nonlinear optics

nonlinear optics [′nän‚lin·ē·ər ′äp‚tiks]

(optics)

The study of the interaction of radiation with matter in which certain variables describing the response of the matter (such as electric polarization or power absorption) are not proportional to variables describing the radiation (such as electric field strength or energy flux).

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Nonlinear optics

A field of study concerned with the interaction of electromagnetic radiation and matter in which the matter responds in a nonlinear manner to the incident radiation fields. The nonlinear response can result in intensity-dependent variation of the propagation characteristics of the radiation fields or in the creation of radiation fields that propagate at new frequencies or in new directions. Nonlinear effects can take place in solids, liquids, gases, and plasmas, and may involve one or more electromagnetic fields as well as internal excitations of the medium. Most of the work done in the field has made use of the high powers available from lasers. The wavelength range of interest generally extends from the far-infrared to the vacuum ultraviolet, but some nonlinear interactions have been observed at wavelengths extending from the microwave to the x-ray ranges. See Laser

Nonlinear materials

Nonlinear effects of various types are observed at sufficiently high light intensities in all materials. It is convenient to characterize the response of the medium mathematically by expanding it in a power series in the electric and magnetic fields of the incident optical waves. The linear terms in such an expansion give rise to the linear index of refraction, linear absorption, and the magnetic permeability of the medium, while the higher-order terms give rise to nonlinear effects. See Absorption of electromagnetic radiation, Refraction of waves

In general, nonlinear effects associated with the electric field of the incident radiation dominate over magnetic interactions. The even-order dipole susceptibilities are zero except in media which lack a center of symmetry, such as certain classes of crystals, certain symmetric media to which external forces have been applied, or at boundaries between certain dissimilar materials. Odd-order terms can be nonzero in all materials regardless of symmetry. Generally the magnitudes of the nonlinear susceptibilities decrease rapidly as the order of the interaction increases. Second- and third-order effects have been the most extensively studied of the nonlinear interactions, although effects up to order 30 have been observed in a single process. In some situations, multiple low-order interactions occur, resulting in a very high effective order for the overall nonlinear process. For example, ionization through absorption of effectively 100 photons has been observed. In other situations, such as dielectric breakdown or saturation of absorption, effects of different order cannot be separated, and all orders must be included in the response. See Electric susceptibility, Polarization of dielectrics

Stimulated scattering

Light can scatter inelastically from fundamental excitations in the medium, resulting in the production of radiation at a frequency that is shifted from that of the incident light by the frequency of the excitation involved. The difference in photon energy between the incident and scattered light is accounted for by excitation or deexcitation of the medium. Some examples are Brillouin scattering from acoustic vibrations; various forms of Raman scattering involving molecular rotations or vibrations, electronic states in atoms or molecules, lattice vibrations or spin waves in solids, spin flips in semiconductors, and electron plasma waves in plasmas; Rayleigh scattering involving density or entropy fluctuations; and scattering from concentration fluctuations in gases. See Scattering of electromagnetic radiation

At the power levels available from pulsed lasers, the scattered light experiences exponential gain, and the process is then termed stimulated, in analogy to the process of stimulated emission in lasers. In stimulated scattering, the incident light can be almost completely converted to the scattered radiation. Stimulated scattering has been observed for all of the internal excitations listed above. The most widely used of these processes are stimulated Raman scattering and stimulated Brillouin scattering.

Self-action and related effects

Nonlinear polarization components at the same frequencies as those in the incident waves can result in effects that change the index of refraction or the absorption coefficient, quantities that are constants in linear optical theory. For example, propagation through optical fibers can involve several nonlinear optical interactions. Self-phase modulation resulting from the nonlinear index can be used to spread the spectrum, and subsequent compression with diffraction gratings and prisms can be used to reduce the pulse duration. The shortest optical pulses, with durations of the order of 6 femtoseconds, have been produced in this manner. Linear dispersion in fibers causes pulses to spread in duration and is one of the major limitations on data transmission through fibers. Dispersive pulse spreading can be minimized with solitons, which are specially shaped pulses that propagate long distances without spreading. They are formed by a combined interaction of spectral broadening due to the nonlinear refractive index and anomalous dispersion found in certain parts of the spectrum. See Soliton

Coherent effects

Another class of effects involves a coherent interaction between the optical field and an atom in which the phase of the atomic wave functions is preserved during the interaction. These interactions involve the transfer of a significant fraction of the atomic population to an excited state. As a result, they cannot be described with the simple perturbation expansion used for the other nonlinear optical effects. Rather they require that the response be described by using all powers of the incident fields. These effects are generally observed only for short light pulses, of the order of several nanoseconds or less. In one interaction, termed self-induced transparency, a pulse of light of the proper shape, magnitude, and duration can propagate unattenuated in a medium which is otherwise absorbing.

Other coherent effects involve changes of the propagation speed of a light pulse or production of a coherent pulse of light, termed a photon echo, at a characteristic time after two pulses of light spaced apart by a time interval have entered the medium. Still other coherent interactions involve oscillations of the atomic polarization, giving rise to effects known as optical nutation and free induction decay. Two-photon coherent effects are also possible.

Nonlinear spectroscopy

The variation of the nonlinear susceptibility near the resonances that correspond to sum- and difference-frequency combinations of the input frequencies forms the basis for various types of nonlinear spectroscopy which allow study of energy levels that are not normally accessible with linear optical spectroscopy.

Nonlinear spectroscopy can be performed with many of the interactions discussed earlier. Multiphoton absorption spectroscopy can be performed by using two strong laser beams, or a strong laser beam and a weak broadband light source. If two counterpropagating laser beams are used, spectroscopic studies can be made of energy levels in gases with spectral resolutions much smaller than the Doppler limit. Nonlinear optical spectroscopy has been used to identify many new energy levels with principal quantum numbers as high as 150 in several elements. See Resonance ionization spectroscopy, Rydberg atom

Many types of four-wave mixing interactions can also be used in nonlinear spectroscopy. The most widespread of these processes, termed coherent anti-Stokes Raman spectroscopy (CARS), offers the advantage of greatly increased signal levels over linear Raman spectroscopy for the study of certain classes of materials.

Phase conjugation

Optical phase conjugation is an interaction that generates a wave that propagates in the direction opposite to a reference, or signal, wave, and has the same spatial variations in intensity and phase as the original signal wave, but with the sense of the phase variations reversed. Several nonlinear interactions are used to produce phase conjugation.

Optical phase conjugation allows correction of optical distortions that occur because of propagation through a distorting medium. This process can be used for improvement of laser-beam quality, optical beam combining, correction of distortion because of mode dispersion in fibers, and stabilized aiming. It can also be used for neural networks that exhibit learning properties. See Optical phase conjugation

Photorefractive effect

The photorefractive effect occurs in many electrooptic materials. A change in the index of refraction in a photorefractive medium arises from the redistribution of charge that is induced by the presence of light. Charge carriers that are trapped in impurity sites in a photorefractive medium are excited into the material's conduction band when exposed to light. The charges migrate in the conduction band until they become retrapped at other sites. The charge redistribution produces an electric field that in turn produces a spatially varying index change through the electrooptic effect in the material. Unlike most other nonlinear effects, the index change of the photorefractive effect is retained for a time in the absence of the light and thus may be used as an optical storage mechanism. Storage times range from milliseconds to months or years, depending upon the material and the methods employed. See Traps in solids

Photorefractive materials are often used for holographic storage. In this case, the index change mimics the intensity interference pattern of two beams of light. Over 500 holograms have been stored in the volume of a single crystal of iron-doped lithium niobate. See Holography

Photorefractive materials are typically sensitive to very low light levels. The photorefractive effect is, however, extremely slow by the standards of optical nonlinearity. Because of their sensitivity, photorefractive materials are increasingly used for image and optical-signal processing applications. See Nonlinear optical devices