Abstract

We investigate the stability of analytic symmetric and asymmetric solutions for guided waves in a symmetric layered structure comprising self-focussing, self-focussing with saturation and self-defocussing. The refractive indices in the guiding, substrate and cladding layers are given by n² = n₀² and n² = n₁² + α|E|² + β|E|⁴, respectively. The stability analysis by means of composite phase portrait construction seems to be in agreement with reference [1]. Instability of the symmetric waves occurs at powers where the asymmetric waves appear. Stability is restored at a second bifurcation point for β < 0 below a certain value (Fig. 1). However, testing the stability numerically via propagation of the analytic solutions, the waves become unstable at higher powers before the bifurcation point in the self-defocussing case.

© 1988 Optical Society of America