This work concerns the vacuum deposition of novel thin films that exhibit nonlinear optical effects due to their unusual microstructure. We discuss four different materials: 1) Tilted columns of aluminum-oxide 2) Gold particles in aluminum-oxide 3) Cadmium sulpho-selenide particles in aluminum-oxide 4) Silver particles in zinc-sulphide. We begin with a description of the vacuum system and some the techniques used to characterize the optical and structural properties of the films. This leads to our study of second-harmonic generation (SHG) in aluminum-oxide thin films deposited at an angle to the evaporant source. We show that SHG is very sensitive to the non-isotropic microstructure that results from such a deposition. and the behavior of the SHG signal with sample orientation provides insight to the symmetry properties of the microstructure. In a related study we show that AU/Al₂O₃ composite films produce a large SHG signal. We investigate the dependence of the strength of the SHG signal with fill-fraction of gold and show that it increases quadratically. in agreement with theory. The third material we discuss is cadmium sulpho-selenide doped aluminumoxide. We describe attempts at nucleating semiconductor crystallites in a variety of hosts through a process of co-deposition and subsequent annealing. We also deposit alternate layers of CdS-Se and Al₂O₃ with the semiconductor layer thin enough that interspersed crystallites form. This results in suspended. isolated crystallites similar to the doped-glass materials of interest to nonlinear optics. A waveguide of a CdS/Al₂O₃ "sandwich" demonstrates optical nonlinearity through a power-dependent prism coupling experiment, and the degree of nonlinearity is much greater than undoped glass, though less than doped glass. The final section of the dissertation is a theoretical description of nonlinear optical behavior in a novel composite material consisting of metal particles in a nonlinear dielectric host. We assume the enhanced field around the resonating particles drives the host locally nonlinear through either a Kerr-type or thermal nonlinearity. We calculate the change in optical properties of the medium due to this effect and show that for a system of silver in zinc-sulphide the nonlinearity can be significant.

The topic of this dissertation, modeling and identification of nonlinear oscillation, represents an area of mathematical systems theory that has received little attention in the past. Primarily, the types of oscillation of interest are those found in biological systems where theoretical foundations for mathematical models are insufficient. These oscillations are also observed in other systems including electrical, mechanical, and chemical. The contributions of this dissertation are a generalized class of autonomous differential equations that are found to exhibit stable limit cycles, and an investigation of a method of system identification that can be used to estimate the model parameters. Here the observed signal is modeled as the response of a nonlinear system that can be described by differential equations. Modeling the signal in this way shifts the emphasis from signal characteristics, such as spectral content, to system characteristics, such as parameter values and system structure. This shift in emphasis may provide a better method for monitoring complex systems that exhibit periodic behavior such as patients under anesthesia. A class of autonomous differential equations, called the generalized oscillator models, are presented as one nᵗʰ-order differential equations with nonlinear coefficients. The coefficients are chosen to change sign depending on the magnitude of the phase variables. The coefficients are negative near the origin and positive away from the origin. Motivated by the generalized Routh-Hurwitz criterion, this coefficient sign changing produces the desired oscillation. Properties of the generalized oscillator model are investigated using the describing function method of analysis and numerical simulation. Several descriptive examples are presented. Based on the generalized oscillator model as a set of candidate models, the system identification problem is formed as a mathematical programming problem. The method of quasilinearization is investigated as method of solving the identification problem. Two examples are presented that demonstrate the method. It is shown that in general, the method of quasilinearization as a solution to the system identification problem will not converge regardless of the initial starting point. This result indicates that although the quasilinearization method is useful for solving two-point boundary value problems, it is not useful (in its present form) for solving the system identification problem.

Two spectral regions of gain exist for a weak probe beam propagating through a medium of two-level-atoms pumped by a strong near-resonance field. Experimentally a cw ring-dye laser is used to explore this gain at the Na D₂ resonance in a vapor. Plane-wave calculations of probe-gain spectra which include the Doppler broadening inherent in a vapor agree well with experimental spectra obtained with a Fabry-Perot interferometer. Such two-beam-coupling gain might have applications as optical pre- or power amplifiers. The gain is also the primary step in four-wave-mixing. Mixing of the pump and sideband which experiences gain produces the medium polarization from which the fourth-wave arises. For phase-matched propagation the fourth-wave, which is at a frequency that experiences little or negative probe-gain (i.e., absorption), grows at nearly the same rate as the primary sideband. Together the two sidebands extract far more than twice as much energy from the pump than does the primary sideband acting alone. Experimentally four-wave-mixing which arises from noise at the gain-sideband-frequency is sometimes accompanied by conical emission at the fourth-wave sideband. Since this sideband is also seen on axis the explanation cannot be simply phase-matching. Simulations which include the full transverse nature of the experiment are currently running on a CRAY supercomputer. These simulations indicate that the radial variation of the medium index of refraction is responsible for conical emission.

In chapter 2 we use functional analytic methods and conservation laws to solve the initial-value problem for the Korteweg-de Vries equation, the Benjamin-Bona-Mahony equation, and the nonlinear Schrodinger equation for initial data that satisfy some suitable conditions. In chapter 3 we use the energy estimates to show that the strong convergence of the family of the solutions of the KdV equation obtained in chapter 2 in H³(R) as ε → 0; also, we show that the strong L²(R)-limit of the solutions of the BBM equation as ε → 0 before a critical time. In chapter 4 we use the Whitham modulation theory and averaging method to find the 2π-periodic solutions and the modulation equations of the KdV equation, the BBM equation, the Klein-Gordon equation, the NLS equation, the mKdV equation, and the P-system. We show that the modulation equations of the KdV equation, the K-G equation, the NLS equation, and the mKdV equation are hyperbolic but those of the BBM equation and the P-system are not hyperbolic. Also, we study the relations of the KdV equation and the mKdV equation. Finally, we study the complex mKdV equation to compare with the NLS equation, and then study the complex gKdV equation.

Nonlinear optical properties of passive and active semiconductors are investigated experimentally and theoretically. Improvement of switching cycle time in optical nonlinear etalons to 40 ps is demonstrated, and strained-layer InGaAs/GaAs quantum well material is used in an asymmetric etalon to greatly improve switching power and contrast. Coherent energy transfer (CET) induced by injection of an external light field is demonstrated in a GaAs quantum well vertical-cavity surface-emitting laser (VCSEL). The evolution of CET induced asymmetric gain with increasing injected power is investigated experimentally and theoretically, and it is found that the CET induced effective gain peak and dip are detuned proportionally with injected power as in homogeneously broadened media and in contrast to other multi-wave effects in GaAs which are detuned proportionally with the light field. Transfer of gain modification between orthogonally polarized modes of the VCSEL and cascading of gain modification within a mode is observed and investigated. The approach of a laser to an injection locked state through increased injected power is investigated experimentally and theoretically, showing new emission frequencies produced which evolve to chaos-like behavior before reaching the phase locked state. CET induced gain modification is used to demonstrate low-power high-contrast switching between polarization modes of the VCSEL with differential gain of 3,510. Switching speed and switching bistability is observed and investigated. Injection induced modification of VCSEL transverse modes is studied experimentally and theoretically. Field defects in the resulting field are observed, and their locations are dependent on the frequency of the injected field, in contrast to the temporally evolving defects normally observed. The rich behavior of nonlinear properties, especially in gain media provide interesting results and valuable applications.

This work investigates the response of the solar atmosphere to mechanical and thermal driving due to global solar oscillations. It was discovered that the coupling of thermal and mechanical modes was very important in reconciling theoretical predictions of the expected change in the solar limb due to solar oscillations and experimental observations of the variability in the solar limb darkening function undertaken at SCLERA (Santa Catalina Laboratory for Experimental Relativity). The coupling between the thermal and mechanical modes occur mainly due to the nonlocal nature of the radiation field. Previous theoretical calculations that used approximations for the radiative transfer that ignored the nonlocal nature of the radiation field predicted expected temperature perturbations (compared to the fluid displacement) that were much too small to be observed. Much larger ratios were found when the radiative transfer was treated properly. A particular solar oscillation can be influenced by the presence of a large number of other modes, if these modes can change the average properties of the medium. If the basic nonlinear equations are statistically averaged, the influence of the "mean field" can be investigated. This nonlinear effect can become important in the analysis for single modes in the upper photosphere.

No description available.

Computer modeling of prism coupling of pulsed laser irradiation at a wavelength of 1064 nm into an organic polymer waveguide with Kerr Law nonlinearities showed that the prism coupling technique was inherent problems that make it difficult to accurately determine the magnitude of the refractive index change. Uncertainty in knowledge of the gap spacing under the prism leads to errors in any estimates of these nonlinear refractive index changes. Results from prism coupling experiments conducted on a polymer waveguide with a pulsed laser are inconclusive.

No description available.

No description available.