Parametric nonlinearities are optical nonlinearities with an instantaneous response based on the χ(2) or χ(3) nonlinearity of a medium. They give rise to effects such as frequency doubling, sum and difference frequency generation, parametric amplification and oscillation, four-wave mixing, self-phase modulation, cross-phase modulation and others.
Usually, phase matching is a condition for achieving a high efficiency in such processes. This occurs only in a limited optical bandwidth. However, by manipulation of the parameters which influence the phase matching, it is possible to shift the wavelength range where the nonlinear interaction is strong.
Parametric processes are usually polarization-dependent: the nonlinearity itself is polarization-dependent, and at least in cases with a χ(2) nonlinearity also the phase matching, because such media exhibit birefringence.
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