Spatiotemporal dynamics of optical parametric oscillators

The coupling of diffraction and the χ⁽²⁾ nonlinearity is shown to lead to pattern formation in parametric oscillators in optical cavities. In particular the threshold for the generation of signal and idler waves is lowered by an off-axis emission for negative detunings. The output intensity is spatially modulated just above threshold while more complicated patterns appear for larger values of the pump amplitude. Competition between domains of rolls with different orientations leads to long transients until boundary effects prevail. In the case of finite-size input beams, the roll orientation is locally perpendicular to the boundary and the pattern tends to rotate. Finally, the effect of spatial structures on the spectrum of quantum fluctuations of the vacuum is considered and discussed.