Exploration Of Optical Propagation In A Nonlinear Dispersive Medium Based On An Incommensurate Spectral Formalism

A recent study involving the propagation of optical signals across a linear/nonlinear interface introduced a formalism based on incommensurate discrete sidebands around a carrier [Banerjee et al, JOSA B 7, 21 (1990)] in order to simplify the analysis of the coupled sideband amplitudes. This approach was shown to be fairly effective not only in the derivation of steady-state transmitted and/or reflected sideband amplitudes for the case of N incommensurate sidebands around an undepleted carrier, but also in the non-steady-state analysis based on a perturbation hierarchy. The first-order perturbation analysis indicated a spatial beating between the upper and lower sidebands with a spatial beat period inversely proportional to the frequency deviation of the pair. In the limit of a pulse where the number of incommensurate pairs is made to approach infinity, and the frequency deviation made to approach zero, the transmitted optical signal in response to an AM pulse was found to contain not only an AM burst, but a narrowband FM "packet" as well (assuming an undepleted carrier and weak nonlinearity). These transmitted "packets" were shown to propagate with distinct phase velocities, resulting in an infinite spatial separation in the asymptotic limit.