© 2003 Springer-Verlag New York Inc. Stability Analysis of Stationary Light Transmission in Nonlinear Photonic Structures

Summary. We study optical bistability of stationary light transmission in nonlinear pe-riodic structures of finite and semi-infinite length. For finite-length structures, the system exhibits instability mechanisms typical for dissipative dynamical systems. We construct a Leray-Schauder stability index and show that it equals the sign of the Evans function in λ = 0. As a consequence, stationary solutions with negative-slope transmission function are always unstable. In semi-infinite structures, the system may have stationary localized solutions with nonmonotonically decreasing amplitudes. We show that the localized so-lution with a positive-slope amplitude at the input is always unstable. We also derive expansions for finite size effects and show that the bifurcation diagram stabilizes in the limit of the infinite domain size