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Mimicking a Kerrlike medium in the dispersive regime of second-harmonic generation

Klimov, A B, Sánchez-Soto, L L, Delgado, J C

Published Jan 31, 2001• 22 citations
OpenAlex

Abstract

We find an effective Hamiltonian describing the process of second-harmonic generation in the far-off resonant limit. We show that the dynamics of the fundamental mode is governed by a Kerrlike Hamiltonian. Some dynamical consequences are examined.

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We present a comprehensive and self-consistent theory of the relative phase between fundamental and harmonic modes in the nonlinear process of second-harmonic generation. We introduce an adequate polar decomposition of the field amplitudes that leads to a truly Hermitian relative-phase operator, whose eigenstates correctly describe the phase properties of the fields. We find the probability distribution for the relative phase and, by using a numerical diagonalization of the interaction Hamiltonian, we study its time evolution. This evolution shows quite different asymptotic behaviours for long times depending on the total number of quanta.