We investigate the transverse and longitudinal modes of a resonator co
nsisting of a spherical mirror, a Gaussian aperture, and a dispersive
phase-conjugate mirror (PCM). The photorefractive PCM introduces spati
al dispersion in the form of lateral and focal shifts along with tempo
ral dispersion. For both degenerate and nondegenerate operation, the d
ecentered Gaussian beam was found to be a mode whose peak intensity is
displaced from the resonator axis. In the nondegenerate case, the com
ponents of a mode oscillating at a pair of frequencies that are up and
down shifted from the pump frequency by the same amount have differen
t spatial distributions, so that the intensity pattern moves periodica
lly across the output mirror. The resonance frequencies of the longitu
dinal modes are calculated numerically. (C) 1997 Optical Society of Am
erica.