Stability of the asymmetric nonlinear mode trapped in symmetric planar waveguides

The authors examine the reliability of the numerical approach for studying the asymmetric nonlinear mode trapped in a thin linear film sandwiched in an infinite self-focusing medium, and thus resolve a controversy in the literature on the stability of the mode trapped between the bifurcation point and the transition point on the dispersion curve reported. They demonstrate that as a result of the instability there exists a class of quasi-periodic solutions arising from the instability in the asymmetric mode on the unstable branch and weakly stable branch. In addition, the effect of loss on the propagation characteristics of the nonlinear mode is investigated. The evolution is shown to follow the dispersion curve adiabatically in the stable region provided the loss is small, whereas the initial excitation on the unstable branch leads to evolution away from oscillation around the dispersion curve