Abstract

A short piece of commercial-grade SMF-28 optical fiber is pumped with a 680 ps high-peak power green laser. Red Stokes and blue anti-Stokes beams are generated spontaneously from vacuum noise in different modes in the fiber via intermodal four-wave mixing. Detailed experimental and theoretical analyses are performed and are in reasonable agreement. The large spectral shifts from the pump protect the Stokes and anti-Stokes from contamination by spontaneous Raman scattering noise. This work highlights the predictive power and limitations of a theoretical model to explain the experimental results for a process that relies on the amplification of quantum vacuum energy over more than 11 orders of magnitude.

© 2015 Optical Society of America

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References

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2015 (1)

2014 (2)

2013 (3)

2012 (2)

J. Cheng, M. E. V. Pedersen, K. Charan, K. Wang, C. Xu, L. Grner-Nielsen, and D. Jakobsen, “Intermodal four-wave mixing in a higher-order-mode fiber,” Appl. Phys. Lett. 101, 161106 (2012).
[Crossref] [PubMed]

C. J. McKinstrie, L. Mejling, M. G. Raymer, and K. Rottwitt, “Quantum-state-preserving optical frequency conversion and pulse reshaping by four-wave-mixing,” Phys. Rev. A 85, 053829 (2012).
[Crossref]

2011 (2)

G. P. Agrawal, “Nonlinear fiber optics: its history and recent progress [Invited],” J. Opt. Soc. Am. B 28, A1–A10 (2011).
[Crossref]

A. M. Rocha, P. Antunes, F. Domingues, M. Facao, and P. S. Andre, “Detection of fiber fuse effect using FBG sensors,” IEEE Sens. J. 11, 1390–1394 (2011).
[Crossref]

2009 (2)

2008 (2)

2007 (1)

Q. Lin, F. Yaman, and G. P. Agrawal, “Photon-pair generation in optical fibers through four-wave mixing: Role of Raman scattering and pump polarization,” Phys. Rev. A 75, 023803 (2007).
[Crossref]

2006 (1)

2005 (2)

X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “optical-fiber source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. 94, 053601 (2005).
[Crossref] [PubMed]

E. Brainis, D. Amans, and S. Massar, “Scalar and vector modulation instabilities induced by vacuum fluctuations in fibers: numerical study,” Phys. Rev. A 71, 023808 (2005).
[Crossref]

2004 (5)

2000 (1)

1998 (1)

1992 (1)

K. Inoue, “Four-wave mixing in an optical fiber in the zero-dispersion wavelength region,” J. Lightwave Technol. 10, 1553–1561 (1992).
[Crossref]

1988 (1)

R. Kashyap and K. J. Blow, “Observation of catastrophic self-propelled self-focusing in optical fibres,” Electronic Letters 24, 47–49 (1988).
[Crossref]

1987 (3)

N. Shibata, R. P. Barun, and R. G. Waarts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber,” IEEE J. Quantum Electron. 23, 1205–1210 (1987).
[Crossref]

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880–883 (1987).
[Crossref] [PubMed]

P. L. Baldec and R. R. Alfano, “Intensity effect on the stimulated four photon spectra generated by picosecond pulses in optical fibers,” J. Lightwave Technol. 5, 1712–1715 (1987).
[Crossref]

1986 (1)

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).
[Crossref] [PubMed]

1985 (1)

M. D. Levenson, R. M. Shelby, and A. Aspect, “Generation and detection of squeezed state of light by nondegenerate four-wave mixing in an optical fiber,” Phys. Rev. A 32, 1550–1562 (1985).
[Crossref] [PubMed]

1982 (2)

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1072 (1982).
[Crossref]

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1072 (1982).
[Crossref]

1981 (2)

1975 (1)

R. H. Stolen, “Phase-matched-stimulated four-photon mixing in silica-fiber waveguides,” IEEE J. Quantum Electron. 11, 100–103 (1975).
[Crossref]

1974 (1)

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24, 308–310 (1974).
[Crossref]

1973 (1)

R. H. Stolen and E. P. Ippen, “Raman gain in glass optical waveguides,” Appl. Phys. Lett. 22, 276–278 (1973).
[Crossref]

Agrawal, G. P.

H. Pourbeyram, G. P. Agrawal, and A. Mafi, “Stimulated Raman scattering cascade spanning the wavelength range of 523 to 1750nm using a graded-index multimode optical fiber,” Appl. Phys. Lett. 102, 201107 (2013).
[Crossref]

G. P. Agrawal, “Nonlinear fiber optics: its history and recent progress [Invited],” J. Opt. Soc. Am. B 28, A1–A10 (2011).
[Crossref]

Q. Lin, F. Yaman, and G. P. Agrawal, “Photon-pair generation in optical fibers through four-wave mixing: Role of Raman scattering and pump polarization,” Phys. Rev. A 75, 023803 (2007).
[Crossref]

Q. Lin and G. P. Agrawal, “Vector theory of four-wave mixing: polarization effects in fiber-optic parametric amplifiers,” J. Opt. Soc. Am. B 21, 1216–1224 (2004).
[Crossref]

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880–883 (1987).
[Crossref] [PubMed]

G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Academic, 2012).

Alfano, R. R.

P. L. Baldec and R. R. Alfano, “Intensity effect on the stimulated four photon spectra generated by picosecond pulses in optical fibers,” J. Lightwave Technol. 5, 1712–1715 (1987).
[Crossref]

Amans, D.

E. Brainis, D. Amans, and S. Massar, “Scalar and vector modulation instabilities induced by vacuum fluctuations in fibers: numerical study,” Phys. Rev. A 71, 023808 (2005).
[Crossref]

Andre, P. S.

A. M. Rocha, P. Antunes, F. Domingues, M. Facao, and P. S. Andre, “Detection of fiber fuse effect using FBG sensors,” IEEE Sens. J. 11, 1390–1394 (2011).
[Crossref]

Antunes, P.

A. M. Rocha, P. Antunes, F. Domingues, M. Facao, and P. S. Andre, “Detection of fiber fuse effect using FBG sensors,” IEEE Sens. J. 11, 1390–1394 (2011).
[Crossref]

Ashkin, A.

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24, 308–310 (1974).
[Crossref]

Aspect, A.

M. D. Levenson, R. M. Shelby, and A. Aspect, “Generation and detection of squeezed state of light by nondegenerate four-wave mixing in an optical fiber,” Phys. Rev. A 32, 1550–1562 (1985).
[Crossref] [PubMed]

Baldec, P. L.

P. L. Baldec and R. R. Alfano, “Intensity effect on the stimulated four photon spectra generated by picosecond pulses in optical fibers,” J. Lightwave Technol. 5, 1712–1715 (1987).
[Crossref]

Barragan, A. M.

Barun, R. P.

N. Shibata, R. P. Barun, and R. G. Waarts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber,” IEEE J. Quantum Electron. 23, 1205–1210 (1987).
[Crossref]

Bickham, S. R.

Bjorkholm, J. E.

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1072 (1982).
[Crossref]

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1072 (1982).
[Crossref]

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24, 308–310 (1974).
[Crossref]

Blow, K. J.

R. Kashyap and K. J. Blow, “Observation of catastrophic self-propelled self-focusing in optical fibres,” Electronic Letters 24, 47–49 (1988).
[Crossref]

Bookbinder, D. C.

Bosch, M. A.

C. Lin and M. A. Bosch, “Large-Stokes-shift stimulated four-photon-mixing in optical fibers,” Appl. Phys. Lett. 38, 479–481 (1981).
[Crossref]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

Brainis, E.

E. Brainis, D. Amans, and S. Massar, “Scalar and vector modulation instabilities induced by vacuum fluctuations in fibers: numerical study,” Phys. Rev. A 71, 023808 (2005).
[Crossref]

Bufetov, I. A.

Callegari, F. A.

F. A. Callegari, J. M. Chavez Boggio, and H. L. Fragnito, “Spurious four-wave mixing in two-pump fiber-optic parametric amplifiers,” IEEE Photon. Tech. Lett. 16, 434–436 (2004).
[Crossref]

Charan, K.

J. Cheng, M. E. V. Pedersen, K. Charan, K. Wang, C. Xu, L. Grner-Nielsen, and D. Jakobsen, “Intermodal four-wave mixing in a higher-order-mode fiber,” Appl. Phys. Lett. 101, 161106 (2012).
[Crossref] [PubMed]

Chavez Boggio, J. M.

F. A. Callegari, J. M. Chavez Boggio, and H. L. Fragnito, “Spurious four-wave mixing in two-pump fiber-optic parametric amplifiers,” IEEE Photon. Tech. Lett. 16, 434–436 (2004).
[Crossref]

Chen, J.

Chen, Y.

Cheng, J.

J. Cheng, M. E. V. Pedersen, K. Charan, K. Wang, C. Xu, L. Grner-Nielsen, and D. Jakobsen, “Intermodal four-wave mixing in a higher-order-mode fiber,” Appl. Phys. Lett. 101, 161106 (2012).
[Crossref] [PubMed]

Cohen, O.

Cruz-Delgado, D.

Cruz-Ramirez, He.

Demas, J.

Desorcie, R. B.

Dianov, E. M.

Domingues, F.

A. M. Rocha, P. Antunes, F. Domingues, M. Facao, and P. S. Andre, “Detection of fiber fuse effect using FBG sensors,” IEEE Sens. J. 11, 1390–1394 (2011).
[Crossref]

Englebert, J. J.

Facao, M.

A. M. Rocha, P. Antunes, F. Domingues, M. Facao, and P. S. Andre, “Detection of fiber fuse effect using FBG sensors,” IEEE Sens. J. 11, 1390–1394 (2011).
[Crossref]

Fang, B.

Fragnito, H. L.

F. A. Callegari, J. M. Chavez Boggio, and H. L. Fragnito, “Spurious four-wave mixing in two-pump fiber-optic parametric amplifiers,” IEEE Photon. Tech. Lett. 16, 434–436 (2004).
[Crossref]

Frolov, A. A.

Garay-Palmett, K.

Grner-Nielsen, L.

J. Cheng, M. E. V. Pedersen, K. Charan, K. Wang, C. Xu, L. Grner-Nielsen, and D. Jakobsen, “Intermodal four-wave mixing in a higher-order-mode fiber,” Appl. Phys. Lett. 101, 161106 (2012).
[Crossref] [PubMed]

Hasegawa, A.

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).
[Crossref] [PubMed]

Hill, K. O.

Hirani, M.

Horak, P.

Inoue, K.

K. Inoue, “Four-wave mixing in an optical fiber in the zero-dispersion wavelength region,” J. Lightwave Technol. 10, 1553–1561 (1992).
[Crossref]

Ippen, E. P.

R. H. Stolen and E. P. Ippen, “Raman gain in glass optical waveguides,” Appl. Phys. Lett. 22, 276–278 (1973).
[Crossref]

Jakobsen, D.

J. Cheng, M. E. V. Pedersen, K. Charan, K. Wang, C. Xu, L. Grner-Nielsen, and D. Jakobsen, “Intermodal four-wave mixing in a higher-order-mode fiber,” Appl. Phys. Lett. 101, 161106 (2012).
[Crossref] [PubMed]

Johnson, D. C.

Johnson, J. J.

Kashyap, R.

R. Kashyap and K. J. Blow, “Observation of catastrophic self-propelled self-focusing in optical fibres,” Electronic Letters 24, 47–49 (1988).
[Crossref]

Kawasaki, B. S.

Kumar, P.

K. F. Lee, J. Chen, C. Liang, X. Li, P. L. Voss, and P. Kumar, “Generation of high-purity telecom-band entangled photon pair in dispersion-shifted fiber,” Opt. Lett. 31, 1905–1907 (2006).
[Crossref] [PubMed]

X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “optical-fiber source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. 94, 053601 (2005).
[Crossref] [PubMed]

J. Chen, X. Li, and P. Kumar, “Quantum theory for two-photon-state generation by means of four-wave mixing in optical fibers,” Proc. SPIE 5551, 121–128 (2004).
[Crossref]

X. Li, j. Chen, P. Voss, J. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communication: Improved generation of correlated photons,” Opt. Express 12, 3737–3744 (2004).
[Crossref] [PubMed]

Lee, K. F.

Levenson, M. D.

M. D. Levenson, R. M. Shelby, and A. Aspect, “Generation and detection of squeezed state of light by nondegenerate four-wave mixing in an optical fiber,” Phys. Rev. A 32, 1550–1562 (1985).
[Crossref] [PubMed]

Lewis, K. A.

Li, M. J.

Li, X.

K. F. Lee, J. Chen, C. Liang, X. Li, P. L. Voss, and P. Kumar, “Generation of high-purity telecom-band entangled photon pair in dispersion-shifted fiber,” Opt. Lett. 31, 1905–1907 (2006).
[Crossref] [PubMed]

X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “optical-fiber source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. 94, 053601 (2005).
[Crossref] [PubMed]

J. Chen, X. Li, and P. Kumar, “Quantum theory for two-photon-state generation by means of four-wave mixing in optical fibers,” Proc. SPIE 5551, 121–128 (2004).
[Crossref]

X. Li, j. Chen, P. Voss, J. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communication: Improved generation of correlated photons,” Opt. Express 12, 3737–3744 (2004).
[Crossref] [PubMed]

Liang, C.

Lin, C.

C. Lin and M. A. Bosch, “Large-Stokes-shift stimulated four-photon-mixing in optical fibers,” Appl. Phys. Lett. 38, 479–481 (1981).
[Crossref]

Lin, Q.

Q. Lin, F. Yaman, and G. P. Agrawal, “Photon-pair generation in optical fibers through four-wave mixing: Role of Raman scattering and pump polarization,” Phys. Rev. A 75, 023803 (2007).
[Crossref]

Q. Lin and G. P. Agrawal, “Vector theory of four-wave mixing: polarization effects in fiber-optic parametric amplifiers,” J. Opt. Soc. Am. B 21, 1216–1224 (2004).
[Crossref]

Lorenz, V. O.

Lundeen, J. S.

Mafi, A.

H. Pourbeyram, G. P. Agrawal, and A. Mafi, “Stimulated Raman scattering cascade spanning the wavelength range of 523 to 1750nm using a graded-index multimode optical fiber,” Appl. Phys. Lett. 102, 201107 (2013).
[Crossref]

Mahou, P.

Malowicki, J.

Massar, S.

E. Brainis, D. Amans, and S. Massar, “Scalar and vector modulation instabilities induced by vacuum fluctuations in fibers: numerical study,” Phys. Rev. A 71, 023808 (2005).
[Crossref]

McDermott, M. A.

McKinstrie, C. J.

C. J. McKinstrie, L. Mejling, M. G. Raymer, and K. Rottwitt, “Quantum-state-preserving optical frequency conversion and pulse reshaping by four-wave-mixing,” Phys. Rev. A 85, 053829 (2012).
[Crossref]

Mejling, L.

C. J. McKinstrie, L. Mejling, M. G. Raymer, and K. Rottwitt, “Quantum-state-preserving optical frequency conversion and pulse reshaping by four-wave-mixing,” Phys. Rev. A 85, 053829 (2012).
[Crossref]

Milam, D.

Monroy-Ruz, J.

Moreno, J. B.

Nolan, D. A.

Ortiz-Ricardo, E.

Pedersen, M. E. V.

J. Cheng, M. E. V. Pedersen, K. Charan, K. Wang, C. Xu, L. Grner-Nielsen, and D. Jakobsen, “Intermodal four-wave mixing in a higher-order-mode fiber,” Appl. Phys. Lett. 101, 161106 (2012).
[Crossref] [PubMed]

Poletti, F.

Pourbeyram, H.

H. Pourbeyram, G. P. Agrawal, and A. Mafi, “Stimulated Raman scattering cascade spanning the wavelength range of 523 to 1750nm using a graded-index multimode optical fiber,” Appl. Phys. Lett. 102, 201107 (2013).
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Ramachandran, S.

Ramirez-Alarcon, R.

Ranka, J. K.

Raymer, M. G.

C. J. McKinstrie, L. Mejling, M. G. Raymer, and K. Rottwitt, “Quantum-state-preserving optical frequency conversion and pulse reshaping by four-wave-mixing,” Phys. Rev. A 85, 053829 (2012).
[Crossref]

Rishøj, L.

Rocha, A. M.

A. M. Rocha, P. Antunes, F. Domingues, M. Facao, and P. S. Andre, “Detection of fiber fuse effect using FBG sensors,” IEEE Sens. J. 11, 1390–1394 (2011).
[Crossref]

Rottwitt, K.

C. J. McKinstrie, L. Mejling, M. G. Raymer, and K. Rottwitt, “Quantum-state-preserving optical frequency conversion and pulse reshaping by four-wave-mixing,” Phys. Rev. A 85, 053829 (2012).
[Crossref]

Sharping, J.

Sharping, J. E.

X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “optical-fiber source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. 94, 053601 (2005).
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[Crossref]

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[Crossref]

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[Crossref]

R. H. Stolen and E. P. Ippen, “Raman gain in glass optical waveguides,” Appl. Phys. Lett. 22, 276–278 (1973).
[Crossref]

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Tai, B.

Tai, K.

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).
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Tandon, P.

Tomita, A.

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).
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URen, A. B.

Voss, P.

Voss, P. L.

K. F. Lee, J. Chen, C. Liang, X. Li, P. L. Voss, and P. Kumar, “Generation of high-purity telecom-band entangled photon pair in dispersion-shifted fiber,” Opt. Lett. 31, 1905–1907 (2006).
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X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “optical-fiber source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. 94, 053601 (2005).
[Crossref] [PubMed]

Waarts, R. G.

N. Shibata, R. P. Barun, and R. G. Waarts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber,” IEEE J. Quantum Electron. 23, 1205–1210 (1987).
[Crossref]

Walmsley, I. A.

Wang, K.

J. Cheng, M. E. V. Pedersen, K. Charan, K. Wang, C. Xu, L. Grner-Nielsen, and D. Jakobsen, “Intermodal four-wave mixing in a higher-order-mode fiber,” Appl. Phys. Lett. 101, 161106 (2012).
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Windeler, R. S.

Xu, C.

J. Cheng, M. E. V. Pedersen, K. Charan, K. Wang, C. Xu, L. Grner-Nielsen, and D. Jakobsen, “Intermodal four-wave mixing in a higher-order-mode fiber,” Appl. Phys. Lett. 101, 161106 (2012).
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Yaman, F.

Q. Lin, F. Yaman, and G. P. Agrawal, “Photon-pair generation in optical fibers through four-wave mixing: Role of Raman scattering and pump polarization,” Phys. Rev. A 75, 023803 (2007).
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Appl. Opt. (2)

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R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24, 308–310 (1974).
[Crossref]

R. H. Stolen and E. P. Ippen, “Raman gain in glass optical waveguides,” Appl. Phys. Lett. 22, 276–278 (1973).
[Crossref]

J. Cheng, M. E. V. Pedersen, K. Charan, K. Wang, C. Xu, L. Grner-Nielsen, and D. Jakobsen, “Intermodal four-wave mixing in a higher-order-mode fiber,” Appl. Phys. Lett. 101, 161106 (2012).
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C. Lin and M. A. Bosch, “Large-Stokes-shift stimulated four-photon-mixing in optical fibers,” Appl. Phys. Lett. 38, 479–481 (1981).
[Crossref]

H. Pourbeyram, G. P. Agrawal, and A. Mafi, “Stimulated Raman scattering cascade spanning the wavelength range of 523 to 1750nm using a graded-index multimode optical fiber,” Appl. Phys. Lett. 102, 201107 (2013).
[Crossref]

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[Crossref]

IEEE J. Quantum Electron. (4)

R. H. Stolen, “Phase-matched-stimulated four-photon mixing in silica-fiber waveguides,” IEEE J. Quantum Electron. 11, 100–103 (1975).
[Crossref]

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1072 (1982).
[Crossref]

N. Shibata, R. P. Barun, and R. G. Waarts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber,” IEEE J. Quantum Electron. 23, 1205–1210 (1987).
[Crossref]

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1072 (1982).
[Crossref]

IEEE Photon. Tech. Lett. (1)

F. A. Callegari, J. M. Chavez Boggio, and H. L. Fragnito, “Spurious four-wave mixing in two-pump fiber-optic parametric amplifiers,” IEEE Photon. Tech. Lett. 16, 434–436 (2004).
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IEEE Sens. J. (1)

A. M. Rocha, P. Antunes, F. Domingues, M. Facao, and P. S. Andre, “Detection of fiber fuse effect using FBG sensors,” IEEE Sens. J. 11, 1390–1394 (2011).
[Crossref]

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M. J. Li, P. Tandon, D. C. Bookbinder, S. R. Bickham, M. A. McDermott, R. B. Desorcie, D. A. Nolan, J. J. Johnson, K. A. Lewis, and J. J. Englebert, “Ultra-low bending loss single-mode fiber for FTTH,” J. Lightwave Technol. 27, 376–382 (2009).
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Opt. Lett. (5)

Optica (1)

Phys. Rev. A (4)

E. Brainis, D. Amans, and S. Massar, “Scalar and vector modulation instabilities induced by vacuum fluctuations in fibers: numerical study,” Phys. Rev. A 71, 023808 (2005).
[Crossref]

M. D. Levenson, R. M. Shelby, and A. Aspect, “Generation and detection of squeezed state of light by nondegenerate four-wave mixing in an optical fiber,” Phys. Rev. A 32, 1550–1562 (1985).
[Crossref] [PubMed]

C. J. McKinstrie, L. Mejling, M. G. Raymer, and K. Rottwitt, “Quantum-state-preserving optical frequency conversion and pulse reshaping by four-wave-mixing,” Phys. Rev. A 85, 053829 (2012).
[Crossref]

Q. Lin, F. Yaman, and G. P. Agrawal, “Photon-pair generation in optical fibers through four-wave mixing: Role of Raman scattering and pump polarization,” Phys. Rev. A 75, 023803 (2007).
[Crossref]

Phys. Rev. Lett. (3)

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).
[Crossref] [PubMed]

X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “optical-fiber source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. 94, 053601 (2005).
[Crossref] [PubMed]

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Proc. SPIE (1)

J. Chen, X. Li, and P. Kumar, “Quantum theory for two-photon-state generation by means of four-wave mixing in optical fibers,” Proc. SPIE 5551, 121–128 (2004).
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Other (2)

G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Academic, 2012).

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

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Figures (7)

Fig. 1
Fig. 1

(a) Stokes and (b) anti-Stokes FWM beams are generated in a short piece of SMF-28 fiber. (c) The FWM spectrum is shown where the insets highlight the main spectral features.

Fig. 2
Fig. 2

The output spectrum is shown when the pump is not properly aligned. In addition to the main FWM peaks at 656 nm and 447 nm, another set at 650 nm and 449 nm is strongly excited. Moreover, two FWM peaks are also strongly generated very close to the pump and a stimulated Raman peak is also observed at 545 nm. The side subfigures are magnified images of the important spectral features in the main figure.

Fig. 3
Fig. 3

The phase matching condition, where the intersection of the linear and parabolic plots shows phase-matched points.

Fig. 4
Fig. 4

Π(y) defined in Eq. (18): (a) has linear behavior for small y, but (b), (c) is exponentially increasing at large y. The argument of Π(y), i.e. gmaxL varies between ≈ 35 and ≈ 60 in our experiments. The vertical axis scale in subfigure (c) is logarithmic.

Fig. 5
Fig. 5

(a) Experimental result of average Stokes power versus average pump power including different same-length fiber samples. Green circles show the repetition of experiment for different fiber samples with the same approximate 25 ± 0.5 cm length and different coupled pump power. The lines are based on Eq. (25) for different values of γ ˜ 1. (b) Experimental measurements are categorized into different fiber samples, where the results for each fiber sample is marked with a distinct symbol.

Fig. 6
Fig. 6

Experimental result indicating that the Stokes peak is blue-shifted as the pump power is increased.

Fig. 7
Fig. 7

(a) Refractive index difference and mode-field diameter at 1550 nm for pump laser at 532 nm. (b) Core radius and index difference for different Stokes wavelengths. Δ ranges have been selected as typical values for single-mode fibers.

Equations (39)

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z A ^ s = 2 i γ s s | A p | 2 A ^ s + i γ s a A p 2 A ^ a exp ( i Δ β z ) ,
z A ^ a = 2 i γ a a | A p | 2 A ^ a + i γ a s A p 2 A ^ s exp ( i Δ β z ) .
2 ω p = ω a + ω s = ω ¯ a + ω ¯ s ,
Δ β = 2 β p ( ω p ) β a ( ω ¯ a ) β s ( ω ¯ s ) ,
[ A ^ s ( ω ¯ s , z ) , A ^ s ( ω ¯ s , z ) ] = 0 , [ A ^ s ( ω ¯ s , z ) , A ^ s ( ω ¯ s , z ) ] = 2 π ω s δ ( ω ¯ s ω ¯ s ) .
[ A ^ s ( τ , z ) , A ^ s ( τ , z ) ] = 0 , [ A ^ s ( τ , z ) , A ^ s ( τ , z ) ] = ω s δ ( τ τ ) ,
A ^ s ( τ , z ) = 1 2 π d ω ¯ s A ^ s ( ω ¯ s , z ) exp ( i ω ¯ s τ ) .
A p ( z ) = P p e i φ p exp ( i γ p p P p z ) ,
A ^ s ( z ) = A ^ s ( 0 ) [ cosh ( g z ) + i κ 2 g sinh ( g z ) ] e i φ s + A ^ a ( 0 ) [ i γ s a P p g sinh ( g z ) ] e i ( φ s + 2 φ p ) ,
A ^ a ( z ) = A ^ a ( 0 ) [ cosh ( g z ) + i κ 2 g sinh ( g z ) ] e i φ a + A ^ s ( 0 ) [ i γ a s P p g sinh ( g z ) ] e i ( φ a + 2 φ p ) ,
φ s = 2 γ s s P p z + κ z / 2 , g = ( γ ˜ 1 P p ) 2 ( κ / 2 ) 2 , γ ˜ 1 = γ s a γ a s , φ a = 2 γ a a P p z + κ z / 2 , κ = Δ β 2 γ ˜ 2 P p , γ ˜ 2 = γ a a + γ s s γ p p .
Δ β ( Ω ) = δ β ( 0 ) + δ β ( 1 ) Ω β ¯ ( 2 ) Ω 2 ,
( 2 π c ) Ω = ω p ω ¯ s = ω ¯ a ω p , δ β ( 0 ) = 2 β p ( ω p ) β a ( ω p ) β s ( ω p ) , β ¯ ( 2 ) = ( 2 π c ) 2 1 2 ( β s ( 2 ) ( ω p ) + β a ( 2 ) ( ω p ) ) , δ β ( 1 ) = ( 2 π c ) ( β s ( 1 ) ( ω p ) β a ( 1 ) ( ω p ) ) ,
β i ( n ) ( ω ) = n ω n β i ( ω ) , i { p , s , a } .
Ω pm = ± 1 2 ( δ β ( 1 ) β ¯ ( 2 ) ) 2 + 4 δ β ( 0 ) β ¯ ( 2 ) + δ β ( 1 ) 2 β ¯ ( 2 ) ,
Ω pm = ± δ β ( 0 ) β ¯ ( 2 ) + δ β ( 1 ) 2 β ¯ ( 2 ) .
β ¯ ( 2 ) λ p D p , where D p = ( 2 π ) λ 2 λ 2 n ( λ ) | λ p .
P s A ^ s ( τ , z ) A ^ s ( τ , z ) ,
P s c ω a = d Ω ˜ ( γ s a P p g ) 2 sinh 2 ( g z ) = ω s ω a Ω ˜ 0 Π ( g max z ) .
Π ( y ) : = d x ( 1 x 2 ) 1 sinh 2 ( y 1 x 2 ) .
g = g max 1 ( Ω ˜ / Ω ˜ 0 ) 2 , Ω ˜ 0 γ ˜ 1 P p | δ β ( 1 ) / 2 β ¯ ( 2 ) Ω pm | γ ˜ 1 P p β ¯ ( 2 ) δ β ( 0 ) .
P s c ω s g max β ¯ ( 2 ) δ β ( 0 ) Π ( g max z ) .
β ¯ ( 2 ) δ β ( 0 ) β ¯ ( 2 ) Ω pm .
P p = E p ( π τ 0 2 ) 1 / 2 exp ( τ 2 / τ 0 2 ) ,
E s d τ P s 1 β ¯ ( 2 ) δ β ( 0 ) c τ 0 L ω s Ψ ( γ ˜ 1 E p π τ 0 2 L ) ,
Ψ ( z 0 ) = d y z 0 e y 2 Π ( z 0 e y 2 ) z 0 1 π 4 2 exp ( 2 z 0 ) .
E s π 32 β ¯ ( 2 ) δ β ( 0 ) c τ 0 L ω s exp ( 2 γ ˜ 1 E p π τ 0 2 ) .
δ Ω pm δ P p = γ ˜ 2 β ¯ ( 2 ) δ β ( 0 ) .
γ ˜ 1 ω s ω a χ ω p χ , γ ˜ 2 ( ω s + ω a ) χ ω p χ = ω p ( 2 χ χ ) .
A p z = i X ω p [ η p p p p χ ( 3 ) ( ω p ; ω p , ω p , ω p ) A p A p * A p + 2 η p p s s χ ( 3 ) ( ω p ; ω s , ω s , ω p ) A s A s * A p + 2 η p p a a χ ( 3 ) ( ω p ; ω a , ω a , ω p ) A a A a * A p + 2 η p p s a χ ( 3 ) ( ω p ; ω s , ω p , ω a ) A s A p * A a Φ * ] ,
A s z = i X ω s [ η s s s s χ ( 3 ) ( ω s ; ω s , ω s , ω s ) A s A s * A s + 2 η p p s s χ ( 3 ) ( ω s ; ω p , ω p , ω s ) A p A p * A s + 2 η s s a a χ ( 3 ) ( ω s ; ω a , ω a , ω s ) A a A a * A s + η p p s a χ ( 3 ) ( ω s ; ω p , ω a , ω p ) A p A a * A p Φ ] ,
η i j k l = d 2 x F i * F j F k * F l , i , j , k , l { p , s , a } ,
d d z ( | A p | 2 + | A s | 2 + | A a | 2 ) = 0
1 2 d N p d z = d N s d z = d N a d z , N i = | A i | 2 / ω i , i = p , s , a ,
χ ( 3 ) ( ω p ; ω s , ω p , ω a ) = χ ( 3 ) ( ω s ; ω p , ω a , ω p ) = χ ( 3 ) ( ω a ; ω p , ω s , ω p ) .
z A p = i γ p p | A p | 2 A p ,
z A s = 2 i γ s s | A p | 2 A s + i γ s a A p 2 A a * Φ ,
z A a = 2 i γ a a | A p | 2 A a + i γ a s A p 2 A s * Φ ,
γ p p = X ω p η p p p p χ ( 3 ) ( ω p ; ω p , ω p , ω p ) , γ s s = X ω s η p p s s χ ( 3 ) ( ω s ; ω p , ω p , ω s ) , γ a a = X ω a η p p a a χ ( 3 ) ( ω a ; ω p , ω p , ω a ) , γ s a = X ω s η p p s a χ ( 3 ) ( ω s ; ω p , ω a , ω p ) , γ a s = X ω a η p p s a χ ( 3 ) ( ω a ; ω p , ω s , ω p ) .

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