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many configurations the sum of the first two photons will be tuned close to a resonant state. However, close to resonances the index of refraction changes rapidly and makes addition four co-linear k-vectors fail to add exactly to zero—thus long mixing path lengths are not always possible as the four component lose phase lock. Consequently, beams are often focused both for intensity but also to shorten the mixing zone.
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In gaseous media an often overlooked complication is that light beams are rarely plane waves but are often focused for extra intensity, this can add an addition pi-phase shift to each k-vector in the phase matching condition. It is often very hard to satisfy this in the sum-frequency configuration
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A condition for efficient generation of FWM is phase matching: the associated k-vectors of the four components must add to zero when they are plane waves. This becomes significant since sum- and difference-frequency generation are often enhanced when resonance in the mixing media is exploited. In
229:
but it is more easily satisfied in the difference-frequency configuration (where the pi phase shifts cancel out). As a result, difference-frequency is usually more broadly tunable and easier to set up than sum-frequency generation, making it preferable as a light source even though it's less
490:
generation. Parametric amplifiers and oscillators based on four-wave mixing use the third order nonlinearity, as opposed to most typical parametric oscillators which use the second-order nonlinearity. Apart from these classical applications, four-wave mixing has shown promise in the
78:
Energy level diagram for a non-degenerate four-wave mixing process. The top energy level could be a real atomic or molecular level (resonant four-wave mixing) or a virtual level, far detuned off-resonance. This diagram describes the four-wave mixing interaction between frequencies
199:
From calculations with the three input signals, it is found that 12 interfering frequencies are produced, three of which lie on one of the original incoming frequencies. Note that these three frequencies which lie at the original incoming frequencies are typically attributed to
220:
and difference-frequency generation. In sum-frequency generation three fields are input and the output is a new high frequency field at the sum of the three input frequencies. In difference-frequency generation, the typical output is the sum of two minus the third.
351:. FWM can be mitigated by using uneven channel spacing or fiber that increases dispersion. For the special case where the three frequencies are close to degenerate, then optical separation of the difference frequency can be technically challenging.
336:(WDM) systems, where multiple optical wavelengths are spaced at equal intervals or channel spacing. The effects of FWM are pronounced with decreased channel spacing of wavelengths (such as in dense WDM systems) and at high signal power levels. High
460:
194:
315:
946:
Takesue, Hiroki; Inoue, Kyo (2004-09-30). "Generation of polarization-entangled photon pairs and violation of Bell's inequality using spontaneous four-wave mixing in a fiber loop".
717:
Fan, Bixuan; Duan, Zhenglu; Zhou, Lu; Yuan, Chunhua; Ou, Z. Y.; Zhang, Weiping (2009-12-03). "Generation of a single-photon source via a four-wave mixing process in a cavity".
1067:
850:
Slusher, R. E.; Yurke, B.; Grangier, P.; LaPorta, A.; Walls, D. F.; Reid, M. (1987-10-01). "Squeezed-light generation by four-wave mixing near an atomic resonance".
643:
Cardoso, GC; Tabosa, JWR (2002). "Saturated lineshapes and high-order susceptibilities of cold cesium atoms observed via a transferred population grating".
893:
Dutt, Avik; Luke, Kevin; Manipatruni, Sasikanth; Gaeta, Alexander L.; Nussenzveig, Paulo; Lipson, Michal (2015-04-13). "On-Chip
Optical Squeezing".
703:
17:
752:
Sharping, Jay E.; Fiorentino, Marco; Coker, Ayodeji; Kumar, Prem; Windeler, Robert S. (2001-07-15). "Four-wave mixing in microstructure fiber".
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357:
347:, or in other words, the phase mismatch between the signals increases. The interference FWM caused in WDM systems is known as interchannel
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The special case of sum-frequency generation where all the input photons have the same frequency (and wavelength) is
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in standard electrical systems. It is a parametric nonlinear process, in that the energy of the incoming
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62:. FWM is a phase-sensitive process, in that the efficiency of the process is strongly affected by
563:"Broadly tunable difference-frequency generation of VUV using two-photon resonances in H2 and Kr"
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Four-wave mixing is also present if only two components interact. In this case the term
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Cardoso, GC; Tabosa, JWR (2000). "Four-wave mixing in dressed cold cesium atoms".
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111:) interact in a nonlinear medium, they give rise to a fourth frequency (f
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455:{\displaystyle f_{ijk}=f_{i}+f_{j}-f_{k},\mathrm {where} \,i,j\neq k}
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in electrical systems. Four-wave mixing can be compared to the
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Rotating-polarization coherent anti-Stokes Raman spectroscopy
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produce two or one new wavelengths. It is similar to the
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360:
257:
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Adverse effects of FWM in fiber-optic communications
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couples three components, thus generating so-called
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Advanced
Optical Communication Systems and Networks
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454:
309:
188:
803:Wang, L. J.; Hong, C. K.; Friberg, S. R. (2001).
533:Optical phase conjugation, phase conjugate mirror
332:FWM is a fiber-optic characteristic that affects
1256:
216:Two common forms of four-wave mixing are dubbed
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678:Cvijetic, Djordjevic, Milorad, Ivan B. (2013).
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208:, and are naturally phase-matched unlike FWM.
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1003:Encyclopedia of Laser Physics and Technology
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702:: CS1 maint: multiple names: authors list (
42:, whereby interactions between two or three
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189:{\displaystyle \pm f_{1}\pm f_{2}\pm f_{3}}
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1016:
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212:Sum- and difference-frequency generation
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1053:Coherent anti-Stokes Raman spectroscopy
310:{\displaystyle f_{0}=f_{1}+f_{1}-f_{2}}
14:
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682:. Artech House. pp. 314 to 217.
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137:, the nonlinear system will produce
1083:Surface-enhanced Raman spectroscopy
1073:Spatially offset Raman spectroscopy
484:Vacuum Ultraviolet light generation
24:
1134:Stimulated Raman adiabatic passage
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343:FWM effects, as the signals lose
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334:wavelength-division multiplexing
1093:Transmission Raman spectroscopy
1088:Tip-enhanced Raman spectroscopy
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925:10.1103/PhysRevApplied.3.044005
561:Strauss, CEM; Funk, DJ (1991).
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238:Third-Harmonic Generation (THG)
233:than sum-frequency generation.
18:Difference-frequency generation
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1197:Journal of Raman Spectroscopy
1078:Stimulated Raman spectroscopy
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630:10.1016/S0030-4018(00)01033-6
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1063:Resonance Raman spectroscopy
486:and in microresonator based
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499:, correlated photon pairs,
322:degenerate four-wave mixing
244:Degenerate four-wave mixing
48:third-order intercept point
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978:10.1103/PhysRevA.70.031802
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470:FWM finds applications in
52:intermodulation distortion
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480:supercontinuum generation
472:optical phase conjugation
99:When three frequencies (f
1204:Vibrational Spectroscopy
1175:Rule of mutual exclusion
522:Lugiato–Lefever equation
476:parametric amplification
218:sum-frequency generation
895:Physical Review Applied
1058:Raman optical activity
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206:cross-phase modulation
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610:Optics Communications
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1109:Raman amplification
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917:2015PhRvP...3d4005D
864:1987JOSAB...4.1453S
821:2001JOptB...3..346W
766:2001OptL...26.1048S
731:2009PhRvA..80f3809F
657:2002OptCo.210..271C
622:2000OptCo.185..353C
579:1991OptL...16.1192S
517:Kerr frequency comb
1039:Raman spectroscopy
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948:Physical Review A
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16:(Redirected from
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1119:Raman laser
528:Kerr effect
44:wavelengths
1259:Categories
1046:Techniques
815:(5): 346.
545:References
540:generation
1270:Photonics
908:1309.6371
880:1520-8540
837:1464-4266
782:1539-4794
698:cite book
447:≠
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345:coherence
341:decreases
295:−
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70:Mechanism
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595:19776917
526:Optical
511:See also
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860:Bibcode
817:Bibcode
762:Bibcode
727:Bibcode
653:Bibcode
618:Bibcode
575:Bibcode
107:, and f
56:photons
1143:Theory
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786:PMID
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