Abstract

Second harmonic generation and subharmonic generation in a cavity are described by the usual master equation (1) for the statistical operator of the system of two modes (fundamental and second harmonic). The master equation is equivalent to a partial differential equation for the Wigner function which is a generalized Fokker-Planck equation involving partial derivatives of the first, second and third order (2). In the semi-classical limit the third order derivatives are negligible and the Wigner distribution satisfies the Fokker-Planck equation equivalent to the Langevin equation with the formally classical Gaussian white noise ξ₁, ξ₂ with the only non-vanishing correlation coefficients β₁, β₂ are the mode amplitudes (normalized to photon numbers), g is the coupling constant, Δ_{1, 2} the frequency mismatch, x is the damping rate, Fp the amplitude of the pump field.

© 1985 Optical Society of America