Theory of Cherenkov optical parametric oscillation

An analysis is made of Cherenkov-type optical parametric oscillation in an optical resonator (optical waveguide having its ends bounded by mirrors) crossed with a Fabry – Perot interferometer. It is assumed that the pump wave is incident on the interferometer at an angle close to one of the transmission bands of the interferometer. Equations describing the dynamics of the interacting fields are derived and investigated. With the onset of parametric oscillation, the following effects are predicted when an incident wave is transmitted by the interferometer: appearance of transmitted and reflected waves in new directions and formation of transmitted and reflected waves at converted frequencies. Expressions are obtained for the appropriate nonlinear transmission and reflection coefficients and their dependences on the incident wave intensity are studied. The intensities of radiation generated in the optical waveguide in the temporally steady-state regime are also investigated as a function of the incident wave intensity and the parameters of the system. Under certain conditions, hard self-excitation of this oscillation is predicted. Attention is drawn to the fact that the threshold values of the incident wave intensity in the proposed optical parametric oscillators may be lower than 10 W/cm${}^2$ and the efficiency of conversion of pump energy into emitted radiation energy may be of the order of unity.