Abstract

The four-wave mixing process in optical fibers is generally sensitive to dispersion uniformity along the fiber length. However, some specific phase matching conditions show increased robustness to longitudinal fluctuations in fiber dimensions, which affect the dispersion, even for signal and idler wavelengths far from the pump. In this paper, we present the method by which this point is found, how the fiber design characteristics impact on the stable point and demonstrate the stability through propagation simulations using the non-linear Schrödinger equation.

© 2013 Optical Society of America

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2013 (1)

2012 (3)

2010 (2)

2008 (4)

2007 (3)

2005 (3)

2002 (1)

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron.8, 506–520 (2002).
[CrossRef]

2001 (2)

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Role of entanglement in two-photon imaging,” Phys. Rev. Lett.87, 123602 (2001).
[CrossRef] [PubMed]

J. E. Sharping, M. Fiorentino, A. Coker, P. Kumar, and R. S. Windeler, “Four-wave mixing in microstructure fiber.” Opt. Lett.26, 1048–1050 (2001).
[CrossRef]

2000 (2)

F. Abdullaev, B. Umarov, M. Wahiddin, and D. Navotny, “Dispersion-managed solitons in a periodically and randomly inhomogeneous birefringent optical fiber,” J. Opt. Soc. Am. B17, 1117–1124 (2000).
[CrossRef]

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett.84, 4729–4732 (2000).
[CrossRef] [PubMed]

1999 (1)

1998 (2)

1997 (2)

1996 (3)

N. Smith, F. Knox, N. Doran, K. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electronics Letters32, 54–55 (1996).
[CrossRef]

S. Watanabe and M. Shirasaki, “Exact compensation for both chromatic dispersion and Kerr effect in a transmission fiber using optical phase conjugation,” J. Lightwave Technol.14, 243–248 (1996).
[CrossRef]

D. Gillespie, “Exact numerical simulation of the Ornstein-Uhlenbeck process and its integral.” Phys. Rev. E54, 2084–2091 (1996).
[CrossRef]

1994 (1)

1993 (1)

S. Watanabe, T. Naito, and T. Chikama, “Compensation of chromatic dispersion in a single-mode fiber by optical phase conjugation,” IEEE Photon. Technol. Lett.5, 92–95 (1993).
[CrossRef]

1992 (2)

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

C. Bennett, F. Bessette, and G. Brassard, “Experimental quantum cryptography,” Journal of Cryptology5, 3–28 (1992).
[CrossRef]

1991 (1)

1987 (1)

N. Shibata, R. Braun, and R. 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]

1985 (1)

M. Levenson, R. Shelby, A. Aspect, M. Reid, and D. Walls, “Generation and detection of squeezed states of light by nondegenerate four-wave mixing in an optical fiber,” Phys. Rev. A32, 1550–1562 (1985).
[CrossRef] [PubMed]

1982 (2)

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

G. J. Dunning and R. C. Lind, “Demonstration of image transmission through fibers by optical phase conjugation,” Opt. Lett.7, 558–560 (1982).
[CrossRef] [PubMed]

Abdullaev, F.

Abouraddy, A. F.

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Role of entanglement in two-photon imaging,” Phys. Rev. Lett.87, 123602 (2001).
[CrossRef] [PubMed]

Agrawal, G. P.

G. P. Agrawal, Lightwave Technology: Telecommunication Systems (Wiley. com,2005).

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2006), 4th ed.

Andersen, T.

Andrekson, P.

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron.8, 506–520 (2002).
[CrossRef]

Andrekson, P. A.

Aspect, A.

M. Levenson, R. Shelby, A. Aspect, M. Reid, and D. Walls, “Generation and detection of squeezed states of light by nondegenerate four-wave mixing in an optical fiber,” Phys. Rev. A32, 1550–1562 (1985).
[CrossRef] [PubMed]

Bang, O.

Bennett, C.

C. Bennett, F. Bessette, and G. Brassard, “Experimental quantum cryptography,” Journal of Cryptology5, 3–28 (1992).
[CrossRef]

Bennion, I.

N. Smith, F. Knox, N. Doran, K. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electronics Letters32, 54–55 (1996).
[CrossRef]

Bessette, F.

C. Bennett, F. Bessette, and G. Brassard, “Experimental quantum cryptography,” Journal of Cryptology5, 3–28 (1992).
[CrossRef]

Bétourné, A.

Bibbona, E.

E. Bibbona, G. Panfilo, and P. Tavella, “The Ornstein-Uhlenbeck process as a model of a low pass filtered white noise,” Metrologia45, S117 (2008).
[CrossRef]

Birks, T. A.

Bjorkholm, J. E.

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

Blow, K.

N. Smith, F. Knox, N. Doran, K. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electronics Letters32, 54–55 (1996).
[CrossRef]

Bouwmans, G.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, vol. 5 of Electronics & Electrical (Academic Press, 2003).

Brassard, G.

C. Bennett, F. Bessette, and G. Brassard, “Experimental quantum cryptography,” Journal of Cryptology5, 3–28 (1992).
[CrossRef]

Braun, R.

N. Shibata, R. Braun, and R. 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]

Bussières, F.

Chen, J.

J. Chen, X. Li, and P. Kumar, “Two-photon-state generation via four-wave mixing in optical fibers,” Appl. Phys. Lett.72, 033801 (2005).

Chen, Y.

Chikama, T.

S. Watanabe, T. Naito, and T. Chikama, “Compensation of chromatic dispersion in a single-mode fiber by optical phase conjugation,” IEEE Photon. Technol. Lett.5, 92–95 (1993).
[CrossRef]

Coker, A.

Corbeil, J.-S.

Darmanyan, S.

Doran, N.

N. Smith, F. Knox, N. Doran, K. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electronics Letters32, 54–55 (1996).
[CrossRef]

Douay, M.

Dunning, G. J.

Fiorentino, M.

François, P. L.

Friedland, L.

O. Yaakobi and L. Friedland, “Autoresonant four-wave mixing in optical fibers,” Phys. Rev. A82, 023820 (2010).
[CrossRef]

Frosz, M. H.

Furusawa, A.

A. Furusawa, “Unconditional quantum teleportation,” Science282, 706–709 (1998).
[CrossRef] [PubMed]

Gillespie, D.

D. Gillespie, “Exact numerical simulation of the Ornstein-Uhlenbeck process and its integral.” Phys. Rev. E54, 2084–2091 (1996).
[CrossRef]

Godbout, N.

Hansen, K.

Hansryd, J.

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron.8, 506–520 (2002).
[CrossRef]

Hedekvist, P.

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron.8, 506–520 (2002).
[CrossRef]

Hilligsøe, K.

Hirano, M.

Hult, J.

Inoue, K.

K. Inoue, “Arrangement of fiber pieces for a wide wavelength conversion range by fiber four-wave mixing,” Opt. Lett.19, 1189–1191 (1994).
[CrossRef] [PubMed]

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

Jennewein, T.

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett.84, 4729–4732 (2000).
[CrossRef] [PubMed]

Karlsson, M.

Keiding, S.

Knight, J. C.

Knox, F.

N. Smith, F. Knox, N. Doran, K. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electronics Letters32, 54–55 (1996).
[CrossRef]

Kudlinski, A.

Kumar, P.

J. Chen, X. Li, and P. Kumar, “Two-photon-state generation via four-wave mixing in optical fibers,” Appl. Phys. Lett.72, 033801 (2005).

J. E. Sharping, M. Fiorentino, A. Coker, P. Kumar, and R. S. Windeler, “Four-wave mixing in microstructure fiber.” Opt. Lett.26, 1048–1050 (2001).
[CrossRef]

Kuo, B. P.-P.

Lacroix, S.

Laegsgaard, J.

Lægsgaard, J.

J. Lægsgaard, “Phase-matching conditions for single-pump parametric amplification in photonic crystal fibers,” J. Opt. A: Pure Appl. Opt.9, 1105–1112 (2007).
[CrossRef]

Larsen, J.

Levenson, M.

M. Levenson, R. Shelby, A. Aspect, M. Reid, and D. Walls, “Generation and detection of squeezed states of light by nondegenerate four-wave mixing in an optical fiber,” Phys. Rev. A32, 1550–1562 (1985).
[CrossRef] [PubMed]

Li, J.

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron.8, 506–520 (2002).
[CrossRef]

Li, X.

J. Chen, X. Li, and P. Kumar, “Two-photon-state generation via four-wave mixing in optical fibers,” Appl. Phys. Lett.72, 033801 (2005).

Lind, R. C.

Mamyshev, P. V.

Mamysheva, N. A.

Moselund, P. M.

Mussot, A.

Naito, T.

S. Watanabe, T. Naito, and T. Chikama, “Compensation of chromatic dispersion in a single-mode fiber by optical phase conjugation,” IEEE Photon. Technol. Lett.5, 92–95 (1993).
[CrossRef]

Navotny, D.

Nielsen, C.

Øksendal, B.

B. Øksendal, Stochastic Differential Equations, 6th ed. Universitext (Springer, Berlin, 2003).

Ould-Agha, Y.

Panfilo, G.

E. Bibbona, G. Panfilo, and P. Tavella, “The Ornstein-Uhlenbeck process as a model of a low pass filtered white noise,” Metrologia45, S117 (2008).
[CrossRef]

Pureur, V.

Quiquempois, Y.

Radic, S.

Reid, M.

M. Levenson, R. Shelby, A. Aspect, M. Reid, and D. Walls, “Generation and detection of squeezed states of light by nondegenerate four-wave mixing in an optical fiber,” Phys. Rev. A32, 1550–1562 (1985).
[CrossRef] [PubMed]

Russell, P. S.

Saleh, B. E. A.

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Role of entanglement in two-photon imaging,” Phys. Rev. Lett.87, 123602 (2001).
[CrossRef] [PubMed]

Sergienko, A. V.

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Role of entanglement in two-photon imaging,” Phys. Rev. Lett.87, 123602 (2001).
[CrossRef] [PubMed]

Sharping, J. E.

Shelby, R.

M. Levenson, R. Shelby, A. Aspect, M. Reid, and D. Walls, “Generation and detection of squeezed states of light by nondegenerate four-wave mixing in an optical fiber,” Phys. Rev. A32, 1550–1562 (1985).
[CrossRef] [PubMed]

Shibata, N.

N. Shibata, R. Braun, and R. 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]

Shirasaki, M.

S. Watanabe and M. Shirasaki, “Exact compensation for both chromatic dispersion and Kerr effect in a transmission fiber using optical phase conjugation,” J. Lightwave Technol.14, 243–248 (1996).
[CrossRef]

Simon, C.

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett.84, 4729–4732 (2000).
[CrossRef] [PubMed]

Slater, J. A.

Smith, N.

N. Smith, F. Knox, N. Doran, K. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electronics Letters32, 54–55 (1996).
[CrossRef]

Stolen, R.

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

Tavella, P.

E. Bibbona, G. Panfilo, and P. Tavella, “The Ornstein-Uhlenbeck process as a model of a low pass filtered white noise,” Metrologia45, S117 (2008).
[CrossRef]

Teich, M. C.

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Role of entanglement in two-photon imaging,” Phys. Rev. Lett.87, 123602 (2001).
[CrossRef] [PubMed]

Thøgersen, J.

Thomsen, C. L.

Tittel, W.

Torounidis, T.

Umarov, B.

Vanvincq, O.

Virally, S.

Waarts, R.

N. Shibata, R. Braun, and R. 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]

Wadsworth, W. J.

Wahiddin, M.

Walls, D.

M. Levenson, R. Shelby, A. Aspect, M. Reid, and D. Walls, “Generation and detection of squeezed states of light by nondegenerate four-wave mixing in an optical fiber,” Phys. Rev. A32, 1550–1562 (1985).
[CrossRef] [PubMed]

Watanabe, S.

S. Watanabe and M. Shirasaki, “Exact compensation for both chromatic dispersion and Kerr effect in a transmission fiber using optical phase conjugation,” J. Lightwave Technol.14, 243–248 (1996).
[CrossRef]

S. Watanabe, T. Naito, and T. Chikama, “Compensation of chromatic dispersion in a single-mode fiber by optical phase conjugation,” IEEE Photon. Technol. Lett.5, 92–95 (1993).
[CrossRef]

Weihs, G.

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett.84, 4729–4732 (2000).
[CrossRef] [PubMed]

Weinfurter, H.

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett.84, 4729–4732 (2000).
[CrossRef] [PubMed]

Westlund, M.

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron.8, 506–520 (2002).
[CrossRef]

Windeler, R. S.

Yaakobi, O.

O. Yaakobi and L. Friedland, “Autoresonant four-wave mixing in optical fibers,” Phys. Rev. A82, 023820 (2010).
[CrossRef]

Zeilinger, A.

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett.84, 4729–4732 (2000).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

J. Chen, X. Li, and P. Kumar, “Two-photon-state generation via four-wave mixing in optical fibers,” Appl. Phys. Lett.72, 033801 (2005).

Electronics Letters (1)

N. Smith, F. Knox, N. Doran, K. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electronics Letters32, 54–55 (1996).
[CrossRef]

IEEE J. Quantum Electron. (2)

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

IEEE J. Sel. Top. Quantum Electron. (1)

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron.8, 506–520 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

S. Watanabe, T. Naito, and T. Chikama, “Compensation of chromatic dispersion in a single-mode fiber by optical phase conjugation,” IEEE Photon. Technol. Lett.5, 92–95 (1993).
[CrossRef]

J. Lightwave Technol. (4)

S. Watanabe and M. Shirasaki, “Exact compensation for both chromatic dispersion and Kerr effect in a transmission fiber using optical phase conjugation,” J. Lightwave Technol.14, 243–248 (1996).
[CrossRef]

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

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