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{{Short description|Parametric oscillator that oscillates at optical frequencies}}
[[File:IR Optical Parametric Oscillator.JPG|thumb|300 px|right|Infrared optical parametric oscillator]]
An '''optical parametric oscillator''' ('''OPO''') is a [[parametric oscillator]] that oscillates at optical frequencies. It converts an input [[laser]] wave (called "pump") with frequency <math>\omega_p</math> into two output waves of lower frequency (<math>\omega_s, \omega_i</math>) by means of second-[[Orders of approximation|order]] [[nonlinear optics|nonlinear optical interaction]]. The sum of the output waves' frequencies is equal to the input wave frequency: <math>\omega_s + \omega_i=\omega_p</math>.<ref>{{Cite journal|
The first optical parametric oscillator was demonstrated by Joseph A. Giordmaine and Robert C. Miller in 1965,<ref>{{Cite journal|title = Tunable Coherent Parametric Oscillation in LiNbO3 at Optical Frequencies|
==Overview==
The OPO consists essentially of an [[Optical cavity|optical resonator]] and a [[Nonlinear optics|nonlinear optical]] crystal. The optical resonator serves to resonate at least one of signal and idler waves. In the nonlinear optical crystal, the pump, signal and idler waves overlap. The interaction between these three waves leads to amplitude gain for signal and idler waves (parametric amplification) and a corresponding deamplification of the pump wave. The gain allows the resonating wave(s) (signal or idler or both) to oscillate in the resonator, compensating the loss that the resonating wave(s) experience(s) at each round-trip. This loss includes the loss due to outcoupling by one of the resonator mirrors, which provides the desired output wave. Since the (relative) loss is independent of the pump power, but the gain is dependent on pump power, at low pump power there is insufficient gain to support oscillation.
The photon conversion efficiency, the number of output photons per unit time in the output signal or idler wave relative to number of pump photons incident per unit time into the OPO can be high, in the range of tens of percent. Typical threshold pump power is between tens of milliwatts to several watts, depending on losses of the resonator, the frequencies of the interacting light, the intensity in the nonlinear material, and its nonlinearity.
There exist both [[continuous-wave]] and [[Pulsed power|pulsed]] OPOs. The latter are easier to build, since the high intensity lasts only for a tiny fraction of a second, which damages the nonlinear optical material and the mirrors less than a continuous high intensity.
In the optical parametric oscillator the initial idler and signal waves are taken from background waves, which are always present. If the idler wave is given from the outside along with the pump beam, then the process is called [[difference frequency generation]] (DFG). This is a more efficient process than optical parametric oscillation, and in principle can be thresholdless.
In order to change the output wave frequencies, one can change the pump frequency or the [[Nonlinear Optics|phasematching]] properties of the nonlinear optical crystal. This latter is accomplished by changing its temperature or orientation or quasi-phasematching period (see below). For fine-tuning one can also change the [[optical path length]] of the resonator. In addition, the resonator may contain elements to suppress mode-hops of the resonating wave. This often requires active control of some element of the OPO system.
If the nonlinear optical crystal cannot be phase-matched, [[quasi-phase-matching]] (QPM) can be employed. This is accomplished by periodically changing the nonlinear optical properties of the crystal, mostly by [[periodical poling]]. With a suitable range of periods, output wavelengths from 700 nm to 5000 nm can be generated in periodically poled [[lithium niobate]] (PPLN). Common pump sources are [[Nd-YAG laser|neodymium lasers]] at
An important feature of the OPO is the coherence and the spectral width of the generated radiation.
When the pump power is significantly above threshold, the two output waves are, to a very good approximation, [[coherent state]]s (laser-like waves). The linewidth of the resonated wave is very narrow (as low as several kHz). The nonresonated generated wave also exhibits narrow linewidth if a pump wave of narrow linewidth is employed. Narrow-linewidth OPOs are widely used in spectroscopy.<ref name = BJO>{{cite book |editor =[[F. J. Duarte|Duarte FJ]] |title=Tunable Laser Applications | edition = 3rd |publisher= [[CRC Press]] |___location=Boca Raton |year=2016 |isbn=9781482261066 |
==Quantum properties of the generated light beams==
[[File:OPO Crystals.jpg|thumb|300 px|right|[[Potassium titanyl phosphate|KTP]] crystals in an OPO]]
The OPO is the physical system most widely used to generate [[squeezed coherent states]] and [[Quantum entanglement|entangled]] states of light in the continuous variables regime. Many demonstrations of quantum information protocols for continuous variables were realized using OPOs.<ref>
The [[Spontaneous parametric down conversion|downconversion]] process really occurs in the single photon regime: each pump photon that is annihilated inside the cavity gives rise to a pair of photons in the signal and idler intracavity modes. This leads to a [[quantum correlation]] between the intensities of signal and idler fields, so that there is squeezing in the subtraction of intensities,<ref>{{cite journal|author1=A. Heidmann |author2=R. J. Horowicz |author3=S. Reynaud |author4=E. Giacobino |author5=C. Fabre |author6=G. Camy |name-list-style=amp |journal=Phys. Rev. Lett. |volume=59|doi=10.1103/PhysRevLett.59.2555 |pmid=10035582 |year=1987|title=Observation of Quantum Noise Reduction on Twin Laser Beams|issue=22|pages=2555–2557 |bibcode=1987PhRvL..59.2555H}}</ref> which motivated the name "twin beams" for the downconverted fields. The highest squeezing level attained to date is 12.7 dB.<ref>{{cite journal | last1 = Eberle | first1 = T. | last2 = Steinlechner | first2 = S. | last3 = Bauchrowitz | first3 = J. | last4 = Händchen | first4 = V. | last5 = Vahlbruch | first5 = H. | last6 = Mehmet | first6 = M. | last7 = Müller-Ebhardt | first7 = H. | last8 = Schnabel | first8 = R. | year = 2010 | title = Quantum Enhancement of the Zero-Area Sagnac Interferometer Topology for Gravitational Wave Detection | journal = Phys. Rev. Lett. | volume = 104 | issue = 25| page = 251102 | doi = 10.1103/PhysRevLett.104.251102 | bibcode=2010PhRvL.104y1102E|arxiv = 1007.0574 | pmid=20867358| s2cid = 9929939 }}</ref>
It turns out that the phases of the twin beams are quantum correlated as well, leading to [[Quantum entanglement|entanglement]], theoretically predicted in 1988.<ref>{{cite journal|author1=M. D. Reid |author2=P. D. Drummond |name-list-style=amp |journal=Phys. Rev. Lett. |volume=60|doi=10.1103/PhysRevLett.60.2731 |year=1988|title=Quantum Correlations of Phase in Nondegenerate Parametric Oscillation|issue=26|pages=2731–2733 |bibcode=1988PhRvL..60.2731R |pmid=10038437}}</ref> Below threshold, entanglement was measured for the first time in 1992,<ref>{{cite journal|author1=Z. Y. Ou |author2=S. F. Pereira |author3=H. J. Kimble |author4=K. C. Peng |name-list-style=amp |journal=Phys. Rev. Lett. |volume=68|doi=10.1103/PhysRevLett.68.3663 |year=1992|title=Realization of the Einstein-Podolsky-Rosen paradox for continuous variables|issue=25|pages=3663–3666 |bibcode=1992PhRvL..68.3663O |pmid=10045765|url=http://authors.library.caltech.edu/6493/1/OUZprl92.pdf}}</ref> and in 2005 above threshold.<ref>{{cite journal|author1=A. S. Villar |author2=L. S. Cruz |author3=K. N. Cassemiro |author4=M. Martinelli |author5=P. Nussenzveig |name-list-style=amp |journal=Phys. Rev. Lett. |volume=95|page=243603|doi=10.1103/PhysRevLett.95.243603 |year=2005|title=Generation of Bright Two-Color Continuous Variable Entanglement|issue=24|bibcode=2005PhRvL..95x3603V|arxiv = quant-ph/0506139 |pmid=16384378|s2cid=13815567 }}</ref>
Above threshold, the pump beam depletion makes it sensitive to the quantum phenomena happening inside the crystal. The first measurement of squeezing in the pump field after parametric interaction was done in 1997.<ref name="KasaiJiangrui1997">{{cite journal|last1=Kasai|first1=K|last2=Jiangrui|first2=Gao|last3=Fabre|first3=C|title=Observation of squeezing using cascaded nonlinearity|journal=Europhysics Letters
It has been recently predicted that all three fields (pump, signal and idler) must be entangled,<ref>{{cite journal|author1=A. S. Villar |author2=M. Martinelli |author3=C Fabre |author4=P. Nussenzveig |name-list-style=amp |journal=Phys. Rev. Lett. |volume=97|page=140504|doi=10.1103/PhysRevLett.97.140504 |year=2006|title=Direct Production of Tripartite Pump-Signal-Idler Entanglement in the Above-Threshold Optical Parametric Oscillator|issue=14|bibcode=2006PhRvL..97n0504V|arxiv = quant-ph/0610062 |pmid=17155232|s2cid=37328629 }}</ref> a prediction which was experimentally demonstrated by the same group.<ref>{{cite journal | last1 = Coelho | first1 = A. S. | last2 = Barbosa | first2 = F. A. S. | last3 = Cassemiro | first3 = K. N. | last4 = Villar | first4 = A. S. | last5 = Martinelli | first5 = M. | last6 = Nussenzveig | first6 = P. | year = 2009 | title = Three-Color Entanglement | url =
Not only intensity and phase of the twin beams share quantum correlations, but also do their spatial modes.<ref>{{cite journal|author1=M. Martinelli |author2=N. Treps |author3=S. Ducci|author3-link= Sara Ducci |author4=S. Gigan |author5=A. Maître |author6=C. Fabre |name-list-style=amp |journal=Phys. Rev. A |volume=67|page=023808|doi=10.1103/PhysRevA.67.023808 |year=2003|title=Experimental study of the spatial distribution of quantum correlations in a confocal optical parametric oscillator|issue=2|arxiv = quant-ph/0210023 |bibcode = 2003PhRvA..67b3808M |s2cid=119471952 }}</ref> This feature could be used to enhance signal to noise ratio in image systems and hence surpass the standard quantum limit (or the [[shot noise]] limit) for imaging.<ref>{{cite journal | last1 = Treps | first1 = N. | last2 = Andersen | first2 = U. | last3 = Buchler | first3 = B. | last4 = Lam | first4 = P. K. | last5 = Maitre | first5 = A. | last6 = Bachor | first6 = H.-A. | last7 = Fabre | first7 = C. | year = 2002 | title = Surpassing the Standard Quantum Limit for Optical Imaging Using Nonclassical Multimode Light | journal = Phys. Rev. Lett. | volume = 88 | issue = 20| page = 203601 | doi = 10.1103/PhysRevLett.88.203601 | pmid = 12005563 | bibcode=2002PhRvL..88t3601T|arxiv = quant-ph/0204017 | s2cid = 20948903 }}</ref>
==Applications==
The OPO is being employed nowadays as a source of squeezed light tuned to atomic transitions, in order to study how the atoms interact with squeezed light.<ref>{{cite journal|author1=T. Tanimura |author2=D. Akamatsu |author3=Y. Yokoi |author4=A. Furusawa |author5=M. Kozuma |journal=Opt. Lett. |volume=31|pages=2344–6|doi=10.1364/OL.31.002344 |year=2006|title=Generation of a squeezed vacuum resonant on a rubidium D1 line with periodically poled KTiOPO4|issue=15|pmid=16832480|arxiv = quant-ph/0603214 |bibcode = 2006OptL...31.2344T |s2cid=18700111 }}</ref>
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==See also==
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