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Nonlinearities

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 the following:

• Parametric nonlinearities occur in certain crystal materials with <$\chi^{(2)}$> nonlinearity, where the nonlinear polarization is proportional to the square (or to products) of electric field strength components. They give 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 the <$\chi^{(3)}$> nonlinearity. 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, four-wave mixing and modulational instability.
• Effects of the delayed nonlinear response related to the <$\chi^{(3)}$> nonlinearity are spontaneous and stimulated Raman scattering (an interaction of light with optical phonons) and Brillouin scattering (acoustic phonons). The latter typically involves counterpropagating waves.
• 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 <$\chi^{(3)}$> tensor, and is generally large for semiconductor media with small band gap 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).
• 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 laser-induced damage of the material. In gases, extremely high optical intensities can be applied, which can lead e.g. to high harmonic generation.

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.

Nonlinear Effects in Fiber Optics

In optical fiber technology, optical nonlinearities are of high interest. In 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 <$\chi^{(3)}$> 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.

Fibers usually not do not exhibit a <$\chi^{(2)}$> nonlinearity due to the symmetry properties of the used glass. Under certain circumstances, this can be changed, e.g. by poling the glass with a strong electric field.

Case Studies

Case Study: Raman Scattering in a Fiber Amplifier

We investigate the effects of stimulated Raman scattering in an ytterbium-doped fiber amplifier for ultrashort pulses, considering three very different input pulse duration regimes. Surprisingly, the effect of Raman scattering always gets substantial only on the last meter, although the input peak powers vary by two orders of magnitude.

More to Learn

Tutorials:

• Tutorial on Passive Fiber Optics, Part 11: Nonlinearities

Case studies:

• Case Study: Raman Scattering in a Fiber Amplifier
• Case Study: Nonlinear Pulse Compression in a Fiber
• Case Study: Parabolic Pulses in a Fiber Amplifier

Encyclopedia articles:

• nonlinear optics
• effective nonlinear coefficient
• laser-induced breakdown
• nonlinear crystal materials
• nonlinear frequency conversion

Blog articles:

• The Photonics Spotlight 2007-09-01