A parametric process is an

optical Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultrav ...

process in which light interacts with matter in such a way as to leave the

quantum state In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution in ...

of the material unchanged. As a direct consequence of this there can be no net transfer of

energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of hea ...

momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass ...

, or

angular momentum In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed sy ...

between the

optical field An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical ...

and the

physical system A physical system is a collection of physical objects. In physics, it is a portion of the physical universe chosen for analysis. Everything outside the system is known as the environment. The environment is ignored except for its effects on the ...

. In contrast a non-parametric process is a process in which any part of the

of the system changes.See Section ''Parametric versus Nonparametric Processes,'' Nonlinear Optics by

Robert W. Boyd Robert William Boyd (born 8 March 1948) is an American physicist noted for his work in optical physics and especially in nonlinear optics. He is currently the Canada Excellence Research Chair Laureate in Quantum Nonlinear Optics based at the U ...

(3rd ed.), pp. 13-15.

Temporal characteristics

Because a parametric process prohibits a net change in the energy state of the system, parametric processes are "instantaneous". For example, if an atom absorbs a

photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are Massless particle, massless ...

with energy E, the atom's energy increases by ΔE = E, but as a parametric process, the quantum state cannot change and thus the elevated energy state must be a temporary

virtual state In quantum physics, a virtual state is a very short-lived, unobservable quantum state. In many quantum processes a virtual state is an intermediate state, sometimes described as "imaginary" in a multi-step process that mediates otherwise forbi ...

. By the

Heisenberg Uncertainty Principle In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the accuracy with which the values for certain pairs of physi ...

we know that ΔEΔt~ħ/2, thus the lifetime of a parametric process is roughly Δt~ħ/2ΔE, which is appreciably small for any non-zero ΔE.

Parametric versus non-parametric processes

Linear optics

In a linear optical system the dielectric

polarization Polarization or polarisation may refer to: Mathematics *Polarization of an Abelian variety, in the mathematics of complex manifolds *Polarization of an algebraic form, a technique for expressing a homogeneous polynomial in a simpler fashion by ...

, P, responds linearly to the presence of an electric field, E, and thus we can write :

= \varepsilon_0\chi = (n_r+in_i)^2,

where ε₀ is the

electric constant Vacuum permittivity, commonly denoted (pronounced "epsilon nought" or "epsilon zero"), is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric const ...

, χ is the (

complex Complex commonly refers to: * Complexity, the behaviour of a system whose components interact in multiple ways so possible interactions are difficult to describe ** Complex system, a system composed of many components which may interact with each ...

)

electric susceptibility In electricity (electromagnetism), the electric susceptibility (\chi_; Latin: ''susceptibilis'' "receptive") is a dimensionless proportionality constant that indicates the degree of polarization of a dielectric material in response to an applied ...

, and n_r(n_i) is the real(imaginary) component of the

refractive index In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, o ...

of the medium. The effects of a parametric process will affect only n_r, whereas a nonzero value of n_i can only be caused by a non-parametric process. Thus in linear optics a parametric process will act as a lossless

dielectric In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the m ...

with the following effects: *

Refraction In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomen ...

* Diffraction *

Elastic scattering Elastic scattering is a form of particle scattering in scattering theory, nuclear physics and particle physics. In this process, the kinetic energy of a particle is conserved in the center-of-mass frame, but its direction of propagation is modif ...

Rayleigh scattering Rayleigh scattering ( ), named after the 19th-century British physicist Lord Rayleigh (John William Strutt), is the predominantly elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength of the ...

Mie scattering The Mie solution to Maxwell's equations (also known as the Lorenz–Mie solution, the Lorenz–Mie–Debye solution or Mie scattering) describes the scattering of an electromagnetic plane wave by a homogeneous sphere. The solution takes the f ...

Alternatively, non-parametric processes often involve loss (or gain) and give rise to: * Absorption *

Inelastic scattering In chemistry, nuclear physics, and particle physics, inelastic scattering is a fundamental scattering process in which the kinetic energy of an incident particle is not conserved (in contrast to elastic scattering). In an inelastic scattering proc ...

Raman scattering Raman scattering or the Raman effect () is the inelastic scattering of photons by matter, meaning that there is both an exchange of energy and a change in the light's direction. Typically this effect involves vibrational energy being gained by a ...

Brillouin scattering Brillouin scattering (also known as Brillouin light scattering or BLS), named after Léon Brillouin, refers to the interaction of light with the material waves in a medium (e.g. electrostriction and magnetostriction). It is mediated by the refr ...

* Various optical emission processes **

Photoluminescence Photoluminescence (abbreviated as PL) is light emission from any form of matter after the absorption of photons (electromagnetic radiation). It is one of many forms of luminescence (light emission) and is initiated by photoexcitation (i.e. pho ...

Fluorescence Fluorescence is the emission of light by a substance that has absorbed light or other electromagnetic radiation. It is a form of luminescence. In most cases, the emitted light has a longer wavelength, and therefore a lower photon energy, ...

Luminescence Luminescence is spontaneous emission of light by a substance not resulting from heat; or "cold light". It is thus a form of cold-body radiation. It can be caused by chemical reactions, electrical energy, subatomic motions or stress on a crysta ...

Phosphorescence Phosphorescence is a type of photoluminescence related to fluorescence. When exposed to light (radiation) of a shorter wavelength, a phosphorescent substance will glow, absorbing the light and reemitting it at a longer wavelength. Unlike fluo ...

Nonlinear optics

In a nonlinear media, the dielectric

P responds nonlinearly to the electric field E of the light. As a parametric process is in general coherent, many parametric nonlinear processes will depend on

phase matching Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform *Phase space, a mathematica ...

and will usually be

dependent. Sample parametric nonlinear processes: *

Second-harmonic generation Second-harmonic generation (SHG, also called frequency doubling) is a nonlinear optical process in which two photons with the same frequency interact with a nonlinear material, are "combined", and generate a new photon with twice the energy of ...

(SHG), or ''frequency doubling'', generation of light with a doubled frequency (half the wavelength) *

Third-harmonic generation Harmonic generation (HG, also called multiple harmonic generation) is a nonlinear optical process in which n photons with the same frequency interact with a nonlinear material, are "combined", and generate a new photon with n times the energy of t ...

(THG), generation of light with a tripled frequency (one-third the wavelength) (usually done in two steps: SHG followed by SFG of original and frequency-doubled waves) * High harmonic generation (HHG), generation of light with frequencies much greater than the original (typically 100 to 1000 times greater) *

Sum-frequency generation Sum-frequency generation (SFG) is a second order nonlinear optical process based on the annihilation of two input photons at angular frequencies \omega_1 and \omega_2 while, simultaneously, one photon at frequency \omega_3 is generated. As with a ...

(SFG), generation of light with a frequency that is the sum of two other frequencies (SHG is a special case of this) * Difference frequency generation (DFG), generation of light with a frequency that is the difference between two other frequencies *

Optical parametric amplification An optical parametric amplifier, abbreviated OPA, is a laser light source that emits light of variable wavelengths by an optical parametric amplification process. It is essentially the same as an optical parametric oscillator, but without the opti ...

(OPA), amplification of a signal input in the presence of a higher-frequency pump wave, at the same time generating an ''idler'' wave (can be considered as DFG) *

Optical parametric oscillation An optical parametric oscillator (OPO) is a parametric oscillator that oscillates at optical frequencies. It converts an input laser wave (called "pump") with frequency \omega_p into two output waves of lower frequency (\omega_s, \omega_i) by mean ...

(OPO), generation of a signal and idler wave using a parametric amplifier in a resonator (with no signal input) *

Optical parametric generation An optical parametric amplifier, abbreviated OPA, is a laser light source that emits light of variable wavelengths by an optical parametric amplification process. It is essentially the same as an optical parametric oscillator, but without the opti ...

(OPG), like parametric oscillation but without a resonator, using a very high gain instead *

Spontaneous parametric down-conversion Spontaneous parametric down-conversion (also known as SPDC, parametric fluorescence or parametric scattering) is a nonlinear instant optical process that converts one photon of higher energy (namely, a pump photon), into a pair of photons (namely, ...

(SPDC), the amplification of the vacuum fluctuations in the low gain regime * Optical

Kerr effect The Kerr effect, also called the quadratic electro-optic (QEO) effect, is a change in the refractive index of a material in response to an applied electric field. The Kerr effect is distinct from the Pockels effect in that the induced index cha ...

, intensity dependent refractive index * Self-focusing *

Kerr-lens modelocking Kerr-lens mode-locking (KLM) is a method of mode-locking lasers via the nonlinear optical Kerr effect. This method allows the generation of pulses of light with a duration as short as a few femtoseconds. The optical Kerr effect is a process whic ...

(KLM) *

Self-phase modulation Self-phase modulation (SPM) is a nonlinear optical effect of light–matter interaction. An ultrashort pulse of light, when travelling in a medium, will induce a varying refractive index of the medium due to the optical Kerr effect. This variation ...

(SPM), a

\chi^

effect *

Optical solitons In optics, the term soliton is used to refer to any optical field that does not change during propagation because of a delicate balance between nonlinear and linear effects in the medium. There are two main kinds of solitons: * spatial solitons: ...

* Cross-phase modulation (XPM) *

Four-wave mixing Four-wave mixing (FWM) is an intermodulation phenomenon in nonlinear optics, whereby interactions between two or three wavelengths produce two or one new wavelengths. It is similar to the third-order intercept point in electrical systems. Four-wave ...

(FWM), can also arise from other nonlinearities *

Cross-polarized wave generation Cross-polarized wave (XPW) generation is a nonlinear optical process that can be classified in the group of frequency degenerate (four-wave mixing) processes. It can take place only in media with anisotropy of third-order nonlinearity. As a resul ...

(XPW), a

\chi^

effect in which a wave with polarization vector perpendicular to the input is generated Sample non-parametric nonlinear processes: * Stimulated Raman scattering *

Raman amplification Raman amplification "Raman effect"
. ''

Two-photon absorption, simultaneous absorption of two photons, transferring the

to a single electron * Multiphoton absorption * Multiple photoionisation, near-simultaneous removal of many bound electrons by one photon

Notes

References

* * {{Citation , last = Paschotta , first = Rüdiger , title =

Encyclopedia of Laser Physics and Technology The ''RP Photonics Encyclopedia'' (formerly ''Encyclopedia of Laser Physics and Technology'') is an encyclopedia of optics and optoelectronics, laser technology, optical fibers, nonlinear optics, optical communications, imaging science, optical ...

, chapter = Parametric Nonlinearities , chapter-url = http://www.rp-photonics.com/parametric_nonlinearities.html Nonlinear optics Quantum optics