Abstract

In an earlier paper [1] we derived a formula describing a modulational instability on the plane or quasi-plane wave background of the field in a passive nonlinear optical ring cavity. This formula was applied to the specific case of the eigenvalue of the linearization of the fixed point going through -1 signifying a period doubling bifurcation. The Ikeda plane wave instability analysis was shown to be invalid, indicating that such fixed points are unstable to transverse fluctuations. We will show that this formula is universally applicable to feedback systems exhibiting strong nonlinear dispersion. We recover, as a special case, the recent mean field result of Lugiato et al. [2] in the case where the above eigenvalue approaches +1, signifying a saddle-node bifurcation. The modulational instability is of widespread occurrence even in situations where the plane wave solution (K_T = 0) is strongly damped. It explains the occurrence of upper bistable branch solitary wavetrains [3] and shows that the dynamical switching from a low to high transmission state with transverse spatial rings occurs via nonlinear generation of higher harmonics in K_T space.

© 1988 Optical Society of America