Nonlinearities

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

Lasers can be used for the generation of light with very high optical intensities. These can give rise to a number of nonlinear optical effects (→ nonlinear optics), the most important of which are:

• Parametric nonlinearities occur in certain crystal materials with χ⁽²⁾ nonlinearity, giving rise to effects such as frequency doubling, sum and difference frequency generation, and parametric amplification (→ nonlinear frequency conversion).
• There are also parametric nonlinearities arising from χ⁽³⁾. The Kerr effect raises the refractive index by an amount which is proportional to the intensity. This is related to effects like self-focusing, self-phase modulation, cross-phase modulation, and four-wave mixing.
• Spontaneous and stimulated Raman scattering is the interaction of light with “optical phonons”.
• Spontaneous and stimulated Brillouin scattering is the interaction of light with “acoustic phonons” and typically involves counterpropagating waves. Brillouin and Raman scattering are related to the non-instantaneous part of the third-order nonlinear response.
• Two-photon absorption is a process where two photons are simultaneously absorbed, leading to an excitation for which a single photon energy would not be sufficient. Its strength is related to the imaginary part of the χ⁽³⁾ tensor, and is generally large for semiconductor media with small bandgap energy.

There are also various other effects which are not directly based on optical nonlinearities, but are nevertheless affecting optical phenomena:

• Saturation of gain occurs particularly in lasers and amplifiers. Similarly, there are nonlinear losses in saturable absorbers, e.g. in SESAMs used for passive mode locking or Q switching.
• Photorefractive effects are observed in certain ferroelectric crystals such as LiNbO₃. They are used for, e.g., holographic data storage, and can be detrimental in nonlinear frequency conversion.
• There are various kinds of effects involving heating, e.g. thermal lensing in laser gain media or thermal detuning of optical resonators (e.g. enhancement cavities).

In optical fibers, there is a particularly long interaction length combined with the high intensity resulting from a small mode area. Therefore, nonlinearities can have strong effects in fibers. Particularly the effects related to the χ⁽³⁾ nonlinearity – Kerr effect, Raman scattering, Brillouin scattering – are often important, despite the relatively weak intrinsic nonlinear coefficient of silica: either they act as essential nonlinearities for achieving certain functions (e.g. pulse compression), or they constitute limiting effects in high-power fiber lasers and amplifiers.

Usually, the strength of nonlinear effects is determined by the peak power. However, there are cases where stronger effects occur for lower peak powers, as explained in a Spotlight article.

Strong nonlinearities also occur at intensities which are high enough to cause ionization in the medium. This can lead to optical breakdown, possibly even associated with damage of the material. In gases, extremely high optical intensities can be applied, which can lead e.g. to high harmonic generation.

Bibliography

See also: nonlinear optics, laser-induced breakdown, nonlinear crystal materials, nonlinear frequency conversion, nonlinear polarization, nonlinear index, saturable absorbers, fibers, Spotlight article 2007-09-01

Categories: fibers and other waveguides, nonlinear optics