Resonant parametric interaction of electromagnetic waves in quadratic nonlinear medium

摘要

We derive nonlinear evolution equations describing parametric up- and down-conversion under the conditions when either of the two interacting waves is in resonance with a material transition, e.g., with plasmonic oscillations. Using perturbation theory in the limit of the large wave-number mismatch we drive analytical expressions for two families of quasi-solitonic solutions. If material transition is in resonance with the second-harmonic then the quasi-solitons are of the Nonlinear-Schrodinger type. If the fundamental frequency is in resonance then the reduced system is the paraxial wave equation coupled to the nonlinear classical oscillator. The latter system is integrated analytically and localized solutions are presented.