a Numerical Model of Optical Beam Propagation in Photorefractive Crystals and Comparisons with Experiment.

This thesis describes the development of a photorefractive beam propagation method. The numerical model is based on the split step method for propagating beams in inhomogeneous media. It is used to simulate the response of photorefractive materials to better understand the mechanisms of their behavior. Numerical techniques for simulating steady-state, two-beam coupling are extended to include diffractive scattering, four wave mixing, and temporal dependence. A scattering method is implemented in which the strength and separation of the scattering regions can be varied. Both volume and surface scattering can be simulated. Good agreement is obtained between simulations and experimental measurements of nonamplified and amplified scattering. A relaxation method is developed in which the space charge field due to counter-propagating beams can be calculated, permitting the simulation of four wave mixing. This method also provides a visualization of quasi-temporal effects. The resulting phase conjugate reflectivities agree well with previous plane-wave studies in which the pump and probe ratios were varied. The transverse beam distributions of the phase conjugate output are qualitatively similar to those found using a Runge-Kutta method for solving the coupled wave equations. These distorted distributions show that the gain is generally higher in the direction of greatest beam overlap, akin to the convective amplification used to describe the behavior of a double phase conjugate mirror (DPCM). A combination of the relaxation and scattering methods is required to model the DPCM, as it depends on scattering to initiate operation, and has two counter-propagating beams for the initial inputs. A study of the transition between oscillator and amplifier behavior is conducted. Preliminary results indicate that the nature of the device depends primarily upon the ratio of the length of the overlap region of the beams with respect to the crystal length. Secondary trap levels are incorporated in the calculation in the space charge field to account for intensity -dependent photorefractive gain and absorption. Although inclusions of these effects in simulations indicated that substantial differences in beam fanning distributions could be observed, limitations in the experimental measurements hindered attempts to verify this. A more accurate method for evaluating finite Fourier transform integrals using an adapted Filon algorithm is presented. This method can be evaluated using FFT's, yielding the speed of the FFT, yet still retaining the improved performance of the original Filon algorithm.