<p> Optical gradient index media have the property where the spatial variation of the index of refraction is continuous along the direction transverse to the optical axis. Many emerging technologies in optics require gradient index components, and a firm understanding of the physics of light propagation in these components is required. Presented here are the mathematical foundations used to analyze light propagation in planar quadratic index profile waveguides. One transverse direction is used in this analysis, and light propagation is seen to have periodic behavior. Also presented here is a comparison of ray bundles and wave intensities in quadratic index waveguides, with the intent to use this machinery to further ray chaos theory.</p>

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Advantages of optics over electronics in signal processing derive from the fact that many operations, such as addition, multiplication, correlation, and filtering, can be performed in parallel on two-dimensional data samples. However, this advantage is attainable only if information can be input/output or processed at sufficient speed and space bandwidth. Although acousto-optic devices have been used to provide impressive throughput, they are inherently one-dimensional and do not possess any information-storage capability beyond the acoustic transit time (≤50 μs). Hence, a high-resolution high-speed two-dimensional transducer (or spatial light modulator, SLM) with real-time update capability is required. Unfortunately, none of the existing SLMs perform well enough to fully utilize the inherent speed and parallelism of the optics. This dissertation addresses the development of an SLM that has the potential to meet most of the performance requirements of advanced optical information-processing applications--the photoemitter membrane light modulator (PEMLM). At the heart of the PEMLM is a microchannel plate (MCP) with a flexible membrane covering each pore. In operation, the write image incident on a photocathode, which is placed on the input side of the MCP, creates an electron image. This electron image is then amplified by the MCP and deposited onto the membrane array. The membrane elements, which are electrically and mechanically isolated from each other, are deflected by the induced electrostatic forces. These deflections represent the stored information. Readout of stored information is accomplished by sensing the phase changes induced in an optical-readout beam reflected from the deformed membrane array. A sandwich-type electrostatic grid structure positioned between the MCP and membrane greatly enhances the versatility of the PEMLM by facilitating the use of secondary emission for active electron removal and various intrinsic operations. The theoretical analysis and experimental characterizations performed on prototype devices indicates that PEMLM is capable of higher throughput than most other SLMs, with expected resolutions approaching 50 lp/mm over 10⁷ resolution elements and framing rates greater than 1 KHz. MCP gains provides quantum-limited sensitivity. The PEMLM also promises information-storage times of minutes to hours, greater than 2π phase modulation, good image quality, and an option for serial addressing. In addition, the PEMLM can intrinsically perform operations such as intensity thresholding, contrast modification, edge enhancement, binary logic, synchronous detection, and image addition/subtraction.

This dissertation presents theories of multiwave mixing in two- and three-level media. The first part of the dissertation treats the semiclassical theories in two-level media. Chapter 2 gives the simple semiclassical theory of four-wave mixing when the two pump frequences differ by more than the reciprocal of the population-difference lifetime. This difference washes out the pump spatial holes as well as one of the two reflection gratings. We compare the results to the degenerate treatment of Abrams and Lind and find significant differences in the reflection coefficient spectra. Chapter 3 presents the semiclassical theory of multiwave in a squeezed vacuum characterized by unequal in-phase and in-quadrature dipole decay times. For a highly squeezed vacuum, we find sharp resonances in both probe absorption and reflection coefficients, which provide sensitive ways to measure the amount of squeezing in the vacuum. The second part of the dissertation treats the quantum theories in two- and three-level media. Chapter 4 develops the fourth-order quantum theory of multiwave mixing to describe the effects of sidemode saturation in two-level media. We derive explicit formulas for the fourth-order quantum coefficients and show that the fourth-order quantum theory reproduces the third-order semiclassical coefficient obtained by truncating a continued fraction. We apply the results to cavity problems and find significant differences in the sideband spectra given by the second- and fourth-order treatments, particularly as the sidemode approaches the laser threshold. The final chapter presents a quantum theory of multiwave mixing in three-level cascades with a two-photon pump. The explicit formulas for the resonance fluorescence spectrum and the quantum combination-tone source term are derived. The theory is applied to the generation of squeezed states of light. We find almost perfect squeezing for some strong pump intensities and good broad-band squeezing for low pump intensities.

A two-dimensional hard-disk model of thin-film deposition is described; it is of the type originally introduced by Henderson, Brodsky, and Chaudhari (1974). We have implemented a simple (and necessarily approximate) way to incorporate the effects of surface diffusion in our model, and a means to connect the input parameters of the computer algorithm to the evaporation parameters of substrate temperature and evaporation rate. In the limit of no surface diffusion (low substrate temperature), the model predicts a dendritic structure with large voids; this is the Henderson model. With sufficient surface diffusion (higher substrate temperature), a structure of closely packed crystallites is predicted, and the root-mean-square surface roughness is less than half that predicted by a Henderson-type simulation. This dependence of microstructure on substrate temperature is similar to a zone transition originally described by Movchan and Demchishin (1969) in metal and oxide films. We consider the effect of changing the angle of vapor incidence from normal to oblique. As this angle is increased, a certain critical angle is reached, at which the film density drops and the surface roughness rises precipitously. Both effects result from large columnar voids that develop; the structure of the material that comprises the columns between the voids is similar to the structure of depositions simulated at normal vapor incidence. In a separate study, we simulate the growth of a thin film in two dimensions with a computer implementation of the molecular dynamics (MD) method. The system consists of a krypton substrate maintained at a temperature of 10 degrees Kelvin, toward which argon atoms are periodically directed (with a velocity corresponding to 120 degrees Kelvin). The resulting argon film follows the (horizontal) spacing of the krypton lattice until the thickness approaches an average thickness of about ten monolayers. As deposition proceeds, the configuration of the film changes to incorporate an edge misfit dislocation at the film-substrate interface; this relieves the interfacial stress. We also apply the MD method to study the relaxation of thin-film structures predicted by the hard-disk growth model.

Gain spectra are characterized as a function of the well-width in GaAs multiple quantum wells with AlGaAs barriers by nanosecond pump-probe spectroscopy. The gain bandwidth is larger for the same peak gain in wider well-width multiple quantum wells and is explained qualitatively. The Iinewidth broadening factor is calculated from the gain spectra and studied as a material parameter. It is shown that the linewidth broadening factor increases with wavelength and decreases with carrier density. MBE-grown integrated-mirror etalons made from GaAs/AlGaAs. in the 800 nm wavelength region. and GaAllnAs/InAlAs. in the 1.3 μm wavelength region. exhibit lasing by optical pumping. Below threshold. the 800 nm integrated-mirror etalon is used for nonlinear switching which. in the architecture presented. is capable of extracting a single 10 ps pulse from a pair of pulses spaced 40 ps apart. Nonlinear optical properties of type II GaAs/AlAs short-period superlattices are presented and show an apparent high energy shift of the absorption band edge at 10K and no shift at 77 K as the absorption is saturated. Type I multiple quantum well structures of similar dimensions show similar high energy band edge shifts for both temperatures. 10K and 77 K due to phase-space filling. In contrast. electrons in type II structures reside in the barrier and do not contribute to the chemical potential. Transitions in GaAs/AlGaAs coupled-well superlattices show transitions that are a function of the center barrier thickness and reveal shorter carrier lifetimes than a GaAs quantum well of equal thickness without a center barrier.

Nonlinear optical switching and grating formation/scattering effects in thin semiconductor samples are modeled utilizing a combined microscopic/macroscopic theoretical approach. The microscopic optical nonlinearities of the materials of interest are treated using the semiconductor plasma theory of Banyai and Koch. Computer simulations are used to evaluate the models developed under both steady-state and dynamic conditions. The overall objective of the simulations is to provide a realistic assessment of the potential performance of semiconductor etalon-based nonlinear optical devices for photonic switching and processing applications. To this end, parameter studies are performed with the goal of finding device designs that can operate cascadably, at subnanosecond speeds, with minimum switching energy. Both bistable and two-wavelength operating modes are investigated, with an emphasis on dynamic determination of system characteristics such as contrast, fanout, and differential gain. For bistable semiconductor etalons, the maximum gain achieveable is found to depend in a fundamental way on the relationship between the pulsed-excitation timescale t(p) and the carrier lifetime τ(R). Significant differential gain is shown to disappear for GaAs etalons as t(p)/τ(R) approaches unity, implying that subnanosecond cascading of bistable devices is impractical in this case. For two-wavelength logic gates, several potential solutions to the well-known input/output-wavelength incompatibility problem are proposed. Through the use of a NOR-gate/upconverter etalon pair, picosecond cascadable operation with a fanout of two and contrast of at least five are predicted, requiring a total input energy of 75 picojoules. Utilizing an injected current and stimulated recombination in an active NOR-gate design, the total input energy can be reduced to about 25 picojoules for cascadable, high-contrast operation. The nonlinear semiconductor field-propagation model is also applied to the case of degenerate four-wave mixing in the Raman-Nath regime. The resulting theoretical framework is compared with widely-used small-signal analyses of DFWM in semiconductors for the case of bulk GaAs. The comparison makes clear the inadequacies of such approaches in extracting nonlinear material properties from DFWM experiments performed using moderate to high input intensities. Dynamic simulations of diffraction efficiency spectra in low-temperature CdS are compared with data from corresponding pulsed experiments, producing good qualitative agreement. On the basis of the observed theory-experiment correlation, several drawbacks of DFWM spectroscopy in comparison to pump-probe techniques are discussed.

Diffusion effects on the stationary TE nonlinear surface waves and guided waves and the beam propagation characteristics at the interface separating two or more nonlinear diffusive Kerr-like media are studied extensively. The shape of the nonlinear surface and guided waves are computed for differing diffusion mechanisms and diffusion lengths. Stability of these waves is determined using the beam propagation method. The power and the shape of the nonlinear surface or guided waves are seen to be sensitive to the scaled diffusion length. However, many features including the stability criteria from the diffusionless case remain in the presence of the diffusion. An equivalent particle theory, describing the propagation of a self-focused light channel at the interface of two nonlinear dielectric media, is extended to include diffusion of the nonlinear excitation within each medium. The theory replaces the computationally intensive beam propagation problem by a much simpler Newtonian dynamical problem of studying the motion of an equivalent particle in an effective potential. This simpler Newtonian dynamical problem provides quantitative information on the asymptotes of the reflected, transmitted or trapped channels as well as the stability of the latter as a function of increasing diffusion length. The main results are that increased diffusion makes light transmission more difficult and tends to wash out the local equilibria of the equivalent potential representing unstable or stable TE nonlinear surface waves. The dynamics of two beams interacting at an interface separating two nonlinear dielectrics is studied. Using the two-soliton solution of the nonlinear Schrodinger equation (NLS) and performing a perturbation analysis, ordinary differential equations (ODE) approximation for the two beam interaction dynamics are derived. The numerical results of the ODE model are verified by comparison with numerical solutions of the governing full partial differential equation (PDE). This ODE model is reduced to a simple form to carry out a useful analysis for a special case where a single beam propagating as a trapped surface wave acts as a power controllable switch to direct a second beam incident at a finite angle to the interface. In this case the shape of the effective potential for the second beam is obtained and predicts the behavior of such a beam using the equivalent particle theory.

In this dissertation, some analysis tools for the study of integrated devices applied in optical-disk memory system are investigated. These applications include the gradient-index media used in waveguide lenses and the waveguide focusing grating coupler. Previous studies of gradient-index components have largely been either strictly geometrical in nature or based on the split-step procedure, which are not sufficient for design and analysis purposes. In this dissertation, some beam propagation methods based on paraxial optics are presented, which facilitate diffraction propagation calculation in all types of optical systems that have modest amounts of aberrations, including gradient-index elements. It is also shown that not only is it possible to apply the beam propagation method accurately to stigmatic gradient-index media, but also a propagation distance of any length may be taken without using the split-step method. The Maxwell's fisheye lens is discussed in detail to show application of these methods. Waveguide focusing grating couplers are modeled in detail. The polarization theory of these devices differs from the theory of conventional gratings because of the conversion of guided waves to radiated waves. A simple theory based on induced dipoles is presented to study the polarization conversion effect in radiated field of grating coupler under general case of oblique incidence. Calculations of this model indicate that TE guided mode will be well-behaved but a high degree of variation of elliptical polarization will be generated by TM guided mode. It is also shown that despite the simplicity of the analytical formulations, the agreement with experiment is high and adequate for practical design purpose. Also, tolerances for fabrication errors in focusing grating coupler are described and a systematic method to evaluate tolerances is presented.

Certain conservative discretizations of the Nonlinear Schroedinger (NLS) Equation can produce irregular behavior. We consider the diagonal discretization as a conservative perturbation of the integrable discretization and study the homoclinic crossings in its nonlinear spectrum. We find that irregularity sets in for the two unstable mode regime and, in this case, many and continual homoclinic crossings occur throughout the irregular time series. We undertake an analysis to determine the mechanism that causes the "chaotic" behavior to appear in this conservatively perturbed NLS equation. This analysis involves the construction of explicit formulas for the homoclinic orbit, a description of the relevant finite dimensional phase space and a Melnikov analysis for the various regimes studied.