Why does ordinary daylight not produce nonlinear effects?

Nonlinear terms in the polarization scale with powers of the field and are extremely small at ordinary intensities; only the concentrated fields of focused laser pulses are strong enough to make these effects appreciable.

What is self-focusing?

Through the intensity-dependent refractive index, an intense beam raises the index most where it is brightest, at its centre, so the medium acts like a lens that focuses the beam on itself, sometimes leading to filamentation or damage.

Nonlinear Optical Processes

When light is intense, a medium's polarization responds nonlinearly to the field, giving rise to a range of processes absent in ordinary linear optics.

Definition

Optical phenomena arising when the polarization of a medium depends nonlinearly on the electric field of intense light, described by a power-series expansion whose higher-order susceptibilities generate new frequencies and intensity-dependent effects.

Scope

This topic covers the origin and classification of nonlinear optical effects. It includes the expansion of the induced polarization in powers of the field and the second- and third-order nonlinear susceptibilities, the symmetry requirements that permit or forbid even-order effects, and the principal third-order phenomena such as the optical Kerr effect, self-phase modulation, self-focusing, and four-wave mixing. It also covers stimulated Raman and Brillouin scattering. It establishes the framework of nonlinear susceptibilities from which specific frequency-conversion devices follow.

Core questions

How does the polarization of a medium become nonlinear in the field?
Why are even-order nonlinear effects forbidden in symmetric media?
What are the main third-order nonlinear phenomena?
How does intensity-dependent refraction lead to self-focusing?

Key concepts

nonlinear polarization
second-order susceptibility
third-order susceptibility
optical Kerr effect
self-phase modulation
self-focusing
four-wave mixing
stimulated Raman scattering

Key theories

Nonlinear susceptibility expansion: The induced polarization is expanded as a power series in the field, with the second-order susceptibility responsible for three-wave mixing and the third-order susceptibility for effects such as the Kerr effect and four-wave mixing; crystal symmetry determines which terms survive.
Optical Kerr effect and self-action: The third-order response makes the refractive index depend on intensity, so an intense beam modifies its own phase and can focus itself, underlying self-phase modulation, self-focusing, and soliton formation.

Clinical relevance

Third-order nonlinear processes underlie coherent anti-Stokes Raman scattering microscopy and other label-free nonlinear imaging methods used to visualize lipids and other molecules in tissue, while self-phase modulation broadens laser spectra used in optical coherence tomography.

History

The systematic theory of nonlinear optical susceptibilities was developed by Bloembergen and co-workers in the early 1960s, for which Bloembergen shared the 1981 Nobel Prize in Physics. Subsequent decades elaborated the third-order phenomena and their exploitation in fibres and crystals, summarized in standard texts by Shen and Boyd.

Key figures

Nicolaas Bloembergen
Yuen-Ron Shen
Robert W. Boyd

Seminal works

boyd2020
shen2003

Frequently asked questions

Why does ordinary daylight not produce nonlinear effects?: Nonlinear terms in the polarization scale with powers of the field and are extremely small at ordinary intensities; only the concentrated fields of focused laser pulses are strong enough to make these effects appreciable.
What is self-focusing?: Through the intensity-dependent refractive index, an intense beam raises the index most where it is brightest, at its centre, so the medium acts like a lens that focuses the beam on itself, sometimes leading to filamentation or damage.