Optical processes where light-matter interaction depends nonlinearly on the light intensity.Nonlinear optics studies phenomena where the response of a material to light is not proportional to the light's intensity. At high intensities, typically from pulsed lasers, the electric field of light becomes strong enough to alter the optical properties of the medium itself, leading to effects like frequency doubling, self-focusing, and four-wave mixing. This field underpins many modern laser technologies, from green laser pointers to ultrafast pulse generation and optical frequency combs.
The field began with the discovery of second harmonic generation by Peter Franken and colleagues in 1961, shortly after the invention of the laser. The theoretical framework was developed by Nicolaas Bloembergen, who won the 1981 Nobel Prize in Physics for his contributions.
In a nonlinear medium, the polarization induced by the electric field of light includes terms proportional to the square, cube, etc., of the field. These higher-order terms act as sources of new frequencies: for example, the second-order term generates light at twice the frequency (second harmonic generation). Similarly, the intensity-dependent refractive index (Kerr effect) causes self-focusing, where a beam creates its own lens, and can lead to filamentation. The corpus titles illustrate diverse nonlinear phenomena: light breaking symmetry in a ring laser, a layered crystal amplifying light sevenfold, and light and particles becoming entangled in a 'dance'.
Nonlinear optics is used in frequency conversion (e.g., green and UV lasers), optical parametric oscillators for tunable light sources, supercontinuum generation for white-light lasers, and in quantum optics for generating squeezed and entangled photon states.
The first demonstration of second harmonic generation produced so little ultraviolet light that the spot on the paper was barely visible, and the editor of the journal mistakenly cropped it out of the published photograph, thinking it was a blemish.
| ω | variable | angular frequency — angular frequency radian per second |
| k | variable | wave number — wave number radian per metre |
| c | variable | propagation speed — wave speed metre per second |
| | | | operator | returns the magnitude of a real number — absolute value operator |













