Radiative effects in the theory of beam propagation at nonlinear interfaces

A theory is presented that describes radiative effects in beam propagation at interfaces separating two (or three) self-focusing dielectric media. The nonlinear interface is formed by two media, both of which are nonlinear, so that in both media the nonlinear wave packet representing the self-focused channel (optical beam) may be described by a soliton solution of the nonlinear Schr\"odinger equation (NLSE), the interface being a steplike inhomogeneity. Assuming the perturbation to be small, we apply the perturbation theory for solitons based on the inverse scattering technique and study adiabatic and radiative effects stipulated by the soliton scattering. In the adiabatic approximation the scattering is described by equations for the soliton parameters that correspond to a motion equation for a classical particle in an effective potential. The reflection coefficient of the beam (the NLSE soliton) is related to a radiation during the scattering, and calculated in the Born approximation of the perturbation theory for the cases of a single and two nonlinear interfaces. An analytical comparison with the scattering of a linear wave packet is carried out. In particular, it is demonstrated that the nonlinear reflection coefficient may be sufficiently smaller than the linear one. We predict also the nonmonotonic dependence of the single-interface reflection coefficient versus the beam power, and analytically describe the nonlinear resonant scattering by two interfaces.

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