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.

This dissertation investigates three different optical instabilities: cw conical emission, bifurcations of optical transverse solitary waves, and asymmetric gain modification in a vertical cavity surface emitting laser (VCSEL). The first two instabilities occur in sodium vapor while the third occurs in a new type of semiconductor laser. For the conical emission instability, the first comparison and agreement between theory and experiment is given. The conical emission process is modeled as a series of nonlinear effects including self-trapping of the pump beam, Doppler-broadened Raman-gain amplification of Doppler-broadened resonance fluorescence, propagational four-wave mixing, and diffraction and pump-induced refraction of the new frequencies. Each step of the emission process is thoroughly examined and explained. Detailed comparisons are made between experimental observables and numerical calculations including near-field and far-field spatial profiles, frequency spectra, and cone angles. All comparisons show good agreement. In a different but related experiment, bifurcations of optical transverse solitary waves are studied for one-way propagation through a sodium vapor cell. Two types of phase encoding seed transverse bifurcations which result in transverse cell-exit profiles with the beauty rivaling that of a kaleidoscope. The cell-exit profiles are stationary in time, reproduce completely when the power or frequency is scanned, and agree well with one-way computations. Evidence is also presented for the first observation of a double-peaked Raman gain. In the third experiment, a temporal instability is examined in a GaAs VCSEL. Strong evidence is presented for an asymmetric gain modification induced when a strong optical signal is injected into the Fabry-Perot transmission peak of the VCSEL while it is lasing. This gain modification results in increased absorption on the high frequency side of the injected signal and increased gain on the low frequency side as manifested by the formation of an optical sideband. The frequency of the sideband depends on the intensity of the injected signal with frequencies (> 50 GHz) well beyond the predicted relaxation oscillation frequency being observed. Very efficient nondegenerate four-wave mixing is also observed.

The application of optimization techniques to the design and analysis of physical optics systems is studied. Optimization techniques such as the method of least squares are commonly applied during design and analysis of geometrical or ray-based optical systems. Many optical systems, such as simple laser oscillator cavities have properties well described by geometrical optics. However, a more general class of optical systems exists where geometric properties do not sufficiently describe the system. For example, ray-based optical descriptions are adequate only in regions away from focal points. In simple laser oscillators, ABCD matrices provide an adequate description, however, when complex apertures or gain media are introduced, the system is no longer adequately described by these geometric properties. These more general optical systems fall under the category of physical optics. Optimization has found widespread use in geometrical optics design. Physical optics design using optimization techniques adapted from geometrical optimization techniques is the primary focus of this research. The key issues were: identification of differences between geometrical and physical optics optimization, development of a suitable optimization algorithm, determination of solutions for dealing with noisy derivatives and singular systems, identification of classes of problems which benefit from optimization techniques, and testing of the algorithm through representative examples. This dissertation discusses aspects of optimization techniques applied to physical optics modeling problems. The method of singular value decomposition is discussed as it applies to the solution of singular least squares matrices. The computational difficulty with noisy derivatives is discussed, and a solution proposed. Physical optics modeling and optimization is described, and several example cases are studied at length.

The scattering of infrared radiation by individual spheres and cylinders on planar surfaces was measured, and a sum-of-fields theory was devised to model the data. A polarization-modulated angle-scanning tunable-wavelength infrared nephelometer was built as part of this work. Reliable data were collected for a variety of sphere/substrate and cylinder/substrate combinations. The modelling calculations were performed by FORTRAN programs, which were developed as part of this work. This model was generally successful in predicting the qualitative scattering behavior of spheres and cylinders on insulating substrates, but only partially successful for systems involving metallic substrates.

We study theoretically the diffraction of atoms by a standing-wave light field. Conceptually the text is divided into two parts. In the first part we deal with the coherent interaction only. We use a band theoretical approach to describe the laser-atom interaction, and to characterize two-beam resonances (Dopplerons and Bragg resonances). These two-beam resonances are major candidates to develop effective atom beam splitters. We study the interaction with classical light fields as well as with quantum fields. In the second part we take incoherent processes, i.e. spontaneous emission, into account and present a numerical scheme for the solution of the generalized optical Bloch equations. This scheme is based on the split-operator technique, and we use it to study numerically the influence of spontaneous emission on the diffraction process. We compare our results with recent experimental data, and investigate the impact of spontaneous emission on the performance of two-beam resonances.

Christiansen filters are scattering filters composed of two materials with dispersion curves (for refractive index) that intersect at one wavelength. These filters transmit unscattered light at the intersection wavelength and incoherently scatter light of other wavelengths. Unlike filters based on optical interference, the transmitted wavelength does not depend on the angle of light incidence on the filter. These filters have been fabricated with solid host matrices by mixing finely ground optical glass powders with pellets of optical grade resins and injection molding the combination into planar filters of various sizes. This method of fabrication can produce filters of any shape or size, limited only by the skill of the mold designer and the size of the molding machine. This dissertation discusses the fabrication, characterization and modeling of solid matrix Christiansen filters. After a brief proposal of our research objectives to motivate this study, the concepts behind and history of these filters are reviewed. A multiple scattering theory of Christiansen filters is discussed and a computer-based search for compatible materials is summarized. After verifying the refractive index dispersions of the selected polymer matrices, a detailed description of the technology and fabrication of these filters follows. Spectral transmission and other measurements are employed to characterize the optical performance of the filters and to compare the filters to theoretical models. We have produced blue, bandpass filters with transmittances ranging from 0.25 to 0.40 at 392 nm; green, bandpass filters with transmittances of 0.20 centered at 510 nm; and near-infrared, edge filters which begin at 700 nm and reach maximum transmittances ranging from 0.30 to 0.50 at 800 nm. The dissertation concludes with recommendations for future improvements and suggestions for possible applications. The results from the computer-based material search and tables of fabrication parameters are included in two appendices.

Optical and electronic properties of semiconductors heterostructures are analyzed, combining many-body and band structure engineering techniques. The Coulomb interaction is considered in different excitation regimes. For the low density excitonic limit, it is shown that superlattices can be modelled as 3D effective anisotropic media and the method is applied to the computation of exciton binding energies. In the high density regime, coupled band optical Bloch equations are obtained, combining Coulomb effects with the solutions of the Luttinger Hamiltonian, and the problem is solved in general under quasi-equilibrium conditions. Expressions for the band gap shift and the Coulomb enhancement in a Pade' approximation are obtained and solved in the context of a quasi-statically screened Coulomb interaction. The resulting equations are used to study the influence of band-structure and many-body effects in the gain and α-factor of both lattice-matched and strained quantum well lasers.

A near infrared hybridly mode-locked dye laser system consisting of a femtosecond oscillator and a high repetition rate dye amplifier was designed and built. This system was then applied to the study of room temperature below-bandgap femtosecond switching and coherent pulse propagation in GaAs/GaAlAs multiple quantum well waveguides. The noise properties of the oscillator output were studied using radio frequency spectrum analysis techniques. Two distinct modes of operation were identified: The first is characterized by the shortest pulse duration and its real-time autocorrelation signal appears more strongly modulated. The second mode of operation, which exhibits a slightly longer pulse duration and a smoother real-time autocorrelation signal, is obtained for a relative cavity length detuning of ΔL = -0.7 μm. Unexpectedly, the second mode features larger pulse duration fluctuations than the first mode and self-pulsing, while the pulse repetition timing and pulse energy fluctuations were found to be similar in both cases, making the first mode preferable for use in time-resolved experiments. Femtosecond all-optical switching under off-resonance room temperature excitation was demonstrated in a passive GaAs/AlGaAs multiple quantum well directional coupler for the first time. The required phase mismatch originates from an ultrafast refractive index change caused by the optical Stark effect. The main obstacle regarding practical device applications is its low transmission (less than 10%). The use of electrically pumped semiconductor waveguides that provide gain promises to remove this disadvantage. Below-resonance, coherent pulse breakup in a room temperature semiconductor waveguide was observed for the first time. Numerical simulations of the coupled semiconductor Maxwell-Bloch equations show that the light-matter interaction can induce enough chirp through self-phase modulation during propagation in order to violate the initial adiabatic following regime and cause pulse breakup. This coherent effect is distinctly different from self-induced transparency, because it does not involve Rabi-oscillations at the start of propagation, from temporal solitons, because it does not require group velocity dispersion, and from self-steepening. However, it should be ubiquitous under off-resonance pulse propagation with a pulse duration less than the polarization dephasing time.

A rigorous model for treating diffraction from arbitrary profile surface-relief gratings is developed. This model is valid for conical incidence geometries and elliptically polarized incident beams. The model is based on the coupled-wave method of Moharam and Gaylord (J. Opt. Soc. Am. 73, 1105-1112 (1983); J. Opt. Soc. Am. 72, 1385-1392 (1982)). The slow convergence of this model for p polarized incident light is analyzed. The source of this slow convergence is determined to be the use of Fourier series expansions for the permittivity and fields in the grating region. The polarization and energy distribution properties of zeroth order gratings are summarized. Designs are presented for zeroth order gratings that function as retardation and polarization conversion elements for specularly reflected beams. Photoresist gratings are fabricated and characterized by ellipsometric techniques to confirm the predictions of the coupled-wave model and to demonstrate these novel designs. The application of zeroth order gratings to optical storage heads is discussed, and novel head designs based on these components are presented.

This dissertation is concerned with the characterization of both the magneto-optic (MO) media and optical system used in MO recording. Amorphous rare earth-transition metal (RE-TM) thin films give rise to magnetic domain walls that are not smooth, but possess varying degrees of jaggedness. A figure-of-merit for domain wall jaggedness could be used to rank films with respect to their suitability for use in MO recording, since domain wall jaggedness has been shown to increase readout noise. Using a specially-constructed static tester, the measured fractal dimension of MO domain walls provides this figure of merit. The basic theory of fractal structures, two measurement techniques, and data from MO samples is presented. At the system level, accurate focusing and tracking is required to reliably and repeatedly write and read data on the media, while track position and focus are maintained. Three focusing and tracking methods are analyzed using scalar diffraction theory, including the effects of residual aberrations and misalignments on their performance. Feedthrough, the false focus error signal due to track crossing in pre-grooved media is also examined and its origin in the astigmatic method is compared with the cause of feedthrough in the obscuration method. The performance of the double astigmatic method, a novel differential method that eliminates feedthrough caused by astigmatism is analyzed. Birefringence of the polycarbonate disk substrate affects tracking and data readout. The focus offset between the position for the best tracking error signal, and that for maximum data readout is shown to be caused by birefringence-induced astigmatism. The effects reducing the track pitch, proper choice of groove depth and pre-format mark depth and their effect on the track crossing signal are investigated. An experimental static focusing/tracking testbed is described along with example data showing the dependence of the tracking error signal on track pitch, objective numerical aperture, groove depth, and polarization orientation, as well as feedthrough performance for the astigmatic focusing/push-pull tracking method.