Thesis (Ph. D.)--Ohio State University, 2008.

Thesis (Ph.D.)--City University of Hong Kong, 2009. / "Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves [85]-91)

Thesis (M.S.)--West Virginia University, 2010. / Title from document title page. Document formatted into pages; contains viii, 95 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 89-95).

Creating compact, efficient, highly-controllable optical systems has been one of the central goals of optics and photonics research. Integrated photonics provides a powerful platform for manipulating light efficiently and flexibly by guiding light in waveguide circuits on chip. Among the rich family of integrated photonic devices, integrated optical modulators and wavefront generators are two types of components for a great many applications such as optical communications, VR/AR displays, and LiDAR. Current approaches to creating these two types of devices – integrated optical modulators based on waveguides, active wavefront transceivers based on phased arrays, and passive wavefront transceivers based on grating couplers or integrated metasurfaces – suffer from large footprint, high power consumption, low beam quality, and limited controllability. It is desirable to improve the performance of such devices by exploring new device physics and architectures.In this thesis, we propose and investigate several novel approaches for efficient optical modulation and wavefront manipulation using integrated photonics. First, we show that efficient optical phase modulation can be achieved using a micro-resonator operating in the strongly over-coupled regime. Theoretical analysis, simulations, and experimental demonstrations of thermally tuned silicon nitride adiabatic micro-ring resonators operating at the visible and near-infrared wavelengths are conducted. Compared with traditional waveguide-based devices, our resonator-based phase modulators operating at the visible wavelengths showed order-of-magnitude reductions in both device footprint and power consumption. Through a statistical study of the device performance, our adiabatic micro-ring device architecture also showed significantly improved robustness against fabrication variations when compared with the regular micro-ring architecture. Second, we invent a new category of integrated wavefront-shaping devices – leaky-wave metasurfaces – that possess the simple form factor of a grating coupler and the capability of complete wavefront manipulation over all the four optical degrees of freedom: amplitude, phase, polarization ellipticity, and polarization orientation. The working principle of the leaky-wave metasurfaces is based on symmetry-broken photonic crystal slabs supporting quasi-bound states in the continuum (q-BICs). We extended the mechanism of q-BICs excited by free-space planewaves into q-BICs excited by guided waves, and developed a semi-analytical model describing the mapping between the four structural parameters and the four optical parameters of a meta-unit. We experimentally demonstrated multiple leaky-wave metasurface devices that convert light confined in an optical waveguide to an arbitrary optical pattern in free space, realizing custom polarization control, phase-amplitude control, and complete wavefront control, and validating the theory and capability of this platform. Lastly, we explore strategies to optimize the beam quality and efficiency of integrated optical phased arrays. We show that a two-dimensional disordered hyperuniform array layout is promising for generating a radiation pattern with high directionality with performance surpassing uniform arrays, constrained random arrays, and non-redundant arrays. We experimentally demonstrated a passive 32-channel phased array operating at the blue wavelength that showed a high percentage of power in the main beam and suppressed side lobes. We further propose and discuss the use of efficient, resonator-based modulators in phased arrays to improve the system compactness, power efficiency, and scalability. The approaches we investigated in this thesis provide a concrete set of solutions for interfacing free-space optics and integrated photonics. These two platforms have traditionally been studied by investigators from different subfields of optics and have led to commercial products addressing different needs. Our work suggests new ways to create “hybrid” systems consisting of partly integrated photonics and partly free-space optics and utilize the best of both worlds to address many emerging applications such as quantum optics, optogenetics, sensor networks, inter-chip communications, and holographic displays.

In this dissertation, I am presenting my research on the fabrication and simulation of the optical properties of 3D photonic crystals and 2D graded photonic super-crystals. The 3D photonic crystals were fabricated using holographic lithography with a single, custom-built reflective optical element (ROE) and single exposure from a visible light laser. Fully 3D photonic crystals with 4-fold, 5- fold, and 6-fold symmetries were fabricated using the flexible, 3D printed ROE. In addition, novel 2D graded photonic super-crystals were fabricated using a spatial light modulator (SLM) in a 4f setup for pixel-by-pixel phase engineering. The SLM was used to control the phase and intensity of sets of beams to fabricate the 2D photonic crystals in a single exposure. The 2D photonic crystals integrate super-cell periodicities with 4-fold, 5-fold, and 6-fold symmetries and a graded fill fraction. The simulations of the 2D graded photonic super-crystals show extraordinary properties such as full photonic band gaps and cavity modes with Q-factors of ~106. This research could help in the development of organic light emitting diodes, high-efficiency solar cells, and other devices.

In this thesis we study elliptic PDEs and PDE systems with e-pcriodic coeffi- cients, for small E, using the theory of two-scale homogenisation. We study a class of PDEs of partially degenerating type: PDEs with coefficients that are not uniformly elliptic with respect to E, and become degenerate in the limit E -t O. We review a recently developed theory of homogenisation for a general class of partially degenerating PDEs via the theory of two-scale convergence, and study two such problems from physics. The first problem arises from the study of a linear elastic composite with periodically dispersed inclusions that are isotropic and (soft' in shear: the shear modulus is of order E2. By passing to the two- scale limit as E -t 0 we find the homogenised limit equations to be a genuinely two-scale system in terms of both the macroscopic variable x and the micro- scopic variable y. We discover that the corresponding two-scale limit solutions must satisfy the incompressibility condition in y and therefore the composite only undergoes microscopic deformations when a (microscopically rotational' force is applied. We analyse the corresponding limit spectral problem and find that, due to the y-incompressibility, the spectral problem is an uncoupled two-scale prob- lem in terms of x and y. This gives a simple representation of the two-scale limit spectrum. We prove the spectral compactness result that states: the spectrum of the original operator converges to the spectrum of the limit operator in the sense of Hausdorff. The second problem we study is the propagation of electro- magnetic waves down a photonic fibre with a periodic cross section. We seek solutions to Maxwell's equations, propagating down the waveguide with wave number k E2-close to some (critical' value. In this setting, Maxwell's equations are reformulated as a partially degenerating PDE system with z-periodic coeffi- cients. Using the theory of homogenisation we pass to the limit as E -t 0 to find a non-standard two-scale homogenised limit and prove that the spectral compact- ness result holds. We finally prove that there exist gaps in the limit spectrum for two particular examples: a one-dimensionally periodic 'multilayer ' photonic crystal and a two-dimensionally periodic two-phase photonic crystal with the in- clusion phase consisting of arbitrarily small circles. Therefore, we prove that these photonic fibres have photonic band gaps for certain k.

The primary research aim in this thesis is to demonstrate the versatility of porous silicon based nanomaterials for biomaterial and photonic applications. In chapter 2 of this thesis, the suitability of porous silicon as a biomaterial was investigated by performing different surface modifications on the porous silicon films and evaluating biocompatibility of these surfaces in vitro. The porous silicon surfaces were characteriszed by means of atomic force microscopy (AFM), scanning electron microscopy (SEM), diffuse reflectance infrared spectroscopy (DRIFT) and interferometric reflectance spectroscopy (IRS). Cell attachment and growth was studied using fluorescence microscopy and cell viability assays. Both fabrication of the porous silicon films and subsequent surface modifications were demonstrated. Polyethylene glycol functionalised porous silicon prevented cell attachment, whilst collagen or fetal bovine serum coating encouraged cell attachment. Surface modifications were also performed on porous silicon films with different pore sizes and the influence of pore size and surface modification on primary hepatocyte growth was recorded over a course of 2 weeks by means of laser scanning confocal microscopy (LSCM), toxicity and metabolic assays. On collagen-coated surfaces with average pore sizes of 30 nm, multilayer cells stacks were formed. This stacking behaviour was not observed on samples with smaller pore sizes (10 nm), or in the absence of collagen. Hepatocytes remained viable and functional (judging by a metabolic assay) for 6 days, after which they generally underwent apoptosis. Collagen-coated porous silicon films showed later onset of apoptosis than porous silicon films not coated with collagen or collagen-coated flat silicon.. In chapter 3 of this thesis, the nitrogen laser of a laser desorption/ionization (LDI) mass spectrometer was used to selectively ablate regions on porous silicon films that had been functionalised with a non-fouling polyethylene oxide layer, affording a microscale patterning of the surface. Surface characterization was performed by means of AFM, SEM, LDI mass spectrometry, DRIFT and IRS. This approach allowed the confinement of mammalian cell attachment exclusively on the laser-ablated regions. By using the more intense and focussed laser of a microdissection microscope, trenches in a porous silicon film were produced of up to 50 micron depth, which allowed the construction of cell multilayers within these trenches, mimicking the organization of liver cords in vivo. Fluorescent staining and LSCM was used to study cell multilayer organization. To gain a better understanding of how surface topography influences cell attachment and behaviour, porous silicon films were fabricated containing a gradient of pore sizes by means of asymmetric anodisation (chapter 4). These gradients allowed the investigation of the effect of subtle changes of pore size on cell behaviour on a single sample. Analysis by means of LSCM and SEM showed that pore size can dictate cell size and area as well as cell density. In addition, a region of pore size where cell attachment and proliferation was strongly discouraged was also identified. This information can prove to be useful for designing non-biofouling surface topographies. Using the same asymmetric anodisation setup, photonic mirrors gradients were produced and overlaid over one another to produce multidirectional lateral photonic mirror gradients that display a series of roving spectral features (photonic stop-bands) from each gradient layer (chapter 4). These multidirectional photonic gradients have the potential to serve as optical barcodes or contributing to the development of graded refractive index devices such as lenses for high quality image relay and graded-index optical fibers.

<p>This Licentiate presents the main results of theoretical study of light propagation in photonic structures, namely lasing disk microcavities and photonic crystals. In the first two papers (Paper I and Paper II) we present the developed novel scattering matrix technique dedicated to calculation of resonant states in 2D disk microcavities with the imperfect surface or/and inhomogeneous refractive index. The results demonstrate that the imperfect surface of a cavity has the strongest impact on the quality factor of lasing modes.</p><p>The generalization of the scattering-matrix technique to the quantum-mecha- nical case has been made in Paper III. That generalization has allowed us to treat a realistic potential of quantum-corrals (which can be considered as nanoscale analogues of optical cavities) and to obtain a good agreement with experimental observations.</p><p>Papers IV and V address the novel effective Green's function technique for studying propagation of light in photonic crystals. Using this technique we have analyzed characteristics of surface modes and proposed several novel surface-state-based devices for lasing/sensing, waveguiding and light feeding applications.</p> / Report code: LIU-TEK-LIC 2006:5

Photonic properties depend on both dielectric contrast in a microscopic composite and the arrangement of the microstructural components. No theory exists for direct prediction of photonic properties, and so progress relies on numerical methods combined with insight into manufacturable composite architectures. We present a discussion of effective photonic crystal production techniques and several numerical methods to predict dispersion relations of hypothetical but fabricable structures. / Singapore-MIT Alliance (SMA)

Lately, there has been an increasing interest in studying the propagation of electromagnetic waves in periodic dielectric structures (photonic crystals). Like the electron propagation in semiconductors, these structures are represented by band diagrams in which gaps can be found where the electromagnetic propagation is forbidden. Much effort is dedicated to find structures that can prohibit the propagation of light in all directions. This effect could lead to light localization. / Singapore-MIT Alliance (SMA)