Effective non-linear coefficients of optical waveguides

Abstract

Using the weakly guiding approximation, and with the assumption that the non-linearities are sufficiently weak so as not to change the transverse mode profile, perturbation theory is used to derive simple expressions for evaluating the modal, or effective, non-linear coefficients of optical waveguide structures based on the non-linear coefficients of the constituent materials. In particular, the third-order and fifth-order optical non-linearities of refraction and absorption are discussed. The expressions are used to estimate the effective modal non-linear refraction coefficients for various types of slab waveguides, focusing primarily on femtosecond refractive non-linearities in semiconductor amplifiers, including quantum-well structures. The results are of particular relevance to the design of all-optical switches based on these effects.