Hamiltonian Dynamics of Parametric Nonlinear Wave Mixing

Abstract

Exact solutions in terms of elliptic integrals to the problem of mixing between a wave and its second-harmonic in a medium with quadratic and/or cubic nonlinearity have been reported in the nonlinear optics literature since the early sixties [1-4]. These solutions involve rather cumbersome expressions which do not lead to an immediate insight into the physics of the conversion process.