Porous silicon (PSi) photonic crystals have aroused research interest as label-free chemical and biological sensing transducers owing to the ease of fabrication, high quality optics and a sensitive optical response to changes in efractive index. A major impediment to using PSi materials as sensors is the relative instability of the silicon surface to oxidation in ambient air and aqueous environments. This thesis reports methods for derivatising PSi towards realisation of 1-D silicon-based photonic materials for applications in biology and medicine. Narrow-linewidth rugate filters, a class of photonic crystal, are fabricated on silicon to display a high reflectivity resonant line in the reflectance spectrum. The position of the resonance is sensitive to changes in refractive index, thus allowing quantification of infiltrating biological species. The efficacy of rugate filters as biosensing transducers requires 1) protection from aqueous degradation, 2) resistance to non-specific adsorption and 3) distal reactivity for coupling of biorecognition molecules. Two chemical strategies based on hydrosilylation of functional alkenes are compared for stabilising the PSi structure against oxidation whilst resisting non-specific adsorption of biomolecules. Immobilisation of peptides to the organic layers is demonstrated for optical detection of protease enzymes. Introduction of protease results in cleavage of the immobilised peptides within the rugate filters, detected by an optical blue-shift to shorter wavelengths. To increase the sensitivity to proteolysis, covalent mmobilisation of biopolymers is evaluated using gelatin as a model substrate. Digestion of gelatin is detected down to 37 attomoles of protease. Furthermore, the surface chemistry allows specific capture of live cells and incubation with stimulated macrophages in tissue culture results in optical detection of released gelatinase enzymes. The generality of the surface chemistry allows for a range of other biological applications to be investigated. An alternative biorecognition interface, hybrid lipid bilayer membranes, containing specific recognition elements for cholera toxin allows optical detection of affinity capture and concentration within the PSi. In addition, the suitability of chemically modified photonic crystals as reservoirs for mass spectrometry is evaluated towards biomolecule quantification after optical detection. A robust and flexible surface chemistry on PSi photonic crystals is critical to performance in a range of biological assays and a necessary requirement for wide-scale employment.

This thesis presents designs and fabrication algorithms for 3D photonic band gap (PBG) material synthesis and embedded optical waveguide networks. These designs are suitable for large scale micro-fabrication using optical lithography methods. The first of these is a criss-crossing pore structure based on fabrication by direct photo-electrochemical etching in single-crystal silicon. We demonstrate that a modulation of the pore radius between pore crossing points leads to a moderately large PBG. We delineate a variety of PBG architectures amenable to fabrication by holographic lithography. In this technique, an optical interference pattern exposes a photo-sensitive material, leading to a template structure in the photoresist whose dielectric-air interface corresponds to an iso-intensity surface in the exposing interference pattern. We demonstrate PBG architectures obtainable from the interference patterns from four independent beams. The PBG materials may be fabricated by replicating the developed photoresist with established silicon replication methods. We identify optical beam configurations that optimize the intensity contrast in the photoresist. We describe the invention of a new approach to holographic lithography of PBG materials using the diffraction of light through a three-layer optical phase mask (OPM). We show how the diffraction-interference pattern resulting from single beam illumination of our OPM closely resembles a diamondlike architecture for suitable designs of the phase mask. It is suggested that OPML may both simplify and supercede all previous optical lithography approaches to PBG material synthesis. Finally, we demonstrate theoretically the creation of three-dimensional optical waveguide networks in holographically defined PBG materials. This requires the combination of direct laser writing (DLW) of lines of defects within the holographically-defined photoresist and the replication of the microchip template with a high refractive index semiconductor such as silicon. We demonstrate broad-band (100-200~nm), single-mode waveguiding in air, based on the light localization mechanism of the PBG as well as sharp waveguide bends in three-dimensions with minimal backscattering. This provides a basis for broadband 3D integrated optics in holographically defined optical microchips.

This thesis presents designs and fabrication algorithms for 3D photonic band gap (PBG) material synthesis and embedded optical waveguide networks. These designs are suitable for large scale micro-fabrication using optical lithography methods. The first of these is a criss-crossing pore structure based on fabrication by direct photo-electrochemical etching in single-crystal silicon. We demonstrate that a modulation of the pore radius between pore crossing points leads to a moderately large PBG. We delineate a variety of PBG architectures amenable to fabrication by holographic lithography. In this technique, an optical interference pattern exposes a photo-sensitive material, leading to a template structure in the photoresist whose dielectric-air interface corresponds to an iso-intensity surface in the exposing interference pattern. We demonstrate PBG architectures obtainable from the interference patterns from four independent beams. The PBG materials may be fabricated by replicating the developed photoresist with established silicon replication methods. We identify optical beam configurations that optimize the intensity contrast in the photoresist. We describe the invention of a new approach to holographic lithography of PBG materials using the diffraction of light through a three-layer optical phase mask (OPM). We show how the diffraction-interference pattern resulting from single beam illumination of our OPM closely resembles a diamondlike architecture for suitable designs of the phase mask. It is suggested that OPML may both simplify and supercede all previous optical lithography approaches to PBG material synthesis. Finally, we demonstrate theoretically the creation of three-dimensional optical waveguide networks in holographically defined PBG materials. This requires the combination of direct laser writing (DLW) of lines of defects within the holographically-defined photoresist and the replication of the microchip template with a high refractive index semiconductor such as silicon. We demonstrate broad-band (100-200~nm), single-mode waveguiding in air, based on the light localization mechanism of the PBG as well as sharp waveguide bends in three-dimensions with minimal backscattering. This provides a basis for broadband 3D integrated optics in holographically defined optical microchips.

We here developed a third-order accurate numerical method for scattering of 3D electromagnetic waves by doubly periodic structures. The method is an intuitively simple numerical scheme based on a boundary integral formulation. It involves smoothing the singular Green's functions in the integrands and finding correction terms to the resulting smooth integrals. The analytical method is based on the singular integral methods of J. Thomas Beale, while the scattering problem is motivated by the 2D work of Stephanos Venakides, Mansoor Haider, and Stephen Shipman. The 3D problem was done with boundary element methods by Andrew Barnes. We present a method that is both more straightforward and more accurate. In solving these problems, we have used the M\"{u}ller integral equation formulation of Maxwell's equations, since it is a Fredholm integral equation of the second kind and is well-posed. M\"{u}ller derived his equations for the case of a compact scatterer. We outline the derivation and adapt it to a periodic scatterer. The periodic Green's functions found in the integral equation contain singularities which make it difficult to evaluate them numerically with accuracy. These functions are also very time consuming to evaluate numerically. We use Ewald splitting to represent these functions in a way that can be computed rapidly.We present a method of smoothing the singularity of the Green's function while maintaining its periodicity. We do local analysis of the singularity in order to identify and eliminate the largest sources of error introduced by this smoothing. We prove that with our derived correction terms, we can replace the singular integrals with smooth integrals and only introduce a error that is third order in the grid spacing size. The derivation of the correction terms involves transforming to principal directions using concepts from differential geometry. The correction terms are necessarily invariant under this transformation and depend on geometric properties of the scatterer such as the mean curvature and the differential of the Gauss map. Able to evaluate the integrals to a higher order, we implement a \mbox{GMRES} algorithm to approximate solutions of the integral equation. From these solutions, M\"{u}ller's equations allow us to compute the scattered fields and transmission coefficients. We have also developed acceleration techniques that allow for more efficient computation.We provide results for various scatterers, including a test case for which exact solutions are known. The implemented method does indeed converge with third order accuracy. We present results for which the method successfully resolves Wood's anomaly resonances in transmission. / Dissertation

The past decade and a half has seen the rapid emergence of a new material class known as photonic crystals (PCs), structures that exhibit 1, 2, or 3, dimensional periodicity of their dielectric constant, resulting in a modification of the dispersion characteristics from the normal w = vk relationship found in isotropic materials. Several remarkable electromagnetic phenomenon result, including the formation of photonic band gaps (PBGs), which are specific energy ranges where electromagnetic wave propagation is forbidden, and the existence of energies where the photon group velocity is slowed drastically from its normal value. The resulting modification of a materials photonic band structure allows unprecedented control of light, resulting in phenomena such as self-collimation, and spontaneous emission modification or lasing threshold reduction through either band edge effects (low group velocity) or microcavity defect incorporation. PCs for operation at visible wavelengths are difficult to form due to the need for nanoscale fabrication techniques. The research described focused on the fabrication of photonic crystal phosphors by using the infiltration and subsequent removal of self-assembled opal templates to make inverted opal-based photonic crystals. This thesis shows the advantages that atomic layer deposition (ALD) has as an important method for use in photonic crystal fabrication, and highlights the exciting results of use of ALD to fabricate luminescent ZnS:Mn and optically inactive titania inverse opals, as well as ZnS:Mntitania luminescent composite inverse opals.

This thesis reports on a new design of photonic crystal waveguides (PCWs) to achieve large guiding bandwidth, linear dispersion, single-mode behavior, good coupling efficiency to dielectric waveguides, and small loss. The design is based on using the linear dispersion region of one PCW in the photonic bandgap (PBG) of another PCW. While perturbing the period can result in a PCW with linear dispersion and large guiding bandwidth, it introduces an odd mode at those frequencies, as well. By using another perturbation scheme, it is shown that single-mode behavior can also be achieved. The linear dispersion of these waveguides and their operation at lower frequencies of the PBG, where the density of states of radiation modes is smaller, gives rise to very small loss coefficients as verified experimentally. Full characterization of a waveguide requires the measurement of not only the transmission coefficient, but also the dispersion and spectral phase. We have developed a real-time characterization technique based on spectral interferometry with femtosecond laser pulses at optical communication wavelengths to measure the spectral phase of waveguides. This haracterization technique can be used to study fast dynamics in timevarying structures and makes the alignment easy.

<p>This thesis presents results in two different neighboring areas of research: the magnetic properties of thin ferrite films and the application of the films in two-dimensional photonic crystals. </p><p>In the first part, we investigate the accuracy of the customary method for determining the magnetic anisotropy constants of ferrite films by ferromagnetic resonance (FMR) experiment. We have improved the method and introduced an experimental procedure to obtain the anisotropy constants with higher precision. The magnetic anisotropy fields are obtained by using FMR on a (111)-oriented yttrium iron garnet (YIG) film made by pulsed laser deposition. Moreover, we found experimentally that the shapes of FMR spectra of laser deposited epitaxial YIG films strongly depend on the orientation of the magnetic bias field with respect to the crystalline axes of the film. Inhomogeneities of the constants of anisotropy throughout the film could be responsible for the complexity of the FMR spectra. We find the special directions of the applied magnetic field in which the contribution of the magnetocrystalline anisotropy has the smallest effect on the ferromagnetic resonance and therefore on the elements of the permeability tensor. </p><p>In the second part, we study the electromagnetic wave propagation in two-dimensional (2D) dielectric and magneto-optic photonic crystals (PCs). We have proposed a 2D PC which is composed of magneto-optic material for the purpose of the enhancement of Faraday rotation in high transmission. It is assumed that the 2D PC contains a bismuth iron garnet (BIG) film either as the PC background medium or as a defect, embedded in the 2D PC. We have examined theoretically and computationally the increase in the Faraday rotation as well as the transmission of a plane-polarized plane wave incident onto these structures in the optical wavelength regime. Several important phenomena, with potential applications, are observed.</p>

Includes bibliographical references (p. 74-79).

We investigate the design, fabrication, and experimental characterization of high quality factor photonic crystal nanobeam cavities, with theoretical quality factors of \(1.4 × 10^7\) in silicon, operating at ~1550 nm. By detecting the cross-polarized resonantly scattered light from a normally incident laser beam, we measure a quality factor of nearly \(7.5 × 10^5\). We show on-chip integration of the cavities using waveguides and an inverse taper geometry based mode size converters, and also demonstrate tuning of the optical resonance using thermo-optic effect. We also study coupled cavities and show that the single nanobeam cavity modes are coupled into even and odd superposition modes. Using electrostatic force and taking advantage of the highly dispersive nature of the even mode to the nanobeam separation, we demonstrate dynamically reconfigurable optical filters tunable continuously and reversibly over a 9.5 nm wavelength range. The electrostatic force, obtained by applying bias voltages directly to the nanobeams, is used to control the spacing between the nanobeams, which in turn results in tuning of the cavity resonance. The observed tuning trends were confirmed through simulations that modeled the electrostatic actuation as well as the optical resonances in our reconfigurable geometries. Finally we demonstrate reconfiguration of coupled cavities by using optical gradient force induced mechanical actuation. Propagating waveguide modes that exist over wide wavelength range are used to actuate the structures and in that way control the resonance of a localized cavity mode. Using this all-optical approach, more than 18 linewidths of tuning range is demonstrated. Using an on-chip temperature self-referencing method that we developed, we determined that 20% of the total tuning was due to optomechanical reconfiguration and the rest due to thermo-optic effects. By operating the device at frequencies higher than the thermal cut-off, we show high speed operation dominated by just optomechanical effects. Independent control of mechanical and optical resonances of our structures, by means of optical stiffening, is also demonstrated. / Engineering and Applied Sciences

The mid-infrared wavelength region (2-20 µm) is of great utility for a number of applications, including chemical bond spectroscopy, trace gas sensing, and medical diagnostics. Despite this wealth of applications, the on-chip mid-IR photonics platform needed to access them is relatively undeveloped. Silicon is an attractive material of choice for the mid-IR, as it exhibits low loss through much of the mid-IR. Using silicon allows us to take advantage of well-developed fabrication techniques and CMOS compatibility, making the realization of on-chip integrated mid-IR devices more realistic. The mid-IR wavelengths also afford the opportunity to exploit Si's high third-order optical nonlinearity for nonlinear frequency generation applications. In this work, we present a Si-based platform for mid-IR photonics, with a special focus on micro-resonators for strong on-chip light confinement in the 4-5 μm range. Additionally, we develop experimental optical characterization techniques to overcome the inherent difficulties of working in this wavelength regime. First, we demonstrate the design, fabrication, and characterization of photonic crystal cavities in a silicon membrane platform, operational at 4.4 μm (Chapter 2). By transferring the technique known as resonant scattering to the mid-IR, we measure quality (Q) factors of up to 13,600 in these photonic crystal cavities. We also develop a technique known as scanning resonant scattering microscopy to image our cavity modes and optimize alignment to our devices. Next, we demonstrate the electro-optic tuning of these mid-IR Si photonic crystal cavities using gated graphene (Chapter 3). We demonstrate a tuning of about 4 nm, and demonstrate the principle of on-chip mid-IR modulation using these devices. We then investigate the phenomenon of optical bistability seen in our photonic crystal cavities (Chapter 4). We discover that our bistability is thermal in origin and use post-processing techniques to mitigate bistability and increase Q-factors. We then demonstrate the design, fabrication, and characterization grating-coupled ring resonators in a silicon-on-sapphire (SOS) platform at 4.4 μm, achieving intrinsic Q-factors as high as 278,000 in these devices (Chapter 5). Finally, we provide a quantitative analysis of the potential of our SOS devices for nonlinear frequency generation and describe ongoing experiments in this regard (Chapter 6). / Engineering and Applied Sciences