Nonlinear Optical Effects

This article gives a brief overview and different categorizations of nonlinear optical effects in optical materials.

We distinguish optical nonlinearities (underlying physical effects) from nonlinear optical effects; the latter are discussed in this article, while for the former we refer to the article on nonlinearities.

Often, nonlinear effects are distinguished and named by their consequences and uses:

Nonlinear effects can be categorized in various ways, e.g.

• by the type of nonlinearity (electronic, vibrational/rotational, thermal, parametric vs. delayed response)
• by the order of the underlying nonlinearity (($\chi^{(2)}$), ($\chi^{(3)}$) )
• spatial vs. time/frequency effects — for example, Kerr lens effects vs. spectral broadening
• temporal vs. spectral effects — for example, temporal pulse broadening or distortion vs. spectral broadening
• self-action vs. cross-action effects — for example, self-phase modulation vs. cross-phase modulation
• polarization aspects (e.g. type I, type II phase matching)
• resonant vs. nonresonant effects — for example, resonant vs. nonresonant frequency doubling

Various quantities and phenomena are often relevant in nonlinear optical effects:

• Chromatic dispersion affects phase matching and group velocity mismatch, i.e., the temporal overlap of interacting light pulses.
• Effective mode area: This often influences the strength of nonlinear interactions, e.g. in fibers, as it affects the optical intensity for a given optical power.
• Effective nonlinear coefficient: Such a coefficient often governs the strength of parametric nonlinearities.
• Nonlinear index: This governs the strength of the Kerr effect.
• Optical intensity: Generally, nonlinear phenomena become relevant only at high enough optical intensities, although interaction lengths and phase matching can also be highly relevant.
• Phase matching: For many nonlinear optical effects, phase matching is important, i.e., such effects can be strong only if phase matching occurs.

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 RP Photonics Spotlight article.

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 exhibit a ($\chi^{(2)}$) nonlinearity due to the symmetry properties of the glass used. Under certain circumstances, this can be changed, e.g. by poling the glass with a strong electric field.

Tutorials

Passive Fiber Optics
Part 11: Nonlinearities of Fibers

We discuss origins and effects of nonlinearities in passive optical fibers.

Case Studies

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.

Case Studies

Supercontinuum Generation in a Germanosilicate Single-mode Telecom Fiber

We explore supercontinuum generation in telecom fibers. This works well for wavelengths beyond the zero dispersion wavelength. For operation with shorter-wavelength pulses, other fibers are required.