Harmonic generation (HG, also called multiple harmonic generation) is a nonlinear optical process in which ${\displaystyle n}$ photons with the same frequency interact with a nonlinear material, are "combined", and generate a new photon with ${\displaystyle n}$ times the energy of the initial photons (equivalently, ${\displaystyle n}$ times the frequency and the wavelength divided by ${\displaystyle n}$).

In a medium having a substantial nonlinear susceptibility, harmonic generation is possible. Note that for even orders (${\displaystyle n=2,4,\dots }$), the medium must have no center of symmetry (non-centrosymmetrical).

Because the process requires that many photons are present at the same time and at the same place, the generation process has a low probability to occur, and this probability decreases with the order ${\displaystyle n}$. To generate efficiently, the symmetry of the medium must allow the signal to be amplified (through phase matching, for instance), and the light source must be intense and well-controlled spatially (with a collimated laser) and temporally (more signal if the laser has short pulses).

A special case in which the number of photons in the interaction is ${\displaystyle n=2}$, but with two different photons at frequencies ${\displaystyle \omega _{1}}$ and ${\displaystyle \omega _{2}}$.

A special case in which the number of photons in the interaction is ${\displaystyle n=2}$. Also a special case of sum-frequency generation in which both photons are at the same frequency ${\displaystyle \omega }$.

A special case in which the number of photons in the interaction is ${\displaystyle n=3}$, if all the photons have the same frequency ${\displaystyle \omega }$. If they have different frequency, the general term of four-wave mixing is preferred. This process involves the 3rd order nonlinear susceptibility ${\displaystyle \chi ^{(3)}}$.

Unlike SHG, it is a volumetric process and has been shown in liquids. However, it is enhanced at interfaces.

Nonlinear crystals such as BBO (β-BaB₂O₄) or LBO can convert THG, otherwise THG can be generated from membranes in microscopy.