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Resonant scattering from three-dimensional optical microcavities formed in two-dimensional waveguide-based… Cheung, Iva Wai-Yun 2004

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R e s o n a n t - s c a t t e r i n g m i c r o c a v i t i e s  f r o m  t h r e e - d i m e n s i o n a l  f o r m e d  w a v e g u i d e - b a s e d  i n  o p t i c a l  t w o - d i m e n s i o n a l  p h o t o n i c  c r y s t a l s  by Iva Wai-Yun Cheung B.Sc, The University of Alberta, 2001 A THESIS S U B M I T T E D IN P A R T I A L F U L F I L M E N T O F T H E REQUIREMENTS FOR T H E D E G R E E OF M A S T E R OF SCIENCE in The Faculty of Graduate Studies (Department of Physics and Astronomy)  We accept this thesis as conforming to the required standard  T H E U N I V E R S I T Y O F BRITISH C O L U M B I A October 27 2004 ;  © Iva Wai-Yun Cheung, 2004  11  Abstract Reflectivity properties of indium phosphide-(InP-)based two dimensional (2D) photonic crystals and photonic crystal microcavities were studied via optical experimentation and numerical simulations. Planar InP waveguides textured with a hexagonal array of air holes were studied with a specular white-light reflectivity apparatus. Their reflectivity as a function of wavenumber. as measured at different incident angles with an F T I R spectrometer, was compared to the results of computer simulations of the structure, based on a Green's function model. The simulation fits were used to determine salient fabrication parameters of the waveguide structures, including the filling fraction of the texturing, as well as the configuration of the layered structure of the waveguide and its substrate. The reflectivity properties of InP-based photonic crystal defect structures, which, in principle, serve as high-finesse (high Q-value) resonant microcavities. were also probed using both localized (2-/xm spot size) 100-fs pulses from an optical parametric oscillator (tunable from 1.44 /im to 1.58 jum) and a broadband white light source. These reflectivity spectra revealed no evidence of modes in the microcavities. Numerical simulations were performed to study the extent to which the Q values and the field distributions of the defect states are affected by known fabrication imperfections such as random variations in radii of the air holes ;  in the microcavity arrays, as well as the slanting of hole sidewalks.  The  simulations were also used to mimic the microreflectivity experiment in order to determine the effect of the relative position of an incident Gaussian beam on the reflectivity properties of ideal photonic crystal defect cavities.  Abstract  iii  The implications and insights arising from this work point to numerous recommendations for future work. These include a sample design comprising both a uniform photonic crystal region as well as a region of several photonic crystal defect microcavities allowing for better characterization of ;  fabrication parameters; modifications to the microreflectivity apparatus and experimental design that would likely yield better resolution of experimentally measured spectral features from resonant modes; and the controlled exploitation of symmetry-breaking to reduce modal volume for potential applications in cavity quantum electrodynamics.  iv  Contents Abstract  ii  Contents  iv  List of Tables  vi  List of Figures  vii  Acknowledgements  x  1 Introduction  1  2 Background 2.1 Photonic crystals 2.2 Defects and microcavities 2.3 Simulation techniques 2.3.1 Green's function model 2.3.2 FDTD model 2.4 Ideal samples  6 6 10 12 12 13 14  3  17 17 17 22 24 26 26 27 29 29 30  Experimental design 3.1 Sample structure 3.1.1 InP microcavity structure and fabrication 3.1.2 InP uniform photonic crystal structure and fabrication 3.2 Microreflectivity apparatus 3.2.1 Light source 3.2.2 Optical components 3.2.3 Positioning mechanics 3.2.4 Spectrometer 3.2.5 Alignment and imaging of photonic crystal arrays . . . 3.3 Broad-spectrum reflectivity apparatus  Contents  3.4 4  5  3.3.1 Light source 3.3.2 Optical components 3.3.3 Positioning mechanics 3.3.4 Spectrometer 3.3.5 Alignment and imaging of photonic crystal arrays . . . Specular reflectivity apparatus  v 32 33 33 33 34 34  Results a n d discussion 4.1 Uniform photonic crystal lattice structure 4.1.1 Green's function model modification 4.1.2 Identifying structural parameters using the simulation . 4.1.3 Experimental results and comparison to simulations . . 4.2 Microcavity structure 4.2.1 Effect of imperfect hole sizes 4.2.2 Effect of tapered holes 4.2.3 Experimental results 4.2.4 Simulations of an incident Gaussian beam on a microcavity  37 37 38 41 49 54 55 62 65  Conclusion  82  Bibliography  72  86  vi  List of Tables 3.1 3.2  4.1 4.2  4.3  Nominal specifications of uniform InP photonic crystal fabrication Parameters of ellipsoidal mirror used in the reflectivity apparatus Structure of uniform InP photonic crystal samples, as determined by fit to Green's function simulations Structure of uniform InP photonic crystal samples: nominal fabrication parameters, parameters as determined by fit to Green's function simulations and as measured with a scanning electron microscope Hexagonal photonic crystal defect array fabrication parameters as measured by S E M  23 28  50  50 66  Vll  List of Figures 2.1 Schematic diagram of a Bragg stack 7 2.2 Schematic dispersion diagram of a semiconductor planar waveguide slab in air 9 2.3 Schematic dispersion diagram of a periodically textured planar waveguide slab in air 10 2.4 Schematic diagram of a defect in a ID photonic crystal . . . . 11 3.1  Schematic diagram of the nominal layer structure of the InP microcavity samples 3.2 Micrograph of an InP defect array 3.3 Schematic diagram of the central region of a hexagonal defect array 3.4 Schematic diagram of a group of nine hexagonal defect arrays 3.5 Schematic diagram of the nominal layer structure of the InP microcavity samples with a l-^,m undercut 3.6 Schematic diagram of the uniform InP photonic crystal samples fabricated by Dan Dalacu at the National Research Council 3.7 Schematic diagram of microreflectivity set-up 3.8 Parameters of ellipsoidal mirror defined 3.9 Sample image of hexagonal microcavity array 3.10. Schematic diagram of the broad-spectrum reflectivity set-up . 3.11 White light specular reflectivity set-up 4.1  18 18 19 20 21 23 25 28 31 32 36  Afc-spacediagram demonstrating the crystal symmetry directions of a 2D hexagonal array 38 4.2 Experimental and simulated reflectivity spectra prior to Green's function code modification 39 4.3 Experimental and simulated reflectivity spectra following Green's function code modification 40  List of Figures 4.4  4.5 4.6 4.7 4.8 4.9 4.10  4.11  4.12 4.13 4.14 4.15 4.16  4.17  4.18 4.19 4.20  Typical reflectivity spectrum of a uniform InP photonic crystal sample showing background Fabry-Perot modulation and narrower spectral features due to photonic crystal bandstructure. Schematic diagram of the uniform photonic crystal samples studied with the specular reflectivity set-up Effect of varying filling fraction on simulated reflectivity spectra of uniform InP photonic crystal samples Effect of varying oxide thickness on simulated reflectivity spectra of uniform InP photonic crystal samples Effect of varying InP-air grating thickness on simulated reflectivity spectra of uniform InP photonic crystal samples Effect of varying epoxy thickness on simulated reflectivity spectra of uniform InP photonic crystal samples Experimental and simulated reflectivity spectra at different angles of incidence of s-polarized light for an InP uniform photonic crystal (Sample I. K crystal direction) Experimental and simulated reflectivity spectra at different angles of incidence of p-polarized light for an InP uniform photonic crystal (Sample I. K crystal direction) Bandstructure diagrams for an InP uniform photonic crystal (Sample III) Schematic diagram of the central region of a square defect lattice Micrograph of the central region of an InP-based microcavity defect structure showing discernible variation in hole radii . . Schematic diagram of a structure simulated to investigate the effect of random variation in hole radius Effect of various amounts of random variation of hole radii (with a uniform distribution) on the Q value of a hexagonal defect array Effect of various amounts of random variation of hole radii (with a uniform distribution) on the Q value of a square defect array Real-space plots of the field intensities surrounding the defect in the simulated hexagonal microcavity arrays Real-space plots of the field intensities surrounding the defect in the simulated square microcavity arrays S E M micrograph of a textured waveguide sample with slanted hole sidewalls  viii  41 42 45 46 47 48  51  52 53 55 56 57  58  59 60 61 62  List of Figures 4.21 Effect of hole sidewall taper on the Q value of a hexagonal defect array 4.22 Effect of hole sidewall taper on the Q value of a square defect array 4.23 Representative reflectivity (normalized reflection) spectra of InP-based microcavity arrays taken with the microreflectivity set-up 4.24 Reflectivity (normalized reflection) spectra of N R C sample EBWII-III. Group A l , Array 5 taken with the broad-spectrum reflectivity apparatus normalized with respect to two different reference spectra 4.25 Representative reflectivity (normalized reflection) spectra of InP-based microcavity arrays taken with the broad-spectrum reflectivity set-up 4.26 Comparison of reflectivity (normalized reflection) spectra taken with the microreflectivity set-up with those taken with the broad-spectrum apparatus 4.27 Schematic diagram showing positions of Gaussian beams incident on a hexagonal defect array studied in an F D T D simulation 4.28 Comparison of simulated apertured reflectivity spectra acquired with an incident Gaussian pulse striking at various distances from the defect centre 4.29 Schematic diagram of the E-field of the mode in a hexagonal defect array and the effects of the positioning of the incident excitation beam 4.30 Simulated electric field intensities of radiation reflected from a hexagonal defect structure 4.31 Simulated electric field intensities of radiation reflected from a hexagonal defect structure apertured at different locations on the sample 4.32 Schematic diagram showing positions of square apertures of side 1.66 jim used to sample reflected light from a hexagonal defect array in an F D T D simulation 4.33 Simulated electric field intensities of radiation reflected from a hexagonal defect structure with various aperture sizes . . . .  ix  64 64  68  ;  69  70  71 73  74  75 77  78  79 80  Acknowledgements I am extremely grateful to my supervisor. Dr. Jeff Young, for allowing me to study and work as part of his research group. His passion for. prowess at and dedication to his craft are genuinely inspiring. Thanks also to Dr. Georg Rieger for his extensive assistance with my optical experiments. Murray McCutcheon for sample preparation, patient help with my simulations and allowing me to pick his brain clean, as well as Mohamad Banaee. Dr. Andras Pattantyus-Abraham. Allan Cowan and Christina Kaiser for their much-needed tidbits of wisdom—scientific or otherwise; solicited or otherwise. I would also like to acknowledge Dan Dalacu at the National Research Council for sample preparation. Justin Ho and Jo Chun Fai Man deserve thanks for their work with the nanopositioning software, as do the students past, including Dr. Jody Mandeville. for establishing the infrastructure in the lab that made this work possible.  Finally. I would like to extend sin-  cere thanks to my family and close friends who provided unwavering support when it was most needed, including Jeff Mottershead. Anne Liptak. Scott Webster and Dr. James Fraser. just to name a few.  i  Chapter 1 Introduction The effort to create smaller, faster and more powerful computers has driven the microelectronics industry to innovate means of increasing the density of devices such as transistors on integrated circuit chips. The miniaturization of microelectronic devices is predicted to reach the physical limits of what conventional silicon-based technology can offer. Thus, within the past decade, scientific curiosity and attention have turned toward quantum computing and all-optical signal processing. Quantum computing not only proposes the possibility of faster computation, but also the ability to harness exclusively quantum phenomena, such as entanglement, to process, store and encrypt information in a manner with no classical analogue. Rather than employing bits of Is and Os for computation, quantum computers make use of quantum bits, or "qubits," the state of which can be any superposition of two basis states [1]. A number of systems have been proposed as potential bases for the storage and manipulation of qubits. including ion traps, nuclear magnetic resonance (NMR) of single molecules, and cavity quantum electrodynamics (cavity QED). There has been extensive development of the last of these, as cavity QED makes use of many of the techniques well-established in the microelectronics industry and allows for the direct manipulation of qubits. The basic system in cavity QED is a two-level emitter interacting resonantly with a single optical cavity mode [2], which can be realized by coupling an atom [3] or a quantum dot (QD)—typically a semiconductor structure with dimensions on the order of a few nanometers, which, by virtue of its electronic properties, acts as an artificial atom—with a high-finesse microcavity, such  Chapter 1.  Introduction  2  as a photonic crystal defect [4]. A photonic crystal [5] is a dielectric material with a spatially periodic variation in refractive index. The periodicity may be in one. two or three dimensions and is essentially an optical analogue of the periodic potential within a semiconductor due to the atoms at crystal lattice sites. While the periodic potentials in semiconductors give rise to an electronic bandgap. the periodicity in a photonic crystal can result in a photonic bandgap. and light within a certain range of frequencies cannot propagate through such a material. A break in the periodicity serves as a defect, and just as defects in semiconductors (due. for example, to impurities) can give rise to a state within the electronic bandgap. a photonic crystal defect can give rise to modes within the photonic bandgap. These modes, because they cannot propagate through the remainder of the crystal, are localized within the vicinity of the defect, and if the defect's dimensions are on the order of a single wavelength of light, it is possible that there be only one allowed mode localized to the defect. In this case, the small region in which the defect modes are localized serves as a single-mode optical microcavity. The lifetime of the mode resonant within a microcavity may be quantified by its Q value, or quality factor, defined as Q =  2ir (oscillating energy) energy loss per cycle of oscillation  (1.1)  The higher the damping, the lower the Q value, and the faster the resonant mode decays. A system of an optical microcavity coherently coupled to a trapped ion or a quantum dot has been proposed as the basis for a two-qubit system, where the quantized field within the microcavity is the "photon qubit" and the ion or QD constitutes a "material qubit." The applications of this cavity QED system to quantum information processing stem from the ability to convert between the quantum states of material qubits and photon qubits. allowing  Chapter 1. Introduction  3  for the development of two-qubit logic phase gate protocols via atom-atom (QD-QD), atom-photon (QD-photon) or photon-photon entanglements [6, 7]. Cavity QED systems hold promise for several proposed ideas involving distributed quantum information processing and communication [8 9. 10]. Additionally, these systems are being considered as robust, controllable sources of single photons [11]. Epitaxial techniques to grow InAs/InP quantum dots in specific predictable locations on a wafer have been developed at the National Research Council's Institute for Microstructural Sciences [12] and their optical emission properties have been well documented [13]. As well, extensive work has already been done in Dr. Young's research group to study the properties of a waveguide-coupled resonant cavity on a silicon ridge waveguide [14]; however, the Q values measured for this cavity were on the order of 300 to 1200. whereas experiments on microcavities formed by defects in 2D photonic crystals [15] have measured Q values in excess of 10 . The eventual aim of a major project in Dr. Young's laboratory is to create the basic primitive for cavity QED by selectively locating epitaxial quantum dots within wavelength-scale optical cavities formed as photonic crystal defect states in InP waveguides. A waveguide used to couple light into and out of the quantum dot and microcavity system would allow for a singlephoton level study of the system's nonlinear optical properties [16]. Before this can be achieved, however, the properties of the optical microcavities must first be thoroughly studied and understood in order to determine the optimal means to achieve the coupling. ;  5  For this thesis, simulations and optical experiments were performed on microcavity defects in InP-based planar semiconductor waveguides textured with a periodic array of air holes in an effort to study the properties of the resonant cavity modes. The goal of these efforts was to ascertain the resonant properties of the defect modes, their Q values and mode volumes in particular. The microcavities available for these studies were fabricated in  Chapter 1.  Introduction  4  the top layer of an InP planar waveguide wafer. This is convenient because a large number of such microcavities can be fabricated with slightly different photonic crystal parameters, and. in principle, their optical properties can be studied by spectroscopically probing the microcavities individually from above. Two viable options for probing the microcavities were considered: one based on a near-field scanning optical microscope (NSOM)[17], which allows for mapping the field distribution of the localized state; and one based on resonant scattering of light from the microcavity. Since an N S O M with a tunable laser source was unavailable and the primary interest was in identifying the energies and linewidths of the resonant modes rather than the field distribution, resonant scattering techniques were developed. The apparatus for resonantly scattering from the wavelength-scale microcavities would ideally have been developed using a sample known to support a well-characterized mode. Unfortunately, the microcavities were being designed and fabricated for the first time in parallel with the development of the microreflectivity apparatus. Negative results from the available samples prompted numerical simulations with two goals: i) determining the impact of fabrication imperfections on the quality factor of the microcavities. and ii) estimating the modulation depth of resonant features in spectra collected from ideal samples, using the assembled apparatus. Chapter 2 gives an overview of the physical principles governing planar photonic crystals and microcavity defects: it also describes the techniques used to numerically simulate the structure and experimental conditions of the microcavities studied. Chapter 3 of this thesis outlines the experimental design, including the apparatus and techniques used in the optical experiments to measure the reflectivity properties of planar photonic crystals as well as defect structures. The chapter also describes the basic fabrication process used to produce the samples studied. Chapter 4 summarizes the simulation and experimental results along with  Chapter 1.  Introduction  5  some of their implications. Finally. Chapter 5 suggests some potential future directions for this research; i n particular, improvements that could be made to the experimental and sample designs that may yield more fruitful results.  6  Chapter 2 Background 2.1  P h o t o n i c crystals  Few would dispute the claim that the understanding and application of semiconductor physics revolutionized technology for the developed world. The electronic bandgap inherent in semiconductors offers unparalleled control over electron flow and the miniaturization of now-ubiquitous electronic devices such as transistors, allowing technologies including computers and lasers to become accessible and affordable to the general public. The proclivity toward miniaturization was documented in 1965. when Gordon Moore observed the empirical trend that the number of transistors on an integrated circuit chip appeared to double roughly every 18 months, a trend now known as 'Moore's law.' Moore's law has remained fulfilled to the present day. but if current miniaturization efforts continue unabated, the physical limits of what semiconductor-based electronics can offer will soon be reached. Photonic crystals are in essence, the optical analogue of the semiconductor, and several researchers have suggested that they might form the basis of information processing technologies that will eventually replace silicon-based electronic devices. Whereas electrons in a semiconductor experience a periodic potential due to the atoms at the crystal lattice sites, giving rise to the electronic bandgap, photons in a photonic crystal experience an analogous periodic 'potential' due to a lattice of periodically varying dielectric media. This periodicity may exist in one, two or three dimensions. A prototypical example of a one-dimensional (ID) photonic crystal is a Bragg stack: a multilayer film composed of alternating materials exhibiting a contrast in ;  Chapter 2. Background  7  refractive index. A schematic diagram of a Bragg stack is shown in Figure 2.1. These multilayer films are used as dielectric mirrors: they efficiently reflect light (with wavelengths in a range of approximately twice the stack's optical period) that impinges upon the stack at normal incidence to the direction of periodicity, where the optical period is the quotient of the vacuum wavelength of the light and the average index of the structure. Light in this forbidden range of wavelengths is diffracted backwards: the reflection is perfect, without losses. Hence, for normally incident radiation, there is a photonic stopband. the width of which is a function of the contrast in refractive index. For an infinite structure, the extinction of transmitted light is perfect; for a finite structure, however, some tunnelling, and hence non-zero transmission of wavelengths within the photonic stopband. is expected. This stopband shifts for light incident off normal to the direction of periodicity, particularly for light incident on other faces of the crystal, and hence a ID Bragg stack cannot possess a complete bandgap.  Figure 2.1: Schematic diagram of a Bragg stack, an example of a ID photonic crystal. The crystal is composed of alternating layers of materials with a refractive index contrast. Light within a certain wavelength range travelling in the direction of periodicity will not be transmitted through the stack.  Three-dimensional (3D) photonic crystals, which are periodic in all three directions, can exhibit a complete bandgap where radiation within a range of wavelengths is not transmitted regardless of its angle of incidence on any  Chapter 2. Background  8  face of the crystal; however. 3D photonic crystals are challenging to fabricate. The periodicity must be comparable to the wavelength of the bandgap—on the order of hundreds of nanometers—for such 3D crystals to be convenient for use in laser and detector technology. Also, only certain lattice types can support a full bandgap and then only if the magnitude of dielectric contrast is sufficiently high. The fabrication of two-dimensional (2D) photonic crystals, on the other hand, is much easier to execute, as it can be based on existing epitaxial growth and lithographic techniques developed in the microelectronics industry. Pure 2D photonic crystals are periodic in two directions and homogeneous in the third; a photonic bandgap can exist for radiation propagating in the plane of periodicity, although such structures also cannot possess a full photonic bandgap. However, by fabricating a 2D photonic crystal in a planar waveguide, many of the useful properties of a photonic bandgap material can be exploited. Both the total internal reflection restricting light to planar propagation within the waveguide, and the in-plane Bragg diffraction property of the photonic crystal, allow one to make use of the photonic pseudo-bandgap of such structures [18]. This thesis deals exclusively with 2D photonic crystal structures made in semiconductor slab waveguides. An untextured planar waveguide, a 2D high-index semiconductor slab in air. for instance, will support bound modes that exhibit a dispersion similar to that shown in Figure 2.2. The dispersion of light in air and within the bulk semiconductor are represented by the straight lines—known as light lines—with slopes proportional to the reciprocal of the refractive index of the corresponding material. Above the air light line, there exists a continuum of radiation modes. Below the slab light line, no electromagnetic modes exist. Between the light lines is a region in which bound modes—modes that are confined to the planar waveguide by total internal reflection at the semiconductor- air interface—exist. When periodic texturing is added, such as a 2D array of air holes, pho-  Chapter 2. Background  9  O) CD C LU  Continuum of radiation modes 1/n* Bound modes  In-plane wavevector Figure 2.2: Schematic dispersion diagram of a semiconductor planar waveguide slab in air.  tonic bands can arise, just as the periodic potentials within a semiconductor give rise to the electronic bands. In accord with Bloch's theorem, the dispersion diagram can be zone-folded into the first Brillouin zone. Some bound mode bands are zone-folded into the region above the air light line, as depicted in Figure 2.3; such modes are considered "leaky" as they have Fourier components radiating out of the slab and hence serve well to couple light into and out of the textured waveguide to probe its optical properties. Such structures can be designed such that there is a full bandgap for bound modes: in this situation, it is the radiation modes that overlap this bound mode that prevent the structure from possessing a true bandgap for light.  Chapter  2.  Background  10  Brillouin zone boundary  CD  *  •  i _  y  CD C HI  Radiation modes  |  /* s  /  1 ; •  ,  ,  s  I  /  11/n ir  /  a  ! •  Leaky mode  r /  •  \ Bound : modes ,  gap  -  f  "  1/flslat tf  A  *~  i  r **"  >  In-plane wavevector Figure 2.3: Schematic dispersion diagram of a periodically textured planar waveguide slab i n air showing bound mode, leaky mode and radiation mode dispersions.  2.2  Defects and microcavities  Defects i n semiconductors; such as impurities i n the crystal structure, can give rise to states within the electronic bandgap. B y analogy, defects in photonic crystals can yield modes w i t h i n the photonic bandgap. A defect i n a photonic crystal is an interruption i n its periodicity. Consider for instance a I D periodic stack i n which one of the layers is wider than the others, as schematically illustrated in Figure 2.4. T h i s layer serves as a defect as it breaks the crystal's periodicity. Depending on the thickness of the defect layer, light w i t h i n the stopband of the I D crystal can be trapped between two perfect reflectors. If the w i d t h of the defect is on the order of a single wavelength, there may be only one frequency at which such a mode can resonate.  11  Chapter 2. Background  Figure 2.4: Schematic diagram of a defect in a ID photonic crystal. The thicker layer serves to interrupt the crystal's periodicity and acts as a defect.  For a planar waveguide textured with an array of air holes, one method of introducing a defect is to shrink, enlarge or omit one of the holes. This results in a microcavity in which a mode can be confined in two directions by the periodic texturing and in the third direction by total internal reflection. States within the bandgap are localized in the vicinity of the lattice defect and thus the localized photonic defect states are essentially 3D optical microcavity modes. A salient property of a resonant cavity mode for the purposes of cavity Q E D is a measure of its lifetime, given by its Q value defined in Equation 1.1. Also of interest for cavity Q E D is the volume of the cavity, V , as the cav  enhancement factor of the cavity structure, defined as to the ratio of spontaneous emission rate within the cavity to that in free space, is proportional to Q and inversely proportional to V  cav  [19]. Applications in optoelectronics  and quantum computing demand a sustained high electric field per photon, achieved with a high Q value and a low cavity volume. In previous experimental studies [15], Q values in excess of 10 and mode 5  volumes of approximately 0.35 (A/2) have been attained. In the 2D photonic 3  crystal waveguide geometry, the Q is ultimately limited by radiation into the upper and lower half-spaces.  Chapter 2. Background  2.3  12  Simulation techniques  2.3.1  Green's function model  In order to study the photonic bandstructure of textured planar waveguides, an existing computer code was used to simulate the response of the waveguide to electromagnetic radiation. This code employs a Green's function technique to solve Maxwell's equations in order to model the scattering of light incident on a planar textured waveguide and its validity has been verified by comparison with experimental results [20] as well as other models [21]. Actual planar waveguide structures consist of numerous layers; an example of the structure studied for this thesis is depicted in Figure 3.6. The code accurately models the behaviour of harmonic plane waves—at any angle of incidence—scattering off of such a layered structure. Any number of layers may be defined, including semi-infinite upper and lower layers. The code solves Maxwell's equations in the waveguide structure by using the periodic polarization within the textured region as the driving term for a Green's function [22]. For a single Fourier component of the field in the grating, the self-consistent solution is given by  E(u,Ki,z)  =  E (u..Ki,z) hom  where co = Coe is the frequency and Ki is the in-plane wavevector of a plane wave incident from the upper half-space. E  h o m  , ^  and ^t^,  as well as the  full Green's function simulation approach, are described in detail in Cowan (2000) [22]. By truncating the Fourier series describing the in-plane components of the field at N, the infinite set of vector integral equations implied in Equation (2.1) can be reduced to 3N scalar algebraic equations. However, this  Chapter 2. Background  13  requires that the textured region being modelled be sufficiently thin such that the fields in the region can be approximated as constant in the z-direction. eliminating the integral over dz' in Equation (2.1). If the textured region is too thick, it may be divided into thinner regions each satisfying the approximation. ;  2.3.2  F D T D model  The finite difference time-domain (FDTD) algorithm was developed by Yee in 1966 [23] as a numerical means of solving Maxwell's equations. Six coupled difference equations; one for every spatial component of each of the electric and the magnetic fields are derived from the differential form of Maxwell's equations and are time-stepped forward in a leapfrog scheme: discretized electric fields are calculated at temporal gridpoints n while discretized magnetic fields are calculated at temporal gridpoints n + 1/2. Because FDTD is grid-based both spatially and temporally, and enforces the boundary conditions at material interfaces, the technique can accurately model the transient response of structures with complex geometries textured on the order of a radiation wavelength. As well, FDTD makes no assumptions regarding time-varying fields or the direction of wave propagation. For these reasons. FDTD is ideal for the simulation of such structures as photonic crystal defects and microcavities., which have essential structural variations at a sub-micron scale. ;  In order to ensure stability in the FDTD simulation, the time-step must be chosen such that it does not overtake the propagating wave. That is for a Ax spatial interval and an electromagnetic wave propagating at c. the timestep A t must satisfy At < c/Ax. The spatial meshing must be chosen such that 10-20 points per wavelength are sampled to avoid numerical dispersion. ;  Boundary conditions must be carefully considered when defining a simulation area in FDTD. Periodic, reflective or absorbing boundary conditions may be used depending upon the nature of the simulation. Symmetric or  Chapter 2. Background  14  antisymmetric boundary conditions may be defined to take advantage of the symmetry of a structure being simulated and reduce the simulation time. The FDTD software used to simulate photonic microcavity structures for this thesis. FDTD Solutions, was developed by Lumerical Solutions. It permits three-dimensional simulation of dielectric structures with a variety of electromagnetic sources. The computer aided design (CAD) interface allows the user to define and visualize the physical structures to be simulated, including structure size and index. The user may introduce electromagnetic sources such as dipoles. plane waves and Gaussian beams, and specify the field amplitude, spectral bandwidth and polarization of each source. For a Gaussian beam, the spot size—defined as the full-width of the beam at half maximum (or central) intensity—is also specified by the user. The user then defines a simulation volume encompassing the structures and sources of interest and defines the boundary conditions on each of the six rectangular faces of the volume. The software permits absorbing boundary conditions by means of a perfectly matched layer [24], as well as symmetric and antisymmetric boundary conditions, which allow for symmetry properties in the simulated structure to be exploited in order to reduce the total simulation volume and hence the simulation time. Finally, the user may introduce monitors into the simulation volume that can record time- and frequency-domain data showing both the transient and steady-state behaviour of the structure being simulated.  2.4  Ideal samples  As will be shown in Chapters 3 and 4. the samples studied for this thesis included uniform photonic crystal arrays 90 p,m across as well as smaller defect arrays that are only roughly 8 jum across. The ultimate aim is to study the microcavity resonance properties of the defect structures. However, inherent in the fabrication of these structure is uncertainty in the fabrication parame-  Chapter 2. Background  15  ters and the actual fabricated structure will likely deviate from the ideal, or from nominal. The effect of this uncertainty can be curtailed by bracketing the controllable fabrication parameters and producing multiple defect arrays: with sufficient bracketing, the hope is that a few of the fabricated arrays will fall within a range of tolerance that will yield observable resonance effects. Once the defect array samples are fabricated, they must be measured to determine their actual structural parameters. However, measuring the pitch and diameter of the holes in the structure with a scanning electron microscope, for example, is subject to the very same drifts that generate the uncertainty in sample parameters and is therefore not necessarily reliable. An example of a contribution to this uncertainty is the natural degradation of the tungsten filament used to generate the electron beam; as the filament's integrity changes, so too does the quality of the electron beam, leading to changes in astigmatism, for instance, which can decalibrate the SEM and yield a systematic error in measurement. Even if one were to recalibrate the SEM with every use. there is uncertainty in determining exactly where on a planar textured waveguide to take a measurement of hole pitch or hole diameter. As shown in Section 4.1, specular light reflectivity spectra of uniform photonic crystal samples and simulations performed with the Green's function code together yield reliable information regarding the filling fraction of the 2D texturing; the defect arrays, on the other hand, are too small to offer information in this regard. Additionally, the specular spectra and simulations of the uniform samples may be jointly used to determine the layer composition of the structure in the third dimension. Although models are inherently imperfect and may. through fitting to experimental data, give average values for sample parameters that deviate from the actual parameter values for a sample, it is possible that a slight shift of the "sample parameters" as used by the imperfect modeL would compensate for the approximations in the model, yielding a more useful result than para-  Chapter 2. Background  16  meter values measured on an ideal SEM. A specific example of this involves fabrication imperfections, some of which are highlighted in §4.2.1. which examines the effect of random variations in hole sizes in a planar microcavity array; and §4.2.2. which examines the effect of tapered—and therefore nonvertical—hole sidewalls. The holes within a real 2D photonic crystal array would most likely not have perfectly vertical sidewalls. Therefore, the upper diameter of these holes, as measured by an SEM. would not give a clear indication of the crystal's total filling fraction, a property that, as shown in §4.1.2. has a substantial effect on the crystal bandstructure. A fit to the Green's function model, on the other hand, would better correspond to the actual filling fraction. Ideal samples should therefore include both a 90 /«m square uniform photonic crystal region as well as bracketed set of defect arrays. The uniform region may be studied with a white light specular reflectivity setup as described below in Section 3.4. The Green's function code could then be used to simulate the structure and the fit to the experimental spectra may be used to garner information regarding sample parameters. In particular, it could be used to provide a reliable measure of filling fraction that may be used to calibrate the measurement of the defect array sample parameters. While such samples were not available for this thesis, the results of this characterization method, as described in Section 4.1, mean that future fabrication efforts will almost certainly adopt this approach in order to facilitate acquisition of a comprehensive understanding of the sample structure.  17  Chapter 3 Experimental design This chapter describes the structure and fabrication of the photonic crystal samples as well as the optical techniques and apparatus used to study them.  3.1  Sample structure  Two principal types of samples are investigated for this thesis: an InP-based microcavity structure and an InP-based bulk photonic crystal lattice structure, both fabricated at the National Research Council (NRC) Institute for Microstructural Sciences (IMS) by Dan Dalacu in Ottawa. Ontario. The optical characterization techniques described in this thesis will also be applied to silicon-based microcavities being developed at UBC.  3.1.1  InP microcavity structure and fabrication  The InP microcavities investigated consist of nine rings of a hexagonal array of nominally identical air holes surrounding a larger central defect hole in an undercut freestanding InP membrane 300 nm thick. The layer structure of the sample is depicted schematically in Figure 3.1. The size of the central hole is modified, and thus serves as the defect in the microcavity structure. A micrograph of an InP defect array is seen in Figure 3.2. The radius r of the holes in the array, the radius of the central defect hole and the centreto-centre pitch a of the holes, as defined in Figure 3.3 are varied from one array to the next. Arrays are patterned in groups of nine, in three columns and three rows.  Chapter 3. Experimental design Untextured j , r e a  Textured region  o r  • •  iH  H  Air undercut  • !•••  18  300 nrr  400 nn-  Figure 3.1: Schematic diagram of the nominal layer structure of the I n P m i crocavity samples. Note that one of the microcavity samples studied underwent additional fabrication steps to yield a 1-jim rather t h a n a 400-nm air undercut. T h a t structure is depicted i n Figure 3.5.  Figure 3.2: M i c r o g r a p h of an InP defect array. T h e undercut is visible as a slightly darker roughly square region surrounding the hexagonal crystal. T h e array was fabricated by D a n D a l a c u at the N R C I M S and the micrograph was taken by M u r r a y M c C u t c h e o n .  Chapter 3. Experimental design  19  OOO OOOO OO0OO OOOO ooo  Figure 3.3: Schematic diagram of the central region of a hexagonal defect array. Parameters a. r and are defined.  In one dimension, r is modified; in the other dimension, is modified; as shown schematically in Figure 3.4. The InP microcavity structures are fabricated at the NRC IMS by Dan Dalacu using electron-beam lithography, inductively coupled plasma (ICP) dry etching and wet etching on an untextured wafer consisting of a 300-nm layer of InP grown on a 400-nm sacrificial layer of Ino.35Gao.65As on a bulk InP substrate. The fabrication begins with a deposition of 30 nm of Si02 on the untextured wafer, followed by a deposition of 25 nm of Cr. 300 nm of ZEP electron beam resist is then spun onto the sample, at which point it is fully prepared for electron beam lithography. Due to the fact that the electrons within the electron beam impinging upon the resist layer have some distribution about the central focus as well as the fact that electrons backscatter from the substrate at an angle through adjacent resist, the electron beam not only affects the size of one hole, but of neighbouring holes as well. This proximity effect results in different values of hole radii within a given array. In particular, holes with the largest number ;  Chapter 3. Experimental design  20  increasing r  # # # Figure 3.4: Schematic diagram of a group of nine hexagonal defect arrays; several of such groups with varying pitch a were fabricated into an InP membrane at the NRC IMS.  of nearest neighbours are larger than those with the fewest; namely, those holes along the edge of the microcavity array. This effect has been exploited by Painter [25] to improve confinement within the microcavity. but for the purposes of this thesis, attempts were made to counteract the proximity effect to achieve more consistent and predictable hole sizes throughout the InP microcavity array. Therefore, in addition to the focused exposure of the electron beam on the sample to produce the desired grating holes in the electron beam resist mask, a ring 1 pm beyond the edge of the array was further exposed to an electron beam dosage of up to 30 pC/cm . Thus, those holes on the array's edge are given as much electron beam exposure as those holes with a full complement of nearest neighbours, producing holes of a more uniform size throughout the array. 2  Following electron beam exposure, the sample is developed for 2 minutes in orthoxylene. The Cr layer is etched by ICP etching in a C ^ / A r / C ^ mixture for 20 minutes. The SiC>2 layer is then etched in an Ar/C^Fs mixture for 1.5 minutes. Finally, the InP is etched with a mixture of CI2/CH4/H2. The Cr mask is stripped by ICP etching in a Cl2/Ar/0 mixture while 2  Chapter  3. Experimental  21  design  the SiC>2 mask is removed with a 7:1 B O E etch.  A mixture of 1:8:320  H S 0 4 : H 0 2 : H 0 is used to undercut the microcavity arrays by removing 2  2  2  the InGaAs layer under the region of the array, leaving a free-standing InP membrane.  Freestanding InP membrane with a 1-pm undercut One sample that was studied underwent additional fabrication steps to yield a freestanding 300-nm InP waveguide layer with a 1-pm undercut. Following the orthoxylene etch, the sample is glued top-down onto a glass substrate with a 1-pm layer of epoxy indexed-matched to glass.  The original bulk  InP substrate and the sacrificial InGaAs layer are both removed, leaving the 300-nm InP membrane on a layer of epoxy. The epoxy is then etched with 0  2 ;  leaving, in the textured regions, a freestanding textured InP membrane  above a 1-^m air undercut. However, under the untextured regions of the membrane, where the oxygen cannot penetrate, the sample structure consists of a 300-nm InP layer directly on a layer of epoxy on top of the glass substrate, as shown schematically in Figure 3.5. Untextured region  Textured region  Epony  Air undercut  Glass substrate  Figure 3.5: Schematic diagram of the nominal layer structure of the InP microcavity samples with a 1-pm undercut.  Chapter 3. Experimental design  22  Other material systems for photonic crystal microcavities The same basic fabrication process—patterning the array of holes onto a resist mask, anisotropic dry etching to generate the pattern of holes in the semiconductor membrane, and wet etching an underlying sacrificial layer to a leave a freestanding membrane—may be applied to a number of different material systems. In-house fabrication of microcavity defect structures with a 213-nm GaAs membrane with a 1150-nm Alo.9s5Gao.015As sacrificial layer has been achieved by Murray McCutcheon, and structures with a 195-nm silicon membrane on a 1200-nm SiC>2 sacrificial layer by Andras PattantyusAbraham. The InP-based defect cavities fabricated at the NRC were the best available for this thesis work.  3.1.2  InP uniform photonic crystal structure and fabrication  The uniform photonic crystal lattice samples investigated were also fabricated by Dan Dalacu at the NRC IMS. They consist of a layer of Si02 on a layer of InP. Arrays of a hexagonal lattice of holes nominally approximately 250 nm in diameter and 460 nm apart, patterned within a square measuring 90 pm on each side are etched through both layers of the material. The photonic crystal was patterned by electron beam lithography and dry-etched using ICP. The InP membrane was then epoxied onto a glass slide; this process resulted in epoxy being pushed into the holes. The epoxy, index-matched to the glass, was etched with 0 from 0 to 2 minutes, leaving a final structure of a top layer of an oxide grating with air-filled holes , a layer of undetermined thickness of an InP grating with air-filled holes, and a layer of undetermined thickness of an InP grating with epoxy-filled holes, all on a glass substrate. A schematic diagram of the structure is shown in Figure 3.6. 2  1  One sample did not undergo O2 etching after it was epoxied onto the slide, and hence had a top layer of oxide grating with epoxy-filled holes. 1  Chapter 3. Experimental design  23  Figure 3.6: Schematic diagram of the uniform InP photonic crystal samples fabricated by Dan Dalacu at the National Research Council.  Three samples were fabricated to the nominal specifications outlined in Table 3.1. It should be noted that many of the final structure parameters of the fabricated samples were found to deviate substantially from the predicted nominal values specified in the table. Please refer to §4.1.3 for parameter values determined by experiment and subsequent simulations. Sample Oxide thickness (nm) InP thickness (nm) Hole diameter (nm) Hole pitch (nm) O2 etch of epoxy (minutes)  Sample I Sample II 100 100 310 310 246 246 460 460 1 0  Sample III 130 310 240 460 2  Table 3.1: Nominal specifications of uniform InP photonic crystal fabrication.  Chapter 3. Experimental design  3.2  24  M i c r o r e f l e c t i v i t y apparatus  In order to study the resonant modes of the microcavity structures, a microreflectivity apparatus was designed and built by the author to probe the effect of impinging E M fields on the localized region of the microcavity defect. Past efforts [17. 26. 27. 28] to map local optical intensity in photonic crystals have employed a near-field scanning optical microscope (NSOM) with an optical fibre to transmit incident light and collect scattered and evanescent fields. With an NSOM technique, the fibre is kept only a few nanometers from the structure's surface, and therefore collects the following radiation: the evanescent fields coupling from the waveguide slab, the vertically radiated photoluminescence (if present), and the radiative scattering of the localized mode resulting from the waveguide texturing. The signal from the first of these gives information about the field distribution of the localized state within the defect. Our objective, however, is to identify the energy and linewidth of the localized state, with minimal perturbation. The microreflectivity apparatus developed for this thesis, schematically shown in Figure 3.7, employs a microscope objective lens rather than a fibre to excite the defect state. It was built to probe the microcavity structure at telecommunications wavelengths near 1.5 pm but is easily adaptable for a broad variety of wavelengths and light sources.  Chapter 3. Experimental design  25  ToFTIR (with InGaAs detector)  s  Ellipsoidal mirror  CCD camera  Microscope objective lens Beamsplitter  :  LV  Nanopositioner  0.9 OD filter Beam stop  Translation stage  Sample  Figure 3.7: Schematic diagram of the microreflectivity set-up. The nanopositioner on which the sample sits, as well as the short focal length of the focusing microscope objective lens, allow for precise localization of the light from the optical parametric oscillator. Precise positioning is achieved with the help of a CCD camera to image the samples. When the camera is removed from the beampath. the beam is focused into an FTIR spectrometer with an ellipsoidal mirror.  Chapter 3. Experimental design  3.2.1  26  Light source  The source of the pulsed coherent infrared radiation in the microreflectivity set-up is an Opal™ synchronously pumped optical parametric oscillator (OPO) manufactured by Spectra-Physics. The OPO has an average output power of 200 mW with a pulse length of approximately 100 fs at an 80 MHz repetition rate and a tuning range from 1.440 pm to 1.580 pm. The OPO is pumped by a Tsunami mode-locked Ti:sapphire laser manufactured by Spectra-Physics centered at 810 nm outputting pulses at 80.803 MHz at 1.75 W. The cavity of this laser is purged with N gas. The Tirsapphire laser is in turn pumped by a Millenia Xs diode-pumped cw visible laser, also manufactured by Spectra-Physics, outputting a wavelength of 532 nm at 9.20 W. 2  3.2.2  Optical components  The fundamental function of the optics in this apparatus is to focus infrared light onto a sample, collect light reflected from the sample and focus it into an FTIR spectrometer. The incident beam emerging from the OPO is first attenuated with a 0.9 metallic OD filter to prevent sample damage. The OPO output used at full power and focused onto the sample can be of sufficient intensity to ablate the sample. Additional neutral density filters are used in the reflected beampath to prevent saturation of the CCD camera described in §3.2.5. or the InGaAs detector for the spectrometer described in §3.2.4. The apparatus includes a 15-mm non-polarizing cube beamsplitter from Edmund Optics, designed to transmit 50% and reflect 50% of incident light in the 1100 nm to 1620 nm range. The beamsplitter transmits incident light onto the sample and ultimately directs the light reflected from the sample toward the FTIR. Incident light is focused onto the sample with a 40 x-magnification Mi-  Chapter 3. Experimental design  27  croPlan microscope objective lens with a numerical aperture of 0.65 from Edmund Optics. The objective lens is mounted on a translation stage along the beam path allowing for the light incident upon the sample to be focused and defocused. The light reflected from the sample is directed by the beamsplitter toward an ellipsoidal mirror, which focuses the light into the FTIR. The ellipsoidal mirror was fabricated out of aluminium by Lumonics Corporation, with the specifications given in Table 3.2 and defined in Figure 3.8. The mirror is mounted on a 3-axis translation stage to facilitate mirror positioning for alignment optimization.  3.2.3  Positioning mechanics  The microcavity sample is temporarily adhered with a modest amount of silicone vacuum grease onto an aluminum disk 1" in diameter and 1/4" thick. The disk is then secured in a 1" mirror mount with x and y tilt control, mounted onto a nanopositioning system. The tilt controls are used to adjust the samples to achieve an angle of incidence as close to normal as possible. The nanopositioning system used is the 3-axis Melles Griot NanoMax TS. which consists of stepper motors as well as piezoelectric actuators. Each stepper motor has a 4-mm range of travel with a resolution of 0.5 fxm. Each piezoelectric actuator has a range of 20 u.m and a resolution of 0.1 yum. Only the stepper motor is used for the experiments conducted for this thesis. The stepper motor is controlled by a LabView VI designed to move the nanopositioner to a specified absolute position and wait, included as part of the Melles Griot nanopositioning system. The program was slightly modified by Jo Chun Fai Man and Justin Ho [30] to offer a more intuitive user interface and to facilitate navigation using the computer keyboard's arrow keys.  Chapter 3. Experimental design  (cm) r (cm) M = Si/S 7"i 2  t  0  (image distance/object distance)  Bi 02  28  150 2 0.013 0.19 ° 14.39 °  Table 3.2: Parameters of ellipsoidal mirror used in the reflectivity apparatus.  Figure 3.8: Parameters of ellipsoidal mirror defined. An ellipse with semiminor axis a and semi-major axis b has two foci: the elliptical mirror collects light from one focus, a distance r i from the centre of the mirror, and focuses it onto the second focus, a distance r from the centre of the mirror. The mirror spans an angle 6i of light from the first focus, and an angle 0 from the second. The numerical values of the parameters of the ellipsoidal mirror used in the optical experiments for this thesis are given in Table 3.2. Figure by W.J. Mandeville [29]. 2  2  Chapter 3. Experimental design  3.2.4  29  Spectrometer  The light reflected off of the sample is analyzed with a Bomem DA8 FTIR spectrometer, which consists of a Michelson interferometer with a quartz beamsplitter and an InGaAs detector. These components allow for spectral measurements in the range of approximately 6000 c m to 12000 c m . - 1  3.2.5  -1  Alignment and imaging of photonic crystal arrays  The microcavities investigated by the microreflectivity apparatus consists of a hexagonal array with a central defect. Each array measures approximately 8 pm across and in order to ensure that the incident laser light is focused on the centre of a particular array, two imaging techniques are employed in concert. The Electrophysics Micronviewer Model 7290A. a CCD camera sensitive to wavelengths in the range of 0.4 pm to 1.9 pm is placed in the path of the reflected beam. The beam is focused and defocused on the camera by adjusting the distance between the microscope objective lens and the sample. Neutral density filters are placed in the beampath to prevent saturation of the camera. The image from the camera is observed on a Panasonic TR-990C CRT monitor. When the beam is defocused with respect to the camera, the arrays become discernible. In order to prevent the collision of the focusing lens and the sample, the defocusing is accomplished by increasing rather than decreasing the distance between the lens and the sample. The aim of this stage of imaging is to achieve an approximate alignment on the beam focus with the centre of the array being investigated. By observing the array position with the camera while the beam is defocused and the beam position while the beam is focused, the sample may be moved by the nanopositioning system such that the two coincide.  Chapter 3. Experimental design  30  The absolute position (y , z ) of the array, according to the Lab View posi0  0  tioning; program introduced in §3.2.3, is recorded, and the camera is removed from the beampath. The focus is then adjusted to achieve collimation in the far field of the reflected beam: r = 150 cm ~ oo. x  To determine the precise location of the array, the sample is scanned in 0.5 p,m increments in each of the y and z directions while the intensity of the reflected light measured by the FTIR's InGaAs detector is recorded with respect to position. A square area delineated by (y - 8 /im. ZQ - 8 0  /im), (y - 8 fim. z + 8 pm). (yo + 8 fxm. z - 8 pm), and (y + 8 fj,m. 0  0  0  0  z + 8 pm) is scanned. A Lab View VI designed by Jo Chun Fai Man and 0  Justin Ho [30] controls the sample position and records position and voltage information from the InGaAs detector in a spreadsheet. The information in the spreadsheet is compiled by a MATLAB program into an image of the array, where variations in voltage are shown as colour gradients for each pixel in the region scanned. A sample image is shown in Figure 3.9. Although the spatial resolution is not high, the location of the array is clearly discernible, and the absolute position of the centre of the array can be recorded. When the sample is moved to those coordinates, the beam is unambiguously focused onto the array centre to within 0.5 pm.  3.3  B r o a d - s p e c t r u m reflectivity apparatus  While the microreflectivity apparatus described in Section 3.2 offers the ability to probe a very small area—the spot size of the light striking the sample is approximately 2 p,m—it has the disadvantage of having a relatively narrow tuning range: the microcavity structures are only probed by light between 1.440 f/,m and 1.580 //m. In order to investigate the microcavity structures with a broader spectrum of wavelengths, a white-light reflectivity apparatus was designed and built by the author both to verify and attempt to reproduce the results of the microreflectivity apparatus, as well as to ascertain whether  Chapter 3. Experimental design  31  1085.4 1087.4 1089.4 1091.4 1093.4 1095.4 1097.4 1099.4  Figure 3.9: Sample image of a hexagonal microcavity array taken w i t h the nanopositioning set-up and I n G a A s detector.  relevant spectral features may be observed beyond the tuning range of the O P O . T h e broad-spectrum reflectivity apparatus developed for this thesis is schematically depicted i n Figure 3.10.  Chapter 3. Experimental design 1-mm aperture  32  CCD camera  Sample on 3-axis translation stage Elliptical mirror  Elliptical mirror  To FTIR  Collimating lens  White light source  Figure 3.10: Schematic diagram of the broad-spectrum reflectivity set-up. W h i t e light is focused onto the sample and the reflected light is collected and directed toward an F T I R spectrometer. A 1-mm aperture is used to isolate a particular defect array of interest, discernible on a C C D camera. T h e camera is then removed, thus allowing the reflected light to reach the F T I R . E a c h of the red paths depicted above is 2 c m i n length, while the violet and cyan paths are each 150 cm.  3.3.1  Light source  T h e broad-spectrum reflectivity set-up uses a 12-V. 100-W O s r a m Xenophot halogen photo optic bulb in an Oriel fibre optic illuminator (Model 77501) w i t h variable intensity control. T h e light is coupled out through a P-600-2V i s / N I R fibre manufactured by Ocean Optics.  Chapter 3. Experimental design  3.3.2  33  Optical components  The fundamental function of the optics in this apparatus is to focus white light onto a sample, collect light reflected from the sample and focus it into an FTIR spectrometer. White light emanating from a fibre coupled to an incandescent bulb is collimated by a 22-mm focal length. 15-mm diameter plano-convex lens into a 15-mm non-polarizing cube beamsplitter from Edmund Optics, designed to transmit 50% and reflect 50% of incident light in the 1100 nm to 1620 nm range. Incident light from the beamsplitter is focused onto the sample with an ellipsoidal mirror with the same specifications as those given in Table 3.2 and defined in Figure 3.8. Reflected light is collected by the same mirror, which produces a magnified image at its focus a distance 150 cm away. The light then diverges to a second identical ellipsoidal mirror, which focuses the reflected light into the FTIR. This last mirror is mounted on a 3-axis translation stage to facilitate mirror positioning for alignment optimization.  3.3.3  Positioning mechanics  The microcavity sample is temporarily adhered with a modest amount of silicone vacuum grease onto a sample stage on a three-axis translation stage. The y and z directions allow for movement of the incident beam around the sample, while the x direction allows for the adjustment of the beam focus on the sample. The first ellipsoidal mirror is mounted onto a mirror mount with x and y tilt control to facilitate the optimization of the focus and sample imaging.  3.3.4  Spectrometer  As with the microreflectivity set-up. the light reflected off of the sample is analyzed with a Bomem DA8 FTIR. described in §3.2.4.  Chapter 3. Experimental design  3.3.5  34  Alignment and imaging of photonic crystal arrays  The microcavities investigated by the broad-spectrum reflectivity apparatus consist of a hexagonal array with a central defect. Each array measures approximately 8 pm across, which is considerably smaller than the incident beam's spot size on the sample. The light from the particular array of interest must be isolated from that reflected off the remainder of the sample. This is accomplished by observing the image at the mid-path beam focus using the Electrophysics Micronviewer Model 7290A CCD camera, which is sensitive to wavelengths in the range of 0.4 pm to 1.9 pm. The camera is placed in the beampath and the image from the camera is observed on a Panasonic TR-990C CRT monitor. The groups of nine arrays, as in Figure 3.4. are discernible as spots of reduced intensity. A 1-mm circular iris aperture is placed in the beampath to isolate the array of interest. The x-axis of the 3-axis translation stage and the x and y tilts of the first ellipsoidal mirror may be adjusted while observing the image with the camera to optimize image quality and focus. Once the desired array is isolated, the camera is removed from the beampath, allowing for the reflected light to reach the FTIR spectrometer.  3.4  Specular reflectivity apparatus  An existing experimental set-up [29] is used to measure the specular reflectivity of a uniform photonic crystal. Light from a fibre-coupled white light source is focused upon the sample with an ellipsoidal mirror. The reflected light is collected with a second ellipsoidal mirror, which produces a magnified image of the sample that can be viewed with a CCD camera. At the focus of the second mirror, a rectangular aperture is used to isolate only the portion of the sample that is of interest; in the case of the experiments performed for this thesis, the aperture was used to isolate the area of the sample contain-  Chapter 3. Experimental design  35  ing a uniform photonic crystal array (refer to §3.1.2) from its surrounding untextured substrate. When the CCD camera is removed from the beampath. the beam is directed toward a third ellipsoidal mirror, which focuses the light into the FTIR spectrometer. A polarizer is placed in the beampath to isolate the contributions of the s- and p-polarized components of the light. A schematic diagram of the set-up is shown Figure 3.11. The sample is mounted with a modest amount of vacuum grease onto a stage with rotational freedom such that the incident angle of light upon the sample may be adjusted to a well-defined value from near normal to approximately 80°.  36  Chapter 3. Experimental design  Light Polarizer  Bomem FTIR .  S EM 3  2 cm  Figure 3.11: Specular reflectivity set-up used to study uniform InP photonic crystal arrays. The sample sits on a rotating platform such that the incident angle at which the light strikes it may be adjusted. Light from a fibre is focused by an elliptical mirror onto the sample; the reflected light is collected by a second elliptical mirror and focused at an image plane, where the image may be viewed by a CCD camera. A field stop aperture is used to select only the part of the sample that is of interest. When the camera is removed from the beampath. the reflected light is sent into an FTIR spectrometer by a third ellipsoidal mirror. A polarizer may be added to selectively probe certain polarizations of light. Figure and apparatus from W.J. Mandeville [29].  37  Chapter 4 Results and discussion Optical experiments employing the set-ups discussed in Sections 3.2. 3.3 and 3.4 were performed on the samples described in Section 3.1. Concurrently, simulations based upon the fabricated structures as well as the experimental optical configurations were performed, both with the FDTD simulation software as well as the Green's function code. Simulation results were compared; where applicable, to the results acquired through experimentation. This chapter discusses these results and some of their implications.  4.1  U n i f o r m photonic c r y s t a l lattice structure  White light spectroscopy measurements, made using the specular reflectivity apparatus described in Section 3.4. were performed on the uniform InP photonic crystal lattice structures described in §3.1.2. Raw measured spectra were normalized with respect to a white light reference: the reflected spectrum off of (white) Teflon tape. The experimentally measured reflected spectra are fitted with a slightly modified version of the Green's function model described in §2.3.1. The model is used to accurately ascertain the structural parameters, such as hole radius r and the thickness of the photonic crystal array experimentally investigated. The samples were fabricated to adhere to a set of nominal parameters, and deviations from those values in the final product may be identified by the model to higher accuracy than an electron micrograph.  Chapter 4. Results and discussion  4.1.1  38  Green's function model modification  Initial efforts to simulate the optical behaviour of the uniform InP photonic crystal made use of an existing Green's function computer code [29], wherein the material is defined by inputting a fixed value of e, the dielectric function. While these attempts yielded promising agreement to experimental spectra at lower energies up to approximately 9000 c m , the simulated results deviate substantially from those obtained experimentally at high energies, as seen in Figure 4.2. The crystal symmetry directions for a hexagonal array, M and K. are defined in Figure 4.1. -1  Figure 4.1: A fc-space diagram demonstrating the crystal symmetry directions of a hexagonal array. The dots shown represent reciprocal lattice vectors. The deviation stemmed from the fact that the dielectric function is kept fixed in the model, while in reality, e is a function of the frequency of the fields in the material. To remedy this problem, a subroutine was added to calculate the value of e(u) of InP [31]. The original Green's function computer code calls this subroutine and employs its calculated frequencydependent value of the dielectric function rather than using a fixed value input by the user. This method takes into account the absorption—the imaginary part of the dielectric function—at energies above the band-edge of InP. This modification to the code significantly improved agreement of the simulation to the experimental results, especially at high energies, as seen in Figure 4.3.  39  Chapter 4. Results and discussion  UOOO  130OC  Waversumber (t  (a)  ~ 30°. M-crystal direction, s-polarization - Sirnuiatior! s • Eitpefimgnl ?  \  5O0O  6000  7O0O  8000  9000  10000  110O0  120O0  i!  1300C  Wavumjmber Ecm '; -  (b) 9 = 45°. K-crystal direction, s-polarization  Figure 4.2: Simulated reflectivity spectra as compared to experiment prior to modification of Green's function code. Thefiguresshow the experimental reflectivity spectra from NRC uniform InP sample I (nominal parameters given in Table 3.1) and simulated spectra with an InP-air grating thickness of 195 nm. an InP-epoxy grating thickness of 100 nm. a hole pitch of 460 nm and a hole diameter of 330 nm. The noise seen at wavenumbers below 6000 c m and above 12000 c m in the experimental spectra is due to the a drop-off in spectrometer sensitivity. Figures provided by Murray McCutcheon. - 1  - 1  Chapter 4. Results and discussion  5000  6000  7000  6000  9000  10COO  1 tOOO  120O0  40  130OC  WavHruimber (cm" ; 1  (a) 0 — 30°. M-crystal direction, s-polarization — Simulation j " ' £xpgfimgn1 \  5000  SOOO  7000  8000  9000  10000  11000  12000  130OC  Wavemjmb&i (cm" ; 1  (b) 9 = 45°. K-crystal direction, s-polarization  Figure 4.3: Simulated reflectivity spectra as compared to experiment following modification of Green's function code. The figures show the experimental reflectivity spectra from N R C uniform InP sample I (nominal parameters given in Table 3.1) and simulated spectra with an InP-air grating thickness of 195 nm. an InP-epoxy grating thickness of 100 nm. a pitch of 460 nm and a hole diameter of 330 nm. The noise seen at wavenumbers below 6000 c m and above 12000 c m in the experimental spectra is due to the a drop-off in spectrometer sensitivity. - 1  - 1  Chapter 4. Results and discussion  4.1.2  41  Identifying structural parameters using the simulation  The reflectivity spectra of the uniform photonic lattices consist of two principal components: (a) a slowly-varying periodic background due to FabryPerot interference within the thin layers of material making up the sample, and (b) narrow but high-contrast features due to the bandstructure of the photonic crystal lattice. A typical reflectivity spectrum of a uniform photonic crystal sample is shown in Figure 4.4.  6000  7000  8000 9000 10000 Wavenumber{cm J  11000  12000  _1  Figure 4.4: Typical reflectivity spectrum of a uniform InP photonic crystal sample showing Fabry-Perot modulation and features due to photonic crystal bandstructure. The shape and positions of these components depend upon a number of structural parameters, but in different ways and to varying degrees. Four of these parameters—the filling fraction (as defined by hole diameter d and hole pitch a), the thickness of the oxide-air grating, ot, the thickness of the InP-air grating, gt. and the thickness of the InP-epoxy grating et were investigated for their effects on simulated spectra, with the aim of devising  Chapter  4. Results and  42  discussion  a systematic method of determining a set of parameters that best describes the experimentally investigated sample. These parameters are depicted in Figure 4.5. The samples fabricated at the NRC were all made to have nominal hole pitches of 460 nm. while the hole diameters were varied from one sample to another. Because both of these parameters directly influence filling fraction, it was decided that, for the sake of simplicity in the simulation investigation of the effect of filling fraction, the pitch in the simulations would be held constant at the nominal value of 460 nm while only the hole diameters were varied.  Figure 4.5: Schematic diagram of the uniform photonic crystal samples studied with the specular reflectivity set-up. The fabrication parameters d. a. ot. gt and et are defined on the figure. 2  One of the samples investigated did not undergo an O2 etch after it was epoxied onto a glass substrate; therefore, rather than a n oxide-air grating, its top layer consisted of a n oxide layer with epoxy holes. 2  Chapter 4. Results and discussion  43  Variation of filling fraction The diameter of the grating holes in a prototypical sample structure, with a hole pitch of a = 460 nm. top oxide-air grating thickness of ot = 58.6 nm. InP-air grating thickness of gt = 195 nm and InP-epoxy grating thickness of et = 100 nm. was varied between 290 nm and 370 nm in increments of 20 nm. It can be seen in Figure 4.6 that both the Fabry-Perot contribution as well as the features due to the photonic crystal bandstructure shift substantially with changing filling fraction, both moving toward higher wavenumbers as d is increased. Variation of oxide thickness The thickness of the top oxide layer of a prototypical sample structure, with a hole pitch of a = 460 nm. holes of diameter d — 340 nm. InP-air grating thickness of gt = 195 nm and InP-epoxy grating thickness of et = 100 nm. was varied between 50 nm and 75 nm in increments of 5 nm. It can be seen in Figure 4.7 that the effect of the variation of oxide thickness is not substantial. Therefore, the nominal value of the oxide thickness. 58.6 nm. was used in subsequent modelling of the uniform photonic crystal structure investigated for this thesis. Variation of InP-air grating thickness The thickness of the grating layer of InP with air-filled holes of a prototypical sample structure, with a hole pitch of a. = 460 nm. holes of diameter d = 340 nm. oxide-air grating thickness of ot = 58.6 nm and InP-epoxy grating thickness of et = 100 nm. was varied between 195 nm to 275 nm in 20 nm increments. It can be seen in Figure 4.8 that while the Fabry-Perot variation shifts substantially, the features due to photonic crystal bandstructure change little. Both appear to move toward lower energies as the grating thickness increases.  Chapter  4. Results and  discussion  44  Variation of InP-epoxy grating thickness The thickness of the grating layer of InP with epoxy-filled holes of a prototypical sample structure, with a hole pitch of a = 460 nm. holes of diameter d = 340 nm. oxide-air grating thickness of ot = 58.6 nm and InP-air grating thickness of gt = 195 nm. was varied between 80 n m to 140 nm in 10 n m increments. It can be seen in Figure 4.9 that while the Fabry-Perot variation shifts substantially, the shift in the features due to photonic crystal bandstructure is not as dramatic, although it is larger than the shift seen due to variation of the InP-air grating thickness. Both appear to move toward lower energies as the InP-epoxy grating thickness increases. The contrast of the Fabry-Perot also appears to increase discernibly as the InP-epoxy grating thickness is increased. Given an experimental spectrum to fit. the strategy for determining its structural parameters through simulation is as follows: vary the filling fraction in the simulation such that the features due to bandstructure are in approximate agreement with those of the experimental results. Next, vary the InP-air grating thickness to achieve positional agreement with the FabryPerot modulation: the position of the features should not change much while the Fabry-Perot component of the spectrum will change substantially. Next, vary the InP-epoxy grating thickness to achieve agreement in the shape of the Fabry-Perot curve. Finally, the agreement of the fit may be fine-tuned by making slight adjustments iteratively to the InP-air grating and the InPepoxy grating thicknesses. This fitting procedure is done for spectra taken over a range of incident angles and a broad spectral range for each sample.  Chapter  7000  4.  Results and  8000  9000  10000  discussion  45  11000  Wavenumber ( c m ; -1  (a) s-polarized incident light  8000  9000 Wavenumber (cm"'  (b) p-polarized incident light  Figure 4.6: Effect of varying filling fraction on simulated reflectivity spectra of uniform InP photonic crystal samples. The simulation was r u n w i t h 9 = 30°, a hole pitch of 460 nm. an oxide-air grating thickness of 58.6 nm. an InP-air grating thickness of 195 n m and an InP-epoxy grating thickness of 100 nm.  Chapter  700C  4.  Results and  8000  9000  10000  discussion  11000  40  12000  1300C  Wavenumber(cm~',  (a) s-polarized incident light  6000  7000  8000  9000  10000  11000  12000  1300C  Wavenumber (cm ; :  (b) p-polarized incident light  Figure 4.7: Effect of varying oxide thickness on simulated reflectivity spectra of uniform I n P photonic crystal samples. T h e simulation was run w i t h 9 = 30°, a hole pitch of 460 n m . a hole diameter of 340 nm. an InP-air grating thickness of 195 n m and an InP-epoxy grating thickness of 100 n m .  Chapter  4.  Results and  discussion  47  (a) s-polarized incident light  —  8' 195 nm g t . 215nm g t - 235 nm gi = 255 nm g t - 275 nm  | 2 ft  (b) p-polarized incident light  Figure 4.8: Effect of varying InP-air grating thickness on simulated reflectivity spectra of uniform InP photonic crystal samples. T h e simulation was run w i t h 9 = 30°, a hole pitch of 460 n m . a hole diameter of 340 n m . an oxide-air grating thickness of 58.6 nm and an InP-epoxy grating thickness of 100 nm.  Chapter  4.  Results and  discussion  48  el = 80nm el 90 nm el = 100 nm — e l . HOnm el > 120 nm e l . 130 nm et = MO nm  —  00  8000  9000  10000  110  Wavenumber 1cm ';  (a) s-polarized incident light  8000  9000  10000  Wavenumber tcrrf , 1  (b) p-polarized incident light  Figure 4.9: Effect of varying epoxy thickness on simulated reflectivity spectra of uniform I n P photonic crystal samples. T h e simulation was run w i t h 0 = 30°, a hole pitch of 460 nm. a hole diameter of 340 nm. an oxide-air grating thickness of 58.6 nm and an InP-air grating thickness of 195 nm.  Chapter  4.1.3  4. Results and  discussion  49  Experimental results and comparison to simulations  The samples described in §3.1.2 were studied with the specular reflectivity set-up described in Section 3.4. Each sample was probed with both s- and ppolarized light at angles of incidence ranging from 10° to 45°. The reflectivity spectra acquired were then compared to simulated spectra; the structural parameters in the simulations were varied as described in §4.1.2 in order to achieve an acceptable fit to experiment. An example of the simulation fit to experimental spectra for Sample I is shown in Figures 4.10 and 4.11. The quality of fit achieved with Samples II and III is comparable. While there is good agreement in the energies of the spectral features, the simulated features still appear to have much higher contrast and narrower linewidths. This is due to the fact that the simulations model an infinite array of perfect holes, while the real samples are finite 90 p,m arrays of holes that are subject to various imperfections, including variation in radii, disorder in position, and taper of sidewalls. some of which are more rigorously explored for the case of microcavity defect arrays in §4.2.1 and §4.2.2. The final simulated parameters that yielded the optimal fits are listed in Table 4.1. Table 4.2 is a comparative listing of the fabrication parameters: nominal, those found by fitting the reflectivity spectra with the Green's function simulation and those measured by scanning electron microscopy (where available). The narrow high-contrast features due to the photonic crystal bandstructure on the experimental and simulated spectra were measured to produce bandstructure diagrams for each sample. The simulation results also yielded information regarding bands that could not be probed with the specular reflectivity set-up. Example dispersion diagrams for Sample III are shown in Figure 4.12.  Chapter  4. Results and  Sample Oxide thickness (nm) InP-air grating thickness (nm) InP-epoxy grating thickness (nm) Hole diameter (nm)  50  discussion  Sample I Sample II Sample III 58.6 58.6 130 217 0 287 90 310 0 345 370 308  Table 4.1: Structure of uniform InP photonic crystal samples, as determined by fit to Green's function simulations. The pitch a was held constant throughout the simulations at the nominal value of 460 nm. While the oxide grating layer is an oxide-air grating for Samples I and III. it is an oxide-epoxy grating for Sample II.  Sample I Oxide-air grating thickness (nm) InP-air grating thickness (nm) InP-epoxy grating thickness (nm) Hole diameter (nm) Hole pitch (nm) Sample II Oxide-epoxy grating thickness (nm) InP-air grating thickness (nm) InP-epoxy grating thickness (nm) Hole diameter (nm) Hole pitch (nm) Sample III Oxide-air grating thickness (nm) InP-air grating thickness (nm) InP-epoxy grating thickness (nm) Hole diameter (nm) Hole pitch (nm)  Nominal 100 310 246 460 Nominal 100 310 246 460 Nominal 130 310 240 460  Simulation fit 58.6 217 90 345 460 Simulation fit 58.6 0 310 370 460 Simulation fit 130 287 0 308 460  SEM measured 58.6 280 87 250 No data SEM measured 58.6 0 366 349 No data SEM measured No data No data No data No data No data  Table 4.2: Structure of uniform InP photonic crystal samples: nominal fabrication parameters, parameters as determined by fit to Green's function simulations and as measured with a scanning electron microscope. Note that in the case of the nominal parameters, there are only data for total InP thickness.  Chapter  4.  Results and  discussion  51  Figure 4.10: Experimental and simulated reflectivity spectra at different angles of incidence of s-polarized light for an InP uniform photonic crystal (Sample I. K crystal direction).  Chapter  6000  7000  52  4. Results and discussion  8000  9000  10000  11000  12000  Wavenumber (cm')  Figure 4.11: Experimental and simulated reflectivity spectra at different angles of incidence of p-polarized light for an InP uniform photonic crystal (Sample I. K crystal direction).  Chapter  4.  Results and  discussion  53  10000  8000  E S  >>  6000  ro l5  4000 2000 01  0.2  0.3  0.4  O.S  0.4  0.5  (a) K crystal direction  0.1  0.2  0.3  (b) M crystal direction  Figure 4.12: Bandstructure diagrams for an InP uniform photonic crystal (Sample III). The points are taken from the experimental spectra w i t h the error bars representing linewidth of the features, while the lines are derived from simulation. The solid lines are derived from simulations w i t h s-polarized incident light while the dashed lines are derived from simulations w i t h p-polarized incident light.  Chapter  4.2  4.  Results and  discussion  54  Microcavity structure  The fabrication of the photonic crystal microcavity structures involves a multi-step process including lithography, developing and etching. Inherent in the final fabricated structures are imperfections due to fabrication parameters that cannot be fully controlled. Small fluctuations in electron beam dosage, for instance, may result in slight variations in the sizes of the holes in a 2D textured waveguide. The etch chemistry of the gases used in electroncyclotron resonance (ECR) etching and the manner in which it interacts with the resist mask as well as the waveguide itself may lead to hole sidewalls that are tapered rather than perfectly vertical. The effect of some of these fabrication imperfections on the mode confinement properties of the defect microcavities were studied via 3D-FDTD simulation. Imperfect structures were subjected to a dipole excitation at a frequency close to that of the predicted mode of the microcavity. The data of the evolution of the resulting field intensities were collected using a time monitor placed where the electric field was expected to be the most intense: just adjacent to the central defect in the hexagonal lattice and in the centre of the defect in the square lattice. The field decay was used to calculate Q values of the structures. The hexagonal defect structure simulated was a 300-nm free-standing membrane with refractive index n — 3.16. an air-hole pitch of a = 415 nm. a hole radius of r = 124.5 nm and a central defect radius of = 186.75 nm. as defined in Figure 3.3. The square defect structure had as its central defect not an enlarged hole, but a missing one. The simulated structure was a 180-nm free-standing membrane with refractive index n = 3.4. an air-hole pitch of a = 525 nm and a hole radius of r = 199.5 nm. A schematic diagram of the central region of the square structure is shown in Figure 4.13. While a square defect structure was not experimentally investigated, it is of interest due to its high Q value [32].  Chapter  4. Results and  a  discussion  55  ;  oo oo o oo oo o oo oo oo oo o oo oo o Figure 4.13: Schematic diagram of the central region of a square defect lattice. The defect is a missing hole in the lattice. Parameters a and r are defined.  4.2.1  Effect of imperfect hole sizes  Fluctuations in electron beam dosage and accelerating voltage during electronbeam lithography, as well as spatial variations in the thickness and composition of the electron-beam resist are only a few factors that result in nonuniformity in hole sizes in a planar textured waveguide. An example is shown in a micrograph in Figure 4.14. The effect of such non-uniformity was studied by simulating structures in which the radii of the holes in the first six rings surrounding the defect in a microcavity structure were varied randomly by a maximum of 0%, 10%, 20% and 30% in both hexagonal and square lattice configurations. A schematic example of a hexagonal structure simulated is shown in Figure 4.15. The pseudorandom list of numbers used to determine the variation of each hole was generated in accord with a uniform distribution from a to b: the mean of the distribution was therefore (a+b)/2 and the standard deviation of the distribution was (b — a)/vT2. For these simulations. b = —a. where b — 0. 0.1, 0.2 and 0.3. The total filling fraction of the holes was held constant to ensure that the same mode was being investigated in  Chapter  4. Results and  discussion  56  each case, and the central positions of the holes were not varied. The monitored field decay within these structures, following a dipole excitation near resonance, was then used to determine the Q value of the resonator. The effect on the Q value due to hole variation is summarized in Figures 4.16 (hexagonal arrays) and 4.17 (square arrays).  Figure 4.14: Micrograph of the central region of an InP-based microcavity defect structure (NRC sample EBWII-II: 300-nm InP membrane on 400-nm air undercut) showing discernible variation in hole radii. Micrograph taken by Murray McCutcheon.  Real-space plots of the field intensities within the sample in the area surrounding the defect for a perfect sample and one that has a hole radius variation of up to 30% are shown in Figure 4.18 for the hexagonal defect array and in Figure 4.19 for the square defect array. The imperfect structures demonstrate much less symmetry than the perfect structure. In the hexagonal imperfect defect array, it can be seen that the six-fold degeneracy of the perfect structure is broken, leaving one lobe of relatively high field. In the imperfect square defect array, the regions of maximum field appear to have little correlation with the actual location of the prescribed defect, although they may be indicative of an unintended defect resulting from the imperfections.  Chapter 4. Results and discussion  57  o o o o o o o o o c o o o o o o o o o o c o o o o o o o o o o o c 0 0 0 0 0 0 °  O O O O O C  OOOOO0OO0OOOOC O O O O O O O 0O0OOOOG  O O O O O 0 0 O O C O 0  0 0 0 c  o O O O O O O oOOOOC OOOOOOOOoOO°OOoOOC 0O0 0 O O o O 0 O ° O o 0 O C OOOOo 0 0 0 O O 0 0 0 0 O O O C o o o o o o o o O o o Q o o o o c OOOOO0O0 ooOOOooc O O O O  0  O  O  0 0 0 0 0 0 0 0 0 0 0 0 0 0 c  O O O o o O ° O O O o o o c O O O O O o O O O ° O O C  o o o o o o o o o o o c o o o o o o o o o o c o o o o o o o o o c Figure 4.15: Schematic diagram of a structure simulated to investigate the effect of random variation in hole radius. T h e radii of the holes in the inner six rings of the defect array (in grey) are subject to a uniformly distributed random variation while the t o t a l filling fraction of the structure is left unchanged from that of a perfect structure w i t h zero variation i n hole radius.  It can be seen that while the square lattice configuration does initially offer a higher-Q mode, the mode appears to be much more sensitive to hole variation.  A t 30% variation, the Q value of the square structure is 6.9%  of that of the perfect structure w i t h no variation, while for the hexagonal configuration, the Q value at 30% variation i n hole radius sits at 34% of the Q value of the perfect structure. T h i s difference may be due to the square array being more sensitive to changes i n lattice symmetry t h a n the hexagonal structure [32].  Chapter  4. Results and  58  discussion  2000 •  5  10  15  20  25  3C  Maximum percentage variation in hole radius  Figure 4.16: Effect of various degrees of random variation of hole radii (with a uniform distribution) on the Q value of a hexagonal defect array. The perfect structure simulated was a 300-nm free-standing membrane with refractive index n = 3.16 and with ten rings of air holes with a = 415 nm and r = 124.5 nm surrounding a central defect of = 186.75 nm. In the imperfect structures, only the inner six rings were subject to this variation.  Chapter  4. Results and  59  discussion  10000  5000  5  10  15  20  25  3C  Maximum percentage variation in hole radius  Figure 4.17: Effect of various degrees of random variation of hole radii (with a uniform distribution) on the Q value of a square defect array. The perfect structure simulated was a 180-nm free-standing membrane with refractive index n = 3.4 and with ten rings of air holes with a = 525 n m and r — 199.5 nm surrounding a central defect (omitted hole). In the imperfect structures, only the inner six rings were subject to this variation.  Chapter  4.  Results and  discussion  60  415 nm  (a) Electric fields in the hexagonal defect structure  perfect  (b) Perfect hexagonal defect structure  (c) Electric fields in the hexagonal defect structure with a variation of hole radius of up to 30%  (d) Hexagonal defect structure with a variation of hole radius of up to 30%  415 nm  Figure 4.18: 4.18(a) and 4.18(c) show real-space plots of the field intensities surrounding the defect in the simulated hexagonal microcavity arrays, depicted respectively in 4.18(b) and 4.18(d), on the same scale. T h e perfect structure has r — 124.5 n m , — 186.75 nm, a = 415 n m in a membrane of index n = 3.16, 180 n m thick. T h e imperfect structure shows less symmetry i n the mode than the perfect structure, and the six-fold degeneracy seen i n the perfect structure is broken.  Chapter  4. Results and discussion  61  »••••••••••••••••••• : c «• « « % • « • • • • « « » « « « • « • • • • • » « 3' I » « © » * « f, « • « .4 l> * < : . ! . - « < • - , •  | » • • • • «ft• * | | f »••••••••• ••••••••• » • • • h  »  #  s  s  I  «  |  «  !  « •|  |  g  11  |  g  I  »••  •  •  »•••••••••••!•••«•••  »••••••••••••••••••• »••••••••••••••••••• >••••••••••••••••••• -• | | • « g I g | | I • • <> | * | • (a) Electric fields i n the perfect square defect structure  9 >««8O®•H##®##««.«s#««®(g  (b) Perfect square defect structure  •••••••••••••••••ft ••••••••••••••••••• • •i 11 • i • • • • * • •  • i •  i §  ••••••••••••••••••• ••••••••••••••••••• ••••••••• ••••••••• ••••••••••••••••••• ••••••••••••••••••• ••••••••••••••••••ft ••••••••••••••••••• •••••••••«••••••••• ••••••••••••••••••• • • • • • • • • • • • • • • • • • • a  • • • • • • • • • • • • • • • • • • a  • • • a • • t • i a a aa a a•••• •  (c) Electric fields in the square defect structure with a variation of hole radius of up to 30%.  •  •  •  •  •  •  •  •  •  •  •  •  s  e  «  a  - 8  (d) Square defect structure with a variation of hole radius of up to 30%.  Figure 4.19: 4.19(a) a n d 4.19(c) are real-space plots of the field intensities surrounding the defect i n the simulated square microcavity arrays, depicted respectively i n 4.19(b) a n d 4.19(d), o n the same scale. T h e perfect structure has r = 199.5 n m and a = 525 n m in a membrane of index n — 3.4, 180 n m thick. T h e regions of m a x i m u m field of the imperfect structure show v i r t u a l l y no correlation w i t h the location of the defect; i n fact, they appear to fall w i t h i n the vicinity of a group of enlarged holes, which may serve as a second microcavity —one w i t h a more readily excited resonant mode.  Chapter  4.2.2  4. Results and  discussion  62  Effect of tapered holes  In E C R etching, the sample is bombarded from above by a plasma of chemicals such as CI2 and BCI3, which anisotropically remove material b o t h chemically and v i a the physical impact of the ions. A sample is typically covered w i t h a mask which selects the areas of the samples are to be etched.  The  rate at which the mask is etched away by the plasma and the rate at which the sample material is etched jointly contribute to determining the shape of the etched pattern. A mask that has high resistance to etching compared to the sample material, for instance, w i l l yield high aspect-ratio etches where the sidewalls of the etch are close to vertical. A mask w i t h lower resistance to etching may result i n sloped sidewalls.  Figure 4.20: S E M micrograph of a textured waveguide sample w i t h slanted hole sidewalls. T h e sample depicted here is a silicon-on-insulator (SOI) sample made w i t h a cross-linked P M M A mask etched for 50 s w i t h 600-W microwave power, -160-V bias and 2 0 - W R F power w i t h 30 seem of CI2 at 5 mTorr, w i t h a chuck temperature of 5°C. T h e sample was fabricated and the micrograph was taken by A . P a t t a n t y u s - A b r a h a m .  Chapter  4. Results and  discussion  63  Sidewall slopes of up to a = 20° have been observed in initial attempts to etch holes for a textured planar waveguide in Si. An example of this phenomenon is shown as an SEM micrograph in Figure 4.20. The effect of this sidewall slope was investigating by simulating defect structures with a = 0°. 5°, 10°, 15° and 20° in both hexagonal and square lattice configurations. The total filling fraction of the holes was held constant to ensure that the same mode was being investigated in each case. The defect hole (for the hexagonal structure) was also left unaltered; otherwise, at maximum taper angle, the maximum hole diameter would exceed the hole pitch. The monitored field decay within these structures, following a dipole excitation near resonance, was then used to determine the Q value of the resonator. The effect on the Q value due to hole taper is summarized in Figures 4.21 and 4.22. It can be seen that the hexagonal defect structure is slightly more sensitive to sidewall taper, as the Q value of a structure with holes having a 20° taper drops to 51% of that of a structure with perfectly vertical sidewalls. whereas for a square defect structure, the Q value of a structure with holes having a 20° taper sits at 60%. The difference between the two structures is not as pronounced as in the study of hole radius variation, nor is the difference between perfect and imperfect samples, as the decrease in Q value is due to homogeneously increased out-of-plane losses and not due to the inherent symmetry or filling fraction of the structures.  Chapter  4. Results and discussion  64  12000 r — ~  2.5  7.5  5  10  12.5  15  17.5  2C  Sidewall angle o with respect to vertical (0.  Figure 4.21: Effect of hole sidewall taper on the Q value of a hexagonal defect array. T h e perfect structure simulated was a 300-nm freestanding membrane w i t h refractive index n = 3.16 and w i t h ten rings of holes w i t h a = 415 n m . r = 124.5 n m surrounding a central defect of r = 186.75 n m . d  25000  15000  10000  5000  2.5  5  7.5  10  12.5  15  17.5  2C  Sidewall angle a with respect to vertical (?>.  Figure 4.22: Effect of hole sidewall taper on the Q value of a square defect array. T h e perfect structure simulated was a 180-nm free-standing membrane w i t h refractive index n = 3.4 and w i t h ten rings of holes w i t h a = 525 n m and r = 199.5 n m surrounding a central defect (omitted hole).  Chapter 4. Results and discussion  4.2.3  65  Experimental results  Three different approaches were attempted in order to study the microcavity structures described in §3.1.1 experimentally. The defect structures were first investigated using the microreflectivity set-up discussed in Section 3.2; however, the experiments only allowed for probing of the sample's reflectivity properties over a small wavelength range, from approximately 1.44 pm to 1.58 pm. In order to study the reflectivity of the sample over a broader spectrum, the specular reflectivity set-up described in Section 3.4 was used. This approach, however, yielded too little signal-to-noise to offer reliable reflectivity spectra for analysis, but motivated a modification of the setup, resulting in the experimental apparatus described in Section 3.3. This apparatus was used to study the reflectivity of the microcavity structures and the results were compared to those taken with the microreflectivity setup to ascertain whether the spectra are reproducible and consistent, as well as whether using a broad-spectrum light source generates any additional information relevant to the analysis. The hope was to observe manifestations of the microcavity's resonant mode in any of the reflectivity spectra. Microreflectivity investigation of microcavity structures The OPO outputs 100-fs pulses of collimated light with an approximate bandwidth of 40 nm. Therefore, in order to study a sample's reflectivity over the entire tuning range of the OPO. reflectivity spectra are taken with the laser output centered at 1.44 pm. 1.46 pm, 1.48 pm, 1.50 pm, 1.52 pm, 1.54 pm, 1.56 pm and 1.58 pm. A spectrum is taken with the light incident on the centre of the microcavity, and a reference spectrum for normalization is taken off the defect array entirely, in an untextured region of the sample wafer. The former is divided by the latter, yielding a normalized spectrum showing only the modifications to the input light that were generated upon reflection off of the sample. In principle, each normalized spectrum would overlap with its preceding and subsequent spectra, thus allowing one to piece together  Chapter  4. Results and  66  discussion  all eight spectra for one comprehensive reflectivity spectrum over the OPO tuning range. The two configurations of InP-based microcavity structures, depicted in Figures 3.1 and 3.5. were studied using the microreflectivity set-up. Representative spectra from each sample are shown in Figure 4.23 and the sample fabrication parameters, as measured on an SEM. including hole pitch a. hole radius r and defect hole radius are given in Table 4.3. While there appears to be modulation of the reflectivity as a function of wavenumber. there is no obvious evidence of spectral features due to the microcavity. ;  Sample  Air undercut (nm) Hole pitch (nm) Hole radius (nm) Defect hole radius (nm)  EBWII-II Group A3 Array 3 400 417 265 375  EBWII-III Group A l Array 7 1000 396 136 195  EBWII-III Group A2 Array 2 1000 413 130 182.5  EBWII-III Group A l Array 5 1000 405 135 187  Table 4.3: Hexagonal photonic crystal defect array fabrication parameters as measured by SEM.  Broad-spectrum investigation of microcavity structures The two configurations of InP-based microcavity structures, depicted in Figures 3.1 and 3.5. were studied using the broad-spectrum reflectivity set-up. The alignment procedure described in §3.3.5 was used to sample only the reflected light from the array of interest. For each array, an input spectrum was taken with the aperture centered on the array itself, and one spectrum was taken off the array for normalization purposes with the apertured field containing nothing but an untextured region of the sample wafer. The former spectrum was divided by the latter, yielding a normalized spectrum showing only the modifications to the incident light due to the sample.  Chapter  4. Results and  discussion  67  Normalization was also attempted with a reference spectrum of light reflected off of a section of Teflon tape, which should provide a diffuse reflection of all incident wavelengths; it was thought that normalizing the input spectra with respect to a reference that mimicked the source would provide more information of the sample's layered structure due the spectral modulation arising from Fabry-Perot interference. It can be seen in Figure 4.24 that the two means of normalizing expectedly yield different results. However, as the normalization with respect an untextured area on the sample more closely corresponds to the normalization performed on the microreflectivity spectra, it. rather than the normalization with respect to Teflon tape, will be used for comparison to the experimental results from the microreflectivity experiments. Representative spectra from each of the two configurations of InP-based microcavity arrays are shown in Figure 4.25. While there appears to be modulation of the reflectivity as a function of wavenumber. there is no obvious evidence of spectral features due to the microcavity.  Comparison of microcavity spectra Figure 4.26 shows sample reflectivity spectra, both those taken with the microreflectivity set-up as well as those taken with the broad-spectrum reflectivity apparatus, for each of the two configurations of InP-based microcavity arrays. Of the spectra taken with the microreflectivity set-up. the differences in modulation contrast between Figure 4.26(a) and the other two plots shown may be due to that sample's smaller air undercut. There may ostensibly be a slight correlation between the modulation of the spectra taken with the microreflectivity set-up and those taken with the broad-spectrum reflectivity set-up. but any correlation is weak. However, it is clear that the microreflectivity spectra typically possess higher contrast modulation than do the spectra taken on the broad-spectrum apparatus. A possible reason for this contrast difference is explored in §4.2.4 below.  Chapter  4.  68  Results and discussion  (a) N R C Sample EBWII-II (400-nm air undercut). Group A 3 . Array 3  e  I  , 6.300  6400  , 6S0»  «600  .  6700  6800  690C  Wavenumber (cm" i. 1  (b) N R C Sample E B W I I - I I I (1 um air undercut), Group A l . Array 7  6.300  6-100  6500  S60CS  670S  6800  69S0  700C  Wavenumber (cm"')  (c) N R C Sample E B W I I - I I I (1 yum air undercut), Group A 2 , Array 2  Figure 4.23: Representative reflectivity (normalized reflection) spectra of InP-based microcavities taken with the microreflectivity set-up. Sample fabrication parameters are given in Table 4.3.  Chapter  4. Results and  discussion  69  Figure 4.24: Reflectivity (normalized reflection) spectra of NRC sample EBWII-III. Group A l , Array 5 (measured sample fabrication parameters are given in Table 4.3) taken with the broadspectrum reflectivity apparatus, normalized with respect to two different reference spectra. The solid line is the spectrum that was obtained by normalizing the input spectrum with respect to a spectrum taken of an untextured region of the sample wafer. The broken line is the result of normalizing the input spectrum with respect to the reflectivity spectrum off of Teflon tape.  Chapter  4.  Results and  70  discussion  (a) N R C Sample E B W I I - I I (400-nm air undercut), Group A 3 . Array 3  Wavenumber (enr ). 1  (b) N R C Sample E B W I I - I I I (1 Group A l . Array 7  6000  7000  &0C0  9500  air undercut),  £0000  U0OC  Wavenumber (cm  (c) N R C Sample E B W I I - I I I (1 fj,m air undercut), Group A 2 , Array 2  Figure 4.25: Representative reflectivity (normalized reflection) spectra of InP-based microcavity arrays taken with the broad-spectrum reflectivity set-up. Sample fabrication parameters are given in Table 4.3.  Chapter  4.  71  Results and discussion  Normalized spectrum, microrellecttvlty apparatus  >  a  Normalized spectrum, broad-spectrum apparatus  £000  4000  Wavenumber (cm"').  (a) N R C Sample E B W I I - I I (400-nm air undercut), Group A 3 , Array 3 Normalized spectrum, microrelieciivity apparatus  Normalized spectrum, broad-spectrum apparatus  N  1  soas sooo Wavenumber (cm" ) 1  (b) N R C Sample E B W I I - I I I (1 /zm air undercut), Group A l . Array 7  \ ^ Normalized spectrum, mrcrorelleclivity apparatus 8008  » 0 0  Wavenumber ( c m j .  (c) N R C Sample E B W I I - I I I (1 jum air undercut), Group A 2 , Array 2  Figure 4.26: Comparison of reflectivity (normalized reflection) spectra taken with the microreflectivity set-up with those taken with the broad-spectrum apparatus. Sample fabrication parameters are given in Table 4.3.  Chapter  4.2.4  4. Results and  discussion  72  Simulations of an incident Gaussian beam on a microcavity  Simulations to study the effect of an incident Gaussian pulse on a hexagonal defect microcavity structure may shed some insight into the experimental results of §4.2.3; in particular, they may elucidate why no evidence of a defect mode in the cavity was observed. Using the FDTD simulation software, the following simulation was performed: a 100-fs Gaussian pulse of amplitude 1 V / m and of spot size 2 was launched from 500 nm above the sample at normal incidence toward a hexagonal microcavity consisting of seven rings of air holes (with r = 124.5 nm and a = 415 nm) surrounding a central defect hole with radius = 186.75 nm in a 300-nm-thick freestanding planar slab of index n — 3.16. The excitation pulse was polarized in the x direction. The field intensities of the reflected radiation were monitored with a field profile monitor placed 700 nm above the sample. This simulation mimics to some extent the microreflectivity experiments performed on the InP microcavities. One simulation was run with the Gaussian pulse incident on the centre of the defect array; another with the pulse incident 275 nm off-centre; and a third with the pulse incident 775 nm off-centre as shown in Figure 4.27. When the z-component of the Poynting vector of the reflected radiation, which represents the radiation travelling to the far field, is integrated over a region whose projection onto the sample contains the defect, it becomes clear, as shown in Figure 4.28. that in the case of an incident Gaussian perfectly centered on the defect, the reflected light yields no information about the defect mode. Even when the Gaussian strikes the sample 278 nm away from the defect centre, any evidence of the defect mode is of too low contrast to be discerned. At 774 nm. there begins to appear some evidence of a feature in the spectrum due to the resonant microcavity. 2  ;  That the resonant mode is not excited with a perfectly symmetric incident beam may be explained as follows: the electric field of the resonant mode  Chapter  4. Results and  QUO® 5>t  v./  0k  discussion  •  O O O (111  A  A  A  *  73  i0  • ' '1/ "S''-.0 O  '^m  J o  O © G o-'"©' ©,er®i$-,e 3 © c l O O v j S d ™ O O "V o |pl  ihm  %m mm $m r * ^  o  : ••- • .,  O * wshowing O O O w Figure 4.27: Schematic diagram positions of Gaussian beams incident on a hexagonal defect array studied in FDTD simulations. One simulation was run with the Gaussian pulse incident on the centre of the defect array, denoted by Position 1: another with the pulse incident 275 nm off-centre, denoted by Position 2; and a third with the pulse incident 775 nm off-centre, denoted by Position 3. The broken circles concentric about each position delineate the 2-^rn spot size of the incident Gaussian beam. of interest in the hexagonal defect array circulates the central defect hole [32], as shown schematically in Figure 4.29(a). Figure 4.29(b) demonstrates that when a beam is centered upon the defect array (with the grey arrow indicating polarization), electrons above and below the defect are pulled in the same direction by an equal magnitude of force. As a result, they cannot establish the mode's circulatory electric field. If the incident beam is offcentre, however, as depicted in Figure 4.29(c), electrons on one side of the defect are pulled with a larger force than electrons on the other; the imbalance allows the mode to be excited.  Chapter  4.  Results and  (a) Incidence on the defect centre  discussion  74  (b) Incidence at 275 nm from the defect centre  (c) Incidence at 775 nm from the defect centre  Figure 4.28: Comparison of simulated apertured reflectivity spectra acquired with an incident Gaussian pulse striking at various distances from the defect hole centre, as shown in Figure 4.27. A feature at approximately 194 THz. corresponding to the resonant mode, is only discernible in the case of the Gaussian striking the sample at 775 nm from the centre of the defect.  Chapter  4.  Results and  discussion  75  E  (a) E-field of the resonant defect mode  (b) Centered polarized beam  (c) Incident beam off-centre  Figure 4.29: Schematic diagram of the E-field of the mode in a hexagonal defect array and the effects of the positioning of the incident excitation beam. Figure 4.29(a) shows that the electric field of the resonant mode of interest circulates the central defect hole. Figure 4.29(b) demonstrates that when a beam (polarized in the direction of the grey arrow) is centered upon the defect array, electrons above and below the defect are pulled in the same direction by an equal magnitude of force. Figure 4.29(c) demonstrates that when the incident beam is off-centre—here, below the defect—the electrons on one side of the defect hole are closer to the excitation beam and hence are pulled with a greater force than those electrons on the opposite side of the defect hole, thus allowing the resonant mode to be excited and sustained.  Chapter  4. Results and  discussion  76  As outlined in §3.2.5. an.attempt was made with the microreflectivity apparatus to centre the incident beam on the defect during experiments. According to the resolution allowed by the imaging procedure described, the centre was generally pinpointed to within 500 nm. These simulations reveal that a pulse incident too close to the cavity centre would not produce resolvable spectral features due to the resonant mode and hence may partially explain the lack of such features in the experimental spectra. Because P = E H — E H , it is instructive to examine the x- and ycomponents of the electric field intensities. The feature at the frequency corresponding to the predicted resonant mode is more evident in the electric field intensities; in particular, the feature is much more prominent in the y-component than in the x-component of the electric field, as shown in Figure 4.30. This would suggest that isolating a particular polarization of the reflected light would assist in resolving the features due to the resonant modes. In this simulation, where the excitation pulse was polarized in the x direction, using a polarizer to isolate the y-component of the electric field would therefore yield a spectrum in which the contrast of the feature due to the resonant mode would be better resolved. Additionally, where the reflected light is sampled can be shown to have a tremendous effect on the ability to resolve spectral features due to resonant modes. For the case of a Gaussian pulse striking the sample at 775 nm from the defect centre. Figure 4.31 shows much higher contrast in the y-component of the electric field for the spectral feature due to the resonant mode for light apertured closer to rather than farther from the defect. Aperturing. in this case, refers to isolating a square window of side 1.66 pm from the total reflected light monitored, and the positions of the aperturing for this set of simulations is shown in Figure 4.32. ;  z  x  y  y  x  Chapter  4.  Results and  discussion  77  Frequency (Hz)  (b) Intensity of the y-component of the electric field  Figure 4.30: Simulated electric field intensities of radiation reflected from a hexagonal defect structure following an incident Gaussian pulse striking the sample 775 nm from the defect centre. The feature at approximately 194 THz. corresponding to the resonant mode, is much more prominent in the y-component of the electric field than in the x-component.  Chapter 4. Results and discussion  (a) Aperture centered on the defect  (b) Aperture centered 415 nm from the defect  (c) Aperture centered 830 n m from the defect  (d) Aperture centered 1245 nm from the defect  78  Figure 4.31: Simulated electric field intensities of radiation reflected from a hexagonal defect structure apertured at different locations on the sample. Contrast in the spectral feature due to the resonant mode decreases as the distance between the defect centre and aperture centre increases. The aperture used in this analysis was a square window of side 1.66 pm.  Chapter 4. Results and discussion  •  W  •  IS  ' * " r* " ) I O '< O '  Q O OO  3 o o •) si© o a > o b Q o  " >O O © ' O O O O C C 0 • © <  1  o o o o o €^  w  o o o o  J  o©  Q.6  ;r;'o < /  o o  O OO O  o o o o  c o ; O O O O .1  o c  (a) Aperture centered on the defect  W  V  " •  o r o o ., • „ S 0 O O O o'T'S'O o o o o o o c o o o © « 9 S D O O O O O © o o o o o o o  (c) Aperture centered 830 nm from the defect  > .* i . • • II  • II  , i  (b) Aperture centered 415 nm from the defect  -m  9 © © i> o o o © O O O c o o o © © @ © # <3 5 o o o o o o o © ®m &© Q > © © O O O O O c o o O O O O O O tit^ © © If^ ^ ^ ^ * O © o © • © © <i ® i  *>J  "> e o s o i  ? o©  Cs*'  79  %J  o o o o  \J  „  z o  o  o o o o s o e , O 3 O O O O C O : o o o o o o •"> * x  0  ") O o o O O O O ••  1 'i -  ,.  O *'  " < ')') " „ o o o  :  O O O O G O O  O O O C O O i  ##•••©  (d) Aperture centered 1245 nm from the defect  Figure 4.32: Schematic diagram showing positions of square apertures of side 1.66 jttm used to sample reflected light from a hexagonal defect array in an FDTD simulation. The black dot indicates the position of the incident Gaussian excitation while the broken circle concentric about the dot delineates the beam's 2-fim spot size.  Chapter  4.  Results and  80  discussion  The size of the aperture appears to have a profound effect on the contrast of the spectral feature due to the resonant mode. The reflected light of the simulation involving a Gaussian pulse incident at 775 nm from the defect centre was apertured with squares of side 830 nm. 1.66 pm, 2.49 pm. and 3.32 pm. It can be seen from Figure 4.33 that the smaller the aperture, the higher the contrast of the spectral feature in the intensity of the y-component of the electric field. I  i  : ^™  i  i  i  <—  0  *  V  • ™~~~^>.-~-~-*™~~~^  (a) Aperture of side 830 nm.  (b) Aperture of side 1.66 /xm.  (c) Aperture of side 2.49 /im.  (d) Aperture of side 3.32 /jm.  Figure 4.33: Simulated electric field intensities of radiation reflected from a hexagonal defect structure with various aperture sizes. Contrast in the spectral feature due to the resonant mode decreases as the size of the aperture increases.  Chapter  4. Results and  discussion  81  When the optical experiments on the InP microcavities were performed on the microreflectivity apparatus, there was no aperturing; all of the reflected light was directed into the spectrometer. It is therefore entirely conceivable that the contrast of any spectral feature would be compromised by the indiscriminate sampling. Thus, the experimental procedure of centering the OPO pulse on the array and sampling the entire reflected beam on the microreflectivity apparatus, and aperturing a large region 8 pm in diameter on the broad-spectrum apparatus, would certainly contribute to a lack of contrast in the spectra feature due to the resonant mode and explain why there appeared to be no evidence of the mode in the experimental results. In order to observe the mode, one would therefore have to modify the experimental design. Suggestions for these modifications are discussed in Chapter 5.  82  Chapter 5 Conclusion The intention of this thesis was to develop a method for characterizing the energy and the Q value of 3D microcavities using resonant light scattering. Photonic crystal microcavities have been proposed as a key component in the realization of the basic cavity QED primitive with potential quantum information processing applications. Both experimental and simulation studies were performed to investigate the reflectivity properties of both uniform photonic crystals, consisting of a periodic array of air holes in InP. as well as microcavity defect arrays, consisting of several hexagonal rings of periodic air holes surrounding a central enlarged defect hole in an InP membrane. The uniform photonic crystal structures were studied with a specular reflectivity apparatus. The reflectivity spectra were compared with those generated through a simulation based on a Green's function code. A systematic method of fitting the simulated to the experimental spectra by modifying certain structural parameters in the simulation was devised, allowing for a reliable determination of the sample parameters including filling fraction of the array of air holes and the layer structure of the wafer used to fabricate the sample. The microcavity structures were studied by three different means, only two of which yielded spectra with an acceptable signal-to-noise ratio. However, neither the spectra taken with the microreflectivity apparatus nor those taken with the broad-spectrum apparatus yielded fruitful information regarding the resonant mode of the microcavity predicted by FDTD simulations. Further simulations performed mimicking the microreflectivity set-up gave  Chapter  5.  Conclusion  83  several clues as to why this was the case: a Gaussian pulse incident too close to the defect centre will fail to yield spectral features from the resonant mode of sufficient contrast to be resolved due to the symmetry properties of the defect mode. Contrast is also compromised if too large an area of the reflected beam is sampled. The logical extension of the studies undertaken for this thesis would be the refinement of the experimental design to increase the likelihood of observing spectral features due to the resonant cavity modes. The simulation results of §4.2.4 would suggest that the alignment procedure of the microreflectivity apparatus should be modified on at least two counts: first, one should aim not to strike the centre of the defect array with the pulse, as had been done for this thesis, but attempt to excite the resonant mode with a pulse off-centre; second, the reflected light must be carefully apertured to isolate only the contribution from a small region centered on the defect. As demonstrated in Figure 4.31, if the reflected light is apertured too far off-centre, the spectral features due to the resonant mode are not of sufficient contrast to discern. Similarly. Figure 4.33 shows that using too large an aperture to sample the reflected light also compromises the contrast of the spectral features. A further modification of introducing a polarizer in the reflected beampath to isolate the polarization yielding the highest contrast in resonant mode spectral feature may also be a potential improvement. Further simulation studies should be conducted to ascertain the optimal position at which to excite the defect mode; clearly, while the limited simulations performed in §4.2.4 reveal that Gaussian pulses incident on the sample further from centre yielded higher contrast spectral features, this relationship certainly is not linear. At some distance from defect centre, the pulse would be too far from the microcavity to excite the resonant mode at all. Contrast would, in principle, be greater with a higher-Q mode; increasing the Q value of the resonant mode may be achieved in fabrication by increasing the number of rings surrounding the defect and by increasing the  Chapter  5.  Conclusion  84  distance between the membrane and the sample substrate. A drawback of these measures is that a larger textured region with a larger undercut has less structural integrity and a membrane with too large an array is prone to collapse. Systematic studies to find an optimal structure—one that has both a sufficiently high Q value and that is structurally robust—may be worth pursuing. Successfully aperturing the reflected beam, however, would require a more drastic modification of the set-up: the beam would first need to be focused at a point along the reflected beampath. The aperture would then need to be placed at the focus. The CCD camera could be employed to determine the correct aperture position in order to isolate the contribution from only a small area surrounding the defect. Modifications to the optics may be needed to magnify the image at the focus such that the size of aperture required not be so small as to render aperture alignment impractical or to decrease the signal entering the FTIR spectrometer to a level at which the resonant mode spectral features become indistinguishable from background noise. If one were to keep the ellipsoidal mirror used to focus the reflected light into the spectrometer, the aperturing image plane would need to be 150 cm (in pathlength) from the ellipsoidal mirror. Once a rigorous set-up and experimental method is developed that adequately resolves the spectral features due to the resonant cavity mode, samples should be fabricated in accord with Section 2.4. with a region of uniform photonic crystal in addition to the defect microcavities. Reflectivity measurements on the uniform photonic crystal structures made with the specular reflectivity set-up. along with the Green's function code simulations, could then be used to determine sample fabrication parameters and give accurate calibrationfiguresto determine the parameters of the microcavity defect structures, to be studied with the modified microreflectivity apparatus. Jointly, these techniques would, in principle, provide exhaustive information regarding the microcavity structures and the resonant modes they support.  Chapter  5.  Conclusion  85  In addition to simulations to study the effect of an incident Gaussian pulse on a defect array, a series of FDTD simulations were performed to investigate the effects of two common fabrication imperfections: the random variation in the radii and the non-verticality of the sidewalls of the holes etched into the planar waveguides. These studies were performed on both hexagonal and square defect structures and found that, in general, the Q value drops as the imperfections become more pronounced. The hexagonal structure appears slightly more sensitive to hole taper than the square structure, although the difference is not large enough to attribute unequivocally to the symmetry differences in the structure. On the other hand, the square array is much more sensitive to hole radii variation than the hexagonal structure, likely due to the fact the latter is more robust to changes in symmetry than the former. The FDTD simulation studies into the effect of fabrication imperfections may shed some light into how irregularities in hole size, for instance, may actually be exploited. As can be seen in Figure 4.18. random variations in hole radii breaks the symmetry of the field profile, and while the intensity of the field and the Q value of the mode may not be as high as for a perfect structure, the mode is now concentrated in one lobe of the hexagon, thus essentially reducing the mode volume six-fold. A full six-fold reduction is unlikely as the mode also tends to extend further from the central defect region, but it appears that some reduction in mode volume should be realizable by this means. If a smaller mode volume is more significant than a high Q value for a particular QED application, one may deliberately, though in a controlled manner, introduce hole radius variations in order to isolate the electric field to a small volume.  86  Bibliography [1] Joachim Stolze. Quantum Computing: A short course from theory to experiment. Wiley-VCH, Weiheim. Germany. 2004. [2] A. Kiraz C. Reese, B. Gayral, Lidong Zhang, W.V. Schoenfeld, B.D. Gerardot. P.M. PetrofL E.L. Hu, and A. Imamoglu. Cavity-quantum electrodynamics with quantum dots. Journal of Optics B: Quantum and Semiclassical Optics, 5:129-137. 2003. ;  [3] Jelena Vuckovic, Marko Loncar, Hideo Mabuchi, and Axel Scherer. Design of photonic crystal microcavities for cavity QED. Physical Review E, 65:016608-1, 2001. [4] Kerry J. Vahala. Optical microcavities. Nature, 424:839-846, 2003. [5] John D. Joannopoulos, Robert D. Meade, and Joshua N. Winn. Photonic Crystals: Molding the flow of light. Princeton University Press, Princeton, 1995. [6] J. Pachos and H. Walther. Quantum computation with trapped ions in an optical cavity. Physical Review Letters. 89:187903, 2002. [7] L. You, X.X. Yi, and X.H. Su. Quantum logic between atoms inside a high-Q optical cavity. Physical Review A, 67:032308, 2003. [8] J.I. Cirac, S.J. van Enk, P. Zoller. H.J. Kimble, and H. Mabuchi. Quantum communication in a quantum network. Physica Scripta. T76:223232, 1998.  87  Bibliography  [9] S.J. van Enk. 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