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, ultravio ...

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 embodies the knowledge of a quantum system. Quantum mechanics specifies the construction, evolution, and measurement of a quantum state. The result is a prediction for the system ...

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

energy Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...

momentum In Newtonian mechanics, momentum (: momenta or momentums; 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. ...

, or

angular momentum Angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of Momentum, linear momentum. It is an important physical quantity because it is a Conservation law, conserved quantity – the total ang ...

between the optical field and the

physical system A physical system is a collection of physical objects under study. The collection differs from a set: all the objects must coexist and have some physical relationship. In other words, it is a portion of the physical universe chosen for analys ...

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

of the system changes.See

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 particles that can ...

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. By the

Heisenberg Uncertainty Principle The uncertainty principle, also known as Heisenberg's indeterminacy principle, is a fundamental concept in quantum mechanics. It states that there is a limit to the precision with which certain pairs of physical properties, such as position a ...

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, P, responds linearly to the presence of an

electric field An electric field (sometimes called E-field) is a field (physics), physical field that surrounds electrically charged particles such as electrons. In classical electromagnetism, the electric field of a single charge (or group of charges) descri ...

, E, and thus we can write :

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

where ε₀ is the electric constant, 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 applie ...

, 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 the ratio of the apparent speed of light in the air or vacuum to the speed in the medium. The refractive index determines how much the path of light is bent, or refrac ...

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 Insulator (electricity), electrical insulator that can be Polarisability, polarised by an applied electric field. When a dielectric material is placed in an electric field, electric ...

with the following effects: *

Refraction In physics, refraction is the redirection of a wave as it passes from one transmission medium, 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 commo ...

Diffraction Diffraction is the deviation of waves from straight-line propagation without any change in their energy due to an obstacle or through an aperture. The diffracting object or aperture effectively becomes a secondary source of the Wave propagation ...

Elastic scattering Elastic scattering is a form of particle scattering in scattering theory, nuclear physics and particle physics. In this process, the internal states of the Elementary particle, particles involved stay the same. In the non-relativistic case, where ...

Rayleigh scattering Rayleigh scattering ( ) is the scattering or deflection of light, or other electromagnetic radiation, by particles with a size much smaller than the wavelength of the radiation. For light frequencies well below the resonance frequency of the scat ...

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

Raman scattering In chemistry and physics, 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 vibrationa ...

** Brillouin scattering * Various optical emission processes ** Photoluminescence **

Fluorescence Fluorescence is one of two kinds of photoluminescence, the emission of light by a substance that has absorbed light or other electromagnetic radiation. When exposed to ultraviolet radiation, many substances will glow (fluoresce) with colore ...

Luminescence Luminescence is a spontaneous emission of radiation from an electronically or vibrationally excited species not in thermal equilibrium with its environment. A luminescent object emits ''cold light'' in contrast to incandescence, where an obje ...

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 fluor ...

Nonlinear optics

In a nonlinear media, the dielectric polarization P responds nonlinearly to the

E of the light. As a parametric process is in general coherent, many parametric nonlinear processes will depend on

phase matching Nonlinear optics (NLO) is the branch of optics that describes the behaviour of light in nonlinear media, that is, media in which the polarization density P responds non-linearly to the electric field E of the light. The non-linearity is typicall ...

and will usually be polarization dependent. Sample parametric nonlinear processes: *

Second-harmonic generation Second-harmonic generation (SHG), also known as frequency doubling, is the lowest-order wave-wave nonlinear interaction that occurs in various systems, including optical, radio, atmospheric, and magnetohydrodynamic systems. As a prototype behav ...

(SHG), or ''frequency doubling'', generation of light with a doubled frequency (half the wavelength) * Third-harmonic generation (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 mixing of two input photons at frequencies \omega_1 and \omega_2 to generate a third photon at frequency \omega_3. As with any \chi^ optical phenomenon in nonl ...

(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 op ...

(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 mea ...

(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 op ...

(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 (name ...

(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 chan ...

, intensity dependent refractive index * Self-focusing * Kerr-lens modelocking (KLM) * Self-phase modulation (SPM), a

\chi^

effect * Optical solitons * Cross-phase modulation (XPM) * Four-wave mixing (FWM), can also arise from other nonlinearities * Cross-polarized wave generation (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 * 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