The colored rings shown in figure 1 are a spectacular manifestation of one type of nonlinear optical frequency conversion: parametric amplification of quantum noise. The amplification in this case is produced by the propagation of an intense pulse of ultraviolet radiation through a crystal of barium borate. When intense electromagnetic radiation propagates through such a material, whose polarization response at optical frequencies manifests a strongly nonlinear dependence on electric field amplitude, nonlinear mixing of the input radiation generates new spectral components. We can exploit this phenomenon to generate coherent radiation at frequencies for which we have no convenient laser sources.
Mixing laser beams of different frequencies in a crystal with nonlinear polarizability can generate coherent output at sum and difference frequencies for which there are no convenient laser sources.