TE wave reflection from a Kerr medium: spatial dynamics and bistability

We analyze transverse-electric (TE) wave reflection at a planar interface between a linear medium and a Kerr nonlinear half-space. Using an amplitude-phase formalism, we derive expressions for the reflection coefficient and the incident intensity as functions of the interface permittivity. For total internal reflection, we obtain the spatial evolution equation for the permittivity, which decays monotonically toward the linear value. The shape of the incident intensity function is examined, yielding conditions for the existence of a maximum on the evanescent branch and a minimum on the propagating branch, which together determine the bistability region. Both self-focusing (α > 0) and self-defocusing (α < 0) Kerr nonlinearities are treated. The propagation constant β appears as a free design parameter, allowing the switching intensity to be adjusted through waveguide geometry. These results may be useful for all-optical switching devices based on nonlinear TE waves.