Encyclopedia … combined with a great Buyer's Guide!

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

Author:

Cite the article using its DOI: https://doi.org/10.61835/sle

Get citation code: Endnote (RIS) BibTex plain textHTML

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.

Bibliography

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

(Suggest additional literature!)

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

Questions and Comments from Users

Here you can submit questions and comments. As far as they get accepted by the author, they will appear above this paragraph together with the author’s answer. The author will decide on acceptance based on certain criteria. Essentially, the issue must be of sufficiently broad interest.

Please do not enter personal data here; we would otherwise delete it soon. (See also our privacy declaration.) If you wish to receive personal feedback or consultancy from the author, please contact him, e.g. via e-mail.

Spam check:

By submitting the information, you give your consent to the potential publication of your inputs on our website according to our rules. (If you later retract your consent, we will delete those inputs.) As your inputs are first reviewed by the author, they may be published with some delay.

preview

Share this with your friends and colleagues, e.g. via social media:

These sharing buttons are implemented in a privacy-friendly way!