RP Photonics logo
RP Photonics
Encyclopedia
Consulting Software Encyclopedia Buyer's Guide

Short address: rpp-con.com

Dr. Paschotta, the founder of RP Photonics, supports your R & D with his deep expertise. Save time and money with efficient support!

Short address: rpp-soft.com

Powerful simulation software for fiber lasers and amplifiers, resonator design, pulse propagation and multilayer coating design.

Short address: rpp-enc.com

The famous Encyclopedia of Laser Physics and Technology provides a wealth of high-quality scientific and technical information.

Short address: rpp-bg.com

In the RP Photonics Buyer's Guide, you easily find suppliers for photo­nics products. As a supp­lier, you can profit from enhanced entries!

Learn on lasers and photonics every day!
VL logo part of the
Virtual
Library

Nonlinear Polarization

<<<  |  >>>  |  Feedback

Buyer's Guide

Use the RP Photonics Buyer's Guide to find suppliers for photonics products! You will hardly find a more convenient resource.

Ask RP Photonics how calculations and simulations of nonlinear processes may benefit your product development.

Definition: the part of the light-induced electric polarization which depends nonlinearly on the electric field of the light

German: nichtlineare Polarisation

Categories: nonlinear optics, physical foundations

How to cite the article; suggest additional literature

When light propagates in a transparent medium, its electric field causes some amount of electric polarization in the medium, i.e. some density of electric dipole moment. (This must not be confused with the polarization of the light field, which is the direction of its electric field.) That polarization propagates together with the electromagnetic field in the form of a polarization wave. Whereas at low light intensities the electric polarization is proportional to the electric field strength, nonlinear contributions become important at high optical intensities, as they can e.g. be produced with lasers.

Second-order Nonlinear Polarization

The second (lowest) order of nonlinear polarization can arise from a χ(2) nonlinearity which can occur only in crystal materials with a non-centrosymmetric crystal structure. (Nonlinear effects at crystal surfaces are an exception.) The nonlinear polarization then has a component which depends quadratically on the electric field of an incident light wave. More precisely, the tensor nature of the nonlinear susceptibility needs to be considered:

nonlinear polarization

where Pi is the i-th Cartesian coordinate of the polarization, χ(2) is the nonlinear susceptibility, and E(t) is the optical electric field. More commonly, this is written as

nonlinear polarization

with the nonlinear tensor d. Many tensor components can actually be zero for symmetry reasons, depending on the crystal class.

The nonlinear polarization contains frequency components which are not present in the exciting beam(s). Light with such frequencies can then be generated in the medium (→ nonlinear frequency conversion). For example, if the input field is monochromatic, the nonlinear polarization also has a component with twice the input frequency (→ frequency doubling). As the polarization has the form of a nonlinear polarization wave, the frequency-doubled light is also radiated in the direction of the input beam. Other examples are sum and difference frequency generation, optical rectification, parametric amplification and oscillation.

Third-order Nonlinear Polarization

The next higher order of nonlinear polarization can arise from a χ(3) nonlinearity, as it occurs in basically all media. This can give rise to various phenomena:

Phase Matching

In many cases, the nonlinear mixing products can be efficiently accumulated over a greater length of crystal only if phase matching is achieved. Otherwise, the field amplitudes at the exit face, generated at different locations in the crystal, essentially cancel each other, and the apparent nonlinearity is weak. Some nonlinear effects, however, are either automatically phase-matched (e.g. self-phase modulation) or do not need phase matching (e.g. Raman scattering).

Bibliography

[1]D. A. Kleinman, “Nonlinear dielectric polarization in optical media”, Phys. Rev. 126 (6), 1977 (1962)

(Suggest additional literature!)

See also: nonlinearities, nonlinear index, polarization waves, nonlinear crystal materials, nonlinear frequency conversion, phase matching

How do you rate this article?

Your general impression: don't know poor satisfactory good excellent
Technical quality: don't know poor satisfactory good excellent
Usefulness: don't know poor satisfactory good excellent
Readability: don't know poor satisfactory good excellent
Comments:

Found any errors? Suggestions for improvements? Do you know a better web page on this topic?

Spam protection: (enter the value of 5 + 8 in this field!)

If you want a response, you may leave your e-mail address in the comments field, or directly send an e-mail.

If you like our website, you may also want to get our newsletters!

arrow

A Quiz Question

taken from the Photonics Quiz:

Parametric fluorescence is

(a) a quantum-mechanical effect occurring in OPOs and OPAs

(b) responsible for the finite threshold pump power of an OPO

(c) an effect in an OPA which is analogous to ASE in a laser amplifier

After selecting your answer(s) and pressing this button, find the explanations on the left side.

– Show all banners –

– Get your own banner! –