Theory of the optical parametric oscillator

Abstract

We have considered the problem of parametric oscillation in the optical region. The mathematical approach consists of solving Maxwell equations in the normal-mode formulation for the amplitudes of the pump (ω_p), signal (ω_s) and idler (ω_i) modes in the presence of a nonlinear optical medium characterized by an SIIG-like tensor x_(ijk) and with ω+p = ω_i + ω_s. The derivation of the equations of motion for the normal mode amplitudes is similar to those of previous resonator analyses. The original contribution of the paper, however, is the extension of the analysis into the nonlinear above threshold region. This requires that the pump energy density inside the optical resonator and the pump power input be considered as two independent physical quantities. The analysis shows that below threshold the two are proportional to each other, while above threshold the pump energy density saturates, in a manner analogous to the single-pass gain of a laser oscillator, at a constant value. The analysis is also used to obtain explicit expressions for the power outputs at ω_i and ω_s as a function of the pumping power. The conditions of optimum coupling are derived and the validity of the Manley-Rowe relations in the presence of losses is established.