Competing nonlinearities

The interaction between two cavity resonant nonlinear processes in an intracavity χ⁽²⁾ medium is studied, namely frequency doubling of a pump field of frequency ω₁ and subsequent down-conversion of the second harmonic to a pair of photons of frequencies ω₁±{}{Δ}. A closed set of semiclassical equations of motion for appropriately chosen quantities of the full system is derived and an explicit stationary solution is given. Its features and stability are discussed, the most striking being a stable plateau in the second harmonic, i.e., the field of frequency ω₂=2ω₁ becomes independent of the pump field scrE₁, provided scrE₁ is larger than a certain threshold value. It is demonstrated that undamped self-pulsing can only prevail, if the ratio of the rates of second harmonic generation over and parametric down-conversion exceeds a value which depends solely on the relative damping rates of the second harmonic and fundamental, which yields a tentative theoretical explanation of the experimentally observed quenching of the self-pulsing.