Absolute instabilities of counterpropagating pump beams in a dispersive Kerr medium, placed inside a Fabry–Perot cavity, are analytically studied 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 complicated nonlinear system in terms of a doubly resonant optical parametric oscillator. We consider the growth of modulation-instability sidebands associated with each pump beam when weak probe signals are injected through one of the mirrors of the Fabry–Perot cavity. The results are used to obtain the threshold condition for the onset of the absolute instability and the growth rate for the unstable sidebands in the above-threshold regime. As expected, the well-known Ikeda instability is recovered at low modulation frequencies. The effects of the group-velocity dispersion are found to become quite important at high modulation frequencies. Although the absolute instability dominates in the anomalous-dispersion regime, it exists even in the normal-dispersion regime of the nonlinear medium. Below the instability threshold, our analysis provides analytic expressions for the probe transmittivity and the reflectivity of the phase-conjugated signal that is generated through a four-wave-mixing process.
© 1998 Optical Society of America
(120.2230) Instrumentation, measurement, and metrology : Fabry-Perot
(190.0190) Nonlinear optics : Nonlinear optics
(190.3270) Nonlinear optics : Kerr effect
(270.3100) Quantum optics : Instabilities and chaos
M. Yu, C. J. McKinstrie, and Govind P. Agrawal, "Temporal modulation instabilities of counterpropagating waves in a finite dispersive Kerr medium. II. Application to Fabry–Perot cavities," J. Opt. Soc. Am. B 15, 617-624 (1998)