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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>
| | Boyd is how he's called but he doesn't like when people use his complete title. Some time in the past I chose to live in Connecticut. Production and preparing is what I do and I'll be promoted quickly. |
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| ==Temporal characteristics==
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| 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" />
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| ==Parametric versus non-parametric processes==
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| ===Linear optics===
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| 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
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| {\mathbf P} = \varepsilon_0\chi{\mathbf E} = (n_r+in_i)^2{\mathbf E},</math>
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| 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.
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| Thus in linear optics a parametric process will act as a lossless [[dielectric]] with the following effects:
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| *[[Refraction]]
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| *[[Diffraction]]
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| *[[scattering|Elastic scattering]]
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| **[[Rayleigh scattering]]
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| ** [[Mie theory|Mie scattering]]
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| Alternatively, non-parametric processes often involve loss (or gain) and give rise to:
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| *[[Absorption (electromagnetic radiation)|Absorption]]
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| *[[scattering|Inelastic scattering]]
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| **[[Raman scattering]]
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| **[[Brillouin scattering]]
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| *Various optical emission processes
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| ** [[Photoluminescence]]
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| ** [[Fluorescence]]
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| ** [[Luminescence]]
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| ** [[Phosphorescence]]
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| ===[[Nonlinear optics]]===
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| 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.
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| '''Sample parametric nonlinear processes:'''
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| * [[Second harmonic generation]] (SHG), or ''frequency doubling'', generation of light with a doubled frequency (half the wavelength)
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| * [[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)
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| * [[High harmonic generation]] (HHG), generation of light with frequencies much greater than the original (typically 100 to 1000 times greater)
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| * [[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)
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| * [[Difference frequency generation]] (DFG), generation of light with a frequency that is the difference between two other frequencies
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| * [[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)
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| * [[Optical parametric oscillation]] (OPO), generation of a signal and idler wave using a parametric amplifier in a resonator (with no signal input)
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| * [[Optical parametric generation]] (OPG), like parametric oscillation but without a resonator, using a very high gain instead
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| * [[Spontaneous parametric down conversion]] (SPDC), the amplification of the vacuum fluctuations in the low gain regime
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| * Optical [[Kerr effect]], intensity dependent refractive index
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| * [[Four-wave mixing]] (FWM)
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| * [[Self-focusing]]
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| * [[Kerr-lens modelocking]] (KLM)
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| * [[Self-phase modulation]] (SPM), a <math>\chi^{(3)}</math> effect
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| * [[Soliton (optics)|Optical soliton]]s
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| * [[Cross-phase modulation]] (XPM)
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| * [[Four-wave mixing]] (FWM), can also arise from other nonlinearities
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| * [[Cross-polarized wave generation]] (XPW), a <math>\chi^{(3)}</math> effect in which a wave with polarization vector perpendicular to the input is generated
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| '''Sample non-parametric nonlinear processes:'''
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| * [[Stimulated Raman Effect#Stimulated scattering and amplification|Stimulated Raman scattering]]
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| * [[Raman amplification]]
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| * [[Two-photon absorption]], simultaneous absorption of two photons, transferring the [[energy]] to a single electron
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| * [[Multiphoton absorption]]
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| * Multiple [[photoionisation]], near-simultaneous removal of many bound electrons by one photon
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| ==See also==
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| *[[Nonlinear optics]]
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| ==Notes==
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| {{Reflist}}
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| ==References==
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| *{{cite book
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| |title = Nonlinear Optics
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| |pages = 13–15
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| |edition = 3rd
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| |last = Boyd
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| |first = Robert
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| |authorlink = Robert W. Boyd (physicist)
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| |year = 2008
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| |publisher = Academic Press
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| |isbn = 978-0-12-369470-6
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| |url = http://www.amazon.com/Nonlinear-Optics-Third-Robert-Boyd/dp/0123694701/ref=sr_1_1?ie=UTF8&qid=1313111421&sr=8-1}}
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| *{{Citation
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| |last = Paschotta
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| |first = Rüdiger
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| |title = [[Encyclopedia of Laser Physics and Technology]]
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| |chapter = Parametric Nonlinearities
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| |url = http://www.rp-photonics.com/parametric_nonlinearities.html
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| }}
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| [[Category:Optics]]
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| [[Category:Nonlinear optics]]
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| [[Category:Quantum optics]]
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Boyd is how he's called but he doesn't like when people use his complete title. Some time in the past I chose to live in Connecticut. Production and preparing is what I do and I'll be promoted quickly.
To collect kites is something that I've done for years. She's not great at style but you may want to check her website: %url
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