Period Doubling Bifurcations From a Linear (Empty) Interferometer

Abstract

In investigations of dynamical instabilities in passive nonlinear optical systems it is often the case that the basic frequencies of oscillation which appear in sequences of dynamical states are those characteristic of the linear relaxation processes of one of the components of the nonlinear system. For example, in the single mode instability in optical bistability the frequency which occurs in the first bifurcation from a time independent steady state is approximately that of the cavity mistuning1, which is likewise the frequency observed in the transient relaxations of the cavity alone. For multimode instabilities that have been discussed by Ikeda and others2,3 the frequencies which occur at subharmonics of the cavity free spectral range are the same as those one can observe in the transient excitation of an empty linear interferometer. Because of this feature it is often difficult to separate nonlinear dynamical behavior observed in the transient regime from the simple transient oscillatory behavior of a linear system.4,5 An essential characteristic of the nonlinear interactions between the individual components is to stabilize what would otherwise be transient oscillations, and in fact to create new time dependent steady states.