nonlinearities (original) (raw)

Author: the photonics expert (RP)

Definition: optical phenomena involving a nonlinear response to a driving light field

Categories: article belongs to category fiber optics and waveguides fiber optics and waveguides, article belongs to category nonlinear optics nonlinear optics

nonlinearities

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DOI: 10.61835/08e Cite the article: BibTex BibLaTex plain text HTML Link to this page! LinkedIn

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What are Optical Nonlinearities?

Interactions of intense light with matter are often of a nonlinear nature. In this article, we focus on the physical origins of such interactions, while a separate article on nonlinear optical effects discusses the observable consequences.

Summary of Important Nonlinearities

Some of the most important nonlinear interactions are briefly summarized below:

($\chi^{(2)}$) nonlinearities are electronic nonlinearities where a nonlinear polarization is proportional to products of electric-field components. Such nonlinearities arise in media without inversion symmetry (certain low-symmetry nonlinear crystal materials), or to some extent even for symmetric materials as surface/interface contributions. Consequences include frequency doubling, sum and difference frequency generation, optical parametric amplification and oscillation, and the electro-optic effect (Pockels effect).
($\chi^{(3)}$) nonlinearities are of third order in electric fields. They include instantaneous electronic responses and delayed contributions from material excitations. Examples of consequences are the Kerr effect, two-photon absorption (related to the imaginary part of the ($\chi^{(3)}$) tensor), Raman scattering and Brillouin scattering.
Non-perturbative high-field interactions going beyond a low-order ($\chi^{(n)}$) description occur in high harmonic generation: Electrons tunnel/ionize, accelerate in the field, and recombine, emitting high-order harmonics (three-step model).
Electronic excitations often shape nonlinear behavior. For example, dopant ions or bands in semiconductors can be driven between levels (→ optical pumping); population changes then modify absorption and gain, yielding saturable absorption (used for passive mode locking of lasers) as well as laser amplification via stimulated emission. Related effects include excited-state absorption and gain saturation.
Thermal nonlinearities (thermo-optic effects like thermal lensing and thermally induced depolarization loss) arise from heating due to absorption. They are delayed and often nonlocal. Additional mechanisms (e.g. Bragg scattering) underlie phenomena such as thermal mode instabilities in high-power fiber lasers and amplifiers. Related photoinduced index changes include the photorefractive effect and free-carrier contributions in semiconductors (free-carrier absorption/dispersion).

Categorization of Nonlinearities

Nonlinearities can be categorized in various ways, e.g.

by the type of underlying nonlinear effects (as above)
by the participating subsystems (e.g. electronic vs. ionic/vibrational/acoustic, free-carrier, thermal, orientational)
by the order of the underlying nonlinearity (($\chi^{(2)}$) , ($\chi^{(3)}$) )
parametric (instantaneous) nonlinearities vs. those involving a delayed nonlinear response (e.g. Raman scattering)
resonant vs. non-resonant (near a material resonance vs. far-off-resonant electronic response)
local vs. nonlocal (response depends only on local intensity vs. spatially averaged, as in many thermal effects)
by tensor symmetry/anisotropy (isotropic vs. birefringent/anisotropic nonlinear response)

Bibliography

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