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A '''parametric process''' is an [[optical]] process in which light interacts with matter in such a way as to leave the [[quantum state]] of the material unchanged.  As a direct consequence of this there can be no transfer of [[energy]], [[momentum]], or [[angular momentum]] between the [[optical field]] and the [[physical system]].  In contrast a '''non-parametric process''' is a process in which any part of the [[quantum state]] of the system changes.<ref name="Boyd NLO">See Section ''Parametric versus Nonparametric Processes,'' '''Nonlinear Optics''' by [[Robert W. Boyd (physicist)|Robert W. Boyd]] (3rd ed.), pp. 13-15.</ref>


==Temporal characteristics==
Since a parametric process prohibits a change in the energy state of the system, parametric processes are considered to be 'instantaneous' processes.  This can be seen as follows; if an atom absorbs a [[photon]] with energy E, the atom's energy will increase by ΔE = E.  Since we are assuming this is a parametric process, the quantum state cannot change and thus this energy state must be a [[Virtual state (physics)|Virtual state]].  By the [[Uncertainty principle#Energy-time uncertainty principle|Heisenberg Uncertainty Principle]] 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.<ref name="Boyd NLO" />


==Parametric versus non-parametric processes==
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===Linear optics===
In a linear optical system the dielectric [[polarization (electrostatics)|polarization]], '''P''', responds linearly to the presence of an [[electric field]], '''E''', and thus we can write
:<math>
{\mathbf P} = \varepsilon_0\chi{\mathbf E} = (n_r+in_i)^2{\mathbf E},</math>
where ε<sub>0</sub> is the [[electric constant]], χ is the ([[Complex number|complex]]) [[electric susceptibility]], and n<sub>r</sub>(n<sub>i</sub>) is the real(imaginary) component of the [[refractive index]] of the medium. The effects of a parametric process will effect only n<sub>r</sub>, whereas a nonzero value of n<sub>i</sub> can only be caused by a non-parametric process.
 
Thus in linear optics a parametric process will act as a lossless [[dielectric]] with the following effects:
*[[Refraction]]
*[[Diffraction]]
*[[scattering|Elastic scattering]]
**[[Rayleigh scattering]]
** [[Mie theory|Mie scattering]]
 
Alternatively, non-parametric processes often involve loss (or gain) and give rise to:
*[[Absorption (electromagnetic radiation)|Absorption]]
*[[scattering|Inelastic scattering]]
**[[Raman scattering]]
**[[Brillouin scattering]]
*Various optical emission processes
** [[Photoluminescence]]
** [[Fluorescence]]
** [[Luminescence]]
** [[Phosphorescence]]
 
===[[Nonlinear optics]]===
In a [[Nonlinear optics|nonlinear media]], the dielectric [[polarization (electrostatics)|polarization]] '''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 [[Nonlinear optics#Phase matching|phase matching]] and will usually be [[Polarization (waves)|polarization]] dependent.
 
'''Sample parametric nonlinear processes:'''
* [[Second harmonic generation]] (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]] (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]] (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]] (OPO), generation of a signal and idler wave using a parametric amplifier in a resonator (with no signal input)
* [[Optical parametric generation]] (OPG), like parametric oscillation but without a resonator, using a very high gain instead
* [[Spontaneous parametric down conversion]] (SPDC), the amplification of the vacuum fluctuations in the low gain regime
* Optical [[Kerr effect]], intensity dependent refractive index
* [[Four-wave mixing]] (FWM)
* [[Self-focusing]]
* [[Kerr-lens modelocking]] (KLM)
* [[Self-phase modulation]] (SPM), a <math>\chi^{(3)}</math> effect
* [[Soliton (optics)|Optical soliton]]s
* [[Cross-phase modulation]] (XPM)
* [[Four-wave mixing]] (FWM), can also arise from other nonlinearities
* [[Cross-polarized wave generation]] (XPW), a <math>\chi^{(3)}</math> effect in which a wave with polarization vector perpendicular to the input is generated
 
'''Sample non-parametric nonlinear processes:'''
* [[Stimulated Raman Effect#Stimulated scattering and amplification|Stimulated Raman scattering]]
* [[Raman amplification]]
* [[Two-photon absorption]], simultaneous absorption of two photons, transferring the [[energy]] to a single electron
* [[Multiphoton absorption]]
* Multiple [[photoionisation]], near-simultaneous removal of many bound electrons by one photon
 
==See also==
*[[Nonlinear optics]]
 
==Notes==
{{Reflist}}
 
==References==
*{{cite book
|title = Nonlinear Optics
|pages = 13–15
|edition = 3rd
|last = Boyd
|first = Robert
|authorlink = Robert W. Boyd (physicist)
|year = 2008
|publisher = Academic Press
|isbn = 978-0-12-369470-6
|url = http://www.amazon.com/Nonlinear-Optics-Third-Robert-Boyd/dp/0123694701/ref=sr_1_1?ie=UTF8&qid=1313111421&sr=8-1}}
 
*{{Citation
|last = Paschotta
|first = Rüdiger
|title = [[Encyclopedia of Laser Physics and Technology]]
|chapter = Parametric Nonlinearities
|url = http://www.rp-photonics.com/parametric_nonlinearities.html
}}
 
[[Category:Optics]]
[[Category:Nonlinear optics]]
[[Category:Quantum optics]]

Revision as of 21:07, 20 February 2014


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