Quantum fluctuation of nonlinear degenerate optical parametric amplification

An analytical solution of the Fokker-Planck equation for the nonlinear degenerate optical parametric amplifier (DOPA) is presented, taking into account the influence of pump depletion on the generation of squeezed light. Results conform to those obtained using perturbation series expansion theory near threshold, and also apply to the whole region far away from threshold. When the nonlinear term(eta -> 0) is neglected, the solution transitions naturally to the linear approximation solution; when the nonlinear term is retained (infinity eta), in the case mu -> 0, the quantum fluctuations are close to vacuum fluctuations; in the case mu >> 1, squeezing increases, and tends to the result obtained using linear theory, 1/(1 + mu).