TEMPORAL-MODULATION INSTABILITIES OF COUNTERPROPAGATING WAVES IN A FINITE DISPERSIVE KERR MEDIUM - II - APPLICATION TO FABRY-PEROT CAVITIES

Absolute instabilities of counterpropagating pump beams in a dispersiv e Kerr medium, placed inside a Fabry-Perot cavity, are analytically st udied by use of the analysis and the results of part I [J. Opt. Soc. B 14, 607 (1998)]. Our approach allows characterization of such a compl icated nonlinear system in terms of a doubly resonant optical parametr ic oscillator. We consider the growth of modulation-instability sideba nds associated with each pump beam when weak probe signals are injecte d through one of the mirrors of the Fabry-Perot cavity. The results ar e used to obtain the threshold condition for the onset of the absolute instability and the growth rate for the unstable sidebands in the abo ve-threshold regime. As expected, the well-known Ikeda instability is recovered at low modulation frequencies. The effects of the group-velo city dispersion are found to become quite important at high modulation frequencies. Although the absolute instability dominates in the anoma lous-dispersion regime, it exists even in the normal-dispersion regime of the nonlinear medium. Below the instability threshold, our analysi s provides analytic expressions for the probe transmittivity and the r eflectivity of the phase-conjugated signal that is generated through a four-wave-mixing process. (C) 1998 Optical Society of America.