Effective non-linear coefficients of optical waveguides

Using the weakly guiding approximation, and with the assumption that the nonlinearities 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.