Reflection and transmission coefficients for nonlinear media: Self-induced transmission, amplified reflection, phase conjugation, third harmonic generation, second harmonic generation

We propose a method using invariant imbedding of integral equations for determining the reflection and transmission coefficients for Helmholtz wave equations which are nonlinear because of nonlinear polarization terms. The present method generalizes previous treatments by (a) properly including reflection and refraction at dielectric interfaces, (b) allowing solution for spacially inhomogeneous and/or absorptive nonlinear media, and (c) bypassing the adiabatic (or slowly varying envelope) approximation. Propagation equations for the reflection and transmission coefficients of the nonlinear phenomena enumerated in the title are presented for various geometries.