A linear model of second harmonic generation in terms of generalized Bose operators

G. S. Agarwal

Matthew J. Collett, R. B. Levien

The input-output theory, originally developed for a linear coupling between cavity mode a and a bath, is extended to a coupling that is quadratic in the cavity mode operator a. We then apply this to second-harmonic generation, in a cavity that is resonant at the fundamental frequency and has an active laser medium working at the fundamental frequency. We find intensity squeezing of 50% below the shot-noise level in the output light at the second-harmonic frequency, whether or not the cavity is resonant at the second-harmonic frequency. To compare the singly resonant cavity to the doubly resonant cavity, we develop in an appendix a general technique for extracting a single mode from a continuum.

Giovanni Chesi

Jacob Katriel, Nimrod Moiseyev

The dynamics of the second-harmonic generation Hamiltonian is studied both exactly and using an approximation involving the application of generalized Bose operators. The limits of validity of the approximate treatment, which is of interest in the context of quantum optics, are established. The transition from a regular to a quasistochastic behavior in this nonlinear system is investigated.

Guoxiang Huang, Xin-Qi Li, Jacob Szeftel

A second-harmonic generation (SHG) is predicted for the Bogoliubov excitations in a two-component Bose-Einstein condensate. It is shown that, because the linear dispersion curve of the excitations displays two branches, the phase-matching condition for the SHG can be fulfilled if the wave vectors and frequencies of fundamental and second-harmonic waves are selected suitably from different branches. The nonlinearly coupled envelope equations for the SHG are derived by using a method of multiple scales. The explicit solutions of these envelope equations are provided and the conversion efficiency of the SHG is also discussed.