Abstract

Deeply saturated fiber optic parametric amplifiers can have very high performance. While it’s a common practice to model the fiber as a longitudinally homogenous entity, we show that the inhomogeneous nature of the fiber leads to a greater performance level which is neither accessible nor accountable using the homogenous model. This indicates that some experimental results cannot be predicted using the homogenous fiber model, even in principle. Consequently, future studies on the performance limit of the system will have to include an inhomogeneous fiber model.

© 2014 Optical Society of America

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References

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2014 (1)

2012 (4)

2011 (1)

B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photonics 5(3), 141–148 (2011).

2010 (1)

2009 (3)

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fiber and their application,” IEEE J. Sel. Top. Quantum Electron. 15(1), 103–113 (2009).
[Crossref]

E. Myslivets, C. Lundström, J. M. Aparicio, S. Moro, A. O. J. Wiberg, C.-S. Bres, N. Alic, P. A. Andrekson, and S. Radic, “Spatial equalization of zero dispersion wavelength profiles in nonlinear fibers,” IEEE Photon. Technol. Lett. 21(24), 1807–1809 (2009).
[Crossref]

E. Myslivets, N. Alic, J. R. Windmiller, and S. Radic, “A new class of high-resolution measurements of arbitrary-dispersion fibers: localization of four-photon mixing process,” J. Lightwave Technol. 27(3), 364–375 (2009).
[Crossref]

2008 (2)

S. Moro, E. Myslivets, J. R. Windmiller, N. Alic, J. M. Chavez Boggio, and S. Radic, “Synthesis of equalized broadband parametric gain by localized dispersion mapping,” IEEE Photon. Technol. Lett. 20(23), 1971–1973 (2008).
[Crossref]

P. A. Andrekson, H. Sunnerud, S. Oda, T. Nishitani, and J. Yang, “Ultrafast, atto-Joule switch using fiber-optic parametric amplifier operated in saturation,” Opt. Express 16(15), 10956–10961 (2008).
[Crossref] [PubMed]

2006 (1)

2005 (2)

2004 (2)

F. Yaman, Q. Lin, S. Radic, and G. P. Agrawal, “Impact of dispersion fluctuation on dual-pump fiber-optic parametric amplifiers,” IEEE Photon. Technol. Lett. 16(5), 1292–1294 (2004).
[Crossref]

M. Farahmand and M. de Sterke, “Parametric amplification in presence of dispersion fluctuations,” Opt. Express 12(1), 136–142 (2004).
[Crossref] [PubMed]

2002 (1)

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

2001 (3)

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87(3), 033902 (2001).
[Crossref] [PubMed]

M. E. Marhic, K. K. Y. Wong, M. C. Ho, and L. G. Kazovsky, “92% pump depletion in a continuous-wave one-pump fiber optical parametric amplifier,” Opt. Lett. 26(9), 620–622 (2001).
[Crossref] [PubMed]

C. J. Chen and W. S. Wong, “Transient effects in saturated Raman amplifiers,” Electron. Lett. 37(6), 371–373 (2001).
[Crossref]

1999 (1)

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence behavior of the Nelder-Mead simplex algorithm in low dimensions,” SIAM J. Optim. 9(1), 112–147 (1999).
[Crossref]

1998 (1)

1997 (1)

A. K. Srivastava, Y. Sun, J. L. Zyskind, and J. W. Sulhoff, “EDFA transient response to channel loss in WDM transmission system,” IEEE Photon. Technol. Lett. 9(3), 386–388 (1997).
[Crossref]

1991 (1)

1990 (1)

1989 (3)

G. Eisenstein, R. S. Tucker, J. M. Wiesenfeld, P. B. Hansen, G. Raybon, B. C. Johnson, T. J. Bridges, F. G. Storz, and C. A. Burrus, “Gain recovery time of traveling-wave semiconductor optical amplifiers,” Appl. Phys. Lett. 54(5), 454–456 (1989).
[Crossref]

R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, “Raman response function of silica-core fibers,” J. Opt. Soc. Am. B 6(6), 1159–1166 (1989).
[Crossref]

D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weidman, “Nonlinear optical susceptibilities of high-index glasses,” Appl. Phys. Lett. 54(14), 1293 (1989).
[Crossref]

1988 (1)

C. J. McKinstrie and G. G. Luther, “Solitary-wave solutions of the generalised three-wave and four-wave equations,” Phys. Lett. A 127(1), 14–18 (1988).
[Crossref]

1986 (1)

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56(2), 135–138 (1986).
[Crossref] [PubMed]

1982 (1)

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18(7), 1062–1072 (1982).
[Crossref]

1973 (1)

R. H. Stolen and A. Ashkin, “Optical Kerr effect in glass waveguides,” Appl. Phys. Lett. 22(6), 294–296 (1973).
[Crossref]

1961 (1)

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7(4), 118–119 (1961).
[Crossref]

Agrawal, G. P.

F. Yaman, Q. Lin, S. Radic, and G. P. Agrawal, “Impact of dispersion fluctuation on dual-pump fiber-optic parametric amplifiers,” IEEE Photon. Technol. Lett. 16(5), 1292–1294 (2004).
[Crossref]

Alic, N.

E. Myslivets, N. Alic, J. R. Windmiller, and S. Radic, “A new class of high-resolution measurements of arbitrary-dispersion fibers: localization of four-photon mixing process,” J. Lightwave Technol. 27(3), 364–375 (2009).
[Crossref]

E. Myslivets, C. Lundström, J. M. Aparicio, S. Moro, A. O. J. Wiberg, C.-S. Bres, N. Alic, P. A. Andrekson, and S. Radic, “Spatial equalization of zero dispersion wavelength profiles in nonlinear fibers,” IEEE Photon. Technol. Lett. 21(24), 1807–1809 (2009).
[Crossref]

S. Moro, E. Myslivets, J. R. Windmiller, N. Alic, J. M. Chavez Boggio, and S. Radic, “Synthesis of equalized broadband parametric gain by localized dispersion mapping,” IEEE Photon. Technol. Lett. 20(23), 1971–1973 (2008).
[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(2), 023808 (2005).
[Crossref]

Andrekson, P. A.

E. Myslivets, C. Lundström, J. M. Aparicio, S. Moro, A. O. J. Wiberg, C.-S. Bres, N. Alic, P. A. Andrekson, and S. Radic, “Spatial equalization of zero dispersion wavelength profiles in nonlinear fibers,” IEEE Photon. Technol. Lett. 21(24), 1807–1809 (2009).
[Crossref]

P. A. Andrekson, H. Sunnerud, S. Oda, T. Nishitani, and J. Yang, “Ultrafast, atto-Joule switch using fiber-optic parametric amplifier operated in saturation,” Opt. Express 16(15), 10956–10961 (2008).
[Crossref] [PubMed]

P. Kylemark, H. Sunnerud, M. Karlsson, and P. A. Andrekson, “Semi-analytic saturation theory of fiber optical parametric amplifiers,” J. Lightwave Technol. 24(9), 3471–3479 (2006).
[Crossref]

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

Aparicio, J. M.

E. Myslivets, C. Lundström, J. M. Aparicio, S. Moro, A. O. J. Wiberg, C.-S. Bres, N. Alic, P. A. Andrekson, and S. Radic, “Spatial equalization of zero dispersion wavelength profiles in nonlinear fibers,” IEEE Photon. Technol. Lett. 21(24), 1807–1809 (2009).
[Crossref]

Ashkin, A.

R. H. Stolen and A. Ashkin, “Optical Kerr effect in glass waveguides,” Appl. Phys. Lett. 22(6), 294–296 (1973).
[Crossref]

Batha, S. H.

Bjorkholm, J. E.

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18(7), 1062–1072 (1982).
[Crossref]

Borrelli, N. F.

D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weidman, “Nonlinear optical susceptibilities of high-index glasses,” Appl. Phys. Lett. 54(14), 1293 (1989).
[Crossref]

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(2), 023808 (2005).
[Crossref]

Bramerie, L.

Bres, C.-S.

E. Myslivets, C. Lundström, J. M. Aparicio, S. Moro, A. O. J. Wiberg, C.-S. Bres, N. Alic, P. A. Andrekson, and S. Radic, “Spatial equalization of zero dispersion wavelength profiles in nonlinear fibers,” IEEE Photon. Technol. Lett. 21(24), 1807–1809 (2009).
[Crossref]

Bridges, T. J.

G. Eisenstein, R. S. Tucker, J. M. Wiesenfeld, P. B. Hansen, G. Raybon, B. C. Johnson, T. J. Bridges, F. G. Storz, and C. A. Burrus, “Gain recovery time of traveling-wave semiconductor optical amplifiers,” Appl. Phys. Lett. 54(5), 454–456 (1989).
[Crossref]

Brilland, L.

Burrus, C. A.

G. Eisenstein, R. S. Tucker, J. M. Wiesenfeld, P. B. Hansen, G. Raybon, B. C. Johnson, T. J. Bridges, F. G. Storz, and C. A. Burrus, “Gain recovery time of traveling-wave semiconductor optical amplifiers,” Appl. Phys. Lett. 54(5), 454–456 (1989).
[Crossref]

Cappellini, G.

Chartier, T.

Chavez Boggio, J. M.

S. Moro, E. Myslivets, J. R. Windmiller, N. Alic, J. M. Chavez Boggio, and S. Radic, “Synthesis of equalized broadband parametric gain by localized dispersion mapping,” IEEE Photon. Technol. Lett. 20(23), 1971–1973 (2008).
[Crossref]

Chen, C. J.

C. J. Chen and W. S. Wong, “Transient effects in saturated Raman amplifiers,” Electron. Lett. 37(6), 371–373 (2001).
[Crossref]

Costa e Silva, M.

Cunningham, J. E.

de Sterke, M.

Dumbaugh, W. H.

D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weidman, “Nonlinear optical susceptibilities of high-index glasses,” Appl. Phys. Lett. 54(14), 1293 (1989).
[Crossref]

Eggleton, B. J.

B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photonics 5(3), 141–148 (2011).

Eisenstein, G.

G. Eisenstein, R. S. Tucker, J. M. Wiesenfeld, P. B. Hansen, G. Raybon, B. C. Johnson, T. J. Bridges, F. G. Storz, and C. A. Burrus, “Gain recovery time of traveling-wave semiconductor optical amplifiers,” Appl. Phys. Lett. 54(5), 454–456 (1989).
[Crossref]

Emplit, Ph.

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87(3), 033902 (2001).
[Crossref] [PubMed]

Farahmand, M.

Franken, P. A.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7(4), 118–119 (1961).
[Crossref]

Galili, M.

Gay, M.

Gordon, J. P.

Haelterman, M.

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87(3), 033902 (2001).
[Crossref] [PubMed]

Hall, D. W.

D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weidman, “Nonlinear optical susceptibilities of high-index glasses,” Appl. Phys. Lett. 54(14), 1293 (1989).
[Crossref]

Hansen, P. B.

G. Eisenstein, R. S. Tucker, J. M. Wiesenfeld, P. B. Hansen, G. Raybon, B. C. Johnson, T. J. Bridges, F. G. Storz, and C. A. Burrus, “Gain recovery time of traveling-wave semiconductor optical amplifiers,” Appl. Phys. Lett. 54(5), 454–456 (1989).
[Crossref]

Hansryd, J.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

Hasegawa, A.

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56(2), 135–138 (1986).
[Crossref] [PubMed]

Hasegawa, T.

Haus, H. A.

Hedekvist, P. O.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

Hill, A. E.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7(4), 118–119 (1961).
[Crossref]

Hirano, M.

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fiber and their application,” IEEE J. Sel. Top. Quantum Electron. 15(1), 103–113 (2009).
[Crossref]

Ho, M. C.

Hu, H.

Huang, Y.

Hvam, J. M.

Jeppesen, P.

Ji, H.

Johnson, B. C.

G. Eisenstein, R. S. Tucker, J. M. Wiesenfeld, P. B. Hansen, G. Raybon, B. C. Johnson, T. J. Bridges, F. G. Storz, and C. A. Burrus, “Gain recovery time of traveling-wave semiconductor optical amplifiers,” Appl. Phys. Lett. 54(5), 454–456 (1989).
[Crossref]

Karlsson, M.

Kazovsky, L. G.

Kikuchi, K.

Krishnamoorthy, A. V.

Kylemark, P.

Lagarias, J. C.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence behavior of the Nelder-Mead simplex algorithm in low dimensions,” SIAM J. Optim. 9(1), 112–147 (1999).
[Crossref]

Le, S. D.

Lee, J. H.

Lee, J.-H.

Lenglé, K.

Li, G.

Li, J.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

Lin, Q.

F. Yaman, Q. Lin, S. Radic, and G. P. Agrawal, “Impact of dispersion fluctuation on dual-pump fiber-optic parametric amplifiers,” IEEE Photon. Technol. Lett. 16(5), 1292–1294 (2004).
[Crossref]

Liu, X.

Lundström, C.

E. Myslivets, C. Lundström, J. M. Aparicio, S. Moro, A. O. J. Wiberg, C.-S. Bres, N. Alic, P. A. Andrekson, and S. Radic, “Spatial equalization of zero dispersion wavelength profiles in nonlinear fibers,” IEEE Photon. Technol. Lett. 21(24), 1807–1809 (2009).
[Crossref]

Luo, Y.

Luther, G. G.

C. J. McKinstrie, G. G. Luther, and S. H. Batha, “Signal enhancement in collinear four-wave mixing,” J. Opt. Soc. Am. B 7(3), 340–344 (1990).
[Crossref]

C. J. McKinstrie and G. G. Luther, “Solitary-wave solutions of the generalised three-wave and four-wave equations,” Phys. Lett. A 127(1), 14–18 (1988).
[Crossref]

Luther-Davies, B.

B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photonics 5(3), 141–148 (2011).

Marhic, M. E.

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(2), 023808 (2005).
[Crossref]

McKinstrie, C. J.

C. J. McKinstrie, G. G. Luther, and S. H. Batha, “Signal enhancement in collinear four-wave mixing,” J. Opt. Soc. Am. B 7(3), 340–344 (1990).
[Crossref]

C. J. McKinstrie and G. G. Luther, “Solitary-wave solutions of the generalised three-wave and four-wave equations,” Phys. Lett. A 127(1), 14–18 (1988).
[Crossref]

Méchin, D.

Mekis, A.

Moro, S.

E. Myslivets, C. Lundström, J. M. Aparicio, S. Moro, A. O. J. Wiberg, C.-S. Bres, N. Alic, P. A. Andrekson, and S. Radic, “Spatial equalization of zero dispersion wavelength profiles in nonlinear fibers,” IEEE Photon. Technol. Lett. 21(24), 1807–1809 (2009).
[Crossref]

S. Moro, E. Myslivets, J. R. Windmiller, N. Alic, J. M. Chavez Boggio, and S. Radic, “Synthesis of equalized broadband parametric gain by localized dispersion mapping,” IEEE Photon. Technol. Lett. 20(23), 1971–1973 (2008).
[Crossref]

Myslivets, E.

R. R. Nissim, E. Myslivets, and S. Radic, “Performance limits of inhomogeneous fiber optic parametric amplifiers operated in saturated regime,” J. Lightwave Technol. 32(21), 3552–3559 (2014).
[Crossref]

E. Myslivets, C. Lundström, J. M. Aparicio, S. Moro, A. O. J. Wiberg, C.-S. Bres, N. Alic, P. A. Andrekson, and S. Radic, “Spatial equalization of zero dispersion wavelength profiles in nonlinear fibers,” IEEE Photon. Technol. Lett. 21(24), 1807–1809 (2009).
[Crossref]

E. Myslivets, N. Alic, J. R. Windmiller, and S. Radic, “A new class of high-resolution measurements of arbitrary-dispersion fibers: localization of four-photon mixing process,” J. Lightwave Technol. 27(3), 364–375 (2009).
[Crossref]

S. Moro, E. Myslivets, J. R. Windmiller, N. Alic, J. M. Chavez Boggio, and S. Radic, “Synthesis of equalized broadband parametric gain by localized dispersion mapping,” IEEE Photon. Technol. Lett. 20(23), 1971–1973 (2008).
[Crossref]

Nagashima, T.

Nakanishi, T.

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fiber and their application,” IEEE J. Sel. Top. Quantum Electron. 15(1), 103–113 (2009).
[Crossref]

Newhouse, M. A.

D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weidman, “Nonlinear optical susceptibilities of high-index glasses,” Appl. Phys. Lett. 54(14), 1293 (1989).
[Crossref]

Nishitani, T.

Nissim, R. R.

Oda, S.

Ohara, S.

Okuno, T.

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fiber and their application,” IEEE J. Sel. Top. Quantum Electron. 15(1), 103–113 (2009).
[Crossref]

Onishi, M.

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fiber and their application,” IEEE J. Sel. Top. Quantum Electron. 15(1), 103–113 (2009).
[Crossref]

Oxenløwe, L. K.

Peters, C. W.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7(4), 118–119 (1961).
[Crossref]

Peucheret, C.

Pu, M.

Radic, S.

R. R. Nissim, E. Myslivets, and S. Radic, “Performance limits of inhomogeneous fiber optic parametric amplifiers operated in saturated regime,” J. Lightwave Technol. 32(21), 3552–3559 (2014).
[Crossref]

S. Radic, “Parametric signal processing,” IEEE J. Sel. Top. Quantum Electron. 18(2), 670–680 (2012).
[Crossref]

E. Myslivets, N. Alic, J. R. Windmiller, and S. Radic, “A new class of high-resolution measurements of arbitrary-dispersion fibers: localization of four-photon mixing process,” J. Lightwave Technol. 27(3), 364–375 (2009).
[Crossref]

E. Myslivets, C. Lundström, J. M. Aparicio, S. Moro, A. O. J. Wiberg, C.-S. Bres, N. Alic, P. A. Andrekson, and S. Radic, “Spatial equalization of zero dispersion wavelength profiles in nonlinear fibers,” IEEE Photon. Technol. Lett. 21(24), 1807–1809 (2009).
[Crossref]

S. Moro, E. Myslivets, J. R. Windmiller, N. Alic, J. M. Chavez Boggio, and S. Radic, “Synthesis of equalized broadband parametric gain by localized dispersion mapping,” IEEE Photon. Technol. Lett. 20(23), 1971–1973 (2008).
[Crossref]

F. Yaman, Q. Lin, S. Radic, and G. P. Agrawal, “Impact of dispersion fluctuation on dual-pump fiber-optic parametric amplifiers,” IEEE Photon. Technol. Lett. 16(5), 1292–1294 (2004).
[Crossref]

Raj, K.

Raybon, G.

G. Eisenstein, R. S. Tucker, J. M. Wiesenfeld, P. B. Hansen, G. Raybon, B. C. Johnson, T. J. Bridges, F. G. Storz, and C. A. Burrus, “Gain recovery time of traveling-wave semiconductor optical amplifiers,” Appl. Phys. Lett. 54(5), 454–456 (1989).
[Crossref]

Reeds, J. A.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence behavior of the Nelder-Mead simplex algorithm in low dimensions,” SIAM J. Optim. 9(1), 112–147 (1999).
[Crossref]

Ren, X.

Richardson, K.

B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photonics 5(3), 141–148 (2011).

Shubin, I.

Simon, J. C.

Srivastava, A. K.

A. K. Srivastava, Y. Sun, J. L. Zyskind, and J. W. Sulhoff, “EDFA transient response to channel loss in WDM transmission system,” IEEE Photon. Technol. Lett. 9(3), 386–388 (1997).
[Crossref]

Stolen, R. H.

R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, “Raman response function of silica-core fibers,” J. Opt. Soc. Am. B 6(6), 1159–1166 (1989).
[Crossref]

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18(7), 1062–1072 (1982).
[Crossref]

R. H. Stolen and A. Ashkin, “Optical Kerr effect in glass waveguides,” Appl. Phys. Lett. 22(6), 294–296 (1973).
[Crossref]

Storz, F. G.

G. Eisenstein, R. S. Tucker, J. M. Wiesenfeld, P. B. Hansen, G. Raybon, B. C. Johnson, T. J. Bridges, F. G. Storz, and C. A. Burrus, “Gain recovery time of traveling-wave semiconductor optical amplifiers,” Appl. Phys. Lett. 54(5), 454–456 (1989).
[Crossref]

Sugimoto, N.

Sulhoff, J. W.

A. K. Srivastava, Y. Sun, J. L. Zyskind, and J. W. Sulhoff, “EDFA transient response to channel loss in WDM transmission system,” IEEE Photon. Technol. Lett. 9(3), 386–388 (1997).
[Crossref]

Sun, Y.

A. K. Srivastava, Y. Sun, J. L. Zyskind, and J. W. Sulhoff, “EDFA transient response to channel loss in WDM transmission system,” IEEE Photon. Technol. Lett. 9(3), 386–388 (1997).
[Crossref]

Sunnerud, H.

Tai, K.

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56(2), 135–138 (1986).
[Crossref] [PubMed]

Tanemura, T.

Thacker, H.

Thual, M.

Tomita, A.

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56(2), 135–138 (1986).
[Crossref] [PubMed]

Tomlinson, W. J.

Toupin, P.

Trillo, S.

Troles, J.

Tucker, R. S.

G. Eisenstein, R. S. Tucker, J. M. Wiesenfeld, P. B. Hansen, G. Raybon, B. C. Johnson, T. J. Bridges, F. G. Storz, and C. A. Burrus, “Gain recovery time of traveling-wave semiconductor optical amplifiers,” Appl. Phys. Lett. 54(5), 454–456 (1989).
[Crossref]

Van Simaeys, G.

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87(3), 033902 (2001).
[Crossref] [PubMed]

Wang, Y.

Weidman, D. L.

D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weidman, “Nonlinear optical susceptibilities of high-index glasses,” Appl. Phys. Lett. 54(14), 1293 (1989).
[Crossref]

Weinreich, G.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7(4), 118–119 (1961).
[Crossref]

Westlund, M.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

Wiberg, A. O. J.

E. Myslivets, C. Lundström, J. M. Aparicio, S. Moro, A. O. J. Wiberg, C.-S. Bres, N. Alic, P. A. Andrekson, and S. Radic, “Spatial equalization of zero dispersion wavelength profiles in nonlinear fibers,” IEEE Photon. Technol. Lett. 21(24), 1807–1809 (2009).
[Crossref]

Wiesenfeld, J. M.

G. Eisenstein, R. S. Tucker, J. M. Wiesenfeld, P. B. Hansen, G. Raybon, B. C. Johnson, T. J. Bridges, F. G. Storz, and C. A. Burrus, “Gain recovery time of traveling-wave semiconductor optical amplifiers,” Appl. Phys. Lett. 54(5), 454–456 (1989).
[Crossref]

Windmiller, J. R.

E. Myslivets, N. Alic, J. R. Windmiller, and S. Radic, “A new class of high-resolution measurements of arbitrary-dispersion fibers: localization of four-photon mixing process,” J. Lightwave Technol. 27(3), 364–375 (2009).
[Crossref]

S. Moro, E. Myslivets, J. R. Windmiller, N. Alic, J. M. Chavez Boggio, and S. Radic, “Synthesis of equalized broadband parametric gain by localized dispersion mapping,” IEEE Photon. Technol. Lett. 20(23), 1971–1973 (2008).
[Crossref]

Wong, K. K. Y.

Wong, W. S.

C. J. Chen and W. S. Wong, “Transient effects in saturated Raman amplifiers,” Electron. Lett. 37(6), 371–373 (2001).
[Crossref]

Wright, M. H.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence behavior of the Nelder-Mead simplex algorithm in low dimensions,” SIAM J. Optim. 9(1), 112–147 (1999).
[Crossref]

Wright, P. E.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence behavior of the Nelder-Mead simplex algorithm in low dimensions,” SIAM J. Optim. 9(1), 112–147 (1999).
[Crossref]

Yaman, F.

F. Yaman, Q. Lin, S. Radic, and G. P. Agrawal, “Impact of dispersion fluctuation on dual-pump fiber-optic parametric amplifiers,” IEEE Photon. Technol. Lett. 16(5), 1292–1294 (2004).
[Crossref]

Yang, J.

Yao, J.

Yvind, K.

Zhang, X.

Zheng, L.

Zheng, X.

Zyskind, J. L.

A. K. Srivastava, Y. Sun, J. L. Zyskind, and J. W. Sulhoff, “EDFA transient response to channel loss in WDM transmission system,” IEEE Photon. Technol. Lett. 9(3), 386–388 (1997).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

R. H. Stolen and A. Ashkin, “Optical Kerr effect in glass waveguides,” Appl. Phys. Lett. 22(6), 294–296 (1973).
[Crossref]

G. Eisenstein, R. S. Tucker, J. M. Wiesenfeld, P. B. Hansen, G. Raybon, B. C. Johnson, T. J. Bridges, F. G. Storz, and C. A. Burrus, “Gain recovery time of traveling-wave semiconductor optical amplifiers,” Appl. Phys. Lett. 54(5), 454–456 (1989).
[Crossref]

D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weidman, “Nonlinear optical susceptibilities of high-index glasses,” Appl. Phys. Lett. 54(14), 1293 (1989).
[Crossref]

Electron. Lett. (1)

C. J. Chen and W. S. Wong, “Transient effects in saturated Raman amplifiers,” Electron. Lett. 37(6), 371–373 (2001).
[Crossref]

IEEE J. Quantum Electron. (1)

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18(7), 1062–1072 (1982).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (3)

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

S. Radic, “Parametric signal processing,” IEEE J. Sel. Top. Quantum Electron. 18(2), 670–680 (2012).
[Crossref]

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fiber and their application,” IEEE J. Sel. Top. Quantum Electron. 15(1), 103–113 (2009).
[Crossref]

IEEE Photon. Technol. Lett. (4)

E. Myslivets, C. Lundström, J. M. Aparicio, S. Moro, A. O. J. Wiberg, C.-S. Bres, N. Alic, P. A. Andrekson, and S. Radic, “Spatial equalization of zero dispersion wavelength profiles in nonlinear fibers,” IEEE Photon. Technol. Lett. 21(24), 1807–1809 (2009).
[Crossref]

S. Moro, E. Myslivets, J. R. Windmiller, N. Alic, J. M. Chavez Boggio, and S. Radic, “Synthesis of equalized broadband parametric gain by localized dispersion mapping,” IEEE Photon. Technol. Lett. 20(23), 1971–1973 (2008).
[Crossref]

F. Yaman, Q. Lin, S. Radic, and G. P. Agrawal, “Impact of dispersion fluctuation on dual-pump fiber-optic parametric amplifiers,” IEEE Photon. Technol. Lett. 16(5), 1292–1294 (2004).
[Crossref]

A. K. Srivastava, Y. Sun, J. L. Zyskind, and J. W. Sulhoff, “EDFA transient response to channel loss in WDM transmission system,” IEEE Photon. Technol. Lett. 9(3), 386–388 (1997).
[Crossref]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. B (4)

Nat. Photonics (1)

B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photonics 5(3), 141–148 (2011).

Opt. Express (4)

Opt. Lett. (3)

Phys. Lett. A (1)

C. J. McKinstrie and G. G. Luther, “Solitary-wave solutions of the generalised three-wave and four-wave equations,” Phys. Lett. A 127(1), 14–18 (1988).
[Crossref]

Phys. Rev. A (1)

E. Brainis, D. Amans, and S. Massar, “Scalar and vector modulation instabilities induced by vacuum fluctuations in fibers: Numerical study,” Phys. Rev. A 71(2), 023808 (2005).
[Crossref]

Phys. Rev. Lett. (3)

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7(4), 118–119 (1961).
[Crossref]

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56(2), 135–138 (1986).
[Crossref] [PubMed]

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87(3), 033902 (2001).
[Crossref] [PubMed]

SIAM J. Optim. (1)

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence behavior of the Nelder-Mead simplex algorithm in low dimensions,” SIAM J. Optim. 9(1), 112–147 (1999).
[Crossref]

Other (2)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).

N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University, 1991), pp. 227.

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Figures (7)

Fig. 1
Fig. 1 An illustration of signal-induced pump depletion in a fiber optics parametric amplifier with a high FoM, operated in deep saturation. When the weak signal enters to the saturated amplifier, the amplification of the signal is accompanied by generation of multiple idlers and noise, all of which draw power from the pump. At the output of the amplifier, the band pass filter blocks the amplified signal and the other byproducts, and shows the depleted pump.
Fig. 2
Fig. 2 Power analysis of a typical pump depletion effect in a highly saturated FOPA: (a) The optical spectrum (50 GHz RBW) at the output of the HNLF in the absence of a signal. Each trace corresponds to the matching color point in (b) (signal OFF), describing the FOPA output spectrum at FoM of 6.8 (blue), 7.7 (green), 8.5 (red), and 9.3 (turquoise). (b) The dependence of the pump power at the output of the amplifier as a function of the FoM in the presence and absence of the input signal using a 50 GHz band pass filter. The first and second strong contrasts are located at FoM of 8.6 and 11.3, respectively. (c) The distribution of the optical power at the output of the HNLF as a function of the FoM in the presence of the signal. The figure shows the power distribution between the pump power, integrated noise power, and the sum of signal and idlers power. The CW components were measured within a 50 GHz BW. The FoM was expressed in terms of the effective length of the fiber, Leff = [1-exp(-α L)]/α, where α is the propagation loss. The FoM was modified by extending the length of a uniform fiber, and was simulated using the following parameters: γ = 17.66 W−1km−1, α = 0.69 dB/km, ZDW at 1550 nm with a dispersion slope of 44.89·10−3 ps/nm2-km, pump wavelength at 1567.06 nm, signal wavelength at 1573.17 nm, and pump and signal input power levels of 30 and −35 dBm.
Fig. 3
Fig. 3 Illustration of ZDW profile representation of a fiber using “static grid”. The profile is represented by six equally spaced nodes where the first and last nodes are positioned at the entrance and exit of the fiber, respectively. The full profile description is given by interpolating the ZDW between the nodes. Each of the double headed arrows represents a degree of freedom. The signal wavelength (λS) remains a free parameter, and a reference is formed by keeping the pump wavelength (λP) fixed.
Fig. 4
Fig. 4 A plot of the optimized ZDW profiles. The dashed line shows the profile of the benchmark. The blue trace (round markers) and green trace (square markers) describe solutions which were made using the six nodes static grid profile representation in the case that the initial guess of the optimizer was set as the benchmark and first peak settings, respectively. The red trace (triangular markers) describes a solution which was made using the ten nodes static grid profile representation in the case that the initial guess of the optimizer was set as the green trace. The markers represent the nodes while traces show the interpolated profile. The pump (dash-dot) and the signal (solid) positions are described by the two uppermost horizontal lines. The optimizations resulted in a practically identical signal wavelength.
Fig. 5
Fig. 5 Illustration of ZDW profile representation of a fiber using “dynamic grid”. The profile is represented by six nodes where the first and last nodes are positioned at the entrance and exit of the fiber, respectively. Each of the nodes, except the first one which is positioned at the entrance of the fiber, is free to be shifted both laterally and vertically. The full profile description is given by interpolating the ZDW nodes. The position of the signal (λS) remains a free parameter; however, the wavelength of the pump (λP) is fixed and acts as a reference.
Fig. 6
Fig. 6 A plot of the optimized ZDW profiles. The dashed line shows the profile of the benchmark. The upper horizontal line (dash-dot) represents the wavelength of the pump. The green trace (triangular markers) describes a solution made by a dynamic grid representation in the case that the initial guess of the optimizer was set as FP. The blue trace (round markers) describes a solution made by optimizing a dynamic grid in the case that the initial guess of the optimizer was set to the solution achieved by the six node static grid (6-First peak). Each of the markers represents a node.
Fig. 7
Fig. 7 A simulation of the pump’s ER dependence on the signal wavelength for different optimized ZDW profiles; the signal position is shown with respect to the pump wavelength.

Tables (1)

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Table 1 Summary of the optimized FOPA performance.

Equations (3)

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Δ β = k S + k I 2 k P
Δ β = 2 π c λ P 2 S ( λ P λ 0 ) ( λ S λ P ) 2 .
d A d z = ( D ^ ( z ) + N ^ α 2 ) A ,

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