Spatial and temporal modes of resonators with dispersive phase-conjugate mirrors

The effects of spatiotemporal dispersion introduced by the phase-conjugate mirror (PCM) on the performance of phase-conjugate resonators (PCRs) is investigated. The PCM is based on four-wave mixing in a nonlinear material in which dispersion arises from the dependence of the mirror reflectivity on the angle of incidence and the temporal frequency. This dispersion is particularly significant when the reflectivity is complex-valued as a result of complex coupling between the four interacting waves.; As a result of spatial dispersion the symmetry of the modes of the ideal PCR, the Hermite-Gaussian beams, is broken. The modes of the dispersive PCR were determined to be the family of Decentered Hermite-Gaussian beams in the degenerate and the nondegenerate case. In the degenerate case, the modes have asymmetric intensity distributions with peaks that are offset from the resonator axis. Such offsets are sensitive to very modest dispersion. The effects of angular dispersion are similar to the effects of misalignments in conventional cavities. Significant distortions in the cavity modes, especially higher-order modes, are introduced by even the smallest dispersion effects in PCRs, and small misalignments in conventional resonators.; In the nondegenerate case, the beating of mode components that are detuned equally above and below the pump frequency, but have different spatial distributions, can result in complex spatiotemporal patterns. The superposition of a number of mode orders with noncommensurate beating frequencies can lead to nontrivial dynamics. This analysis serves to indicate the range of spatiotemporal dynamics that can be attributed to the dispersion associated with the complex coupling in the four-wave mixing process.