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Parametric Nonlinearities

Definition: instantaneous optical nonlinearities based on the <$\chi^{(2)}$> or <$\chi^{(3)}$> nonlinear tensor of a transparent medium

More general term: optical nonlinearities

German: parametrische Nichtlinearitäten

Category: physical foundations


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Parametric nonlinearities are optical nonlinearities with an instantaneous response based on the <$\chi^{(2)}$> or <$\chi^{(3)}$> 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.

The term “parametric” comes from models where one considers the effect of a (typically oscillating) disturbance of a parameter. For example, cross-phase modulation can be described as a modulation of the refractive index (a parameter) affecting some other wave.

Usually, phase matching is a condition for achieving a high efficiency in parametric 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 <$\chi^{(2)}$> nonlinearity also the phase matching because such media exhibit birefringence.

Processes involving a change of the quantum state of the optical medium are not called parametric. For example, absorption processes can lead to a nonlinear response of non-parametric type.


[1]G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams”, J. Appl. Phys. 39 (8), 3597 (1968), DOI:10.1063/1.1656831
[2]S. Radic, “Parametric amplification and processing in optical fibers”, Laser & Photon. Rev. 2 (6), 498 (2008), DOI:10.1002/lpor.200810049

See also: nonlinearities, nonlinear polarization, nonlinear crystal materials, phase matching, group velocity mismatch

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