Spatiotemporal behavior and nonlinear dynamics in a phase conjugate resonator

Abstract

The work described in this dissertation can be divided into two parts. The first part is an investigation of the transient behavior and stability property of a phase conjugate resonator (PCR) below threshold. The second part is an experimental and theoretical study of the PCR's spatiotemporal dynamics above threshold.

The time-dependent coupled wave equations for four-wave mixing (FWM) in a photorefractive crystal, with two distinct interaction regions caused by feedback from an ordinary mirror, was used to model the transient dynamics of a PCR below threshold. Analytical expressions of the steady state cavity's fields for the case of nondepleted pumps and an absorption free medium were derived and used to determine the self-oscillation conditions. The solutions, through simple frequency domain transformation techniques, were used to define the PCR's transfer function and analyse its stability.

Taking into account pump depletion and medium absorption, the transient buildup and decay times of the cavity's fields as well as the specularly reflected and phase conjugate reflected intensities were numerically calculated as functions of a number of system parameters such as the coupling parameter and the pump and probe ratios. General trends were unveiled and discussed in view of the possible use of the PCR in image storage or processing architectures. Experimental results for the buildup and decay times confirmed qualitatively the predicted behavior.