Spatiotemporal dynamics of a photorefractive phase-conjugate resonator
Korwan, Daniel R.
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The spatiotemporal dynamics of a photorefractive phase-conjugate resonator (PPCR) is studied both experimentally and analytically. The resonator is a confocal cavity bounded by a dielectric mirror and a phase-conjugate mirror in a four wave mixing geometry. The effect of the Bragg mismatch, which is caused by the misalignment of the pump fields, is experimentally shown to break the cylindrical symmetry of the system and to increase the speed of the dynamics. By studying the first non stationary state at a cavity Fresnel number of F=2.0, the effect of the transverse component of the mismatch is shown to add a transverse phase to the wavefront of the phase-conjugate field, leading to the periodic nucleation of a pair of phase defects. A model of this state is developed in terms of the competition of a few transverse patterns. The model is experimentally verified using a holographic optical correlator designed to identify the modes presumed by the model. The dynamics are also studied using a Karhunen-Loeve decomposition in which the eigenvectors of the covariance matrix are calculated. The covariance matrix is obtained from the transverse intensity fluctuations of the cavity field and the eigenvectors are interpreted as the active cavity modes of the resonator. The results of the application of this experimental method to the F=2.0 state match those obtained by the correlator. This demonstrates its validity as a useful tool for studying the system. Application of the decomposition to states at higher F reveal that aperiodic and periodic states can have very similar active mode structures. An analytical model of the PPCR is then developed using a plane wave decomposition of the cavity field and the n1aterial variables contained in Kukhtarev's equations. Numerical simulations using the model demonstrate its accuracy. In addition, the different effects of the longitudinal and transverse components of the Bragg mismatch on the dynamics and defect nucleation are revealed. The relevant assumptions involved in the development of the model are discussed in detail.
- Doctoral Dissertations