Theory of optical parametric oscillation internal to the laser cavity

Since the fields inside a laser cavity are much higher than the external fields, an analysis of a parametric oscillator with the nonlinear crystal internal to the laser is performed. Using self-consistency equations as the starting point, the equations of motion of such an oscillator are derived. Depending on various cavity, pumping, and nonlinearity parameters, these lead to several types of oscillation with distinctly different operating characteristics: (1) efficient parametric oscillation similar to that of previous analyses; (2) inefficient parametric oscillation resulting from the fact that the nonlinear interaction drives the phases rather than the amplitudes of the signal, idler, and pump; and (3) a pulsing output from the oscillator with repetitive pulses of the signal and idler. A stability analysis of these various regions shows that they are mutually exclusive and can be experimentally chosen by changing the laser gain, the oscillator output coupling, or the strength of the nonlinear interaction. It is shown that the internal oscillator efficiency rapidly approaches the Manley-Rowe limit, as the available pump power becomes several times greater than that required for threshold. The efficiency of an external oscillator having a triply resonant optical cavity is found to be generally less than that of the corresponding internal oscillator.