Nonlinear optics
Branch of optics studying intensity-dependent optical properties of matter.
Nonlinear optics (NLO) is a branch of optics that studies the case when optical properties of matter depend on the intensity of the input light. Nonlinear phenomena become relevant only when the input light is very intense, typically requiring an electromagnetic field larger than 10⁸ V/m, comparable to the atomic electric field. In nonlinear optics, the superposition principle no longer holds, and the polarization of the material responds non-linearly to the electric field, often expressed as a polynomial sum in the perturbative limit.
This nonlinear response arises from several physical mechanisms, including the motion of bound electrons, field-induced vibrational or orientational motions, optically induced acoustic waves, and thermal effects. The motion of bound electrons is particularly important for ultrafast nonlinear optics due to its very short response timescale. A semiclassical model for this behavior treats the bound electron as an anharmonic oscillator, where the Coulomb force between the ion core and electron acts like a spring, and nonlinearities emerge when the oscillator is stretched or compressed enough to change its effective elastic constant. Because Maxwell's equations are linear in vacuum, all nonlinear optical processes require a material medium, though quantum electrodynamics predicts that vacuum itself can become nonlinear above the Schwinger limit. The standard perturbative description of nonlinear optics applies when input intensities remain below 10¹⁴ W/cm², allowing the polarization density to be written as a polynomial series. At higher intensities, the field of nonperturbational or extreme nonlinear optics studies high-order harmonic generation, attosecond pulses, and relativistic effects. Historically, two-photon absorption was predicted by Maria Goeppert Mayer in 1931, but the field advanced rapidly after the first laser was built, leading to the observation of two-photon absorption at Bell Labs and the discovery of second-harmonic generation by Peter Franken et al. at the University of Michigan in 1961. Some nonlinear effects were known before the laser, and the theoretical foundation for many processes was later consolidated in Bloembergen's monograph "Nonlinear Optics."
- field
- Optics
- known_for
- Study of light-matter interactions where optical properties depend on light intensity, including second-harmonic generation and two-photon absorption
Lore & Background
Nonlinear optics studies how the optical properties of a material change when the incoming light is extremely intense, typically requiring an electric field strength greater than 108 V/m, which approaches the atomic electric field of roughly 1011 V/m. Under such conditions, the polarization density of the material no longer responds linearly to the light’s electric field; the superposition principle fails, and the polarization can be expressed as a polynomial sum of order n in the perturbative limit. The necessary intensity is achieved only with laser sources. Various physical mechanisms cause these nonlinearities, including the motion of bound electrons, field-induced vibrational or orientational motions, optically induced acoustic waves, and thermal effects. The motion of bound electrons has a very short response time, making it especially important for ultrafast nonlinear optics. A semiclassical model of this behavior uses an anharmonic oscillator to represent the forced oscillations of a bound electron, where the Coulomb force governs the binding and nonlinearities arise from changes in the elastic constant when the oscillator is stretched or compressed significantly. Nonlinear processes occur only in media, as Maxwell’s equations are linear in vacuum, though quantum electrodynamics predicts vacuum nonlinearity above the Schwinger limit. The standard perturbative description applies when input intensity remains below 1014 W/cm2, allowing a Taylor series expansion of the polarization density. At higher intensities, the field of nonperturbational or extreme nonlinear optics studies high-order harmonic generation, attosecond pulse generation, and relativistic effects.
Reader's Guide
Nonlinear optics is significant because it explains how intense light can alter the optical properties of materials, leading to a host of phenomena such as frequency doubling, high-harmonic generation, and self-focusing. Its legacy includes enabling technologies like laser mode-locking, optical parametric oscillators, and attosecond pulse generation. The field is divided into perturbative nonlinear optics, valid below 10¹⁴ W/cm², and nonperturbational or extreme nonlinear optics, which investigates extremely high-order harmonics and relativistic effects. Nonlinear optics also underpins practical devices such as electro-optic modulators and acousto-optic modulators, and its study continues to advance understanding of light-matter interactions at the most fundamental levels.
Did You Know?
- Maxwell's equations are linear in vacuum, so nonlinear processes only occur in media, though quantum electrodynamics predicts vacuum nonlinearity above the Schwinger limit.
- The motion of bound electrons has a very short response timescale, making it particularly relevant for ultrafast nonlinear optics.
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