Bifurcation of asymmetric solutions in nonlinear optical media

We study the propagation of monochromatic fields in a layered medium, The m athematical model is derived from Maxwell's equations. It consists of a non linear eigenvalue problem on the real axis with coefficients depending on t he various layers. A systematic analysis is carried out to uncover the vari ous mechanisms leading to the bifurcation of asymmetric solutions even in a completely symmetric setting. We derive two particular simple conditions f or the occurence of asymmetric bifurcation from the symmetric branch. One o f these conditions occurs at a matching of the refractive indices across th e interface while the other corresponds to a switching of the peak from the core to the cladding. The rich bifurcation structure is illustrated by num erical calculations. Further stability considerations are included.