Harmonic generation is a nonlinear optical effect which can be used to access higher frequencies than might conventially be available using the available equipment. High electric field strengths are required in the optical beam and so pulsed lasers are an obvious choice for this technique.

Harmonic generation involves frequency addition. Generally, some crystal is used with a relatively high second-order nonlinear susceptability (X⁽²⁾). This is used for second-harmonic generation, known also as frequency doubling. However, it is possible to access higher harmonics.

How does it work?

Second-Harmonic

When an intense optical field is incident on a transparent medium, the respose of the medium to the field need not be linear. In particular, if the medium has a response which is partially dependent on the square of the field strength, it is possible to get three-wave mixing.¹ In this process, some of the incident light is converted to its second-harmonic. This means, for example, that two red photons can mix and combine to form one blue photon. The frequency of the light has been doubled, but energy is conserved as the total energy of the two red photons should be identical to the energy of the blue one.

Third-Harmonic

Third-harmonic generation is a four-wave mixing process, and so instead of X⁽²⁾, we need to use X⁽³⁾. This means that the interaction will be weaker; however, it is still relatively simple to perform. In this case, the condition that there need not be centrosymmetry does not apply, and all transparent materials have a non-zero value of X⁽³⁾.

Higher harmonics

To access higher harmonics, one needs to have n-wave mixing, where n is one higher than the harmonic you wish to generate. This means that one needs materials with χ(n-1), and as we increase the order of nonlinearity we decrease the interaction strength. Harmononics of orders higher than 50 have been generated, but this level needs exceptionally high optical intensities.