (reprinted from [11]). (d) FDTD calcu-lation of the electric field intensity distribution resulting fromincidence plane wave illumination of a nanopillar at λ = 974nm. Intensity enhancement, that is, intensity normalized toincident intensity |E|2/|EINC|2, is plotted. Peak intensity en-hancement is 490 times, although upper limit of colour scaleis chosen to be 20 times for visualization. The scale bar is 200nm (reprinted from [11]). (e) Electric field amplitude distribu-tion of a nanoantenna with 80 nm arm and 25 nm gap. Theinset shows the SEM image of a fabricated nanoantenna with10 nm gap. The scale bar is 100 nm (reprinted from [12]). (f)Double-hole nanotweezers with a 15 nm tip separation usedfor trapping 12 nm silica spheres (reprinted from [13]). . . . . 21xiiiFigure 1.10 (a) Schematic of a microtoroid coupled to an optical fiber (notto scale) (reprinted from [14]). In this system, a frequency-tuned laser beam is evanescently coupled to a 90 µm diametermicrotoroid by an optical fiber (red). The microtoroids haveloaded Qs (i.e. Q of a cavity when connected to waveguidesin a circuit) of 1× 105–5× 106 in water at 633 nm and cantrap 5 nm silica nanoparticles. (b) SEM images of a 5 µmradius microring nanotweezers with Q factor of 860 (reprintfrom [15]). Polystyrene particles with diameters of 500 nmcan be stably trapped and propelled along the microring res-onator with speeds of 110 µm/s at 9 mW in the bus waveguide.(c)-(d) The top-view schematic of a microdisk resonator withtwo bus waveguides along with the normalized electric fieldamplitude distribution of its modes. The corresponding zoom-in-view images near the coupling gap are shown in the insets(reprinted from [16]). A 30 µm diameter, 700 nm thick SiNmicrodisk resonator has been demonstrated [17] to trap 1 µmpolystyrene particles with∼ 7 mW of input power with qualityfactors from 3000-6000. . . . . . . . . . . . . . . . . . . . . 23Figure 1.11 (a) Schematic of a 1D PC resonator for enhanced optical trap-ping. (b) Simulated electric field intensity profile of the cavitymode showing the strong field confinement and amplificationwithin the one-dimensional resonator cavity. The black arrowsindicate the direction and magnitude of the local optical forces(reprinted from [18]). (c) SEM image of a silicon nitride PCcavity along with FDTD simulation showing the electric fieldintensity distribution near the resonator cavity (arbitrary unit).Strong field enhancement can be seen within the small hole atthe center of the cavity. Scale bars are 1 µm (reprinted from [19]). 25xivFigure 1.12 (a) Schematic of a 2D PC hollow resonator along with its simu-lated electric field intensity profile of the cavity mode showingthe strong field confinement and amplification within hollowregion. (b) SEM image of device showing the hollow cavityand the PC waveguide. (c) The side view of the hollow cavityand the profile of the field intensity showing the good overlapbetween the field and the trapped particle. The experimen-tal Q factor is 2000 and the mode volume is 0.2 time cubicwavelength. For stable trapping of 500 nm dielectric particles,120 µW of power is launched into the PC waveguide (reprintedfrom [20]). . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Figure 2.1 Layout of a full device SC1 including the grating couplers,cavity and waveguides sitting on SiO2 substrate (in red). Thegratings are separated by 680 microns. The input/output lightis injected/collected at 17◦ angle to the normal to grating plane. 31Figure 2.2 Transverse electric field profile of the quasi-TE mode in a SOI-based slot waveguide. The origin of the coordinate system islocated at the center of the waveguide, with a horizontal x-axisand a vertical y-axis. nH is the refractive index of silicon andnC is the refractive index of SiO2. (a) Contour of the electricfield amplitude and the electric field lines. (b) 3D surface plotof the electric field amplitude (reprinted from [21]). . . . . . . 33xvFigure 2.3 [(a)-(b)] FDTD simulation layout of the SOI grating couplerthat diverts the excitation laser into a parabolic tapered waveg-uide connected to a single mode channel waveguide. Its po-larization and injection directions are shown with pink arrows.All feature sizes are described in 2.2.1. The picture scale alongx and y axes are the same but different than the z axis scale. (c)The transmission of this structure is calculated using two mon-itors (yellow lines in (a)). The blue curve is the transmissionfrom the source up to the beginning of the tapered waveguide(monitor M1) and the black is the efficiency of the whole struc-ture (i.e. from the source up to the channel waveguide (monitorM2). The red curve, which is the division of the black curveto the blue curve, is showing the transmission efficiency of thetapered waveguide (the structure between the two monitors). . 35Figure 2.4 (a) Layout of a SC1 slot-cavity with input/output channel waveg-uides. The channel waveguides have a width of 450 nm. Amode source is used to send light into the input channel waveg-uide and a monitor (M1 in yellow color) is located at the outputchannel waveguide to calculate the transmission of the devicefrom input to output channel waveguides (spectrum shown inFig. 2.5c). (b) Enlarged image of the cavity region at the centerof the structure. The 30 different color holes near to the slotare shifted away from it to create two defect modes. Similarcolor holes are shifted the same amount. The hole shifts ares1 = 12 nm, s2 = 8 nm and s3 = 4 nm, going from inner ringof holes outward. The two smaller coupling holes at the end ofPC waveguides in black color have radius rc = 110 nm. Theradius for the rest holes of the PC is r = 160 nm and the latticeperiod is a = 490 nm. The width of the slot is 90 nm. . . . . . 37xviFigure 2.5 The normalized electric field intensity profile of Mode 1 (a)and Mode 2 (b) of the SC1 slot-cavity overlapped with the cav-ity structure. (c) The transmission efficiency of the structure inFig. 2.4 showing two high quality modes of this cavity. The Qfor Mode 1 (λ1 = 1567.4 nm) is 7400 and Mode 2 (λ2 = 1586.6nm) is 8100. (d) The TE transmission band of W1 PC waveg-uides overlapped with SiO2 light line (black sloped line) andtwo resonances of the SC1 cavity (Mode 1 in red and Mode2 in blue color). (e) The two TE transmission bands of thePCS waveguide. The red curve has the same characteristics asMode 1 of the cavity and blue curve corresponds to Mode 2.Again, the dashed lines are the SC1 cavity resonance modes. . 39Figure 2.6 (a) Layout of the FDTD simulation for calculating the powerloss in the W1 PC waveguides of the structure in Fig. 2.4. Thelength of the W1 PC waveguide in this simulation is 29 pitches,equivalent to the total length of W1 PC waveguides in Fig. 2.4.All feature sizes are similar to the structure in Fig. 2.4. (b) Thetransmission spectrum (blue), reflection spectrum (red) and thesum of them (black) for the structure in (a) calculated frominput to output channel waveguide. The dashed line shows thewavelength of Mode1 of the cavity. The transmission value forthe structure in (a) at Mode1 resonance is ∼ 67%. . . . . . . . 40Figure 2.7 (a) Layout of the FDTD simulation for calculating the powerloss in different parts of the structure in Fig. 2.4. All featuresizes are similar to the structure in Fig. 2.4 and the color ofthe holes are modified for better distinction from the yellowpower monitors. (b) The enlarged image around one of thetwo coupling holes of this structure (in black color) shows thepower monitor (small yellow box around the coupling hole)that measures the vertical losses occurring at this coupling hole. 41xviiFigure 2.8 The optical trapping potential (absolute value) of the SC1 cav-ity (see Fig. 2.4), calculated for Mode 1 (a) and Mode 2 (b) ona 50 nm diameter Au nanosphere. The injected power in theinput channel waveguide (the top waveguide in Fig. 2.4a) is 1mW. The unit of the colorbar is in kBT . . . . . . . . . . . . . 42Figure 2.9 Layout of the full SC2 device including the grating couplers,cavity and waveguides. The channel waveguides are curvedwith radius of 5 µm. . . . . . . . . . . . . . . . . . . . . . . 43Figure 2.10 [(a)-(b)] The FDTD simulation layout showing the size of thesimulation region (orange rectangle) and the location of y-polarizedelectric dipole source (double-side blue arrow). The yellowcrosses are the point time monitors to record the decay of thecavity electric field in time domain. The radius of the holesis r = 150 nm, the slot width is s = 100 nm and the cav-ity hole shifts are s1 = 6 nm (black color holes), s2 = 4 nm(pink color holes) and s3 = 2 nm (blue color holes). The FastFourier Transform (FFT) of the electric field of mode 1 mea-sured by time monitors for SC2 (c) versus SC1 (d) cavity de-sign. The cavity is unloaded and is sitting on Buried Ox-ide (BOX) layer (3 µm thick SiO2 on top of a millimeter thicksilicon) and hexane is the upper cladding. The Q-factor ofMode 1 for SC2 cavity design (c) is 18500 while for SC1 cav-ity design (d) is 9600. The mode volume of Mode 1 in SC2structure is VMode1 = 0.14( λ1nhex )3, while in SC1 structure wasVMode1 = 0.1( λ1nhex )3. . . . . . . . . . . . . . . . . . . . . . . . 45xviiiFigure 2.11 (a) Transmission band structure of the W1 PC waveguide cal-culated using 3D FDTD simulations (PC hole radius of 160nm). The solid black line is the light-line for SiO2 under-cladding and the dashed line is the resonance of mode1 of theinitial design (i.e. Fig. 2.10d). (b) Transmission band struc-ture of a PCS waveguide with hole radius of 150 nm and slotwidth of 100 nm. The first row of holes adjacent to the slot areshifted by 15 nm (red), 25 nm (pink), and 40 nm (blue) fromtheir lattice point to lower the waveguide band frequency sothat it intersects with the cavity mode to guide light in/out ofit. Again, the solid black line is the light-line for SiO2 under-cladding. But the dashed line is the resonance of mode1 of theimproved cavity (i.e. Fig. 2.10c). . . . . . . . . . . . . . . . . 46Figure 2.12 (a) The proposed nanowire to slot waveguide structure is out-lined in white along the outer extremities and in black along theslot. The intensity profile at λ = 1550 nm is plotted along thez= 0 plane for a coupler with L= 400 nm, and a= 100 nm andcoupling efficiency 92%. For positive (negative) a, the slot endis outside (inside) of the tapered region. Mode intensity profileis plotted for (b) the fundamental silicon nanowire mode, and(c) the lowest order slot waveguide mode at λ = 1550 nm. . . 47Figure 2.13 The transmission is plotted as a function of (a) the couplerlength L (with a = 100 nm), and (b) the position of the slotend a (with L = 400 nm), for λ = 1550 nm. . . . . . . . . . 48xixFigure 2.14 [(a)-(b)] The simulation layout of the optimized PCS waveg-uide in SC2 structure that offers higher transmission efficiency(no cavity exists in this simulation). The colored holes (otherthan yellow and white holes) have been modified to reduceinsertion loss. The radius of the holes (r) and their distancefrom slot center (y) are optimized using FDTD simulations.For black holes r = 120 nm, y = 570 nm, blue holes r = 120nm, y = 450 nm, pink holes r = 128 nm, y = 526 nm, greenholes r = 190 nm, y = 950 nm, and red holes r = 180 nm,y = 890 nm. The rest of the nearest holes to the slot are shiftedaway from the slot by 40 nm with respect to their lattice pointto make the PCS waveguide. All holes on the edge of the sil-icon slab will show up as half circles after fabrication (seeFig. 3.4d-e). The refractive index of these holes is the sameas the background refractive index (nhex), therefore having fullholes on the silicon edge instead of half-holes does not changethe simulation results. . . . . . . . . . . . . . . . . . . . . . 49Figure 2.15 (a) Simulated transmission (blue), reflection (red) spectra, andthe sum of them (black) calculated at the input and outputchannel waveguides of the structure in Fig. 2.14. (b) Simu-lated transmission (blue), reflection (red) spectra, and the sumof them (black) for the same structure without modification ofthe radii and location of the 10 holes at the entrance and theexit of PCS waveguide. (c) Simulated transmission (blue), re-flection (red) spectra, and the sum of them (black) for the samestructure as (b) without the Y-branch. The black dashed-line inthese three figures is the resonance of Mode 1 of the modifiedcavity (Fig. 2.10c). The transmission of the improved structurein (a) at the cavity resonance is increased from 19% to 59% byusing the Y-branch adapter and modifying the holes. . . . . . 51xxFigure 2.16 [(a)-(b)] Simulation layout for optimized SC2 PCS cavity. Theholes in the PCS waveguide region have the same size and lo-cation as Fig. 2.14. There are 10 un-shifted holes in betweenthe PCS waveguides and the cavity region (blue color holes atthe center). The cavity hole shifts are s1 = 6 nm, s2 = 4 nm,s3 = 2 nm. The hole radius for the regular PC holes is 150 nm.Slot width is 100 nm and the Y-branch adapting part betweenthe single mode and PCS waveguide is explained in Fig. 2.12except for the change of slot width to 90 nm. (c) The trans-mission efficiency of the full SC2 structure calculated usingpower monitor at the output channel waveguide. The Q of thisloaded cavity is 8400 and its maximum transmission (althoughnot completely resolved) is 17.5%. . . . . . . . . . . . . . . . 52Figure 2.17 (a) The trapping potential calculated for Mode 1 of SC2 cav-ity in Fig. 2.16 on a 50 nm diameter Au nanosphere. (b) Theoptical trapping potential of mode 1 of SC1 cavity design de-scribed in Fig. 2.4 on a 50 nm diameter Au nanosphere. Theinjected power in the input channel waveguide for both figuresis 1 mW and the unit of the colorbar is in kBT . . . . . . . . . 53Figure 2.18 (a) 2D FDTD simulation layout for optimization of 1D double-tooth grating coupler. Instead of having partly etched trenches,a double-tooth geometry is chosen for easier fabrication. Theoptimization parameters are the teeth spacing (t), the period(a) and trench width (w). All three parameters are optimizedat the same time within reasonable amount of simulation time.(b)The optimized values are t = 192 nm, a = 800 nm, w = 114nm as shown in the figure. . . . . . . . . . . . . . . . . . . . 54xxiFigure 2.19 (a) Final optimized double-tooth grating design (for SC2 de-vices) connected to a tapered waveguide. The grating area is20 µm × 20 µm. (b) The transmission efficiency of optimizeddouble-tooth design from a Gaussian focused source to the be-ginning of the tapered waveguide (blue). The peak transmis-sion value is 52% and Full Width at Half Maximum (FWHM)is 75 nm. The excitation angle with normal to silicon sur-face is 18◦. The transmission from tapered waveguide to thechannel waveguide is shown in the black curve. Dividing thetwo curves gives the transmission efficiency of the waveguidesthat is improved compared to the red curve in Fig. 2.3c thanksto better wavefront shape matching between the double-toothgrating and the waveguides. . . . . . . . . . . . . . . . . . . 55Figure 3.1 (a) Layout of the Chip EB312 based on SC1 designed de-scribed in Chapter 2. There are 12 groups of 3× 3 deviceson this chip. The row and column label of each group is lo-cated on the left side of the group. (b) Group EB312R2C2consists of devices that are full SC1 structures. (c) GroupEB312R4C1 consists of devices with no photonic crystal inbetween the channel waveguides. (d) Group EB312R4C2 con-sists of devices that have only grating couplers, tapered, chan-nel and photonic crystal waveguides without any PCS cavityin between them. . . . . . . . . . . . . . . . . . . . . . . . . 59xxiiFigure 3.2 (a) Layout of the Chip EB485. There are 6 groups of 19 de-vices on this chip. In each group there are 12 SC2 devicesalong with 7 reference devices that do not have cavity in themto let us test the efficiency of other elements of SC2 photoniccircuit. (b) Zoomed out layout of group EB485R2C2. The 4squares on the right side of the devices are showing the labelof the group. (c) The layout of the first 3 devices of groupEB485R2C2, which show two reference devices for measur-ing the transmission of the grating couplers and waveguidesand one full SC2 device that include PCS cavity. . . . . . . . 61Figure 3.3 SEM image of a fabricated (a) grating and [(b)-(c)] cavity onchip EB312. Blackened areas are due to electron-beam-inducedcarbon deposition on the chip during SEM imaging. . . . . . 65Figure 3.4 (a) SEM image of the fabricated chip EB485 [4]. (b) Pic-ture of a full SC2 device, (c) a device without a cavity inbetween PCS waveguides, [(d)-(e)] adapting parts and (f) adouble-tooth grating coupler. . . . . . . . . . . . . . . . . . 66Figure 3.5 The structure of the liquid cell (Harrick Scientific Products 1)used for immersing the chips in a liquid medium (reprintedfrom manufacturer’s website), composed of a pair of quartzglass window separated by two half-ring Teflon spacers be-tween which the photonic SOI chip is placed during measure-ments. Once assembled the volume between the windows isfilled with solution. . . . . . . . . . . . . . . . . . . . . . . . 67xxiiiFigure 3.6 The top-view of the experimental setup used for transmissionmeasurements and optical trapping experiments. The rotationstages allow the angle between the incident light and the sur-face of the chip to be varied, which is necessary for optimalcoupling to grating couplers at different wavelengths. The ex-citation optics include a polarizer and two plano-convex lensesheld in a lens tube. One of the lens collimates the laser beamcoming out of a single mode optical fiber (blue line in the fig-ure) and the second lens focuses it on the chip. This one-to-onefocusing system results in focusing the laser light to the samesize as the beam at the output of the single mode optical fiber(∼ 10 µm).The detailed description of this experimental setupis explained in Ref. [22]. . . . . . . . . . . . . . . . . . . . . 69Figure 3.7 (a) Simulation (black) versus experimental transmission effi-ciency of device EB312R4C1(2,1) (green), EB312R4C1(2,2)(blue), EB312R4C1(2,3) (red). These transmission are frominput grating coupler to output grating coupler through thechannel waveguide. The incident angle of the laser with thegrating surface normal is 18◦ for both simulation and experi-ment. (b) Black curve is the same curve as in (a) and the bluecurve is the simulated transmission spectra when the radius ofthe grating holes is reduced by 15 nm to 135 nm. . . . . . . . 70xxivFigure 3.8 (a) The experimental transmission spectra of two nominallyidentical devices that have photonic crystal W1 waveguide with-out any cavity in between them. The blue curve is for the de-vice EB312R4C2(2,2) while the red is for EB312R4C3(2,2).These transmission values are for the full devices (i.e. grat-ing couplers and photonic crystal waveguides). (b) Simula-tion (black) versus experimental transmission spectra (blue andred) from input channel waveguide through the photonic crys-tal W1 waveguide to the output channel waveguide. These ex-perimental curves are the result of dividing transmissions in (a)by the transmission of device EB312R4C1(2,1) (green curve inFig. 3.7). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Figure 3.9 Resonant transmission spectra from input to output ridge waveg-uides through slot-cavity for device EB312R22(2,2) in Table 3.3.The simulation curve is in blue and the experimental curve isin black. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Figure 3.10 Simulation (blue) versus experimental (black) transmission frominput grating coupler to output grating coupler through chan-nel waveguide, for device EB485R2C2n1. The incident angleis 18°. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74Figure 3.11 (a) Experimental transmission efficiencies for devices EBEB485R1C1n1(black) and EB485R1C1n5 (blue) measured at 19° incident an-gle. EB485R1C1n1 is a device with no photonic crystal re-gion, which allowed the efficiency of the grating couplers tobe measured and EB485R1C1n5 includes the PCS waveguidein addition. By dividing the blue curve by the black one (FabryPerot oscillations of the black spectrum are filtered out duringdivision), it is possible for us to find the transmission of thisPCS waveguide. The result is the black curve in (b). (b) Sim-ulation (blue) versus experimental (black) transmission frominput channel waveguide through PCS waveguide to outputchannel waveguide. The photonic crystal hole radius is 150nm and the slot width is 90 nm. . . . . . . . . . . . . . . . . 75xxvFigure 3.12 (a) Resonant transmission spectra from input to output ridgewaveguides through the slot-cavity for device EB485R1C1n6.The simulation curve is blue and the experimental data areplotted in black. The photonic crystal holes are 150 nm withslot width of 90 nm. The Q value of the fabricated device is4400 as compared to 7400 from simulation. The peak resonanttransmission efficiency for the fabricated device is 6% as ap-posed to the simulated value of 17%. (b) Experimental trans-mission spectra of three SC2 devices: EB485R1C1n3 (black),EB485R2C1n7 (blue), and EB485R1C1n7 (red). . . . . . . . 77Figure 4.1 Normalized resonant transmission spectra, fitted with a Fanoline-shape, for (a) device EB312R22(1,1) and (b) EB312R22(1,2)in hexane (blue) and acetone (red). In figure (a) Qhexane =5450, Qacetone = 5700 and for figure (b) Qhexane = 3980, Qacetone =4100. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81Figure 4.2 The full SSC1 photonic circuit [1] used for trapping is illus-trated schematically at the bottom (lateral dimensions to scale).It includes an input and an output grating coupler at each endthat symmetrically connects to the photonic crystal microcav-ity region at the center, through single mode channel waveg-uides, as shown in the scanning electron microscope (SEM)image at the top, right. The calculated electric field intensityprofile of the cavity mode excited in these experiments is alsoshown at the top, left. . . . . . . . . . . . . . . . . . . . . . . 83xxviFigure 4.3 (a) Normalized transmission time series from a device with aninitial empty-cavity Q factor of ∼ 4500 when the laser is tunedclose to the peak transmission in the empty-cavity state (blackvertical dashed line in (b)), and the guided power in the inputchannel waveguide is ∼ 0.75 mW. The shaded regions indicatewhen the laser is turned off to release the transiently trappedparticles. (b) The transmission spectrum before any trappingevents (blue) and after permanently attaching an Au particle(green), both obtained at a power of ∼ 0.75 mW. The blackcircles and horizontal dashed lines show the nominal transmis-sion values at the trapping laser wavelength corresponding tothe empty cavity and the cavity with a permanently attachedAu particle, as also indicated by the dashed lines in (a). . . . . 84Figure 4.4 (a) The transmission of the cavity when the laser is tuned to ∼97% of the empty-cavity peak transmission on the red side. (b)The transmission of the same device under the same conditionsbut with the laser tuned to ∼ 82% of the empty-cavity peaktransmission (on the red side). . . . . . . . . . . . . . . . . . 85Figure 4.5 (a) A transmission time series obtained at an input power inthe waveguide of 0.3 mW at a red detuning set at 73% of theempty-cavity peak transmission. (b) Experimental (red) his-togram of the time series data in the range indicated by the lefthorizontal bar in (a), and the simulated histogram (blue), usinga mean particle diameter of 24.8 nm. (c) Experimental (red)histogram of the time series data in the range indicated by theright horizontal bar in (a), and the simulated histogram (blue),using a mean particle diameter of 30.0 nm. The y-axes of bothhistograms are re-normalized and therefore their units are ar-bitrary. The total count number for (b) is 2.5×106 and for (c)is 3.75×106. . . . . . . . . . . . . . . . . . . . . . . . . . . 86xxviiFigure 4.6 (a) A graph of the cavity resonance wavelength shift versus Auparticle diameter at the center of the cavity (~rp = (0,0,0)). (b)A graph of the resonance shift versus the position of a 40 nmdiameter Au particle along the z axis at (x = y = 0). For bothfigures, the solid black line shows the full-FDTD simulationresults and the dashed color lines are the approximated reso-nance shifts from Equation 4.1 scaled by three different fac-tors; blue, red and magenta correspond to scaling Equation 4.1by 2, 2/1.5 and 1, respectively. . . . . . . . . . . . . . . . . . 88Figure 4.7 This diagrammatic representation illustrates the workflow ofmodelling a TTE histogram for a given particle size and laserdetuning. The initial electric field intensity is calculated us-ing FDTD simulator and the rest of the modelling steps areperformed using MATLAB programming. The yellow boxesshow the output of each simulation step. . . . . . . . . . . . . 89xxviiiFigure 4.8 (a) The electric field intensity profile in the x-y plane (i.e. theplane that cuts through the middle of the silicon slab), fromFDTD simulations with 0.3 mW of resonant modal power inthe input ridge waveguide. The unit of the intensity is (Vm)2.(b) The profile of the ∆(~rp) function, which is the detuning(units of nm) of the laser wavelength from the cavity reso-nance wavelength with a particle of diameter 30 nm locatedat~rp, calculated using ∆(~rp) = ∆0−δλ (~rp). (c) The transmis-sion function T (~rp;∆0) plotted versus ∆ . The laser wavelengthis detuned to 73% of the peak transmission wavelength of theempty-cavity, on the red side. (d) The transmission functionT (~rp;∆0) profile in x-y plane. Note that at the center of thecavity T = 0.2, showing when the particle of diameter 30 nmis located at the center of the cavity, the transmission of thedevice is expected to drop to 0.2 of its maximum because ofthe shift in the cavity resonance (backaction effect). (e) Thetrapping potential energy including the backaction in units ofkBT (Boltzmann factor) calculated using Equation 4.3. (f) Theprobability distribution calculated using Equation 4.4. Thisprobability distribution is used in calculating the histogramshown in Fig. 4.5c. . . . . . . . . . . . . . . . . . . . . . . . 91Figure 4.9 (a) Normalized transmission time series obtained at an inputpower in the waveguide of 0.3 mW at a red detuning set at31% of the empty-cavity peak transmission. (b) Experimen-tal (red) histogram of the time series data in the range indi-cated by the horizontal bar in (a), and the simulated histogram(blue), obtained using a fixed particle diameter of 33.8 nm.(c) The same experimental histogram as in (b) (red) is plottedwith a histogram (blue) obtained by averaging over a normal(Gaussian) distribution of particle diameters centered at 32.6nm with standard deviation of 3%. The total count number forthe experimental histogram is 5×106. . . . . . . . . . . . . 92xxixFigure 4.10 The graph of log10(χ2) as a function of particle diameter andGaussian averaging standard deviation. The best fit histogramis determined by finding the minimum of the χ2. . . . . . . . 94Figure 4.11 [(a)-(e)] An experimental histogram (red) versus simulated his-tograms (black) of particles with various average diameter (D)and a fixed standard deviation of 1.1% for Gaussian averag-ing. All histograms are obtained for an input power in thewaveguide of 0.3 mW and a red detuning set at 31% of theempty-cavity peak transmission. The total count number forthe experimental histogram is 15×106. . . . . . . . . . . . . 95Figure 4.12 [(a)-(e)] Experimental histogram (red) versus simulated his-tograms (black) of Au nanospheres with a fixed average diam-eter (D) of 35.36 nm and various standard deviation for Gaus-sian averaging. All histograms are obtained for an input powerin the waveguide of 0.3 mW and a red detuning set at 31% ofthe empty-cavity peak transmission. . . . . . . . . . . . . . . 96Figure 4.13 (a) The electric field intensity profile (in arbitrary units) ofthe second cavity mode in the x-y plane, calculated from aFDTD simulation. (b) The experimentally measured, normal-ized, empty-cavity transmission at the second cavity mode res-onance of a device almost identical to the one discussed inthe manuscript (see text for explanation of the difference); theguided power is 0.28 mW. The dashed line indicates the trap-ping laser wavelength used to obtain the 6 sets of experimental(red) and modelled (blue) histograms shown in (c)-(h) asso-ciated with 6 distinct TTEs. The estimated diameter (percentvariation) of trapped Au particles extracted from these mod-elled histograms are shown in each plot. . . . . . . . . . . . . 97xxxFigure 5.1 (a) A prolate spheroid in the cavity coordinate system. (b) Thecalculated normalized electric field intensity profile of Mode 1of a SC1 cavity, which is used for trapping nanorods, with slotwidth of 90 nm and hole radius of 150 nm. The cavity mode ispolarized along the y-axis at its center. . . . . . . . . . . . . . 102Figure 5.2 The amount of cavity resonance shift when different size andorientation nanorods are placed at the center of a SC1 cavitywith slot width of 90 nm and hole radius of 150 nm. For (a)-(b) the nanorod is perpendicular to the slot (θ = pi2 , ϕ = pi2 )and (a) is the resonance shift as a function of nanorod diame-ter (length of 40 nm) and (b) shows the dependance on nanorodlength (diameter of 12 nm). (c) and (d) show the same relation-ships as (a) and (b) respectively, except that the rod is orientedalong the slot (i.e. θ = pi2 , ϕ = 0) for these two plots. Thefilled circles are the result from simulations and the curves arecalculated from Equation 5.8 with m = 1.5 and assumption ofperfect cylindrical shape for the nanorods. . . . . . . . . . . . 104Figure 5.3 [(a)-(d)] Histogram of 4 different spheroids with same shortdiameter of 32 nm and different aspect ratios calculated withthe anisotropic trap model including torques. The aspect ratiosare 1 (a), 1.1 (b), 1.2 (c), and 1.4 (d), respectively. The emptycavity transmission (i.e. without any particle in the cavity) isshown with blue dashed line in all graphs. . . . . . . . . . . . 106Figure 5.4 [(a)-(d)] The dependence of the device transmission on the ϕorientation of 4 different spheroids with same shorter diameterof 32 nm and different aspect ratios. The aspect ratios are 1(a), 1.1 (b), 1.2 (c), and 1.4 (d), respectively and their θ anglefor all 4 particles is 90 degrees. All particles are located at theintensity antinode of the cavity mode. . . . . . . . . . . . . . 107xxxiFigure 5.5 (a) Experimental histogram (red) during trapping of Au nanospherealong with fitted histogram (black) assuming a perfectly spher-ical shape of diameter 36.4 nm. (b) Same experimental (red)histogram as in (a), with the simulated histogram (black), us-ing a normal distribution of sizes of mean diameter 35.36 nmand 1.1% standard deviation. (c) The same experimental his-togram (red) is fitted (black) assuming a spheroid shape for thetrapped nanoparticle. The extracted size of the spheroid is 34.4nm ×37.1 nm. . . . . . . . . . . . . . . . . . . . . . . . . . 108Figure 5.6 (a) Scanning electron microscope (SEM) image of a 90nmwide slot cavity [1] used for trapping. (b) SEM image of theAu nanorods used in the trapping experiments. The averagesize of the rods, extracted from SEM images, is 44 nm ×12nm with 15% standard deviation. . . . . . . . . . . . . . . . 109Figure 5.7 [(a)-(f)] 6 different nanorod experimental (red) histograms areillustrated along with the calculated (black) histograms fits basedon theory accounting for the nanoparticles’ anisotropy. The in-sets show the corresponding normalized transmission time se-ries collected during the trapping experiment and the dashedblack lines show the range for which the experimental his-togram is collected. (a)-(c) are for laser power of 0.2 mW inthe waveguide and the estimated nanorod size based on the fitsare 14 nm×46 nm, 14 nm×50 nm and 38 nm×39 nm respec-tively. The actual total count number for the experimental his-tograms in these three plots are 105, 6.25×104, and 1.25×105respectively. (d)-(f) are at 0.25 mW power and the estimatedsizes based on the fits are 13 nm ×42.5 nm, 12 nm ×43 nmand 12 nm ×46 nm. The total count number for the experi-mental histograms in these three plots are 2×105, 8.75×104,and 7.5×104 respectively. . . . . . . . . . . . . . . . . . . . 110xxxiiGlossaryBOX Buried OxideC.O.M Center Of MassCMOS Complementary Metal Oxide SemiconductorCW Continuous WaveDI Deionized WaterFDTD Finite Difference Time DomainFEM Finite Element MethodFWHM Full Width at Half MaximumGPIB General Purpose Interface BusLPP Localized Plasmon PolaritonsMST Maxwell Stress TensorPAE Permanent Attachment EventPBG Photonic Band GapPC Photonic CrystalPCS Photonic Crystal SlotPLC Photonic Lightwave CircuitsxxxiiiSEM Scanning Electron MicroscopeSOI Silicon-on-InsulatorTE Transverse ElectricTIR Total Internal ReflectionTM Transverse MagneticTTES Temporary Trapping EventsxxxivAcknowledgmentsFirst and foremost, I would like to express my gratitude to my supervisor, Dr. JeffYoung for his inspiration, guidance and continuous support during my PhD study.My special thanks to Ellen Schelew, Jonathan Massey-Allard, Dr. Charles Foell fortheir support throughout this work. They have been a source of friendships as wellas good advice and collaboration. It was a pleasure working with you! Thanks tothe rest of the Nanolab members for their help and good company during my stayin the lab, Dr. George Rieger, Dr. Mohsen Keshavarz Akhlaghi and Dr. MarioBeaudoin.Lastly, I would like to thank my family for all their love and encouragement.For my parents, my sister and most of all for my loving, patient wife, who sup-ported me in all my pursuits. Thank you!xxxvChapter 1Introduction1.1 MotivationThe work described in this thesis demonstrates how modern nanofabrication tech-niques can be used to engineer the strength of light-matter interactions to opti-cally trap and confine single sub-50 nm dimension nanoparticles with sub-micronprecision, using less than 1 mW of continuous wave laser excitation. The keychallenge - routing laser radiation of a specific wavelength into a nanophotoniccavity with dimensions less than a cubic wavelength, and keeping it confined for∼ 10,000 optical cycles - was achieved using textured silicon planar waveguidesthat were immersed in a solvent bath containing a dispersion of Au nanoparticles.The basic design concepts are common to related structures designed to enhancelight-matter interactions for nonlinear optics [23], single photon sources [24], andsensing applications [25–28]. The results add to a growing body of work thataims to optically manipulate, detect, and/or characterize nanoparticles in solutionusing the strong “dipole” forces exerted by confined light on small dielectric parti-cles [3, 12, 25, 29].The project was originally motivated by wanting to use such structures to opti-cally trap and then permanently attach single nanoscale semiconducting nanocrys-tals, or “quantum dots” at the antinode of high quality factor cavities formed insilicon photonic circuits [30]. These quantum dots can act effectively as quantumemitters, and when resonant with microcavity modes, they can be used to produce1Figure 1.1: Layout of a full device designed and fabricated in this work foroptical trapping and sensing experiments. It includes the diffractiongrating couplers, cavity and waveguides all patterned in a 220 nm siliconslab sitting on top of SiO2 substrate (in red). The gratings, which consistof a 2D lattice of holes etched in silicon, are separated by 680 microns.The input/output light is injected/collected at a 17◦ angle to the normalto grating plane. The vertical scale bar is different than the in-planescale bar for better visibility.2non-classical, single photon sources [31–33], or as mediators of nonlinear opticalprocesses at the single photon level, both of which are key ingredients for optically-based quantum information processing. To be resonant with silicon-based micro-cavities, Pb-based nanocrystals must be on the order of ∼ 5 nm in diameter. Thecircuits described in this thesis are not currently capable of trapping such smallparticles, but only small improvements are necessary to realize this original goal.The structures used to achieve this level of confinement of infrared laser lightwith wavelengths ∼ 1.5 µm are made by two dimensionally (2D) patterning ∼ 200nm thick planar silicon slabs supported on a thick silicon dioxide cladding layer(see Fig.1.1). The high refractive index of silicon (nSi = 3.45) compared to silica(nSiO2 = 1.45) below, and air or solvent above (n = 1−1.37), means that light canpropagate in 2D, without loss, via bound, planar waveguide modes, due to totalinternal reflection. 2D patterns are defined in mask layers using electron beamlithography, and transferred to the silicon slab by chemically etching through theentire slab, as shown in Fig.1.2. The patterns are designed to i) couple light fromfree space into and out of the bound waveguide modes via diffraction gratings, ii)further confine the bound modes to propagate along distinct paths within the slabvia channel waveguides (effectively integrated optical fibers), and iii) define ultra-small, ultra-high quality factor 3D resonant cavities that are efficiently coupled tothe waveguides.Silicon was chosen as the base waveguide material because of its high re-fractive index, but also because many industries are rapidly leveraging decadesof silicon processing expertise to develop integrated photonic/electronic chips forclassical telecommunication applications [34–37]. The starting SOI wafers are rel-atively inexpensive [37, 38], there is a solid base of advanced, silicon-specific pho-tonic circuit design tools [38], and several optical and electron-beam processing“foundries” are readily accessible to researchers [38, 39]. Successful integration ofmultiple optical components such as waveguides, resonators and filters, in the formof planar photonic integrated circuits, have been already demonstrated on siliconwafers [1, 39, 40] and progress is constantly being made toward replacing opticalcomponents with equivalent photonic nanostructures.The novelty of this thesis work has to do with the design of the 3D micro-cavities and how they couple to previously designed channel waveguides and grat-3Figure 1.2: (a) Typical silicon-on-insulator (SOI) dimensions used for fab-ricating photonic integrated circuits. (b) Example fabrication processfor creating pattern on silicon slab. Additional functionality may beachieved by lithographic integration of metal contacts, ion doping, anddeposition of other materials [5].ing couplers. While much silicon photonic work utilizes ring [15] or disk res-onators [16] to confine light with high quality factors (Q: the number of opticalcycles that light remains trapped in the cavities), the need for both high Q, and lowmode volumes, motivated the use of microcavities based on 2D, in-plane PhotonicCrystal (PC) concepts [1, 3].These novel photonic circuits were successfully used to optically trap individ-ual Au nanospheres and nanorods with dimensions < 50 nm using less than 1 mWof Continuous Wave (CW) laser power [3]. These particles perturb the dielectricenvironment of the microcavity significantly, shifting the resonant frequency byup to a few linewidths. This “backaction” leads to a nanoparticle-position depen-dent transmission of the excitation laser, and a corresponding change of the powercoupled into the cavity mode. A detailed model of the optical forces and torquesoperating on the trapped nanoparticles, including the backaction, was developedand used to extract the size and shape of the trapped nanoparticles with nanometer4sensitivity, using only the variation in transmitted light intensity associated withthe Brownian motion of the particles in the cavity. It is believed that this structureand analysis can be of great interest in not only the physics community but also tothe biology and medicine communities for the study of single biological particles.The rest of this chapter introduces different concepts that are exploited to con-duct this research.1.2 Silicon Photonic Integrated CircuitsCommunications technology was revolutionized when optical fibers and semicon-ductor lasers enabled transmission of information using coded optical signals ratherthan electrical currents. Data processing and transmission are therefore currentlydone on two separate platforms: microelectronic Complementary Metal OxideSemiconductor (CMOS) chips and optical fiber networks, respectively. Many op-tical network components (e.g. lenses, filters, beam splitters, etc.) have graduallyshrunk in size, but until very recently, they have remained largely stand-alone,bulk elements. In late 80s, the idea of integrating multiple optical components ona small silicon chip was suggested for the first time [34–37]. The motivation wasto replace separate bulky optical components with miniature optical chips that stilloutput electrical signals to be processed using CMOS electronics. Silicon attractsmost attention in this field due to its compatibility with the mature silicon inte-grated circuit manufacturing enterprise, having the lowest cost per unit area, thehighest crystal quality of any semiconductor material, small optical absorption innear-infrared (IR), high thermal conductivity, high optical damage threshold, andhigh third-order optical nonlinearities [38]. Availability in the form of high qualitySOI wafers is another reason for choosing silicon as an ideal platform for creatingplanar waveguide circuits [38]. The ultimate goal of much of the current siliconphotonic circuit research and development is to successfully realize a wide rangeof photonic circuit elements in silicon at a relatively low cost that perform bothswitching and routing tasks without a need for signal conversion between opticaland electrical elements [22].There exists a huge body of work behind the development of the two funda-mental building blocks of SOI-based photonic circuits: grating input/output cou-5plers, and single Transverse Electric (TE) polarized mode “photonic wires” [41–53]. Fig. 1.3 shows a schematic of a generic photonic circuit. Grating couplersare all essentially diffraction gratings designed so that light incident from a fo-cused laser or an optical fiber near-normally incident on the wafer will diffractinto the plane of the silicon slab where it will be guided due to Total Internal Re-flection (TIR). The active area of the grating couplers is therefore on the orderof 10 µm2, and they typically incorporate some adiabatic transition to couple thediffracted beam into the single mode channel waveguides that have been optimizedto have cross sections ∼ 200 nm ×500 nm (for wavelengths around 1550 nm), asshown in Fig.1.1. Etching and chemical polishing techniques have been optimizedto minimize side-wall roughness on the etched silicon surfaces that define the pat-terned features, to the extent that losses as low as∼ 0.8 dB/cm through these singlemode waveguides can be achieved [51, 53, 54].In the current work, the key operational element connected to the channel inputand output waveguides is a high Q, small mode volume microcavity. Very highQ (up to several million) microcavities have been made in photonic circuits byetching smooth-edged disks or ring waveguides (see Fig. 1.10 in Section 1.4.2),with typical radii of ∼ 10 µm. While some optical trapping of particles has beendemonstrated using such cavities [14–17], the fact that the high intensity regionof the resonant cavity modes lies within the silicon means that the particles onlyinteract with the confined light field via the evanescent fields that penetrate thesolvent overlayer. Furthermore, the mode volume V of these type of resonatorsis typically several cubic wavelengths. These factors translate into the need forrelatively high input laser powers (∼ 10 mW) to trap even large (500 nm) dielectricparticles [14–17].To reduce the required power, the present work employed microcavities de-fined by introducing defect states within quasi-2D photonic crystals etched into thesilicon, as described in the following section.1.3 Photonic Crystal NanostructuresAs mentioned above, TIR within the 2D device layer of SOI circuits reduces thesize of optical components significantly compared with bulk counterparts. It is also6Figure 1.3: (a) Schematic of a generic SOI photonic integrated circuit con-sisting of different active and passive photonic elements such as gratingcouplers, waveguides, splitters, filters, switches, etc. The minimum sizeof splitters, is limited by how tightly channel waveguides may be bentbefore break down of TIR, which is dictated by relative indices of re-fraction of the waveguide and surrounding cladding.7Figure 1.4: Example structures taken from the literature (not work done aspart of this thesis); (a) Scanning Electron Microscope (SEM) image ofone-dimensional (1D) PC made of successive layers of AlInN (darker)and GaN (brighter) (reprinted from [6]). (b) SEM image of a two-dimensional (2D) PC made of macroporous silicon lattice (reprintedfrom [7]). (c) SEM micrographs of a three-dimensional (3D) photoniccrystal. Left image is the top view of a completed four-layer structureand the right image is the cross-sectional view of the same 3D pho-tonic crystal. The rods are made of polycrystalline silicon (reprintedfrom [8]).8responsible for in-plane light confinement in channel waveguides (typically with afew hundred nanometers width and vertical walls), which are effectively opticalfibers that route light in planar photonic integrate circuits.In the 80s, a different and more powerful photon confinement mechanism wasdeveloped based on the Photonic Band Gap (PBG) concept that was first intro-duced separately by Yablonovich [55] and John [56]. Confinement based on thePBG effect allows for even further light confinement and therefore optical deviceminiaturization. John and Yablonovich showed that by creating multidimensionalperiodic structures (Fig. 1.4) with periods on the order of an optical wavelengthand sufficiently high refractive index contrast, it is possible to artificially createa band of frequencies (PBG) within which there are no propagating solutions tothe Maxwell’s equations (i.e. photonic density of states of zero). These so-calledPC structures are the photonic analog of an atomic lattice for electrons, which in-stead of obeying Schro¨dinger’s equations, follow Maxwell’s wave equations. Likeelectrons in atomic lattices, photons in PCs exhibit band structure and dependingon the lattice type and scattering properties of the unit cell, these band structuresmay or may not exhibit full band gaps; a range of optical frequencies for whichlight propagation is prohibited in all directions for all polarizations (Fig. 1.5). Bymodifying the structure of PCs (e.g. their periods, refractive indices, shapes etc.)and therefore, their band-structures, it is possible to engineer the photonic den-sity of states, which leads to various applications from controlling of spontaneousemission through the Purcell effect [55, 57] to enhancing laser efficiencies [58–60],guiding light through sharp bends [61] and propagation speed of light for nonlinearoptics [62].Complete PBG for all propagation directions can only be realized in 3D PCswith sufficient index contrast and lattice structure. For other periodic structures(e.g. 1D, 2D or “2D planar”), only quasi PBG can exist for some specific propaga-tion direction and polarization. For instance, in Fig. 1.5, for a 2D planar PC lattice(called planar because the holes have finite depth), one can at best only achieve aquasi-PBG for TE modes propagating in the xy plane. Thus, although in 1D and2D PC structures, there is no complete PBG, one can still can use these structuresas a very effective means of in-plane light confinement of radiation modes withspecific polarization properties.9Figure 1.5: [(a)-(b)] Schematic of a 2D planar hexagonal lattice PC structurein a SOI photonic circuit with two types of propagating modes: TE(with only in-plane electric field polarization) and TM (with only in-plane magnetic field polarization). (c) Example photonic band structurefor the 2D planar PC above the substrate in (a) (reprinted from [5]). Thegray light-cones show the area above substrate light-line, where the TIRfails and leads to coupling of the PC modes to continuum modes andtherefore to intrinsic out-of-plane diffraction losses in the PC region.10Figure 1.6: (a) Schematic of a line defect (also known as W1) PC waveguidewhich is created by removing a row of holes in a hexagonal lattice ofholes. (b) Example band structure of a W1 waveguide showing twoguided TE modes (the red has even symmetry and the blue has oddsymmetry) in the projected bulk PC bandgap (yellow region).Quasi-2D PC like the one shown in Fig. 1.5 can be used to confine light morestrongly than TIR alone by introducing appropriate defects within the 2D PC uni-form host crystal. Fig. 1.6 illustrates how, by leaving out a row of holes in anotherwise uniform hexagonal PC lattice, one can form 1D connected waveguideswith effective bend-radii on the order of the lattice constant. There are variety ofways for introducing a linear defect into a crystal, and therefore a variety of guidedmodes. The only requirement is that the structure has discrete translational sym-metry in the waveguiding direction [63]. By tuning the size/location of holes in thebend region, light inside a 1D waveguided TE mode, can be transmitted with over90% efficiency per bend [64]. One remarkable property of PC waveguides is theability to guide light primarily outside higher-index material, which shows theirfundamentally different light guiding mechanism (for an example see waveguidedesigns in Chapter 2). In contrast with traditional waveguides that solely operatebased on index guiding (TIR), in PC waveguides, in-plane light confinement canalso occur strictly due to the existence of the 2D bandgap in the region surround-ing the 1D defect. To form an ultra-small 3D localized cavity, one introduces a11localized defect, such as in Fig. 1.7. This particular “L3” cavity actually supportsseveral modes with distinct frequencies and associated mode profiles.Figure 1.7: (a) Schematic of a PC L3 cavity, consisting of a defect (threemissing holes) in a hexagonal lattice of holes in a silicon slab. (b) Asketch of the local photonic density of states at the cavity center.The in-plane confinement of the defect modes is due to PBG of the PC andout-of-plane confinement is a result of TIR. But these confinement elements arenot perfect in reality, which in the case of cavities, results in coupling of cavitymodes to continuum modes not confined to the slab. Therefore, the energy inthe cavity modes decays exponentially, which gives a Lorentzian line-shape to thecavity mode ( the defect mode in Fig. 1.7b). This exponential decay can be char-acterized by a parameter called the “Quality Factor” (Q), which is related to theLorentzian linewidth, γ , the angular resonant frequency of the cavity, ω0 and cavityphoton lifetime, τ through the following relationQ = ω0τ = ω0γ . (1.1)Referring again to Fig. 1.7, the various localized L3 cavity modes have widelyranging Q values.The cavities act like resonators and their Q is a measure of field enhancementin these resonators. For most photonic applications that rely on light-matter inter-actions, cavities with higher Q are beneficial because they produce a higher fieldintensity for a given input laser power associated with a larger local density of pho-tonic states. As mentioned previously, the other important factor that influences the12maximum field intensity in the cavity when resonantly exciting a particular modeis its mode volume (V ), which is defined asV =∫d3rε(r)|E(r)|2max(ε(r)|E(r)|2) . (1.2)In the above equation, E(r) is the electric field associated with the confined cavitymode [65] and ε(r) is the dielectric constant at location r in the cavity. As willbe shown in the following chapters, PC based defect state microcavity modes canhave mode volumes less than ( λ√ε)3, in which case the peak internal field intensityis approximately Q times the incident field intensity when the Q of that mode isdetermined by its coupling to a single input/output waveguide channel. In contrast,the peak field intensity in ring and disk resonators is reduced in proportion to 1V .As discussed later in this chapter, the optical forces on nanoparticles are re-lated to the gradient of cavity electric field intensity. Therefore, both smaller modevolume and higher Q lead to larger optical forces. This is because smaller modevolume means more spatially-confined cavity modes, which increases the field in-tensity “gradient”, and higher Q means more enhancement of the cavity’s maxi-mum electric field, which leads to larger electric field intensity and therefore opticalforce.In this thesis, we design a cavity structure that operates at around 1.55 µm,which is the optical telecommunications wavelength. The PC in this design isformed by a 2D triangular lattice of holes drilled in a silicon slab of thickness 220nm. The triangular lattice is selected because of its higher degree of symmetry,which creates omnidirectional PBG for TE polarized light propagating in any di-rection within the silicon slab. The structure of the cavity is optimized to havehigh-Q in fluidic medium where the optical trapping and sensing is taking place.The detail of the cavity design is described in Chapter 2.1.4 Optical TweezersIt has been a few centuries since Johannes Kepler hypothesized the presence of“radiation pressure” on objects. But it took nearly three centuries for experimentalconfirmation of radiation pressure by Lebedev [66] in 1901. Later in 1936 Richard13Beth [67] at Princeton University experimentally demonstrated angular momentumtransfer between light and the matter. Invention of Lasers revolutionized opto-mechanics and led to a new class of tools, named “Optical Tweezers”.Since being established in the 1980s [68], optical tweezers [68–70] have beenone of the most useful tools used to trap and manipulate the position of meso-scopic objects, giving rise to rapid progress in various nanoscience areas [71–74].The tightly focused laser beams (Fig. 1.8a) present in these tools cause dipolarcoupling of light and small particles, resulting in optical forces/torques being ex-erted on the particles toward the focus of the laser beam. These forces/torques,which are described in the next sub-sections, enable trapping and non-contact ma-nipulation of micro and nanoparticles with extremely high accuracy [9] (Fig. 1.8b).For instance, laser tweezers enable following the movements, forces, and strains inmolecular structures during a reaction [75]. By attaching glass or latex beads tomacromolecules, it is possible to trap them at the laser focus and do high-accuracyposition and force/torque measurements directly [9, 69, 72, 76–79]. Some otherapplications of laser tweezers in biology include measuring elastic properties ofDNA [80, 81], characterizing the mechanical unfolding of proteins [82–84], andmeasuring the force in single myosin molecules [85]. All of these demonstrationsare performed in fluidic environments, where the main force competing with theoptical force is due to Brownian motion. This force, which is a function of thermalenergy of particles, pushes them out of the equilibrium point in a random fashion.The overall motion of the particles depends on the temperature of the environmentand the strength of optical forces. To keep the particles stably in the optical trap,laser tweezers typically have to produce trapping potential energies with minimumdepth of 10kBT , where kB is the Boltzmann constant and T is the temperature ofthe system.1.4.1 Optical ForceMaxwell Stress TensorSince light radiation carries energy and momentum, it is intuitively understoodthat it can transfer its energy and momentum to an object placed in its path and14Figure 1.8: (a) Schematic focused beam of laser propagating downward thatproduces optical forces on a particle that has larger refractive index thanits surrounding. Two rays of light (R1 and R2) are showing the lightrefraction in the particle. Since R2 is coming from the focal centerof the beam, its intensity is stronger, and therefore it transfers largermomentum to the particle compared to R1. Therefore, the conservationof momentum dictates the particle experiences a force toward the beamfocal center. This force, which is a result of laser intensity variationand in the direction of light intensity gradient, is called the gradientforce. Also, both rays exert “scattering force” in the direction of lightpropagation because of momentum transfer from refracted or absorbedlight. This force tries to push the particle out of the laser trap. (b) Anexperimental example of optical manipulation of multiple micron-sizecolloidal silica spheres using laser tweezers (reprinted from [9]).15hence exert an optical force on the object. If the size of a particle is much largerthan the wavelength of the light (Mie Regime), the optical force can be understoodusing ray optics. When a transparent particle enters a tightly localized radiationfield, the light rays will reflect and refract and this leads to a change in the light’smomentum. From Newton’s third law, the particle experiences the same amount ofmomentum change in the opposite direction. In a non-uniform field like a Gaussianbeam, this force is towards higher light intensity regions (when the refractive indexof the particle is higher than the medium). As illustrated in Fig. 1.8, the particleis attracted towards the region with higher intensity of light (in the direction of thegradient of light intensity) by this “gradient force” and pushed away from the laserfocus by axial forces due to the absorption and scattering of light.Analytical calculations of optical forces on arbitrary objects are usually verycomplicated, as it requires solving Maxwell’s equations to find electric and mag-netic fields in different media both inside and outside the objects. Therefore,optical force calculations rely on numerical methods like Maxwell Stress Ten-sor (MST) [86]. In this method, the total electromagnetic field distribution includ-ing the particle is self-consistently evaluated using Finite Difference Time Do-main (FDTD) or Finite Element Method (FEM) solvers [87, 88], which discretize(mesh) the whole physical system and solve Maxwell’s equations numerically tofind electric and magnetic fields in that system. Once these fields are evaluated,the MST is integrated over a surface surrounding the particle to calculated opticalforces, as explained below.When a particle is placed in an electromagnetic field (electric field E and mag-netic field B), it gets polarized and the Lorentz force (F) on the induced charges(with charge and current densities ρ and J) inside the particle (at location r andtime t) would be [89]F(r, t) =∫[ρ(r, t)E(r, t)+J(r, t)×B(r, t)]dV. (1.3)From Maxwell’s equations we can write∇×E× ε0E =−∂B∂ t × ε0E (1.4)16and∇×B×µ0H = [ 1c2∂E∂ t +µ0J]×µ0H (1.5)and adding these two equations givesε0(∇×E)×E+µ0(∇×H)×H =− 1c2∂H∂ t ×E+1c2∂E∂ t ×H+J×B. (1.6)The two terms on left hand side of Equation 1.6 can be written asε0(∇×E)×E+µ0(∇×H)×H = ∇ · [ε0E⊗E− ε02 E2←→I ]−ρE−∇ · [µ0H⊗H+ µ02 H2←→I ],(1.7)where ⊗ refers to tensorial product and ←→I is identity tensor. As a result, Equa-tion 1.6 simplifies to∇ ·←→T = ρE+ 1c2∂ (E×H)∂ t +J×B, (1.8)where ←→T is MST and is defined as (for material floating in vacuum background):←→T = ε0E⊗E−µ0H⊗H− 12(ε0E2 +µ0H2)←→I . (1.9)In the case of non-vacuum background, ε0 and µ0 in equation should be replacedwith those of the background medium (i.e. ε and µ). Integrating Equation 1.8 overan arbitrary volume V with surface A that encloses all charge and current densities(ρ , J) results in∮A←→T ·dA =∫V(ρE+J×B)dV + 1c2ddt∫VE×HdV. (1.10)On the right-hand side, the first term is the Lorentz force on the polarized particle(Equation 1.3) under illumination and the second term is the time variation of thefield momentum. For steady state, the second term becomes zero when the timedependence of the fields is described as e−iωt which is zero when averaged over afull optical cycle [90]. Therefore, after averaging Equation 1.10 over a full optical17cycle and using Equation 1.3, we can write〈F〉=∮A←→T ·dA. (1.11)Thus, to rigorously find the radiation force on a particle we should define a closedsurface surrounding the particle and then integrate the MST on this closed surface.The result is the average force on the particle. To compute the optical force on aparticle, only E and H on a closed surface are required, and these fields are self-consistent, meaning they are the sum of incident and scattered fields. SimilarlyMST can also be used to calculate the optical torque as demonstrated in Ref. [91].Although MST is a rigorous method, for practical purposes it is computation-ally expensive to perform. As mentioned above for finding the optical forces, theelectromagnetic fields are needed over a closed surface. This means that to find theoptical forces on a particle that is in motion, all self-consistent calculations of thefields have to be done for each position of the particle. As will be discussed in thenext chapter, each simulation that calculates the fields takes a few hours to run forour optical tweezers, and this makes it impractical to study the motion of a particlein out optical tweezers. In the next sub-section, an approximation is explained thatcan be applied to tiny nanoparticles (<< λ ) and greatly reduces the computationalcost of force calculation. Since the particles that we are dealing with in this re-search are in this category, all force calculations in this work are performed basedon this approximation.Dipole ApproximationWhen the size of a particle is much smaller than the illumination wavelength (lessthan 120 of the wavelength according to Ref. [92]), we can assume the polarizationdensity inside the particle’s volume is uniform and only dependent on the incidentfield at the center of the particle. In this regime (“Raleigh regime”), the particle’sresponse to the incident field can be assumed to be like a point dipole which getsuniformly polarized in the radiation field. This assumption is known as the “DipoleApproximation” and as shown below, it significantly simplifies and speeds up theforce and torque calculations.The radiation force on a dipole-like particle that possesses no static dipole mo-18ment and responds linearly to an external electric field with polarizability α isgiven in Ref. [89]:F(r, t) = (p(r, t) ·∇)E(r, t)+ ddt [p(r, t)×B(r, t)] , (1.12)where F(r, t) is the total dipole force, E(r, t) and B(r, t) are the electric and mag-netic fields, andp = αE (1.13)is the dipole moment of the particle. If we assume the particle is moving slowlyin an optical cycle, we can time average the optical force on a full cycle and byassuming time harmonic electromagnetic fields, the second term on the right side inEquation 1.12, which corresponds to the momentum of the incident light vanishes.As a result, Equation 1.12 becomes〈F(r, t)〉= 〈(p(r, t) ·∇)E(r, t)〉 , (1.14)which, considering harmonic fields of the form E(r, t) = E0(r,ω)ei(−ωt+φ(r)) anda complex polarizability of α = α ′+ iα ′′, can be reformulated as〈F(r,ω)〉= α′(ω)4∇(|E0(r,ω)|2)+ α′′(ω)2|E0(r,ω)|2 ∇φ(r). (1.15)The first term of Equation 1.15 corresponds to the gradient of intensity, which isalso known as the dipole term. This part of the force comes from the interactionbetween the external electric field and the induced dipole moment of the particleand acts in the direction of the gradient of electric field intensity. The secondterm, which corresponds to the dissipative part of the polarizability, results fromtransfer of momentum of light to the particle (usually known as scattering force).In the case of lossless particles or standing waves (the case that corresponds to PCcavity modes) the second term in Equation 1.15 vanishes. This is one advantage ofstanding waves over propagating waves, because the scattering force can move theparticle out of the stable trapping point defined by the dipole term (i.e. the pointwith highest intensity). For this case, it is possible to define a potential energy for19the trapping force field that takes the formU(r,ω) =−α′(ω)4|E0(r,ω)|2 . (1.16)The depth of this potential is the figure of merit for the effectiveness of the opticaltrap for overcoming the random Brownian motion of the particles. As a rule ofthumb, a minimum potential depth of 10kBT is needed for stable trapping [29].With the same procedure and again within the dipole approximation it is possibleto derive the mechanical torque generated by optical radiation on a dipole-likeparticle [89], which isτ =12Re[p∗×E]. (1.17)To calculate the optical force and torque on a particle in the dipole approximation,we only need to know the polarizability of the particle to be trapped, and the spatialdistribution of the incident electric field (not the self-consistent field), which isextremely less expensive computationally compared to the more rigorous MSTmethod.1.4.2 NanoTweezersOptical tweezers – tightly focused laser beams that trap and manipulate micron-size particles [68–70] – have enabled a truly impressive array of scientific break-throughs [71–74]. But as demonstrated in the previous section (see Equation 1.15),the trapping force is dependent on the gradient of the electric field intensity, whichrelies on the focusing power of the laser tweezers’ microscope objective and there-fore is ultimately diffraction-limited. Since a Rayleigh particle’s polarizabilityis proportional to its volume, large laser powers are required to trap nanoscaleparticles. In standard optical tweezers, a 100 nm polystyrene sphere requires 15mW [68] of laser power. This implies that for a 10 nm sphere ∼ 15 W of laserpower would be needed [93]. Increasing the laser power to above 10 mW mayeasily cause photo-damage to the trapped particles (especially biological objects)and increased Brownian motion because of the heat it produces [94].To overcome these drawbacks of conventional laser tweezers, namely cubicwavelength trapping volumes and large laser power requirements, a novel class20Figure 1.9: (a) Schematic of a plasmonic nanotweezers experimental set-up,in which a pattern of micrometre-sized gold structure is illuminatedunder the Kretschmann configuration through a glass prism. The redarrows give the direction of the incident and reflected light (reprintedfrom [10]). (b)-(c) SEM and atomic force microscope images of fabri-cated gold nanopillars. Scale bar is 1 µm (reprinted from [11]). (d)FDTD calculation of the electric field intensity distribution resultingfrom incidence plane wave illumination of a nanopillar at λ = 974 nm.Intensity enhancement, that is, intensity normalized to incident inten-sity |E|2/|EINC|2, is plotted. Peak intensity enhancement is 490 times,although upper limit of colour scale is chosen to be 20 times for vi-sualization. The scale bar is 200 nm (reprinted from [11]). (e) Electricfield amplitude distribution of a nanoantenna with 80 nm arm and 25 nmgap. The inset shows the SEM image of a fabricated nanoantenna with10 nm gap. The scale bar is 100 nm (reprinted from [12]). (f) Double-hole nanotweezers with a 15 nm tip separation used for trapping 12 nmsilica spheres (reprinted from [13]).21of “Nanotweezers” has emerged [69, 93], which relies on strong local enhance-ment of the exciting laser intensity. These new types of tweezers, which aremostly plasmon-based [10] or dielectric cavity-based [95], confine light into ex-tremely small regions and enhance its intensity, allowing for ultra-accurate andnon-invasive positioning of single nano-objects at low excitation powers. Further-more, because of their considerably smaller footprint, they enable optical trappingand manipulation of small particles on Lab-on-Chip systems at reduced costs.The collective resonant excitations of plasmons in metallic nanostructures (known as Localized Plasmon Polaritons (LPP)) gives rise to a large electric fieldenhancement in the near-field of the nanostructures. Because of the small featuresof these nanostructures (see Fig. 1.9), their plasmonic resonances have a very largeelectric field gradient and thus, produce a strong optical gradient force [96]. Thefirst experimental demonstration of metallic nanotweezers was done with micron-sized polystyrene particles with metallic nanopillars patterned on a glass substrate.The LPP of the pillars was excited by the evanescent light of a laser passing througha prism by TIR [97] (see Fig. 1.9a-d). Smaller metallic “nano-antennas” with dif-ferent shapes have subsequently been fabricated and used to trap (Fig. 1.9e-f) 10nm gold nanoparticles [12] and 12 nm silica spheres [13]. In another more signif-icant demonstration [98], a single 3.4 nm Bovin serum albumin protein moleculehas been trapped using double-hole nanotweezers with∼ 10 mW of incident power.The huge improvement in the size of the trapped nanoparticles in these metallicnanostructures is because of the extreme sub-wavelength concentration of the field,which gives rise to enormous field enhancements near the surface of the metal.Another benefit of these nanotweezers is their compatibility with microfluidic in-tegration as demonstrated in Ref. [99].A second type of nanotweezer is based on dielectric photonic microcavities(resonators) that only confine light down to volumes on the order of a cubic wave-length in the host dielectric, but that can have high Q factors [3]. The high Qfactors can, to a large degree, offset the lesser confinement (compared to plas-monic nanotweezers), by resonantly building up a larger modal field intensity fora given CW excitation power. These dielectric cavity structures also offer the sig-nificant advantage of being easily integrated with other optical elements on Pho-tonic Lightwave Circuits (PLC) for more complex nanomanipulation like sorting22Figure 1.10: (a) Schematic of a microtoroid coupled to an optical fiber (notto scale) (reprinted from [14]). In this system, a frequency-tuned laserbeam is evanescently coupled to a 90 µm diameter microtoroid byan optical fiber (red). The microtoroids have loaded Qs (i.e. Q ofa cavity when connected to waveguides in a circuit) of 1× 105–5×106 in water at 633 nm and can trap 5 nm silica nanoparticles. (b)SEM images of a 5 µm radius microring nanotweezers with Q factorof 860 (reprint from [15]). Polystyrene particles with diameters of 500nm can be stably trapped and propelled along the microring resonatorwith speeds of 110 µm/s at 9 mW in the bus waveguide. (c)-(d) Thetop-view schematic of a microdisk resonator with two bus waveguidesalong with the normalized electric field amplitude distribution of itsmodes. The corresponding zoom-in-view images near the couplinggap are shown in the insets (reprinted from [16]). A 30 µm diameter,700 nm thick SiN microdisk resonator has been demonstrated [17] totrap 1 µm polystyrene particles with ∼ 7 mW of input power withquality factors from 3000-6000.23and storing [15, 18–20, 100].One group of cavity-based nanotweezers (Fig. 1.10) includes microdisks [17],microtoroids [14] and microrings [15] which confine light through TIR (also knownas “Whispering Gallery Mode” resonators). They have Q factors from a few hun-dreds to several millions and can trap particles ranging from 5 nm to a few micronswith about 10 mW of power [15–17]. The other main category of cavity-basednanotweezers exploit PC microcavities that were described in Section 1.3. Lightin these nanotweezers is confined to a defect region in a photonic band-gap struc-ture, where light propagation of a certain range of frequencies is inhibited. Thesecavities have comparable Q factors as WGM resonators but they can have muchsmaller mode volumes, which reduces the required power for optical trapping byincreasing the light-matter interaction strength.In 2010, the first experimental demonstration (Fig. 1.11a-b) of optical trappingusing PC nanotweezers was done [18] on ∼ 50 nm polystyrene nanoparticles witha 1D PC resonator (also known as a “nanobeam” cavity). The loaded Q for thisdevice is 2500 in water. In the same article, the ability of these nanotweezers totransport, trap, and manipulate larger nanoparticles by simultaneously exploitingthe propagating nature of the light in a coupling waveguide was demonstrated.This class of optical nanotweezers lays the groundwork for photonic platformsthat could eventually enable complex all-optical single molecule manipulation anddirected assembly of nanoscale material [18]. Two years later, the same group de-veloped a new 1D silicon-nitride PC nanotweezer ((Fig. 1.11c) that can trap andrelease quantum dots, and 22 nm polymer particles [19]. This nanobeam cavityhas a Q factor of ∼ 5000 and mode volume of ∼ 4.4 cubic wavelengths, whichoperates with ∼ 10 mW of coupled power into the resonator. In Ref. [101], a1D nanobeam cavity with Q factor of ∼ 2000 and mode volume of a cubic effec-tive wavelength (i.e. the wavelength inside silicon which is the cavity material),was exploited for the auto-assembly of 1 µm dielectric particles inside an optoflu-idic cell designed to enable the assembly of multiple particles with different stableconformations at 0.3mW injected power. The same group in a proof-of-conceptdemonstration [102], used multiple coupled nanobeam cavities to create a recon-figurable nanotweezers, which upon switching the excitation wavelength betweendifferent resonances of the nanotweezers, could manipulate the orientation of the24Figure 1.11: (a) Schematic of a 1D PC resonator for enhanced optical trap-ping. (b) Simulated electric field intensity profile of the cavity modeshowing the strong field confinement and amplification within the one-dimensional resonator cavity. The black arrows indicate the directionand magnitude of the local optical forces (reprinted from [18]). (c)SEM image of a silicon nitride PC cavity along with FDTD simulationshowing the electric field intensity distribution near the resonator cav-ity (arbitrary unit). Strong field enhancement can be seen within thesmall hole at the center of the cavity. Scale bars are 1 µm (reprintedfrom [19]).trapped microspheres.Although the first predictions [103, 104] about the use of PC nanotweezers foroptical trapping referred to 2D PC cavities, it was not until 2013 that the first andonly other experimental demonstration was published [20]. In this work, as shownin Fig. 1.12, 500nm dielectric particles were optically trapped in a cavity with Qfactor of 2000 and injected power of 120 µW in the waveguide. The main advan-tage of this structure compared to previously discussed 1D PC nanotweezers, is thegood overlap between the cavity mode electric field and the trapped nanoparticle25Figure 1.12: (a) Schematic of a 2D PC hollow resonator along with its sim-ulated electric field intensity profile of the cavity mode showing thestrong field confinement and amplification within hollow region. (b)SEM image of device showing the hollow cavity and the PC waveg-uide. (c) The side view of the hollow cavity and the profile of the fieldintensity showing the good overlap between the field and the trappedparticle. The experimental Q factor is 2000 and the mode volume is 0.2time cubic wavelength. For stable trapping of 500 nm dielectric parti-cles, 120 µW of power is launched into the PC waveguide (reprintedfrom [20]).(Fig. 1.12c). The work described in this thesis builds on this concept, by modifyingthe cavity and coupling geometries to achieve high Q values and higher trappingforces for a given coupled laser power.1.5 Sensing and Backaction EffectAs mentioned above, nanotweezers in general (both plasmonic and dielectric cavity-based nanotweezers) generate enhanced electric fields that are confined to tiny vol-umes. They also possess an additional interesting feature that is not intrinsic to con-ventional laser tweezers, which is their resonant behavior. All of these structuresoperate at well-defined resonance wavelengths that are defined by the local dielec-tric environment where the modal light field is enhanced. A particle trapped in the26near field of a nanotweezers’ mode can therefore, in general, modify the microcav-ity’s resonant frequency by changing that dielectric environment. The influenceof the particle on the resonant frequency depends in general on its polarizabilityand its location within the microcavity. This is a major difference compared to thephysics of laser tweezers where the particle does not have a noticeable influence onthe exciting laser field. This effect, which is known as “backaction” [94, 105, 106],complicates the dynamics of the trapping mechanism (the coupled laser power be-comes dependent on the position of the particle), but it also provides a powerfulmeans by which to easily study the dynamics of the trapped particle, as discussedbelow.In Ref. [94], the authors exploited a plasmonic nanotweezers made of a nanoaper-ture in a metal film to trap a 50nm polystyrene sphere that has an active rolein enhancing the restoring force. They demonstrated experimentally that whena particle gets near to the nanoaperture mainly by random Brownian motion, thetransmittance of the nanoaperture gets influenced by the presence of the particlebecause of the refractive index changes it induces in the nanoaperture environ-ment (backaction effect). As a result of this backaction effect, which in their casewas an increase in the transmittance of the nanoaperture, the light intensity andtherefore optical forces on the particle is enhanced thus effectively deepening thetrapping potential. On the same basis, in Ref. [27] a double-hole plasmonic nan-otweezers (Fig. 1.9) enabled trapping of a 20-nm biotin-coated polystyrene parti-cle in a solution containing streptavidin. Of particular note in [27], because thebackaction modifies the transmission, the dynamics of the trapped particle couldbe easily monitored by simply taking time-series data of the transmitted laser in-tensity. This makes these nanotweezers an excellent single-molecule-resolutionsensor for studying biomolecular interactions and dynamics at a single moleculelevel [27, 28, 107].The backaction of trapped particles on dielectric cavity-based nanotweezershas also been studied in recent years [20, 26, 95, 105, 106, 108, 109]. All ofthese demonstrations are based on measuring the amount of shift in the resonanceof the cavities because of the trapped particles’ backaction. Using perturbativecalculations [105], this shift for a cavity with a spherical Rayleigh particle (smaller27than λ20 [92]) inside it is predicted to beδλ = λ0α ′|E(r)|22∫d3rε(r)|E(r)|2 , (1.18)where λ0 is the original resonance of the cavity before trapping the particle (emptycavity resonance), α ′ is the real part of particle’s polarizability (for spherical par-ticles the polarizability is defined in Equation 4.2), r is the permittivity of themedium at location r and E(r) is the empty cavity electric field at the locationof the particle r. The integral at the denominator of this equation is the energystored in the cavity which depends on the mode profile of the cavity. This rela-tionship shows the dependence of the cavity resonance on the trapped particle’spolarizability and location.The resulting position-dependent shift of the cavity resonance gives rise to achange in the amount of energy coupled into the cavity and therefore complicatesthe optical trapping physics from what it would be if the intensity of the trappingfield inside the cavity was independent of the particle’s position. However, in anal-ogy with the effect of backaction in the plasmonic nanotweezers, the fact that thetransmission of the trapping laser depends on the position of the trapped parti-cle means that the transmitted intensity time-series data contains a fingerprint ofthe particle’s dynamics, and hence offers a relatively simple means of sensing theproperties of the trapped particle.Our objectives in this project are first to design an efficient 2D PC nanotweezerthat produces larger trapping forces compared to previous designs and secondly toexploit them for simultaneous trapping and sensing of sub-50 nm Au nanoparticles.The designed PC nanotweezers have small mode volume (0.1 cubic wavelength),high-Q factor (up to 7000) and more importantly large overlap between the cavitymode profile and the trapped particles (i.e. in contrast to disk and ring resonators,the mode lives in the space outside the dielectric medium, which can be filled withsolution containing the particles to be trapped), which results in extreme sensitivityto backaction of trapped particles.In Chapter 2, the design of these devices is described. The process includesinvestigating the influence of various design parameters on the performance of thedevices and optimizing them using a commercial FDTD Maxwell equation solver.28In Chapter 3, the fabrication process and the experimental setup for testing thefabricated devices are described in detail. Furthermore, the initial testing resulton the fabricated devices is presented and compared with the simulation results toinvestigate the agreement between them. The results of this chapter and Chapter 2are published in Refs. [1, 2].In Chapter 4, the fabricated devices are used for trapping spherical gold (Au)nanoparticles and sensing the change in the refractive index of the medium. A self-consistent model is presented to analyze the backaction of the trapped particles onthe optical transmission signal of the devices during trapping experiments, whichled us to estimate the size of trapped nanoparticles. This work shows that transienttransmission time series data alone can be used, together with a self-consistentelectrodynamic model of the perturbed cavity transmission, to quantify the size ofnominally spherical Au nanoparticles with nanometre sensitivity, and to quantifythe fluctuation of the particle’s effective polarizability while in the trap. The resultsof this chapter are published in Ref. [3].In Chapter 5, the model present in the previous chapter is generalized to includeanisotropic particles and then the modified model is applied to the experimental re-sults from trapping Au nanorods. It is explained how the rotation of the anisotropicparticles modifies the transmission signal of the devices and this distinct behav-ior is exploited to differentiate particles with different degrees of anisotropy in theoptical trap. The trapping results in this chapter are to our knowledge the firstexperimental demonstration of trapping sub-50 nm anisotropic particles using PCcavity-based nanotweezers.Chapter 6 is the concluding chapter. An outlook of PC nanostructures for vari-ous applications is presented and the limitations and possible improvements of ouranalysis are discussed.29Chapter 2Device Design2.1 IntroductionThe present chapter focuses on designing SOI PLCs and exploits the design flex-ibility of PCs to integrate high Q, low mode volume (V ) microcavities whereinthe mode energy resides almost entirely in the background dielectric (vacuum or asolvent) with more conventional SOI-based grating couplers, and silicon channel(ridge) waveguides, where the field is predominantly in the silicon.Such structures (Fig. 2.1) are of interest for applications where one wants toenhance the interaction of circuit-bound photons with matter that cannot be em-bedded within the silicon. The relevant applications for our project are opticaltrapping of nanoscale objects dissolved in solution using optical forces and opticalsensing, where small amounts of some material in solution is detected due to itseffect on the refractive index of background medium.In the next section of this chapter, a PLC design is introduced that allows op-eration in fluidic medium, which is necessary for the applications discussed above.The basic elements of a PLC for confining laser light are grating couplers for cou-pling laser light into the silicon slab, different types of waveguides for reshaping thelight wavefront and guiding it through the PLC with minimum loss, and resonatorsfor the ultimate light confinement. Different aspects of this design that influenceits performance are investigated, and in Section 2.3 some modifications are ap-plied to the original PLC design to enhance light confinement inside the cavity and30Figure 2.1: Layout of a full device SC1 including the grating couplers, cav-ity and waveguides sitting on SiO2 substrate (in red). The gratings areseparated by 680 microns. The input/output light is injected/collectedat 17◦ angle to the normal to grating plane.approach the optimal performance. The goal of the modifications is to minimizeout-of-plane losses in the waveguides and increase the efficiencies of different in-terconnections of the PLC. To show the effectiveness of these modifications, theoptical trapping force of the cavity mode on a 50 nm Au nanosphere is calculatedand compared for both designs. These two designed structures are referred to asSC1 and SC2, respectively. They are studied using finite-difference time-domain(FDTD) simulation software from Lumerical Solutions [87].All data and simulations in this thesis correspond to samples with a 220 nmthick silicon layer on top of a 3 µm thick buried oxide layer that robustly supportsall circuit elements. The refractive index of the top cladding in all simulations ofthis chapter is assumed to be nhex = 1.365. This is the refractive index of hexanewhich is a common non-polar solvent for suspending some nanoparticles (like col-loidal Pb-based quantum dots). On the other hand, this number is also close to therefractive index of isopropanol (nipa = 1.37), a typical polar solvent for suspend-ing another class of nanoparticles (Au, Ag nanoparticles). Therefore, the results ofsimulations in this Chapter are potentially applicable for trapping a wide range ofnanoparticles.312.2 SC1 StructureThe full SC1 photonic circuit that is initially designed includes a Photonic CrystalSlot (PCS) Cavity, input/output grating couplers, single mode silicon ridge waveg-uides, and 1D PC coupling waveguides (see Fig. 2.1). Two 2D PC grating cou-plers [39] are used to launch light from a tunable laser diode, via parabolic taperedwaveguides, into and out of single mode silicon channel waveguides that connectto the PCS cavity region.As illustrated in Fig. 2.1, the channel waveguides of SC1 devices are curvedso that the input and output grating couplers do not sit on the same line. Thismakes the experimental signal measured at the output grating coupler less noisy, asthe scattered light from the input grating coupler that is guided through the under-cladding layer does not get detected. The design of the PCS cavity originatedfrom “slot-waveguide” structures (see Fig. 2.2) developed by the authors in [21]that support propagating modes in channel waveguides wherein most of the modeprofile is concentrated in the air/solvent gap between two silicon ridges. These havebeen used extensively in the sensor community [110, 111]. The authors in [112]showed theoretically that if such a slot waveguide was surrounded by a 1D PC oneither end, a fully 3D localized mode could be trapped in a volume less than a tenthof a cubic half (free space) wavelength (< 0.1(λ/2)3). This design assumed a slotwidth of only 20 nm.It is subsequently suggested [113] a slot waveguide structure surrounded by a2D PC that could achieve almost as small a mode volume, but for larger slot widthsthat should be easier to fabricate. Their cavity was defined by locally modifyingjust a few of the holes in the PC, nearest to the waveguide. In [114], the authorsdemonstrated high-Q values and strong sensitivity of resonant frequencies to thebackground refractive index in slot cavities defined by varying the pitch of thesurrounding PC along the slot waveguide axis. These, as well as subsequent [115]high-Q PC based slot cavities, are based on “free-standing” structures where theunderlying cladding layer is removed after the PC structures are etched into thesilicon. They also required butt-coupling of the excitation source to the waveguide.The design details of each segment of the full SC1 circuit are described in thefollowing sub-sections.32Figure 2.2: Transverse electric field profile of the quasi-TE mode in a SOI-based slot waveguide. The origin of the coordinate system is locatedat the center of the waveguide, with a horizontal x-axis and a verticaly-axis. nH is the refractive index of silicon and nC is the refractive indexof SiO2. (a) Contour of the electric field amplitude and the electricfield lines. (b) 3D surface plot of the electric field amplitude (reprintedfrom [21]).332.2.1 Grating Couplers and Slab Waveguides (device SC1)The grating couplers consist of a 2D rectangular lattice of holes in a 220 nm siliconslab. This design is selected because Young’s lab had experience with this type ofrelatively simple and efficient coupler [39]. The radius and the pitch of the gratingcoupler holes (see Fig. 2.3) are chosen so that the transmission efficiency of thegrating coupler is a maximum at the resonant wavelength of the cavity and theincident angle required by experiment conditions. Each grating occupies an areaof ∼ 20 µm ×20 µm and is designed for operating with y-polarized excitation.The light diffracted in-plane from a grating coupler is transferred first to atapered multimode waveguide that gradually shrinks and connects to a single modewaveguide (Fig. 2.3a). The long 300 µm parabolic shaped waveguide ensures lowdissipation light transfer to the single mode channel waveguide of width 450 nm.Using FDTD simulations, a y-polarized (refer to Fig. 2.3) Gaussian beam withwaist diameter of 10 µm is launched into the grating coupler at a 17 degree incidentangle with the z-axis. The source is located 90 nm above the silicon slab and itscenter is 5 µm away from the beginning of the tapered waveguide along the x axis.This x distance is optimized to have highest transmission efficiency for the gratingcoupler. The transmitted power in the beginning of the tapered waveguide and theend of single-mode channel waveguide are calculated using 2D frequency-domainpower monitors (yellow lines are monitors in Fig. 2.3a). The total transmissionefficiency of the whole structure as well as transmission of each of its sections isillustrated in Fig. 2.3c. The hole radius of this grating coupler is 230 nm with 795nm and 750 nm pitches along the x and y axes, respectively. The width of the ta-pered waveguide at its beginning is 14 µm. The simulation region is uniformlymeshed with mesh sizes of (39.75 nm,37.5 nm,22 nm) along x,y,z directions re-spectively. These numbers are an integer factor of the lattice pitch of the gratingalong the x and y directions. In the z direction since the structure is not periodic,the mesh size is selected based on the smallest feature size, which is the siliconslab thickness (i.e. 220 nm). These meshing considerations ensure the periodicityof the PC structures is not destroyed by discretization.34Figure 2.3: [(a)-(b)] FDTD simulation layout of the SOI grating coupler thatdiverts the excitation laser into a parabolic tapered waveguide connectedto a single mode channel waveguide. Its polarization and injection di-rections are shown with pink arrows. All feature sizes are described in2.2.1. The picture scale along x and y axes are the same but differentthan the z axis scale. (c) The transmission of this structure is calcu-lated using two monitors (yellow lines in (a)). The blue curve is thetransmission from the source up to the beginning of the tapered waveg-uide (monitor M1) and the black is the efficiency of the whole structure(i.e. from the source up to the channel waveguide (monitor M2). Thered curve, which is the division of the black curve to the blue curve,is showing the transmission efficiency of the tapered waveguide (thestructure between the two monitors).352.2.2 Photonic Crystal Slot Cavity (SC1 device)Here we designed a PCS cavity (Fig. 2.4) based on a design in [113, 115] thatsupports high-Q, small volume modes in solution without having to remove thesilicon dioxide layer beneath the cavities. The background PC region comprisesa hexagonal array of circular holes separated by 490 nm, and with hole radius ofr = 160 nm, which was designed to have a TE PBG from 1495 nm to 1800 nm.To transfer laser light to the PCS cavity, the other end of single mode channelwaveguide is connected via a short impedance matching region [40, 116] to W1PC waveguides that simply omit a row of holes from the background PC.Various defects are introduced into the background PC to excite a 3D local-ized mode in the center of the PC (see Section 1.3). A narrow 90 nm slot runshorizontally, through the middle of the PC, forming a distinct 1D waveguide. TheW1 waveguides intersect the slot at 60 degrees (Fig. 2.4). The light in the W1waveguides propagates primarily in the silicon, while the slot waveguide confinesthe light primarily in the air or solvent gap. When the position of the 3 rings ofholes adjacent to the slot waveguide (different color holes in Fig. 2.4b) betweenthe two W1 waveguides are intentionally shifted away from the slot, two 3D local-ized modes (Fig. 2.5a-b) are drawn out of the slot waveguide continuum [113], andthese 3D localized modes are exploited in this circuit design. The 4 closest holesto the slot are shifted by s1 = 12 nm, the next ring of holes (10 holes) are shiftedby s2 = 8 nm, and the third ring of holes (16 holes) are shifted by s3 = 4 nm.Figure 2.4b also shows how the two different waveguide types are connectedvia a single “coupling hole” (black color holes) with radius (rc) that can vary fromdevice to device to adjust the coupling efficiency between the 1D waveguides andthe cavity. This geometry, though not fully optimized in this design, allows inde-pendent access to the slot waveguide from the ends, which may be advantageousfor some applications. Also, this angled coupling between the waveguides allowsfor exciting both high-Q modes of the cavity which are polarized orthogonallyat the cavity center. Figure 2.5a-b shows the electric field intensity distributionin the vicinity of the SC1 slot-cavity modes in hexane. Mode 1 (Fig. 2.5a) withresonance wavelength λ1 = 1567.4 nm is more concentrated in the slot and it ismainly y-polarized and has a smaller mode volume (VMode1 = 0.1( λ1nhex )3). Mode 236Figure 2.4: (a) Layout of a SC1 slot-cavity with input/output channel waveg-uides. The channel waveguides have a width of 450 nm. A mode sourceis used to send light into the input channel waveguide and a monitor (M1in yellow color) is located at the output channel waveguide to calculatethe transmission of the device from input to output channel waveguides(spectrum shown in Fig. 2.5c). (b) Enlarged image of the cavity regionat the center of the structure. The 30 different color holes near to the slotare shifted away from it to create two defect modes. Similar color holesare shifted the same amount. The hole shifts are s1 = 12 nm, s2 = 8 nmand s3 = 4 nm, going from inner ring of holes outward. The two smallercoupling holes at the end of PC waveguides in black color have radiusrc = 110 nm. The radius for the rest holes of the PC is r = 160 nm andthe lattice period is a = 490 nm. The width of the slot is 90 nm.(Fig. 2.5b) which is mainly in the four central holes of the cavity, is x-polarized atcavity center and has mode volume VMode2 = 0.4( λ2nhex )3, where λ2 = 1586.6 nm.Figure 2.5c shows the theoretical transmission of the device shown in Fig. 2.4.A TE-polarized mode with well-defined power in the input silicon channel waveg-uide is launched towards the cavity region, and the corresponding power in the out-put silicon channel waveguide is calculated using a 2D frequency-domain powermonitor, from which the theoretical transmission of each mode is obtained. TheFDTD simulation for calculating the transmission spectra of this structure with1240×1402×100 gridpoints and using 256 processors takes ∼ 40 hours to finish.37The simulation length is set to 40 ps, to obtain good resolution (∼ 25 GHz) on thefrequency-domain data.2.2.3 SC1 Device Performance DiscussionThe simulated resonant transmission of Mode 1 for the structure in Fig. 2.4 is2.1%. The Q factor of this structure when the W1 PC waveguides are omitted(QU ) is 9600 while the loaded Q (QL) is 7400. In the absence of losses in waveg-uide regions, the expected theoretical resonant transmission of this structure isT = (QU−QLQU )2 = 5.25%, which is bigger than what the FDTD simulation givesus (i.e. 2.1%). This means 60% of the power that is supposed to be transmittedto the output channel waveguide is dissipated in the waveguides and junctions. Byrunning more simulations with power monitors at different locations, it is foundthat this power loss is caused by three main factors:The first reason is evident from the W1 PC waveguide band structure shownin Fig. 2.5d. At the cavity resonant wavelengths, the PC waveguide band is lo-cated above the SiO2 substrate light-line, which leads to coupling to continuummodes and therefore to intrinsic out-of-plane diffraction losses in the PC waveg-uide region. The second reason is because of out-of-plane scattering at the junctionbetween channel and PC waveguides. In fact, nearly 33% of the injected power inthe input single mode channel waveguide dissipates during traveling through thereference PC waveguide structure, as illustrated in Fig. 2.6b. In this figure, thestructure consists of only channel and W1 PC waveguides with no cavity betweenthem. Again, the first TE mode of the input silicon channel waveguide is excitedand the output power is measured using power monitors. The transmission and re-flection efficiencies are shown in Fig. 2.6b. The 33% power loss in this simulationis a result of scattering at the intersection of waveguides (14%) and out-of-planescattering (19%) along the PC waveguide. The reflection is negligible at the reso-nance of the cavity (∼ 1%).Unfortunately, there is not much room below the light-line to be used forimproving transmission efficiency through the PC waveguide section. Also, thewaveguide band is almost flat below the light-line, which means slow group veloc-ity and therefore higher losses due to scattering from rough surfaces of fabricated38Figure 2.5: The normalized electric field intensity profile of Mode 1 (a) andMode 2 (b) of the SC1 slot-cavity overlapped with the cavity structure.(c) The transmission efficiency of the structure in Fig. 2.4 showing twohigh quality modes of this cavity. The Q for Mode 1 (λ1 = 1567.4 nm)is 7400 and Mode 2 (λ2 = 1586.6 nm) is 8100. (d) The TE transmis-sion band of W1 PC waveguides overlapped with SiO2 light line (blacksloped line) and two resonances of the SC1 cavity (Mode 1 in red andMode 2 in blue color). (e) The two TE transmission bands of the PCSwaveguide. The red curve has the same characteristics as Mode 1 of thecavity and blue curve corresponds to Mode 2. Again, the dashed linesare the SC1 cavity resonance modes.39devices. The other problem with such a small range of frequency is that with fab-rication imperfections, it is almost impossible to achieve the target frequency.Figure 2.6: (a) Layout of the FDTD simulation for calculating the power lossin the W1 PC waveguides of the structure in Fig. 2.4. The length ofthe W1 PC waveguide in this simulation is 29 pitches, equivalent tothe total length of W1 PC waveguides in Fig. 2.4. All feature sizes aresimilar to the structure in Fig. 2.4. (b) The transmission spectrum (blue),reflection spectrum (red) and the sum of them (black) for the structurein (a) calculated from input to output channel waveguide. The dashedline shows the wavelength of Mode1 of the cavity. The transmissionvalue for the structure in (a) at Mode1 resonance is ∼ 67%.The third important source of power loss is the scattering and reflection at thecoupling hole at the end of the PC waveguide (see Fig. 2.7). It is found that atthe resonance of Mode 1, nearly 23% of the power that passes the end of input PCwaveguide reflects and dissipates around the coupling hole region. This is a largesource of loss which is due to poor mode matching between the PC waveguidemode and the cavity modes. This measurement means that the overall transmissionefficiency of input+output coupling holes is (1− 0.23)2 = 60%, which reducesthe device overall efficiency. With these fundamental losses, even by varying thecoupling hole radius (see Fig. 2.4), it is not possible to get the optimized 25%efficiency required to have maximum energy in the cavity.Despite all these sources of power dissipation, we tried to measure the func-40Figure 2.7: (a) Layout of the FDTD simulation for calculating the power lossin different parts of the structure in Fig. 2.4. All feature sizes are similarto the structure in Fig. 2.4 and the color of the holes are modified forbetter distinction from the yellow power monitors. (b) The enlargedimage around one of the two coupling holes of this structure (in blackcolor) shows the power monitor (small yellow box around the couplinghole) that measures the vertical losses occurring at this coupling hole.tionality of the SC1 device as optical tweezers by calculating the optical trappingpotentials (see Equation 1.16) generated in both modes of this cavity (see Fig. 2.8).These plots show the trapping potential energy for a 50 nm Au nanosphere pro-duced in Mode 1 and 2 of this cavity when 1 mW (maximum power available inour experimental setup) of continuous laser power is injected into the input channelwaveguide. This low laser power prevents photo-damaging of the trapped nanopar-ticles as often happens in more common laser tweezers.For stable trapping, a potential depth of at least 10kBT is needed [9, 29, 68],where kB is the Boltzman constant and T is the temperature (here assumed to be300 Kelvin). As illustrated in Fig. 2.8, the maximum potential depth of Mode 1 is212kBT and for Mode 2 this number is 17kBT . Therefore, even with large losses inthe waveguides and inefficient coupling of this structure, both modes of this cavitytheoretically produce large enough optical force to confine and trap a 50nm Auparticle at mW-level laser power. For Mode 1, this calculation suggests that only410.05 mW of power in the input channel waveguide is required to trap such particles.The main reasons for producing such strong traps at low laser power, peculiar tothese particular PCS cavities, are the small volume of the modes (especially Mode1 of the cavity) and the fact that the high intensity part of the cavity modes isoutside the silicon slab and is therefore directly accessible by nanoparticles in thesolution.Figure 2.8: The optical trapping potential (absolute value) of the SC1 cav-ity (see Fig. 2.4), calculated for Mode 1 (a) and Mode 2 (b) on a 50nm diameter Au nanosphere. The injected power in the input channelwaveguide (the top waveguide in Fig. 2.4a) is 1 mW. The unit of thecolorbar is in kBT .2.3 SC2 StructureAlthough the SC1 design in the previous section has a promising ability to produceenough optical force for trapping 50 nm Au particles, it has low transmission ef-ficiency, which limits the trapping potential of this device especially, for trappingsub-10 nm particles like semiconductor quantum dots. The ability to trap thesesmall light sources precisely at the cavity anti-node would be very useful for build-ing low-threshold single quantum dot lasers[24] or controlling spontaneous emis-sion of single quantum dots for cavity quantum electrodynamics[23]. To increasethe optical trapping forces, an improved PCS cavity-based design, named “SC2”,was created, which is schematically illustrated in Fig. 2.9. The goals in designingSC2 are first to enhance the unloaded cavity Q-factor (hence reduce out-of-planeenergy loss in the cavity region) and then increase the coupling efficiency of dif-ferent parts of the device. All these improvements are performed for Mode 1 of thecavity as its better light confinement produces stronger optical forces compared42to Mode 2. To enhance the PCS cavity Q, some feature sizes in the PCS cavitystructure are modified. And to increase coupling efficiencies for cavity Mode 1,angled coupling in the SC1 design is replaced with a butt-coupling geometry. Ad-ditionally, to further improve the SC1 design, a new grating coupler is includedSC2 devices that offers larger bandwidth and slightly higher transmission. Duringthe design process, it is attempted to avoid partially etching the silicon slab or un-deretching the device undercladding, which keeps the fabrication process simplewith only a single lithography/single etch step.Figure 2.9: Layout of the full SC2 device including the grating couplers,cavity and waveguides. The channel waveguides are curved with radiusof 5 µm.2.3.1 PC Slot Cavity Q Factor Enhancement (SC2 devices)By simulating slot cavities with different sets of cavity hole shifts, it is found thatreducing the shift of the holes increases the Q factor of the unloaded cavity. There-fore, the hole shifts in the SC1 structure get halved to s1 = 6 nm, s2 = 4 nm, s3 = 2nm in SC2 devices. The minimum shift is held at 2 nm for an easier fabricationprocess. Since reducing the hole shift increases cavity effective refractive indexand hence the resonance wavelength of the cavity, we modified the radius of thebackground PC holes as well as the width of the slot to keep the cavity resonancenearly the same as the SC1 cavity. The reason is to keep the resonance in the mid-dle of our laser working range (1520 nm to 1630 nm). The hole radius of the SC2PC is reduced by 10 nm to 150 nm and the pitch of the PC lattice is kept at thesame value of 490 nm. The slot width is 100 nm for this design.43The theoretical Q of Mode 1 of SC2 cavity, when no waveguide is connectedto it, is 18500, as shown in Fig. 2.10. This number is increased compared to the Qof SC1 cavity (9600 for Mode 1), which means less vertical loss in the new cavitydesign.2.3.2 Photonic Crystal Slot (PCS) Waveguide Optimization (SC2device)As discussed in 2.2.3 the losses in the W1 PC waveguides are limiting the transmis-sion of SC1 devices due to vertical losses. Therefore, in SC2 devices, we attemptedto find a better way of loading the cavity. Since Mode 1 is mostly concentrated inthe slot and its shape is basically a perturbed version of the PCS waveguide mode,it is expected that a butt-coupled geometry through the PCS waveguides would bea more efficient way of exciting cavity Mode 1. Therefore in the SC2 design, weexploited the PCS waveguides to couple light into cavity Mode 1.To be able to guide light in PCS waveguides, the nearest row of holes nextto the slot are moved away from the slot in SC2 design. By shifting the nearestrow of holes away from the slot, it is possible to shift down the PCS waveguidemode into the bandgap and transfer light through it. The amount of side-shift isdetermined by considering two factors: i) The group velocity of the mode whichdetermines the scattering loss in the PCS waveguide, ii) the mode profile matchingbetween the PCS waveguide mode and Mode 1 of the cavity which influencesthe coupling strength between the modes. It is found a hole shift of 40 nm is agood compromise of both factors. Larger shifts lead to worse mismatch betweenmode profiles, and smaller shifts result in slow group velocities, which cause higherscattering losses. Figure 2.11 shows the band structure of PCS waveguides (shownin Fig. 2.14 with three different side-shifts for the first row of holes) compared to aW1 PC waveguide. Reducing the amount of hole shifts gives rise to shifting up thePCS waveguide band, which means the cavity resonance (black dashed line) willintersect the PCS waveguide band at its flat end. This shallow slope of the PCSwaveguide mode causes higher scattering losses.44Figure 2.10: [(a)-(b)] The FDTD simulation layout showing the size of thesimulation region (orange rectangle) and the location of y-polarizedelectric dipole source (double-side blue arrow). The yellow crossesare the point time monitors to record the decay of the cavity electricfield in time domain. The radius of the holes is r = 150 nm, the slotwidth is s = 100 nm and the cavity hole shifts are s1 = 6 nm (blackcolor holes), s2 = 4 nm (pink color holes) and s3 = 2 nm (blue colorholes). The Fast Fourier Transform (FFT) of the electric field of mode1 measured by time monitors for SC2 (c) versus SC1 (d) cavity design.The cavity is unloaded and is sitting on BOX layer (3 µm thick SiO2on top of a millimeter thick silicon) and hexane is the upper cladding.The Q-factor of Mode 1 for SC2 cavity design (c) is 18500 while forSC1 cavity design (d) is 9600. The mode volume of Mode 1 in SC2structure is VMode1 = 0.14( λ1nhex )3, while in SC1 structure was VMode1 =0.1( λ1nhex)3.45Figure 2.11: (a) Transmission band structure of the W1 PC waveguide cal-culated using 3D FDTD simulations (PC hole radius of 160 nm). Thesolid black line is the light-line for SiO2 under-cladding and the dashedline is the resonance of mode1 of the initial design (i.e. Fig. 2.10d). (b)Transmission band structure of a PCS waveguide with hole radius of150 nm and slot width of 100 nm. The first row of holes adjacent to theslot are shifted by 15 nm (red), 25 nm (pink), and 40 nm (blue) fromtheir lattice point to lower the waveguide band frequency so that it in-tersects with the cavity mode to guide light in/out of it. Again, the solidblack line is the light-line for SiO2 under-cladding. But the dashed lineis the resonance of mode1 of the improved cavity (i.e. Fig. 2.10c).2.3.3 1D Nanowire to Slot Waveguide Adapter (SC2 device)Since ridge or nanowire waveguides are most often used for routing signals inphotonic circuits, it is important and nontrivial to efficiently couple light from theminto slot-style waveguides. The challenge is rooted in the effective index and modeprofile mismatch between typical nanowire and slot waveguide modes.Several proposed designs for efficient coupling between nanowire and slotwaveguide modes include structures in which tapers delocalize the mode from thenanowire and the evanescent fields are coupled into the slot [117–120]. High trans-mission efficiencies (∼ 97%) have been achieved with tapered structures [117, 118]which are approximately 10 µm in length.46Figure 2.12: (a) The proposed nanowire to slot waveguide structure is out-lined in white along the outer extremities and in black along the slot.The intensity profile at λ = 1550 nm is plotted along the z = 0 planefor a coupler with L= 400 nm, and a= 100 nm and coupling efficiency92%. For positive (negative) a, the slot end is outside (inside) of the ta-pered region. Mode intensity profile is plotted for (b) the fundamentalsilicon nanowire mode, and (c) the lowest order slot waveguide modeat λ = 1550 nm.Here, we propose a compact Y-branch nanowire-to-slot waveguide coupler thathas smaller footprint (< 500 nm in length) and has > 90% efficiency for bothforward and reciprocal coupling, both in air and solvent, over a bandwidth of∼ 200nm.The structure shown in Fig.2.12 is designed to efficiently couple light betweenthe fundamental transverse electric (TE) mode of a 500 nm wide nanowire waveg-uide (this is wider than 450nm, which is used in SC1 devices, to increase the cou-pling efficiency to the slot waveguide) in a 220 nm silicon slab and the lowest orderTE slot waveguide mode of two 350 nm wide dielectric slabs, separated by an 80nm wide slot. The silicon nanowire is linearly expanded over length L out to the47Figure 2.13: The transmission is plotted as a function of (a) the couplerlength L (with a = 100 nm), and (b) the position of the slot end a(with L = 400 nm), for λ = 1550 nm.two dielectric slabs. The slot is truncated with a circular end cap, positioned adistance a away from the slot waveguide end. The silicon slab lies on top of sili-con dioxide, and is immersed in either air or hexane with refractive index 1.365 at1.55 µm.The structure is studied using FDTD simulations. The nanowire TE-polarizedmode is launched and the transmission through the cross-section of the slot waveg-uide is monitored. To determine the coupling efficiency of light into the lowest or-der slot waveguide mode, the overlap integral between the transmitted field and theslot mode profile is calculated. The nanowire and slot waveguide mode intensityprofiles in the cross-section plane are plotted in Fig. 2.12(b) and (c), respectively.The width of the two dielectric slabs of the slot waveguide are chosen such thatlight is primarily coupled into the mode shown in Fig. 2.12(c), and there is minimalcoupling to other slot waveguide modes, which have lower concentration of lightin the slot region.The structure is optimized based on the transmission from the nanowire to theslot waveguide, as measured by the monitor. Figure 2.13(a) shows that the trans-mission varies slowly as a function of the taper length for L = 200 to 700 nm anda= 100 nm. A coupler length of 400 nm yields a transmission efficiency of > 94%,48Figure 2.14: [(a)-(b)] The simulation layout of the optimized PCS waveguidein SC2 structure that offers higher transmission efficiency (no cavityexists in this simulation). The colored holes (other than yellow andwhite holes) have been modified to reduce insertion loss. The radiusof the holes (r) and their distance from slot center (y) are optimizedusing FDTD simulations. For black holes r = 120 nm, y = 570 nm,blue holes r = 120 nm, y = 450 nm, pink holes r = 128 nm, y = 526nm, green holes r = 190 nm, y = 950 nm, and red holes r = 180 nm,y = 890 nm. The rest of the nearest holes to the slot are shifted awayfrom the slot by 40 nm with respect to their lattice point to make thePCS waveguide. All holes on the edge of the silicon slab will show upas half circles after fabrication (see Fig. 3.4d-e). The refractive indexof these holes is the same as the background refractive index (nhex),therefore having full holes on the silicon edge instead of half-holesdoes not change the simulation results.and offers a desirable balance between efficiency and footprint. The transmissionis further investigated by adjusting the position of the slot end, a, as plotted inFig. 2.13(b). The transmission for a coupler that is 500 nm long (L = 400 nm anda = 100 nm) is 94%, and the coupling efficiency of light into the lowest order slotwaveguide mode is 92% at λ = 1550 nm. The reciprocal coupling efficiency, forlight propagation from the slot waveguide mode to the nanowire waveguide modeis also found to be 92% for the same coupler design. To simulate a solvent environ-ment, as might be used in sensing or trapping applications, the background indexof refraction, n, was changed from air to hexane (n = 1.365) and the new coupling49efficiency at 1550 nm is found to be 94%. The coupling efficiency is found to be> 90%, over a 200 nm bandwidth centered at λ = 1550 nm, for both forward andreciprocal couplings in air and hexane.To reduce the insertion loss from this adapter to the PCS waveguide in SC2structure, the slot width of the Y-branch is increased to 90 nm and the y-coordinateand radius of 10 PCS waveguide holes (Fig. 2.14) have been modified. The radiiand y-coordinates are optimized using FDTD simulations. The optimization of theradii and y-coordinates of the holes are done for one hole at a time to reduce thesimulation time and the structure is symmetrical across the slot. The 3D FDTDsimulation time for optimizing multiple design parameters has power-law depen-dence on the number of parameters to be optimized. Therefore, it is not practicalto optimize the radius of all PCS waveguide holes simultaneously to find the least-power-dissipating design. As illustrated in Fig. 2.14, the order of optimization isblack, blue, pink, green and finally red color holes.Figure 2.15 shows the transmission efficiency of the optimized structure (a) is14% higher compared with the case without any hole radii and location changes(b). More importantly, the transmission of the optimized structure (a) is signif-icantly improved as opposed to the structure without the Y-branch adapter andhole modifications (c). The PCS waveguide transmission at the cavity resonanceis increased from 19% to 59% indicating the benefit of Y-branch adapter and holemodifications. It is important to note that to obtain higher transmission efficiencyin the optimized structure, the slot in the Y-branch is not connected to the slot inPC. A distance of 1 pitch (490 nm) was found to offer highest transmission.Comparing this waveguide-only (no cavity) net transmission of 59% with thatobtained in the corresponding SC1 design (Fig. 2.6), there is no net benefit. Thereason is the difference of the adapting parts in the two designs. The improvementin the PCS waveguide transmission gets hindered by the lower transmission effi-ciency between the Y-branch adapter and PCS waveguide. Therefore, there is stillno real advantage in the transmission efficiency of the waveguides in SC2 geome-try. The real advantage in this SC2 configuration described in the next sub-section,when the transmission of the whole SC2 structure (waveguides plus cavity) is sim-ulated.50Figure 2.15: (a) Simulated transmission (blue), reflection (red) spectra, andthe sum of them (black) calculated at the input and output channelwaveguides of the structure in Fig. 2.14. (b) Simulated transmission(blue), reflection (red) spectra, and the sum of them (black) for thesame structure without modification of the radii and location of the10 holes at the entrance and the exit of PCS waveguide. (c) Simu-lated transmission (blue), reflection (red) spectra, and the sum of them(black) for the same structure as (b) without the Y-branch. The blackdashed-line in these three figures is the resonance of Mode 1 of themodified cavity (Fig. 2.10c). The transmission of the improved struc-ture in (a) at the cavity resonance is increased from 19% to 59% byusing the Y-branch adapter and modifying the holes.51Figure 2.16: [(a)-(b)] Simulation layout for optimized SC2 PCS cavity. Theholes in the PCS waveguide region have the same size and location asFig. 2.14. There are 10 un-shifted holes in between the PCS waveg-uides and the cavity region (blue color holes at the center). The cavityhole shifts are s1 = 6 nm, s2 = 4 nm, s3 = 2 nm. The hole radiusfor the regular PC holes is 150 nm. Slot width is 100 nm and the Y-branch adapting part between the single mode and PCS waveguide isexplained in Fig. 2.12 except for the change of slot width to 90 nm. (c)The transmission efficiency of the full SC2 structure calculated usingpower monitor at the output channel waveguide. The Q of this loadedcavity is 8400 and its maximum transmission (although not completelyresolved) is 17.5%.522.3.4 SC2 Device Performance DiscussionFigure 2.16c shows the transmission efficiency of the SC2 structure including thecavity. This plot tells the real advantage of the butt-coupling structure over theoriginal SC1 design (i.e. Fig. 2.4), which is due to better coupling between thePCS waveguides and the cavity mode. The peak transmission efficiency of SC2 inFig. 2.16c is 17.5%. Considering the loaded and unloaded Q factor of SC2 cav-ity design, the transmission through the cavity is approximately T = (QU−QLQU )2 =( 18500−840018500 )2 = 30%. Therefore, knowing the efficiency of the waveguides in SC2design (i.e. 59%), one can estimate the coupling efficiency from the PCS waveg-uides to the cavity. This number for SC2 design is√17.5%30%×59% = 98%, which meansonly 2 percent of the power that reached the end of the input PCS waveguide is dis-sipated and reflected in the coupling region between the input PCS waveguide andthe cavity. This number is significantly lower compared to the 23% lost in eachof the coupling holes of SC1 design, which confirms the effectiveness of the butt-coupled geometry. Both the cavity Q factor and the transmission peak have beenenhanced for the SC2 design and the optical trapping potential profile of the SC2cavity illustrated in Fig. 2.17 quantifies the improvement in the trapping ability ofthis design.Figure 2.17: (a) The trapping potential calculated for Mode 1 of SC2 cavity inFig. 2.16 on a 50 nm diameter Au nanosphere. (b) The optical trappingpotential of mode 1 of SC1 cavity design described in Fig. 2.4 on a 50nm diameter Au nanosphere. The injected power in the input channelwaveguide for both figures is 1 mW and the unit of the colorbar is inkBT .532.3.5 1D Grating Coupler (SC2 device)To slightly increase the amount of coupled power into the PCS cavity, a new 1Dgrating coupler has been designed for the SC2 structure using the optimizationmethod described in [121, 122], which has three benefits: 1) because of its 1Dstructure, its optimization can be done using 2D FDTD simulations, which aremuch faster than full 3D simulations, 2) it gives rise to a few percent higher trans-mission efficiency and 3) its operation bandwidth is larger than the SC1 gratingcoupler design, which is useful for some applications. The optimized parametersand the corresponding transmission spectra are shown in Fig. 2.18.Figure 2.18: (a) 2D FDTD simulation layout for optimization of 1D double-tooth grating coupler. Instead of having partly etched trenches, adouble-tooth geometry is chosen for easier fabrication. The optimiza-tion parameters are the teeth spacing (t), the period (a) and trenchwidth (w). All three parameters are optimized at the same time withinreasonable amount of simulation time. (b)The optimized values aret = 192 nm, a = 800 nm, w = 114 nm as shown in the figure.2.4 ConclusionIn conclusion, we have reported the design of two different silicon-based photonicintegrated circuits (SC1 and SC2) consisting of a PCS cavity, waveguides and grat-ing couplers, operating at telecommunication wavelengths in a fluidic medium.The structure was designed to offer a robust means to enhance electric field in-tensity and hence light-matter interactions at a precise location inside a fluidicmedium, while minimizing fabrication complexity and maximizing ease-of-use.54Figure 2.19: (a) Final optimized double-tooth grating design (for SC2 de-vices) connected to a tapered waveguide. The grating area is 20 µm× 20 µm. (b) The transmission efficiency of optimized double-toothdesign from a Gaussian focused source to the beginning of the taperedwaveguide (blue). The peak transmission value is 52% and FWHM is75 nm. The excitation angle with normal to silicon surface is 18◦.The transmission from tapered waveguide to the channel waveguide isshown in the black curve. Dividing the two curves gives the transmis-sion efficiency of the waveguides that is improved compared to the redcurve in Fig. 2.3c thanks to better wavefront shape matching betweenthe double-tooth grating and the waveguides.3D FDTD simulations demonstrate that such circuits, exhibit Q factors > 7500and mode volumes as small as V ∼ 0.1(λn)3, with resonant transmission as highas T ∼ 17% (from input channel waveguide to output channel waveguide), whenoperated in hexane. These structures theoretically have the ability to easily trap50 nm Au particles with modest coupled power of 1 mW (the maximum powerour laser can deliver) in the channel waveguide. In fact, for the improved SC2design, Mode 1 produces theoretically provides the required 10kBT trapping po-tential for particles as small as 15 nm in diameter with just 1 mW of coupled laserpower. A summary of the performance of the two designed devices are presentedin Table 2.1.The SC2 design shows improved performance, compared to the SC1 structure,55Table 2.1: Summary of the transmission efficiency of different parts of SC1and SC2 designs for the Mode1 of the PCS cavity. The second columnshows the peak transmission efficiency of grating couplers. The thirdcolumn is showing the FWHM of the grating couplers. The fourth col-umn summarizes the transmission of the reference devices in Fig. 2.6 andFig. 2.14. The fifth column is the coupling efficiency from the end of theinput PC(S) waveguides into the PCS cavities.DesignnameGC peaktrans-mission(%)GCFWHM(nm)Channel toPC/PCS tochannel WGtransmission(%)PC/PCSWG tocavitytrans-mission(%)UnloadedQLoadedQSC1 50 50 67 77 9600 7400SC2 52 75 59 98 18500 8400thanks to its butt-coupled geometry and higher Q factor. The main advantage of thebutt-coupled geometry is the better matching between the mode profiles of the PCSwaveguides and the cavity. It is possible to further improve light confinement inthese structures by modifying the PCS cavity structures. For example, by shiftingmore than 3 rings of holes around the cavity center and optimizing their sizes andlocations, it is possible to create more gradual perturbation to the PCS waveguidemodes thus causing less vertical loss in the cavity. Also, if the fabrication limitationallows it, reducing the slot width causes more field-enhancement in the slot asdiscussed in [112] and [21].56Chapter 3Device Characterization AndSensing Application3.1 IntroductionThe first part of this Chapter describes the photonic chip layouts, chip fabricationprocess and the transmission set-up used for measuring the transmission of devicesdetailed in Chapter 2. This is followed by a comparison of the experimental andsimulated transmission spectra of a few fabricated devices.3.2 Chip LayoutThe chip layouts for fabricating photonic chips are generated using Mentor Graph-ics software and exported in “.gds” format to University of Washington Micro-fabrication Facility, a member of the NSF National Nanotechnology InfrastructureNetwork [4], for fabrication. In the following two sub-Sections, the layout of twochips, on which all measurements in this thesis are done, is described in detail.In creating layout files, different device feature sizes are bracketed over a certainrange. This design strategy guarantees that despite the unavoidable fabricationimperfections, at least a few devices will possess the expected feature sizes andoperate as expected. The first chip layout is based on the SC1 device described inChapter 2 and the second chip layout contains SC2 structures.57Table 3.1: The feature sizes for SC1 devices that are used in chip EB312layout.Grating coupler PC hole slot width (nm) coupling holehole radius (nm) radius (nm) radius (nm)230,250,270 150,160,170 70,90,100 80,110,1403.2.1 Chip EB312 Layout (SC1 design)In the chip layout demonstrated in Fig. 3.1, the grating couplers are similar to theones illustrated in Fig. 2.3 (i.e. with 795 nm and 750 nm pitches along x and yaxis) and the cavity structure is similar to Fig. 2.4 (i.e. with pitch size of 490 nm).The four bracketed features that are varied across this chip layout are summarizedin Table 3.1.These features each have 3 different possible values, resulting in a total of34 = 81 devices for this chip layout. These 81 devices are grouped into 9 arraysof 3× 3 devices with each given a row and a column label. The devices in eachof these 9 groups have the same radius for grating coupler and photonic crystalcavity holes. In each group of 9 devices, the slot width and coupling hole radiusvary along that group’s column and row device axes, respectively (see Fig. 3.1).Going from one group of devices to another, the grating coupler hole radius variesalong the group row axis while the PC hole radius varies along the group columnaxis. The group row and column number are located on the left side of each group(see Fig. 3.1b-d). The labels are formed from two column of squares; the numberof squares in the left column specifies the group row number while the number ofsquares in the right column specifies the group column number. For example, thelabel of the group shown in Fig. 3.1c is row 4 and column 1. In this thesis eachspecific device is referred to in the following format; “chip name + R + grouprow number + C + group column number + (device row number, device columnnumber)”. For example the device in the top-left corner of the group shown inFig. 3.1c is referred to as “EB312R4C1(3,1)” and the device just below it is referredas “EB312R4C1(2,1)”.Other than the 9 groups of devices described above, the chip also includes3 groups of reference devices that were designed for measuring the waveguide58Figure 3.1: (a) Layout of the Chip EB312 based on SC1 designed describedin Chapter 2. There are 12 groups of 3×3 devices on this chip. The rowand column label of each group is located on the left side of the group.(b) Group EB312R2C2 consists of devices that are full SC1 structures.(c) Group EB312R4C1 consists of devices with no photonic crystal inbetween the channel waveguides. (d) Group EB312R4C2 consists ofdevices that have only grating couplers, tapered, channel and photoniccrystal waveguides without any PCS cavity in between them.59transmission efficiencies (i.e. no PCS cavities exist in these devices). GroupEB312R4C1 (Fig. 3.1c) contains devices with only a channel waveguide betweentwo tapered waveguides. The grating coupler hole radius varies along the de-vice row axis but there are no features bracketed along the device column axisof this group. The other two groups EB312R4C2 and EB312R4C3 are identical(see Fig. 3.1d) and each of them consists of 9 devices each with a W1 photoniccrystal waveguide but without the usual cavity in the middle. In these two groups,the grating coupler hole radius varies along the device row axis and the photoniccrystal hole radius varies along the device column axis. The length of the photoniccrystal waveguides are identical to the length of input plus output photonic crystalwaveguide in a full SC1 device.3.2.2 Chip EB485 Layout (SC2 design)This chip (Fig. 3.2) is based on the improved SC2 design described in Chapter 2.Since the double-tooth grating coupler is periodic in one-dimension (1D), it can besimulated with relatively good accuracy in 2D FDTD simulations, which are veryshort. Therefore, optimizing this structure to find best performance can be donequickly. As a result, instead of bracketing over all 3 feature sizes of this gratingcoupler (i.e. period (a), tooth spacing (t) and tooth width (w)), which requires fab-ricating many devices and increased fabrication costs, all three parameters wereoptimized at the same time to find 3 grating designs that operate with 3 differentcentral frequencies. Using FDTD simulations and following the same steps as de-scribed in Chapter 2, all three grating parameters are simultaneously varied for op-timized operation at three wavelengths of 1550 nm, 1575 nm and 1600 nm. Thesewavelengths are selected based on previous fabricated devices that demonstratedthat fabrication imperfections (mainly in the size of the grating coupler featureslike hole diameter, etc.) may cause up to a 40 nm mismatch between the centralwavelengths of simulated and fabricated grating couplers. Therefore, these threedifferent grating designs maximizes the likelihood that at least one set of gratingparameters would work in the range of the excitation laser (1520 nm - 1630 nm).The incident laser angle with the normal of the grating coupler plane is kept at 18◦in designing all three gratings.60Figure 3.2: (a) Layout of the Chip EB485. There are 6 groups of 19 deviceson this chip. In each group there are 12 SC2 devices along with 7 refer-ence devices that do not have cavity in them to let us test the efficiencyof other elements of SC2 photonic circuit. (b) Zoomed out layout ofgroup EB485R2C2. The 4 squares on the right side of the devices areshowing the label of the group. (c) The layout of the first 3 devices ofgroup EB485R2C2, which show two reference devices for measuringthe transmission of the grating couplers and waveguides and one fullSC2 device that include PCS cavity.61Table 3.2: The feature sizes for SC2 devices that are used in chip EB485layout.Double-tooth grating PC hole Slot width PCS waveguidecoupler parameters (nm) radius (nm) (nm) length (pitch)a t w793 204 124 140,150,160 90,100 9,10800 192 114803 223 120The grating parameters and three other bracketed features corresponding to thecavity region are shown in Table 3.2. The 3 grating coupler designs, 3 photoniccrystal hole radii, 2 slot widths and 2 different lengths of PCS waveguides yield36 devices in the chip layout. For the devices with photonic crystal hole radiusof 150nm, the radii of the modified holes at the entrance of the PCS waveguidesare the same as described in Fig. 2.14. However, when the radius of the regularphotonic crystal holes changes to 140 nm or 160 nm, the modified hole radii varywith the same relative percentage change. Similarly, when the slot width is 100nm, the width of the slot in the Y-branch is 90 nm (see Fig. 2.16) but when the slotwidth changes by 10% to 90 nm the Y-branch slot width changes with the samepercentage amount to 81 nm. Since the total length of the photonic crystal latticeis kept fixed, by changing the PCS waveguide length, the distance between the endof the PCS waveguides and the cavity varies. This allows control of the couplingbetween the cavity and PCS waveguides which determines the loaded cavity Qfactor.Figure 3.2 shows that Chip EB485 has 6 groups with 19 devices in each ofthem. Each group is identified with a label that shows its group row and columnnumber (similar to EB312 chip). The right and left half of chip EB485 are identical.Devices in one group have the same grating coupler parameters and these parame-ters vary from one group to the other. Each specific device on this chip has a namein the format “chip name + R + group row number + C + group column number +n + device number counted from bottom of a group”. For instance, the third devicefrom the bottom of the group shown in Fig. 3.2b, is named “EB485R2C2n3”.The first device in each group (i.e. device n1) does not have a photonic crystal62and is for measuring the transmission efficiency of the grating couplers and taperedand channel waveguides. There are another 6 reference devices in each group (n2,n5, n8, n11, n14, n17) that do not have any cavity in between PCS waveguidesfor measuring the PCS waveguide transmission efficiency. Devices n2, n5 and n8in each group have similar slot width (90 nm) but different photonic crystal holeradii. Similarly, devices n11, n14 and n17 have the same slot width (100 nm) butvarying photonic crystal hole radius. In between each of these 6 reference devices,two full devices (i.e. devices that have cavities) exist which have identical featuresizes except for the length of their PCS waveguides. The common feature sizes ofthese two full devices are identical to the reference device (i.e. the device with aPCS waveguide by no cavity) underneath them. For example, devices n3 and n4have the same slot width and photonic crystal hole radius as device n2 and in thesame way devices n6 and n7 have the same slot width and photonic crystal holeradius as reference device n5. To summarize, in total each group has 12 full SC2devices, which, along with the other 2 groups in their column, account for all 36combinations of feature sizes.3.2.3 FabricationThe photonic chips are fabricated [4] using a 100 keV JEOL JBX-6300FS electronbeam writing system. ZEP-520A resist (Nippon-Zeon Co. Ltd.) for chip EB312and hydrogen silsesquioxane resist (HSQ, Dow-Corning XP-1541-006) resist forchip EB485 served as the etch mask. It is absolutely crucial to set the shot pitch[4]for the electron beam lithography at most equal to the minimum hole shift in thecavity region ( i.e. 4 nm for SC1 design and 2 nm for SC2 design). Otherwise thecavity will not appear in the final fabricated photonic crystal. The beam currentfor patterning these chips is 1 nA. Etching was done using an Oxford PlasmaLabSystem 100 with chlorine gas. The complete circuit requires only one lithographystep and one etch step.Figure 3.3 shows the grating coupler and cavity region of a SC1 device on chipEB312 (layout in Fig. 3.1), while Fig. 3.4 shows some of the devices that were fab-ricated on chip EB485 with the layout shown in Fig. 3.2. The radius of the photoniccrystal holes are within 7 nm of the designed values. Before using the fabricated63chips, they are rinsed with various organic solvents (acetone, methanol and iso-propanol (IPA)) to remove any leftover resist residue from their surface. If someresist remains after rinsing, the chips can be illuminated with UV light for a fewminutes and then rinsed with acetone to completely remove them. Thereafter, it isoften necessary to clean the chip again to ensure optimal operation especially afterexperiments where the chip surface is exposed to sources of organics and nanopar-ticles (i.e. after trapping experiments). Depending on the experiment, more aggres-sive cleaning processes are needed such as Piranha 1 and Aqua Regia 2. Piranha isrequired for cleaning heavy organic contamination and Aqua Regia is necessary fordissolving Au particles. Although it is possible to remove organic contaminationwith the less aggressive “RCA” cleaning method 3, due to the fact that RCA resultsin oxidization of the silicon slab which can blue-shift cavity resonances by up toabout ∼ 7 nm, a combination of Piranha and Aqua Regia (less than a nanometerblue shift for each run) is recommended instead.3.3 Measurement Setup3.3.1 Liquid CellTo perform measurements in a highly volatile fluidic medium, a leak-free demount-able liquid cell (Harrick Scientific Products 4) (Fig. 3.5) is used to immerse thesilicon chip in solution. Specifically, hexane is more challenging to use than other1For Piranha etch, H2SO4 is slowly mixed into H2O2 with 5 : 1 ratio in a glass container. Thecontainer is placed on a hotplate until its temperature reaches 100◦C. Then the chips are placedinto the solution with a pair of Teflon or stainless steel tweezers for 15 minutes, maintaining thetemperature between 100◦C and 110◦C. Once finished, the container is removed from the hotplateand the chip is removed and rinsed with Deionized Water (DI) water. Piranha etch is an extremelydangerous process and needs proper training and safety equipment to perform.2After Piranha etch, if the sample was used for trapping with Au particles, the Aqua Regia processis necessary to clean the Au particles stuck on the chip surface. The Aqua Regia preparation involvesmixing two strong acids; nitric acid (HNO3) into hydrochloric acid (HCl) with 1 : 3 molar ratio.The reaction is very exothermic and produces poisonous vapors which require proper ventilation andstrict safety protocols during usage. Chips covered with Au nanoparticles are soaked in Aqua Regiafor 5 seconds and rinsed with DI water afterwards. It is important to not leave the chip in Aqua Regiafor more than a few seconds to minimize silicon oxidization which will affect the performance of thedevices on the chips.3http://www.nanofab.ubc.ca/processes/cleaning/rca-1-si-wafer-cleaning/4http://www.harricksci.com/ftir/accessories/group/Demountable-Liquid-Cells64Figure 3.3: SEM image of a fabricated (a) grating and [(b)-(c)] cavity on chipEB312. Blackened areas are due to electron-beam-induced carbon de-position on the chip during SEM imaging.solvents because it is highly volatile and also much more reactive to different typesof sealant (like tapes, vacuum grease, rubber cement, etc.). Therefore, using thetypical glass cuvettes with loose fitting Teflon caps was neither appropriate nor safefor optical measurements of the chip in solvents like hexane. Figure 3.5b shows alldifferent parts of the liquid cell used for the measurements presented in this thesis.The photonic chips are placed in between the quartz windows, where two 1 mmspacers are located to create a small volume for immersing the chip in solution.Another benefit of that liquid cell is the possibility of doing experiments in a flowcondition by connecting Teflon tubes and syringes to the cell. This setup would en-able measurements with time-varying concentration of nanoparticles in the future.Using the same cleaning procedure as above, the glass windows and the caps ofthis cell are cleaned after each round of experiments that result in contamination.65Figure 3.4: (a) SEM image of the fabricated chip EB485 [4]. (b) Picture ofa full SC2 device, (c) a device without a cavity in between PCS waveg-uides, [(d)-(e)] adapting parts and (f) a double-tooth grating coupler.3.3.2 Transmission SetupThe experimental setup, which was mainly built by Ellen Schelew [22] for devicetransmission measurements, is shown in Fig. 3.6. The chips containing devicesare placed inside the liquid cell and the cell is mounted on top of a rotation stage.The position of the cell is adjusted using x-y translational stages to place it at thecenter of the rotation stage. The devices are excited using a tunable diode laser(Newport TLB-6600 Venturi) with the wavelength range of 1520 nm to 1630 nmand a maximum power of 9.5 mW. The laser source is guided through an opticalfiber (blue line in Fig. 3.6) into an optical system consisting of a polarizer and a5http://www.harricksci.com/ftir/accessories/group/Demountable-Liquid-Cells66Figure 3.5: The structure of the liquid cell (Harrick Scientific Products 5)used for immersing the chips in a liquid medium (reprinted from manu-facturer’s website), composed of a pair of quartz glass window separatedby two half-ring Teflon spacers between which the photonic SOI chip isplaced during measurements. Once assembled the volume between thewindows is filled with solution.set of lenses that focuses laser light on the devices in the cell. The optical systemis also sitting on a concentric rotation stage. This rotation stage along with thecell’s own rotation stage enable us to control the angle between the incident andtransmitted beam. The focused laser light is incident on the input grating coupler ofa device and the transmitted light gets out-coupled from the output grating couplertoward an elliptical mirror that focuses the output light on its second focal point,where an InGaAs photodiode power meter ( Model 818-IG from Newport Inc.)is located. The power meter can be swapped with a ElectroPhysics Microviewer(Model 7290A) CCD camera for imaging and alignment purposes. The reflectedlight from the elliptical mirror is redirected using a second flat mirror and passed67through a cross-polarized polarizer that filters the unwanted scattered light fromchip surface. The elliptical mirror has focal lengths of 15 cm and 150 cm, whichresults in 10× magnification. The devices are at the first focus (15 cm distance) ofthe elliptical mirror and the magnified image of the devices, which is formed on aCCD camera, is at the second focus (150 cm distance). The light path is shown byorange dashed lines in Fig. 3.6. A Labview [123] program operates the laser andrecords the data via a General Purpose Interface Bus (GPIB) controller from thepower meter. For measuring transmission spectra, it sweeps (rate of 100 nm/s) thelaser through a 10 nm range of wavelengths and upon receiving the trigger signalfrom the laser, which indicates the start of the sweep, the program starts recordingoutput of the power meter (sampling rate of 10 kHz)to create the transmissionspectra.3.4 Experimental CharacterizationAfter receiving the fabricated chips, the transmission efficiencies of different de-vices were measured. The results of the transmission measurements are summa-rized in the next two sub-Sections. The first sub-Section summarizes measure-ments corresponding to devices on chip EB312 which are based on the SC1 designwhile the following sub-Section details the chip EB485 measurements which arebased on the SC2 design. All of the experimental characterization in this Sectionwas performed when the chips were immersed in pure hexane.3.4.1 Chip EB312 MeasurementsThe first test for a newly fabricated chip is measuring the transmission spectra ofdevices with no photonic crystal in between grating couplers. This step determineswhether the grating couplers are operating in the laser range or not. Figure 3.7shows measurement of three nominally identical devices versus the simulation re-sult. It is clear that the three devices are performing similarly in terms of peaktransmission, central wavelength and bandwidth. But the agreement between sim-ulation and experiment is poor as demonstrated by the∼ 35 nm difference betweenthe simulated and measured central wavelength. This suggests that systematic sizedifferences exist between the fabricated grating couplers and their original design.68Figure 3.6: The top-view of the experimental setup used for transmissionmeasurements and optical trapping experiments. The rotation stagesallow the angle between the incident light and the surface of the chip tobe varied, which is necessary for optimal coupling to grating couplersat different wavelengths. The excitation optics include a polarizer andtwo plano-convex lenses held in a lens tube. One of the lens collimatesthe laser beam coming out of a single mode optical fiber (blue line inthe figure) and the second lens focuses it on the chip. This one-to-onefocusing system results in focusing the laser light to the same size asthe beam at the output of the single mode optical fiber (∼ 10 µm).Thedetailed description of this experimental setup is explained in Ref. [22].69After measuring hole radius of some of the fabricated grating couplers using SEMimages, it was discovered that the grating couplers radii are ∼ 15 nm smaller thanthe designed values. This is consistent with a subsequent FDTD simulation of agrating coupler with 15 nm smaller radius, which shows a 40 nm red shift in thecentral wavelength of grating coupler spectra (Fig. 3.7b).Figure 3.7: (a) Simulation (black) versus experimental transmission effi-ciency of device EB312R4C1(2,1) (green), EB312R4C1(2,2) (blue),EB312R4C1(2,3) (red). These transmission are from input grating cou-pler to output grating coupler through the channel waveguide. The in-cident angle of the laser with the grating surface normal is 18◦ for bothsimulation and experiment. (b) Black curve is the same curve as in (a)and the blue curve is the simulated transmission spectra when the radiusof the grating holes is reduced by 15 nm to 135 nm.The Fabry-Perot reflections between input and output grating couplers create aperiodic modulation of the transmission spectra which can be seen as fluctuationsat the transmission peak in Fig. 3.7. The period of these fluctuations is ∼ 0.5 nm,which agrees very well with the ∼ 650 µm distance from input to output gratingcoupler. Also, the amplitude of these Fabry-Perot fringes is small relative to thepeak of the transmission spectra, which is advantageous for having fairly uniformtransmission values during operation in a short range of wavelengths.The next step in characterization of the chip is measuring the transmission70Figure 3.8: (a) The experimental transmission spectra of two nominally iden-tical devices that have photonic crystal W1 waveguide without any cav-ity in between them. The blue curve is for the device EB312R4C2(2,2)while the red is for EB312R4C3(2,2). These transmission values arefor the full devices (i.e. grating couplers and photonic crystal waveg-uides). (b) Simulation (black) versus experimental transmission spectra(blue and red) from input channel waveguide through the photonic crys-tal W1 waveguide to the output channel waveguide. These experimentalcurves are the result of dividing transmissions in (a) by the transmissionof device EB312R4C1(2,1) (green curve in Fig. 3.7).spectra of devices with a photonic crystal W1 waveguide but no cavity in them.Figure 3.8 (a) shows two experimental transmission spectra of this type of device,which are performing similarly. By dividing the transmission of these devices bythe transmission of devices in Fig. 3.7, the performance of the photonic crystal W1waveguides can be studied separately. When the spectra are divided, the FabryPerot fringes in the spectra of the grating coupler reference devices is filtered outso the only the Fabry Perot effect of the photonic crystal waveguide devices is in-cluded in the division result. Figure 3.8 (b) shows that the fabricated devices are∼ 20% less efficient compared to what the FDTD simulation predicted and sug-gests some size differences exist between fabricated and designed features. SEMimages of the photonic crystal holes in this chip confirm that the fabricated devices71Figure 3.9: Resonant transmission spectra from input to output ridge waveg-uides through slot-cavity for device EB312R22(2,2) in Table 3.3. Thesimulation curve is in blue and the experimental curve is in black.have on average 7 nm smaller PC hole radii compared to the designed values.Finally, Fig. 3.9 shows the experimentally measured transmission spectrumthrough a full-structure device (EB312R22(2,2)), in hexane, on an absolute scale(left curve). To make a correspondence with simulated transmission from in-put ridge waveguide to output ridge waveguide (through the cavity), these cavitytransmission spectra are normalized by the transmission measured through iden-tical reference devices where the entire PC region is replaced by a simple con-tinuation of the ridge waveguide (i.e. devices in Fig. 3.7). The agreement be-tween the experimental and simulated spectrum for this device is one of the bestamong all measured full device on this chip. Table 3.3, summarizes the measuredand simulated parameters for 5 different full-structure devices (absolute trans-mission data only for 3 of the 5). Devices EB312R22(1,2), EB312R22(2,2) andEB312R22(3,2) differ only in the radius of the coupling hole. Both EB312R22(1,2)and EB312R22(2,2) yield good agreement with the simulations, while all parame-ters for device EB312R22(3,2) are noticeably different, indicating the presence offabrication imperfections. EB312R22(2,2), EB312R22(2,1) and EB312R22(2,3)differ only in the width of the slot, and the predicted shift and change in Q valueare in good agreement between experiment and simulation.72Table 3.3: Summary of the results from simulations and transmission mea-surements on 5 different devices. All of these devices are on chip EB312.The transmission values are from input channel waveguide to outputchannel waveguide. rc is the nominal radius of the coupling hole at theend of W1 photonic crystal waveguides that controls the coupling of thewaveguides to the cavities. s is the nominal width of the slot waveguide.Device s(nm) rc(nm) Simulation Experimentλ(nm)Q T (%) λ(nm)Q T (%)R22(1,2) 90 80 1567.8 5640 4.8 1564.3 3800 3.1 ±0.4R22(2,2) 90 110 1567.8 7390 2.1 1563.9 6100 2.3 ±0.3R22(3,2) 90 140 1567.8 8480 0.49 1564.8 4400 0.29±0.08R22(2,1) 80 110 1596 8900 – 1595.4 7650 –R22(2,3) 100 110 1535.4 4720 – 1545.2 4400 –These Q values are higher than those reported for cavities operating in solventsin Refs. [101, 114, 124] despite not having removed the silicon dioxide under-cladding. Simulations suggest that by undercutting these cavities, the intrinsic(i.e. stand-alone, unloaded) Q value of the cavity in hexane should increase from10× 103 to 25× 103 as compared to the hexane-over-SiO2 structure studied here.As discussed in detail in Section2.2.3, the transmission values are limited partiallyby the fact that the W1 photonic crystal waveguide modes lie above the light linein these samples, and because the single-variable-hole coupler between the W1waveguide and the slot waveguide causes excess scattering.3.4.2 Chip EB485 CharacterizationChip EB485 consists of the improved SC2 structures and its characterization resultsare presented in this sub-Section. Similar to the previous chip, characterizationstarts with devices that only possess grating couplers and waveguides. Figure 3.10shows the measurement for device EB485R2C2n1 versus the FDTD simulation73result. In this device the photonic crystal section is replaced with a channel waveg-uide to test the performance of the grating couplers and the tapered and channelwaveguides. It is clear that this device is performing differently than the simula-tions due to differences between the fabricated and designed feature sizes. Thereis ∼ 20 nm difference between the central wavelength of the simulated spectra ascompared with the experimental result and the peak transmission value is smallerby 50% in the fabricated device. However, the experimental peak transmissionvalue of this double-tooth design is nearly 3 times higher than the previous grat-ing design (Fig. 3.7), while keeping the Fabry-Perot reflection amplitude relativelysmall. Also, because the separation between input and output grating couplers issimilar to SC1 device types, the Fabry-Perot fringes have similar wavelength spac-ing.Figure 3.10: Simulation (blue) versus experimental (black) transmissionfrom input grating coupler to output grating coupler through channelwaveguide, for device EB485R2C2n1. The incident angle is 18°.Next, devices with grating couplers, slab waveguides and PCS waveguideswithout cavities are tested. In Fig. 3.11, the performance of the PCS waveguideis tested. The overall shape of the measured spectra is in good agreement withthe expected simulation result, however it is shifted by ∼ 13 nm, again due to dif-ferences between the fabricated and designed feature sizes. Although the double-branch adapter dissipates power in the butt-coupled configuration (see Chapter 2),74because of lower losses in the PCS waveguide the overall experimental transmis-sion of the butt-coupled PCS waveguide is slightly improved compared with theprevious PC W1 design (Fig. 3.8). This transmission efficiency comparison isbased on the transmission at the cavity resonance wavelengths of Mode 1 of thetwo designs (i.e. Fig. 3.9 for SC1 design and Fig. 3.12a for SC2 design).Figure 3.11: (a) Experimental transmission efficiencies for devicesEBEB485R1C1n1 (black) and EB485R1C1n5 (blue) measuredat 19° incident angle. EB485R1C1n1 is a device with no photoniccrystal region, which allowed the efficiency of the grating couplersto be measured and EB485R1C1n5 includes the PCS waveguide inaddition. By dividing the blue curve by the black one (Fabry Perotoscillations of the black spectrum are filtered out during division),it is possible for us to find the transmission of this PCS waveguide.The result is the black curve in (b). (b) Simulation (blue) versusexperimental (black) transmission from input channel waveguidethrough PCS waveguide to output channel waveguide. The photoniccrystal hole radius is 150 nm and the slot width is 90 nm.Finally, the full SC2 devices with cavities are tested. The transmission of de-vice EB485R1C1n6 is shown in Fig. 3.12a. As can be seen, the resonance of thecavity (the small peak on the low energy side of the spectrum) is very close to theband edge of the PCS waveguide and the peak resonance transmission value of this75device is 6%. This is significantly lower than simulation result (blue curve) andthe resonance is shifted by ∼ 15 nm compared to the simulation. The experimentalspectra have some Fabry-Perot oscillations with periodicity of ∼ 1 nm, which per-fectly matches the distance between PCS cavity and output grating coupler. Theseoscillations do not appear in the simulation result as the simulated structure onlyincludes channel waveguides and the PCS cavity.Despite the fact that the experimental resonance transmission efficiency of thisSC2 device is higher than all SC1 devices in Table 3.3, the expected enhancement(Fig. 2.16c) was not achieved. The reason lies in the amount of side-shift for theholes at the cavity center. The three rings of holes in the SC2 cavity design areshifted by a third of the shifts in the SC1 cavity design. Smaller shifts result in res-onance wavelengths that are very close to the edge of the photonic crystal bandgap.This makes the device performance especially sensitive to the fabrication imperfec-tions in the EB485 chip, as is shown in Fig. 3.12b. This figure shows some devicesfor which the cavity transmission peak is adversely influenced by the imperfec-tions in the fabrication process. This issue affected most of the fabricated devices,which highlights the fabrication challenges for this type of cavity with such smallhole shifts. Due to this limitation, it is recommended to fabricate future deviceswith the same cavities but larger hole shifts while maintaining the butt-coupled ge-ometry to preserve the higher transmission efficiency of the grating couplers andPCS waveguides. More importantly, the PCS waveguide has a major advantage asdiscussed in Chapter 2; its coupling to cavity Mode 1 is better due to the similarityin their mode profiles.3.5 ConclusionIn conclusion, the fabrication and characterization of silicon-based photonic inte-grated circuits consisting of PCS cavities, waveguides and grating couplers, oper-ating at telecommunication wavelengths in a fluidic medium, have been reported.The structures, whose designs are described in the previous Chapter, offer a robustmeans to enhance electric field intensity and hence light-matter interactions at aprecise location inside a fluidic medium, while minimizing fabrication complex-ity and maximizing ease-of-use. Both 3D FDTD simulations and the experimental76Figure 3.12: (a) Resonant transmission spectra from input to output ridgewaveguides through the slot-cavity for device EB485R1C1n6. Thesimulation curve is blue and the experimental data are plotted in black.The photonic crystal holes are 150 nm with slot width of 90 nm. TheQ value of the fabricated device is 4400 as compared to 7400 fromsimulation. The peak resonant transmission efficiency for the fabri-cated device is 6% as apposed to the simulated value of 17%. (b) Ex-perimental transmission spectra of three SC2 devices: EB485R1C1n3(black), EB485R2C1n7 (blue), and EB485R1C1n7 (red).77transmission measurements demonstrate that such circuits, which are fabricatedin a single lithography/single etch process without having to undercut the cavity,exhibit Q factors > 7500 and resonant transmissions as high as T ∼ 6%, when op-erated in hexane. Using a butt-coupled configuration improved the design notablyby increasing the transmission efficiency of all major parts of a full device. How-ever due to the fabrication imperfections, the cavity Q and peak transmission wasnot as high as simulation predicted. Their performance could be improved by i) us-ing the original ( 12 nm, 8 nm, 4 nm) hole shifts for the SC1 cavity and preservingthe butt-coupling geometry to have both high-Q and high transmission efficienciesand ii) by using a different cladding layer thickness to increase the grating couplingefficiency.78Chapter 4Optical Trapping And SensingUsing Photonic Crystal SlotCavities4.1 IntroductionIn this chapter, we focus on the capabilities of SC1 PCS cavities as high-sensitivitynanotweezers, which not only can trap tiny sub-50 nm Au nanospheres with verylow laser power but also enable us to deduce the size of the trapped nanosphere withnanometer sensitivity without using fluorescent particles and/or ancillary imagingapparatus [95, 101, 106].In the first part of this chapter, the high sensitivity of the PCS cavity resonantfrequency is demonstrated by measuring the peak transmission frequency in twodifferent solvents (namely, hexane and acetone) with different refractive indices.In the second part, these devices are immersed in a solution of Au nanospheres andit is found that when ≥ 0.1 mW of resonant CW laser power is launched into theinput waveguides, the temporal behaviour of transmitted light through the cavitiesoscillates in a random fashion when individual nanoparticles are drawn into thecavity region by the large gradient forces associated with the built-up optical powerin the cavity. By modelling the time-series data with numerical simulations of79how a small dielectic particle shifts the resonant frequency of the cavity modedepending on where in the cavity it is located, it is shown that the size of theparticle can be determined with roughly single nanometre sensitivity.4.2 Refractive Index SensingThe fundamental ingredients for achieving large, 3D local field enhancements ofCW light from 1D waveguides - critical coupling of the 1D waveguide with the3D microcavity, small 3D mode volume, and relatively high-Q value, including thewaveguide coupling - also imply that the cavity mode resonant frequency can shiftby a significant fraction of its linewidth when the dielectric environment insidethe cavity is perturbed. By measuring the resonant frequency, one can determinethe background refractive index in the cavity. PCS cavities are specifically suitedfor this kind of sensing application as their electric field mode profiles are mainlyconcentrated outside of the silicon slab which allows the particles to maximallyinteract with the strongest intensity region of the cavity mode.This Section describes how the resonant frequency of Mode 1 of SC1 cavi-ties depends on the solvent refractive index. Figure 4.1 shows the Mode 1 spectrafor two devices measured in hexane (n = 1.365) and acetone (n = 1.346). In bothdevices, the cavity resonance wavelength red shifts by∼ 7 nm in the large index en-vironment, consistent with simulations. The largest shift in nm per unit variation inrefractive index (sensitivity) observed in chip EB312 is 370 nm RIU−1 (RIU refersto Refractive Index Unit), for device EB312R22(2,2). This is less than that reportedfor some samples in Ref. [114] because their structures are undercut, and becausethey have larger slot widths. Using EB312R22(2,2) cavity Q value, sensitivity, andour signal to noise ratio (SNR) of 33 dB with 0.8 mW excitation power launchedinto the input ridge waveguide, the detection limit (DL) [125] of these structuresis estimated to be 2.3× 10−5 RIU. This is comparable to other photonic crystalsensors [114, 124, 126, 127] based on undercut cavities. Despite the fact that the Qvalues of our devices, reported in Table 3.3 are lower than Refs. [128, 129], thesedevices have larger sensitivity as a result of shifting the field maximum from insidethe silicon slab into the fluid. The fact that our samples require no undercuttingmeans that they are remarkably robust: we have cleaned and reused the same chip80over 20 times, over a period of 2 years.Figure 4.1: Normalized resonant transmission spectra, fitted with a Fano line-shape, for (a) device EB312R22(1,1) and (b) EB312R22(1,2) in hexane(blue) and acetone (red). In figure (a) Qhexane = 5450, Qacetone = 5700and for figure (b) Qhexane = 3980, Qacetone = 4100.4.3 Optical Trapping Of Au Nanospheres4.3.1 Experiment SetupThe experiment setup for optical trapping is the same as transmission measurementsetup depicted in Fig. 3.6. The only difference is that the laser wavelength is keptfixed around cavity resonance (instead of sweeping in the case of measuring trans-mission spectra) and the output of the power meter is recorded by the computerto create transmission time-series. The data used in Fig. 4.3 of this chapter wassampled at 1 kHz, while all of the remaining data shown or used for analysis wassampled at 250 kHz.The optical trapping reported here employs SC1 devices in which photoniccrystal (PC) slot microcavities are integrated with single mode channel waveguidesand grating couplers in a 220 nm thick silicon layer supported on a SiO2 claddinglayer (SOI). These devices are located on chip EB355. This chip has exactly the81same design as chip EB312 which is fully described in Chapter 3 and the specificdevice used to collect the data shown here is EB355R1C1(2,2) with the followingnominal feature sizes; the diameter of the PC holes is 300 nm, the slot width is 90nm, the grating coupler holes are 460 nm in diameter, and the coupling holes havea diameter of 220 nm.Instead of hexane, the devices are immersed in an Isopropyl alcohol (IPA) solu-tion containing polyvinylpyrrolidone (PVP)-encapsulated Au particles (with PVPlayer thickness of ∼ 2− 4 nm) of mean Au diameter ∼ 50 nm (14% standarddeviation), and a mean hydrodynamic diameter of ∼ 80 nm, at a concentrationof 1.1× 1011 mL−1 ( as reported in the data-sheet from nanoparticle manufac-turer [130]). IPA is chosen for dispersing Au nanoparticles (NanoComposix Inc.)because of its low absorption at ∼ 1.6 µm (most cavity resonances are at wave-lengths from 1.53 µm to 1.63 µm when immersed in IPA) and the good stabilityof PVP-coated Au particles in it.4.3.2 Trapping ExperimentA schematic of a full SC1 device and its Mode 1 profile is shown in Fig. 4.2,which clearly illustrates that the confined electromagnetic energy is concentratedalmost exclusively in a small volume within the slot (solution filled) region of themicrocavity [113, 115]. This concentration of the electric field in the solvent, ratherthan the silicon, distinguishes these cavities from some other planar-waveguide-based three dimensional (3D) microcavities recently used to trap ∼ micrometerdiameter polystyrene beads [101, 106].When the CW optical power in the input channel waveguide is ∼ 0.75 mW theresonant transmission through the cavity fluctuates as shown in Fig. 4.3a. Duringthe first ∼ 230 s, the laser is turned on and off six times, and after each turn-on,there is a period when the transmission is relatively stable at ∼ 90%, after whichit abruptly starts to fluctuate with large amplitude. The fluctuations are due toperturbations of the cavity resonance frequency when a PVP-coated Au particle istrapped in the vicinity of the mode antinodes (backaction). Since the transmissionreturns to its nominal, empty-cavity value after turning off and on the laser in thesesix instances, they are referred to as Temporary Trapping Events (TTES). The sev-82Figure 4.2: The full SSC1 photonic circuit [1] used for trapping is illustratedschematically at the bottom (lateral dimensions to scale). It includes aninput and an output grating coupler at each end that symmetrically con-nects to the photonic crystal microcavity region at the center, throughsingle mode channel waveguides, as shown in the scanning electron mi-croscope (SEM) image at the top, right. The calculated electric fieldintensity profile of the cavity mode excited in these experiments is alsoshown at the top, left.enth off/on cycle that occurs near ∼ 250 s is different, because the transmissionprior to turning off the laser is relatively constant, and it does not return to theempty-cavity value after turning on the laser. This is due to a Permanent Attach-ment Event (PAE) occurring at∼ 230 s. Figure 4.3b shows the transmission spectrameasured just before and just after the trapping sequence shown in Fig. 4.3a. Thealmost rigid redshift, and relatively small change in linewidth after a particle hasbecome permanently attached to the microcavity, quantifies the backaction effecton the transmission. The amount of the shift is proportional to the real part of theAu particle’s polarizability, and the electric field intensity of the mode at the loca-tion of the particle. For a fixed incident power and initial detuning, ∆0, from thepeak empty-cavity transmission, the range over which the transmission fluctuatesduring any given TTE depends on the particle’s polarizability, as it explores thecavity under the influence of Brownian forces.83Figure 4.3: (a) Normalized transmission time series from a device with aninitial empty-cavity Q factor of ∼ 4500 when the laser is tuned close tothe peak transmission in the empty-cavity state (black vertical dashedline in (b)), and the guided power in the input channel waveguide is∼ 0.75 mW. The shaded regions indicate when the laser is turned off torelease the transiently trapped particles. (b) The transmission spectrumbefore any trapping events (blue) and after permanently attaching an Auparticle (green), both obtained at a power of ∼ 0.75 mW. The black cir-cles and horizontal dashed lines show the nominal transmission valuesat the trapping laser wavelength corresponding to the empty cavity andthe cavity with a permanently attached Au particle, as also indicated bythe dashed lines in (a).4.3.3 Time-series AnalysisFor the purpose of quantifying the dynamics of the particles during TTEs, it is con-venient to work at lower laser powers for which no PAEs occur. Figure 4.4 showsseveral examples of TTEs obtained with 0.3 mW of power in the input waveg-uide, for two different initial detunings of the trapping laser. Qualitatively similartransmission dynamics were observed for many similar devices, for injected opticalpowers ranging from 0.2 mW to 0.4 mW. For a fixed power and initial detuning,a diverse set of TTEs are always observed: in time series data, distinct TTEs aremost obviously identified by the minimum value of the fluctuating transmission,84Figure 4.4: (a) The transmission of the cavity when the laser is tuned to ∼97% of the empty-cavity peak transmission on the red side. (b) Thetransmission of the same device under the same conditions but with thelaser tuned to ∼ 82% of the empty-cavity peak transmission (on the redside).but also sometimes by its maximum value when the mode resonance is not sweptthrough the laser frequency as the particle moves about in the cavity. These distinctTTEs likely correspond to situations when a single particle is temporarily trappedin the vicinity of the cavity, but eventually escapes and is replaced, or is knockedout by a different particle.Histograms of the fluctuating transmission provide a more detailed descriptionof the dynamics associated with distinct TTE, and can actually be used to definethem: for a “distinct TTE”, histograms generated using any sub-interval are essen-tially identical to the histogram generated using the entire interval. Figures 4.5band 4.5c show two experimental histograms (in red) corresponding to the distinctTTEs identified in Fig. 4.5a.To simulate the histograms of the transmission data, the presence of an Au par-ticle at a position~rp in the vicinity of the mode of interest is assumed to rigidly andadiabatically red shift the empty-cavity spectrum by an amount δλc(~rp) (althoughnot exact, Fig. 4.3b shows that this is a reasonable approximation). Assuming theparticle size is small compared to the length over which the mode intensity varies(typically < λ20 [92]), and that its impact on the mode shape can be treated pertur-85Figure 4.5: (a) A transmission time series obtained at an input power in thewaveguide of 0.3 mW at a red detuning set at 73% of the empty-cavitypeak transmission. (b) Experimental (red) histogram of the time seriesdata in the range indicated by the left horizontal bar in (a), and the sim-ulated histogram (blue), using a mean particle diameter of 24.8 nm. (c)Experimental (red) histogram of the time series data in the range in-dicated by the right horizontal bar in (a), and the simulated histogram(blue), using a mean particle diameter of 30.0 nm. The y-axes of bothhistograms are re-normalized and therefore their units are arbitrary. Thetotal count number for (b) is 2.5×106 and for (c) is 3.75×106.batively, δλc(~rp) can be approximated as [131]δλc (~rp)λc=α ′Au |E (~rp)|22∫ε (~r) |E (~r)|2 d3~r . (4.1)The integral in the denominator is taken over the mode excited in the cavity region(which is well defined for these high-Q modes). The E(~rp) in the numerator is theelectric field at the location of the particle, and the shift is independent of excitationpower due to the normalization. α ′ is the real part of the particle polarizability in86a background medium with dielectric constant εm and for a spherical particle withvolume Vp,α = 3Vpε0εmεp− εmεp +2εm, (4.2)where εp is the dielectric constant of the particle.The cavity resonance shift can also be numerically calculated more preciselyusing an FDTD electrodynamic solver. As shown in the next sub-Section, compar-ison of these full FDTD simulations with Equation 4.1 suggest that the factor of2 in the denominator of Equation 4.1 should be replaced with 1.5, but otherwiseEquation 4.1 provides the correct behaviour for different~rp and αAu.To test Equation 4.1, a full FDTD simulation of the cavity is performed asfollows. The simulation region, which includes a slot-cavity, an Au particle andan electric dipole source for excitation, is enclosed with perfectly-matched bound-ary layers. The mesh sizes are non-uniform to make the simulations run fasterand more efficiently: a ∼ 5.5 nm mesh is used around the spherical Au parti-cle while a ∼ 22 nm mesh is used elsewhere. The simulation time is set to 20 ps.Figure 4.6 compares this full FDTD-calculated (black data) shift of the cavity reso-nance (δλ (~rp)) for a range of Au particle sizes (Fig. 4.6a) and positions (Fig. 4.6b)in the cavity, with that obtained using Equation 4.1 with the empty-cavity modeprofile (blue line). While the agreement is reasonable, it can be significantly im-proved by scaling the expression in Equation 4.1 by a factor of 2/1.5 (red curve).While the linewidth of the resonance also changes slightly due to the particle’spresence, the effect is much smaller than the shift, and it is neglected in the currentanalysis (see also the experimental data in Fig. 4.3).The next part of the modelling involves self-consistently determining the ef-fective optical potential experienced by a particle at a position ~rp, including thebackaction. The empty-cavity transmission spectra are not typically Lorentzian, orsymmetric, so the experimentally measured transmission spectrum at the trappingpower, in the absence of trapped particles, is numerically fit using 8 Gaussians,as shown in Fig. 4.8c. This defines the normalized transmission function, T (∆),where ∆ is the detuning of the laser wavelength from the cavity resonance. In thepresence of a particle at position~rp, ∆ is the initial detuning of the laser wavelengthwith respect to the empty cavity resonance (∆0) minus δλ (~rp), as calculated using870 20 40 6001234Diameter (nm)δλ(nm)Z (nm)δλ(nm)−50 0 50 1000.20.40.60.81baFigure 4.6: (a) A graph of the cavity resonance wavelength shift versus Auparticle diameter at the center of the cavity (~rp = (0,0,0)). (b) A graphof the resonance shift versus the position of a 40 nm diameter Au parti-cle along the z axis at (x = y = 0). For both figures, the solid black lineshows the full-FDTD simulation results and the dashed color lines arethe approximated resonance shifts from Equation 4.1 scaled by threedifferent factors; blue, red and magenta correspond to scaling Equa-tion 4.1 by 2, 2/1.5 and 1, respectively.Equation 4.1 with the 2/1.5 scaling factor included.For a given incident power and initial detuning, the force on a particle at po-sition ~rp, that includes the backaction of the particle on the cavity resonance, iscalculated as follows (all these steps are summarized in the flowchart diagram inFig. 4.7);1. The δλ (~rp) is estimated using the scaled version of Equation 4.1 and thefield intensity profile obtained from a full FDTD simulation of the empty-cavity region excited by a guided mode incident in the channel waveguide(example in Fig. 4.8a).2. δλ (~rp) is then subtracted from ∆0 to find the total detuning, ∆(~rp), of thelaser wavelength from the shifted cavity resonance (example in Fig. 4.8b).88Figure 4.7: This diagrammatic representation illustrates the workflow ofmodelling a TTE histogram for a given particle size and laser detuning.The initial electric field intensity is calculated using FDTD simulatorand the rest of the modelling steps are performed using MATLAB pro-gramming. The yellow boxes show the output of each simulation step.3. The relative transmission at each ~rp is calculated by mapping ∆(~rp) to thenormalized transmission spectrum of the cavity shown in Fig. 4.8c. Theresulting function is T (~rp;∆0) (example in Fig. 4.8d).4. The empty-cavity optical gradient force is calculated using the first term ofEquation 1.15 from Chapter 1 with empty cavity electric field intensity foundfrom FDTD simulations. For the simulations reported here, it was assumedthat εm =(1.37)2 and εp =−97.4+11.2i corresponding to the medium (IPA)and Au dielectric constants, respectively. There is also, in general, a “radia-tion force” associated with directionally-differential absorption of radiationby the particle, but this is negligible in resonantly excited cavities where thefields are essentially standing waves.5. The empty-cavity force field is multiplied by T (~rp;∆0) to obtain the finalforce field that now takes into account the backaction of the particle.6. After finding the trapping force field, the trapping potential (U(~rp)) of a89particle located at~rp is determined (example in Fig. 4.8e) byU(~rp) =−∫ ~rp0~F(~r) ·d~r. (4.3)The reference point of the integral is selected to be the center of the slot(~r =(0,0,0)), but the resulting histograms are insensitive to the starting pointor path of integration.7. Given the full trapping potential profile, the probability distribution for thetime spent by the particle at a given position (example in Fig. 4.8f) is esti-mated [132] usingp(~rp) = e−U(~rp)kBT . (4.4)8. Equation (4.4) along with T (~rp;∆0) are used to calculate the histogram ofthe device transmission by adding the probability of the points that share thesame transmission value.9. As discussed in the following paragraph, in order to explain the experimen-tally measured transmission histograms, it is also necessary to average sev-eral such simulated histograms over a narrow Gaussian distribution of polar-izabilities.Figures 4.9b and 4.9c compare the measured and simulated histograms forthe several-second-long TTE identified in Fig. 4.9a. The calculated histogram inFig. 4.9b is generated using a single particle polarizability corresponding to an Audiameter of 33.8 nm, which is the value one might simply estimate based on theminimum transmission value achieved during the relevant TTE, using Equation 4.1.The much better agreement between simulated and experimental histograms shownin Fig. 4.9c, is obtained by averaging over a range of polarizabilities with a 3%standard deviation about a mean value of 32.6 nm. The significantly improvedagreement obtained by averaging over particle polarizability is a general result ob-served in all TTE simulations. There are at least two possible physical phenomenathat might be contributing to this requirement to average over a range of polarizati-blities. Transmission electron microscope images of the particles indicate they arenot spherical, so Brownian rotation of a trapped particle in the polarized field of the90bad−0.5 0 0.500.51∆(nm)T∆0cfeX (µm)Y (µm)X (µm)Y (µm)X (µm)Y (µm)X (µm)Y (µm)X (µm)Y (µm)Figure 4.8: (a) The electric field intensity profile in the x-y plane (i.e. theplane that cuts through the middle of the silicon slab), from FDTD sim-ulations with 0.3 mW of resonant modal power in the input ridge waveg-uide. The unit of the intensity is (Vm)2. (b) The profile of the ∆(~rp) func-tion, which is the detuning (units of nm) of the laser wavelength fromthe cavity resonance wavelength with a particle of diameter 30 nm lo-cated at~rp, calculated using ∆(~rp) = ∆0−δλ (~rp). (c) The transmissionfunction T (~rp;∆0) plotted versus ∆ . The laser wavelength is detunedto 73% of the peak transmission wavelength of the empty-cavity, on thered side. (d) The transmission function T (~rp;∆0) profile in x-y plane.Note that at the center of the cavity T = 0.2, showing when the particleof diameter 30 nm is located at the center of the cavity, the transmis-sion of the device is expected to drop to 0.2 of its maximum becauseof the shift in the cavity resonance (backaction effect). (e) The trappingpotential energy including the backaction in units of kBT (Boltzmannfactor) calculated using Equation 4.3. (f) The probability distributioncalculated using Equation 4.4. This probability distribution is used incalculating the histogram shown in Fig. 4.5c.91Figure 4.9: (a) Normalized transmission time series obtained at an inputpower in the waveguide of 0.3 mW at a red detuning set at 31% ofthe empty-cavity peak transmission. (b) Experimental (red) histogramof the time series data in the range indicated by the horizontal bar in (a),and the simulated histogram (blue), obtained using a fixed particle di-ameter of 33.8 nm. (c) The same experimental histogram as in (b) (red)is plotted with a histogram (blue) obtained by averaging over a normal(Gaussian) distribution of particle diameters centered at 32.6 nm withstandard deviation of 3%. The total count number for the experimentalhistogram is 5×106.cavity could be one contributing factor. The PVP coating on the outside of the par-ticles (interpreted as being responsible for the difference between the Au diameterand the hydrodynamic diameter) is expected to be fluctuating in its configuration,which could also be contributing. The relatively small difference in dielectric prop-erties of PVP and the solvent make us suspect that the non-spherical shape of theAu is most important. This issue is investigated in Chapter 5 by performing fur-ther trapping experiments on more anisotropic nanoparticles and generalizing ourhistogram analysis.92The two distinct TTE histograms simulated in Figs. 4.5b and 4.5c for fixedlaser excitation conditions, agree well with the experimental histograms. The meandiameters of the particles in the two cases are 24.8 nm (with 3% standard deviation)and 30.0 nm (with 4% standard deviation). These and many similar simulations fora wide variety of histograms observed at different (red and blue) detunings, indicatethat most distinct TTEs correspond to particles of different sizes that explore thefull mode distribution in the slot. The best fitted histograms are selected based onminimization of the χ2 as a goodness of the fit parameter, which is defined asχ2 = ∑i=histogram bin(eci− sci)2sci. (4.5)The sum in this equation runs over each bin of the histograms. eci denotes thecount number of bin i of the experimental histogram and sci is the correspondingcount number for the simulated histogram. Figure4.10 shows an example of the χ2function calculated for a TTE. The best fit histogram, calculated by minimizationof χ2, is shown in Fig. 4.11c and Fig. 4.12c. Along with the best fitted histogramin these two figures, the calculated histograms for slightly different nanospherediameters and anisotropies are also plotted to demonstrate the extreme sensitivityof this histogram model. It is obvious that for even a small change of < 0.5 nmin the mean diameter of the trapped nanosphere, the calculated histogram changessignificantly and the fit quality decreases. This is also true for the anisotropy ofthe particle. The model is quite sensitive to < 1% anisotropy variations. Theseestimates of the sensitivity of the fits to the fitting parameters are not yet basedon rigorous χ2 analysis, but rather on comparing plots as shown in Fig. 4.11 andFig. 4.12 “by eye”. More work along the lines reported in Ref. [133] is required toproduced statistically significant uncertainties for these fit parameters.4.3.4 Cavity Mode 2 and Size Sensing In Heterogeneous SolutionFrom many comparisons of model and experimental histograms similar to thoseshown in Figs. 4.5 and 4.9, the maximum diameters of modeled Au particles cap-tured in the trap is ∼ 34 nm, considerably smaller than the mean diameter in solu-tion. To verify that the relatively small size (compared to the mean particle diam-93Figure 4.10: The graph of log10(χ2) as a function of particle diameter andGaussian averaging standard deviation. The best fit histogram is deter-mined by finding the minimum of the χ2.eter of 50 nm, or the most probable diameter of 56 nm) of the particles trapped inthe slot cavity mode is indicative of some physical hindrance, rather than an arti-fact of the model, the same analysis is applied to trapping data obtained using thesecond mode supported by this type of microcavity [115]. Figure 4.13 shows thesimulated mode profile and resonant transmission spectra associated with a devicethat is identical to the one discussed in the manuscript except that its slot widthis 100 nm rather than 90 nm. The highest intensity regions for this mode, wheretrapping occurs, are not in the slot, but at the edges of the 300 nm diameter holesadjacent to the slot. There should be no hindrance for any of the particles in solu-tion accessing these holes, and indeed, several simulations of various TTEs fromthis mode (examples of which are shown in Fig. 4.13c-h) yield particle sizes thatare completely consistent with the average size of the nanoparticles reported by themanufacturer [130].4.4 ConclusionIn this chapter, two applications of SC1 devices, as high-sensitivity tools, aredemonstrated experimentally. Both of these applications exploit the strong light-94Figure 4.11: [(a)-(e)] An experimental histogram (red) versus simulated his-tograms (black) of particles with various average diameter (D) anda fixed standard deviation of 1.1% for Gaussian averaging. All his-tograms are obtained for an input power in the waveguide of 0.3 mWand a red detuning set at 31% of the empty-cavity peak transmission.The total count number for the experimental histogram is 15×106.95Figure 4.12: [(a)-(e)] Experimental histogram (red) versus simulated his-tograms (black) of Au nanospheres with a fixed average diameter (D)of 35.36 nm and various standard deviation for Gaussian averaging.All histograms are obtained for an input power in the waveguide of 0.3mW and a red detuning set at 31% of the empty-cavity peak transmis-sion.96Figure 4.13: (a) The electric field intensity profile (in arbitrary units) of thesecond cavity mode in the x-y plane, calculated from a FDTD sim-ulation. (b) The experimentally measured, normalized, empty-cavitytransmission at the second cavity mode resonance of a device almostidentical to the one discussed in the manuscript (see text for expla-nation of the difference); the guided power is 0.28 mW. The dashedline indicates the trapping laser wavelength used to obtain the 6 setsof experimental (red) and modelled (blue) histograms shown in (c)-(h) associated with 6 distinct TTEs. The estimated diameter (percentvariation) of trapped Au particles extracted from these modelled his-tograms are shown in each plot.97matter interactions in these PCS cavities due to the fact that the majority of electricfield intensity in this structure is located outside of the silicon slab. As nanotweez-ers, these devices require very low optical power for trapping sub-50 nm particlesas demonstrated in Table 4.1. As a refractive index sensor, these un-optimizedstructures have a detection limit for refractive index change of ∼ 2× 10−5 RIUwhich is comparable with best photonic crystal cavity based sensors [114, 124,126, 127]. Their performance can be further enhanced by undercutting the cavity(removing SiO2 undercladding will increase the refractive index contrast and re-duce out-of-plane loss by enhanced TIR) and using a butt-coupled geometry forexciting the cavity.A self-consistent, quantitative model of optical backaction and optical gradientforces in a PC-based silicon slot waveguide microcavity quantitatively describesthe dynamics of cavity transmission as influenced by Au nanoparticles as smallas ∼ 24 nm diameter, transiently trapped using sub-mW CW excitation powers.The backaction footprint of trapped particles on cavity transmission dynamics candistinguish mean particle diameters at the single nanometer level, and polarizabil-ity anisotropies at the 1% level without requiring fluorescent tagging or ancillaryimaging apparatus. This low-power, silicon-wafer-based device geometry, togetherwith the sensitivity of the transmission analysis technique, present exciting op-portunities for further advancing the science and application of nanoscale photon-ics [93].98Table 4.1: Summary of trapping performance of various tweezers.TweezerTypeOperatingWave-length(nm)Particle Mate-rialParticleDiameter(nm)TrappingPower(mW)ReferenceLaserTweezers514.5 polystyrene 100 15 [68]dipoleantennas808 gold 10 2 [12]nanopillar 974 polystyrene 110 10 [11]doublenanoholes975 silica 12 10 [13]microring 1550 polystyrene 500 9 [15]microdisk 1550 polystyrene 1000 7.6 [17]PCnanobeam1548 polystyrene 48 NA [18]PCnanobeam1064 polymer 22 11 [19]PCnanobeam1585 polystyrene 1000 0.3 [101]PC hol-lowcavity1500 polystyrene 250 0.36 [106]our PCScavity1570 gold 25 0.3 [3]99Chapter 5Optical Trapping of Nanorods5.1 IntroductionThe results presented in the previous chapter strongly suggest that the time serieshistograms of TTEs are very sensitive to not only the overall size of the trappedparticle but also any anisotropy in its shape. This chapter describes a generaliza-tion of the histogram model described in Chapter 4 to include particle anisotropy.Using this model, we validate the conjecture that the particle anisotropy was thereason that averaging over sphere size was required to get good agreement withexperimental data in Chapter 4, and then demonstrate how this generalized modelcan also be used to extract the size and shape of highly anisotropic Au nanorodstrapped in the same cavity as in Chapter 4. The corresponding experimental datarepresent the first, to our knowledge, report of using nanotweezers to trap sub-50nm size nanorods. While the importance of including rotational potential energyof anisotropic particles in polarized laser beams has been recognized [76, 134–138], the closest work to that reported here involved the use of 1D photonic crystalnanotweezers to trap several micron long carbon nanotubes [139].In Section 5.2, we first generalize our histogram-fitting model to explicitly ac-count for nanoparticle anisotropy by considering the rotational motion introducedby optical torques on ellipsoidally-shaped trapped nanoparticles. The main differ-ence in the new model is the use of a tensor-form polarizability and the inclusion ofoptical torques in addition to the Center Of Mass (C.O.M) optical forces, when eval-100uating the optical potential for a particle located at any point, and any orientation inthe cavity. Then in Section 5.3, it is demonstrated that with this more generalizedmodel, we obtain high-quality histogram fits for Au nanospheres without averagingover sphere sizes as was done in Chapter 4 (i.e. the new model predicts extremesensitivity of the transmission histograms to slight particle asymmetries). In Sec-tion 5.4 we present new experimental optical trapping data obtained with solutionscontaining sub-50 nm long, < 15 nm diameter Au nanorods and show that the his-tograms can be accurately fit with the generalized model to extract the size andaspect ratio of such particles. The qualitatively different nature of the anisotropichistograms is intuitively explained, and the future applications of this technique toidentify the size and shape of nanoscale particles in solution is discussed in Sec-tion 5.5.5.2 Self Consistent Model Including AnisotropicParticlesTo simulate the trapping of anisotropic particles, both the rotational and c.o.m mo-tion of a particle in the presence of an electric field must be accounted for. As isexplained in Chapter 1, for small nanoparticles, the optical trapping force on thecenter of mass of the particle can be described using the dipole approximation:F =12Re[ ∑i=x,y,zpi∗∇Ei]. (5.1)where pi and Ei are the components of the complex valued dipole moment andexternal electric field respectively and ∗ denotes the complex conjugate. Under thesame approximation, the optical torque generated in the cavity electric field on apoint dipole is:τ =12Re[p∗×E], (5.2)The induced dipole moment depends on the polarizability α of the trapped parti-cles:p = α ·E, (5.3)101Figure 5.1: (a) A prolate spheroid in the cavity coordinate system. (b) Thecalculated normalized electric field intensity profile of Mode 1 of a SC1cavity, which is used for trapping nanorods, with slot width of 90 nmand hole radius of 150 nm. The cavity mode is polarized along the y-axis at its center.For anisotropic particles, the polarizability necessarily becomes a tensor. We as-sume that the particles can be approximated as prolate spheres in order to take ad-vantage of analytical expressions for the polarizability tensor of prolate spheroids.Specifically, in the particle coordinate system (x′y′z′) with the particle’s long axisparallel to z′-axis, the polarizability takes the form:α ′ =αS 0 00 αS 00 0 αL (5.4)where αL,S are the polarizabilities along the long and short axes of a prolate spheroidof radius R and length L with:αL,S = εmε0VAuεAu− εmεm + xL,S(εAu− εm) (5.5)where εm and εAu are the dielectric constant of the background medium and theAu nanoparticles respectively, VAu is the nanoparticle volume and xL and xS are thewell-known ellipsoidal depolarization factors given in [140].102When the anisotropic particle is oriented in the cavity such that its long axis isat an angle θ to the z-axis and azimuthal angle of ϕ to the x-axis (see Fig. 5.1 forcavity coordinate system xyz), the polarizability tensor α(θ ,ϕ), in the cavity frameof reference, is calculated using two rotational transformations:α(θ ,ϕ) = Rα ′R−1, (5.6)whereR =cos(ϕ) −sin(ϕ) 0sin(ϕ) cos(ϕ) 00 0 1cos(θ) 0 sin(θ)0 1 0−sin(θ) 0 cos(θ) . (5.7)Since the slot cavity mode has a small mode volume and high-Q factor, thepresence of a single nanoparticle translating and rotating in the vicinity of the modevolume can significantly shift the resonance wavelength of the cavity and thereforechange the amount of electromagnetic energy coupled to the cavity mode at thelaser wavelength. In the previous chapter, we included this backaction effect inour model by renormalizing the electric field intensity of the cavity (E(r)) by atransmission function (T (δλ )), where δλ was the shift of the cavity resonance dueto the backaction (see Chapter 4 for details). The shift δλ can be approximatedin terms of the nanoparticle’s dipole moment (which now has a tensor form forpolarizability) and cavity electric field as:δλ (r,θ ,ϕ) = λ0Re[{α(θ ,ϕ)E(r)}∗ ·E(r)]m∫ε0ε(r) |E(r)|2 dr, (5.8)λ0 is the empty cavity resonance wavelength, ε(r) denotes the dielectric functionof the device and m is a prefactor that enhances the dipole approximation accuracy.Following the same steps as in Chapter 4, for modelling experimental histograms,the prefactor m in Equation 5.8 is found by fitting the result of simulations of cavityresonance wavelength, when different size and orientation nanoparticles are placedat cavity center. Figure 5.2 shows the best fitting results that happen for m = 1.5.The total trapping potential energy U(r,θ ,ϕ) of a spheroid inside the cavityis found by calculating the work done by both the optical force and torque on thespheroid located at the origin and aligned to z-axis (i.e. r = 0, θ = 0, ϕ = 0)103Figure 5.2: The amount of cavity resonance shift when different size and ori-entation nanorods are placed at the center of a SC1 cavity with slotwidth of 90 nm and hole radius of 150 nm. For (a)-(b) the nanorod isperpendicular to the slot (θ = pi2 , ϕ = pi2 ) and (a) is the resonance shiftas a function of nanorod diameter (length of 40 nm) and (b) shows thedependance on nanorod length (diameter of 12 nm). (c) and (d) showthe same relationships as (a) and (b) respectively, except that the rod isoriented along the slot (i.e. θ = pi2 , ϕ = 0) for these two plots. The filledcircles are the result from simulations and the curves are calculated fromEquation 5.8 with m = 1.5 and assumption of perfect cylindrical shapefor the nanorods.104to a final center of mass location and orientation. From the trap potential energymap, a simulated transmission histogram for a certain laser power and detuningand particle geometry can be calculated following the same procedure as shown inFig. 4.8 of Chapter 4.As demonstrated in Fig. 5.3, the overall shapes of calculated histograms showdistinct qualitative differences based on the particle’s degree of anisotropy. High-aspect ratio spheroids will have a large impact on δλ as they rotate in and outof alignment with the cavity mode polarization, which results in larger variation ofdevice transmission (as shown in Fig. 5.4). Therefore, when comparing histogramsof particles of similar diameters, but different anisotropy, the transmission distri-bution is expected to be larger in total range for nanoparticles that are relativelymore anisotropic (as demonstrated in Fig. 5.3). As the aspect ratio increases froma perfect spherical shape to more anisotropic spheroids, the histograms shift to theleft but maintain their long tail to higher transmissions. The shift to the left is dueto the large δλ when the long axis of the higher aspect ratio rods is aligned withthe electric field at the cavity mode antinode.5.3 Explaining the Need to Average Histograms forImperfect NanospheresAnother notable impact of including rotational motion in the model is that it nat-urally yields smooth simulated histograms without requiring averaging. As dis-cussed in Chapter 4, a model accounting only for translational degrees of freedom(which was appropriate for isotropic particles) can only match the smoothness ofexperimental histograms of nominally, but not precisely spherical particles, by av-eraging simulated histograms over a narrow distribution of nanosphere diameters.This is illustrated in Fig. 5.5a-b where the relatively poor fit of an experimen-tal transmission histogram of a gold nanosphere TTE using the isotropic particlemodel without averaging is shown. It was posited that the averaging requirementwas because the Au nanospheres are not actually perfectly spherical but possessshape irregularities and surface corrugation that give the particle’s polarizability aslight anisotropy. These irregular spheres rotate in the cavity mode, which effec-tively samples different size spheres, averaging out the transmission histograms.105Figure 5.3: [(a)-(d)] Histogram of 4 different spheroids with same shortdiameter of 32 nm and different aspect ratios calculated with theanisotropic trap model including torques. The aspect ratios are 1 (a),1.1 (b), 1.2 (c), and 1.4 (d), respectively. The empty cavity transmission(i.e. without any particle in the cavity) is shown with blue dashed linein all graphs.106Figure 5.4: [(a)-(d)] The dependence of the device transmission on the ϕ ori-entation of 4 different spheroids with same shorter diameter of 32 nmand different aspect ratios. The aspect ratios are 1 (a), 1.1 (b), 1.2 (c),and 1.4 (d), respectively and their θ angle for all 4 particles is 90 de-grees. All particles are located at the intensity antinode of the cavitymode.107Figure 5.5: (a) Experimental histogram (red) during trapping of Aunanosphere along with fitted histogram (black) assuming a perfectlyspherical shape of diameter 36.4 nm. (b) Same experimental (red) his-togram as in (a), with the simulated histogram (black), using a normaldistribution of sizes of mean diameter 35.36 nm and 1.1% standard de-viation. (c) The same experimental histogram (red) is fitted (black) as-suming a spheroid shape for the trapped nanoparticle. The extractedsize of the spheroid is 34.4 nm ×37.1 nm.Figure 5.5c shows how this explanation is supported by including rotation in thetrap potential model. The same nanosphere TTE transmission data is fit with thenew model, which naturally yields the slight anisotropy of the imperfect sphere andthe consequently smooth histograms (the nanoparticle size extracted from both his-tograms in Fig. 5.5b-c agree very well, which confirms both models predict similaramount of anisotropy for the trapped particle.). This highlights the importanceof including optical torques in the trap potential calculations even for nominallyspherical Au particles due to the impressive sensitivity of the trapping devices toeven the slightest particle non-uniformity.5.4 Trapping Gold NanorodsThe trapping experiments are accomplished in Mode 1 of a SC1 PCS cavity (de-vice EB355R1C1(2,2)) with a 90 nm wide slot and hole diameter of 300 nm thatis immersed in a methanol solution of polyvinylpyrrolidone (PVP) coated goldnanorods with average size of 44 nm ×12 nm 1. Figure 5.6 shows the SEM images1These nanorods are synthesized by Jonathan Massey-Allard based on a procedure described inRef. [141]108of the cavity and nanorods. The slot-cavity structure is designed to support a cav-ity mode with a relatively high-Q (∼ 5200) (when immersed in methanol) and withantinodes located in the slot where they are easily accessible to the nanoparticles.These characteristics of the PCS cavity result in trapping sub-50 nm nanorods atcoupled laser power as small as only 0.2 mW (this is the estimated power in theinput channel waveguide).Figure 5.6: (a) Scanning electron microscope (SEM) image of a 90nm wideslot cavity [1] used for trapping. (b) SEM image of the Au nanorodsused in the trapping experiments. The average size of the rods, extractedfrom SEM images, is 44 nm ×12 nm with 15% standard deviation.Similar to nanosphere trapping in previous chapter, TTEs of nanorods areclearly evident as sudden high-amplitude fluctuations in the transmission signalthrough the photonic circuit (shown in insets of Fig. 5.7), which are due to backac-tion effect.The distribution of transmission signal amplitudes during a TTE are arrangedin histograms that provide a rich description of the dynamics associated with thattrapping event. Histograms corresponding to various nanorod trapping events areshown (in red) in Fig. 5.7a-f. Best fits to the experimentally obtained histogramsusing the above described model are shown in black in Fig. 5.7a-f. The extractedsizes agree well with the average size of the nanorods as measured from SEMimages (Fig. 5.6b). Among these histograms, Fig. 5.7c has significantly narrowerdistribution, which by looking at the extracted size, it is noticed that this particle isvery low-aspect ratio, which explains its histogram shape and indeed SEM imagesof these nanorods confirm that there are some low-aspect ratio nanorods in the109solution (some of them are observable in Fig. 5.6b).Figure 5.7: [(a)-(f)] 6 different nanorod experimental (red) histograms areillustrated along with the calculated (black) histograms fits based ontheory accounting for the nanoparticles’ anisotropy. The insets showthe corresponding normalized transmission time series collected dur-ing the trapping experiment and the dashed black lines show the rangefor which the experimental histogram is collected. (a)-(c) are for laserpower of 0.2 mW in the waveguide and the estimated nanorod size basedon the fits are 14 nm×46 nm, 14 nm×50 nm and 38 nm×39 nm respec-tively. The actual total count number for the experimental histograms inthese three plots are 105, 6.25×104, and 1.25×105 respectively. (d)-(f)are at 0.25 mW power and the estimated sizes based on the fits are 13nm ×42.5 nm, 12 nm ×43 nm and 12 nm ×46 nm. The total countnumber for the experimental histograms in these three plots are 2×105,8.75×104, and 7.5×104 respectively.Another fact about these fitted histograms is that although the fits are accept-able, they are not as good as sphere histogram fits in the previous chapter. Themain reason for the lower quality of fitting is the shape of the nanorods that donot have uniform uniform diameters along their lengths. As is shown in Fig. 5.6b,110the ends of the nanorods have a larger diameter compared to their waists. Thismakes their polarizability tensor different than a perfect cylindrical shape, whichresults in inaccurate resonance shift estimation based on FDTD simulations of per-fect cylinders and fits to the tensor-polarizability function of an ellipsoid. To solvethis issue, it is important to find the average shape of the nanorods in the solutionand try to use FDTD simulations to estimate the resonance shift of the cavity whenthis shape nanorod is placed in it and from that find a more accurate value for theprefactor m in Equation 5.8.5.5 ConclusionThis chapter reports the recent advances in trapping sub-50 nm gold nanorods usingan SOI cavity-based nanotweezers at sub-mW injected power. It is demonstratedthat the strong sensitivity of the PCS cavity to the presence of a single trappedparticle can be utilized to study the size and shape of the trapped particles sim-ply from the device’s transmission signal during a trapping event by modeling thelinear and rotational motion of a nanorod in the trapping potential of the cavityand including the backaction of the nanorod on the cavity resonance. Using thisstatistical model to fit the transmission histograms during a trapping event we areable to estimate the dimensions of trapped nanorods in the solution. Distinct sig-natures in the transmission histograms of different aspect ratio particles suggestthat our imaging-free method can be used to differentiate the shapes of the trappedparticles in heterogeneous solutions.111Chapter 6Conclusions and Outlook6.1 ConclusionsTwo slightly different and unique planar photonic circuits made using silicon-on-insulator wafers were designed and characterized. Both were intended to serveas robust chips that could be immersed in a solvent containing small dielectricnanoscale particles that would be attracted to and trapped within sub-micron sizedmicrocavities using the optical gradient forces available when< 1 mW of∼ 1.5 µmlaser radiation was coupled into the circuits. The microcavities in both cases werebased on locally modified slot photonic crystal waveguides, and the differences inthe two designs were in how light was coupled to the cavities via a series of gratingcouplers and waveguides.A series of samples based on the first design (SC1), that used photonic crys-tal waveguides to couple at a 60 degree angle to microcavities with cavity-defininghole shifts of 12, 8, and 4 nm in 3 rings of PC holes adjacent to the cavity, exhibitedQ factors and overall transmission values in reasonable agreement with simulationswhen deviations of the fabricated patterns from the designs were taken account of.To our knowledge, the highest Qs of 7500, are one of the best reported for sup-ported PC cavity structures operating in solvent. By comparing the transmissionspectra from one of the best samples using hexane and IPA solvents, a detectionlimit for sensing refractive index changes in the environment of 2.3× 10−5 RIUwas determined, which is comparable to other optical-chip based sensor structures112reported in the literature.Despite this design suffering scattering losses in the coupling waveguides andtheir connections to each other and the microcavity, both Au spheres of diame-ters down ∼ 20 nm, and Au nanorods as small as 13 nm ×42 nm were successfullytrapped using less than 0.5 mW of CW laser power coupled into the channel waveg-uides. The experimental results from a series of samples fabricated based on thesecond design (i.e. SC2), which used in-line butt-coupling between channel andPC slot waveguides, and cavity-defining hole shifts of 6, 4, and 2 nm in 3 ringsadjacent to the cavity, were less satisfactory. While transmission results from teststructures that did not include the microcavity, but did include the butt-coupledchannel/PC waveguides, agreed quite well with the design specifications, only afew cavities exhibited the desired transmission characteristics. The reason is mostlikely due to the fact that with the small hole-shifts defining the cavity, its resonantfrequency is very close to the photonic band-edge of the slot waveguide mode fromwhich it derives, so even small fabrication imperfections can be expected, in retro-spect, to “lose” the cavity mode. Nevertheless, the one sample that came closest tothe design specifications did in fact exhibit a 3 fold improvement in net transmis-sion over the best of the first designed samples (theoretically it should have been 5fold better), and its Q value was 4400. Preliminary trapping experiments with thisone sample based on the second design proved that it was capable of trapping Auspheres with diameters down to 15 nm with < 0.5 mW of power launched in theinput channel waveguide.The most significant and interesting results of the work came from develop-ing a fully self-consistent model for the statistics of the laser transmission duringindividual transient trapping events. This novel approach to analyzing the trans-mission histograms of individual trapped particle took into account the backactionof the particle on the cavity resonance spectrum while undergoing Brownian mo-tion (both translation and rotation), leaving the particles size and shape (assumingthe functional dependence of a particles polarizability to be that of a ellipsoid) tobe fit by comparison to the experimental transmission data, plotted as a histogram.Several experiments with both nominally spherical and high aspect ratio Au (∼ 8)nanorods convincingly demonstrated that the histogram shapes are sensitive to theoverall size and shape of the trapped particle, with approximately single nanometer113sensitivity.6.2 Future WorkThe advances in this work in building nanotweezers and exploiting them for trap-ping and sensing tiny particles holds great promises in terms of applications. Forinstance it is possible to use these high-Q, small mode volume nanotweezers topermanently trap and self-assemble tiny photon emitters like colloidal quantumdots and quantum rods for increasing their spontaneous emission rates and creat-ing on-chip single photon sources for quantum communication circuitry. Similarlybecause of their enhanced electric field, single molecule cavity-enhanced spectro-scopic analysis and low-threshold single quantum dot lasers can be demonstratedin this platform.Based on these applications, the main goal of future works is to push down thesize of the particles that can be trapped in these tweezers (to a few nanometers)and find a controllable way to permanently localize trapped particles in the cavity.Some of the challenges that need to be faced along the way, are discussed below.1. To increase the trapping forces, the first thing to try is repeating butt-couplinggeometry as SC2 design, but with the larger hole-shift cavities, and test thefabricated devices by trapping few-nm Au particles to indicate how muchsmaller particles they can trap with up to 1 mW of coupled power. Also morework can be done on optimizing structure parameters like under-claddingthickness, slot width, cavity hole location and radii. Undercutting the cavitywould also improve the Q factor because of better vertical confinement.2. Upon confirmation of trapping smaller Au particles, it is possible to use thenew devices for trapping other particles like colloidal quantum dots. Switch-ing the particles requires totally different chemistry which in its own is abig challenge. Solvents and stabilization methods for new types of particlesare different. For instance, we tried SC1 and SC2 devices for trapping PbSequantum dots without successful results. One of the main issues is the Oleicacid molecules that are used for functionalization of quantum dots to makethem stable in solvents. These Oleic acid can easily cover the surface of the114PC and stops dots from reaching to the cavity center. New functionalizationmethods in different solvents needs to be developed to solve this issue.3. It is crucial to develop controllable ways to integrate single nanoparticlesinto the cavity. In our nanosphere trapping, it was observed that by increas-ing the laser power it is possible to permanently localize single trapped par-ticles. This power dependence needs to be further investigated in detail.Also it is important to find a way to flush out the rest of nanoparticles inthe solution without removing the trapped particle or cover the surface ofthe cavity with contamination. Developing microfluidic channels or work-ing with syringe pumps to create a controlled flow of solvent might be asolution. Another benefit of microfluidic channels, is that it enables creatinga reservoir of nanoparticles and then have a slot waveguide passing throughit and delivering nanoparticles to the cavity in a controlled way.4. As it is mentioned in Chapter 3, after each round of trapping experiments,the chip needs to be cleaned. One of the reasons is having particle trappedaway from the cavity at locations like coupling holes, adapters etc. whichinterferes with the transmission efficiency of devices. Increasing the op-tical forces for a given input power is crucial to reduce these incidents asincreasing the laser power will cause more trapping in unwanted areas. Alsodeveloping microfluidic channels will help solving this issue because it caneliminate exposure of nanoparticles to unwanted areas of the chip.5. To improve the theory of backaction and the accuracy of the self-consistenthistogram analysis, the first thing to do is include Q factor changes associatedwith particle motion/orientation in our model, specially when the trappedparticle has a dielectric resonance near the cavity resonance. Under theseconditions it is not possible to ignore the impact of the particle field on thecavity mode field and a more general theory is needed to accurately describeparticle-cavity optomechanical interactions.6. The strong size-dependent backaction in this system, allows one to developsize-selective tweezers. By fully investigating the influence of different pa-rameters (e.g. laser detuning, power, location of trapped particles) on the115depth of trapping potential, one can exploit these tweezers to specificallytrap a certain size/shape particles in a heterogeneous solution.116Bibliography[1] S. Hamed Mirsadeghi, Ellen Schelew, and Jeff F. Young. 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