Bifurcation of asymmetric solutions in nonlinear optical media

Abstract.

We study the propagation of monochromatic fields in a layered medium. The mathematical model is derived from Maxwell's equations. It consists of a nonlinear eigenvalue problem on the real axis with coefficients depending on the various layers.¶A systematic analysis is carried out to uncover the various mechanisms leading to the bifurcation of asymmetric solutions even in a completely symmetric setting. We derive two particular simple conditions for the occurence of asymmetric bifurcation from the symmetric branch. One of these conditions occurs at a matching of the refractive indices across the interface while the other corresponds to a switching of the peak from the core to the cladding.¶The rich bifurcation structure is illustrated by numerical calculations. Further stability considerations are included.