Abstract

The effect of random fluctuations in the zero-dispersion wavelength is considered for fiber four-wave mixing. Theoretical expressions for average parametric gain, phase-conjugation conversion efficiency, and gain bandwidth are obtained and found to be in good agreement with experiments. Possible limitations on the noise figure in phase-sensitive amplifiers based on fiber four-wave mixing are also discussed.

© 1998 Optical Society of America

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  1. R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1072 (1982).
    [Crossref]
  2. N. Kagi, T.-K. Chiang, M. E. Marhic, and L. G. Kazovsky, “Fiber optical parametric amplifier operating near zero-dispersion wavelength,” Electron. Lett. 31, 1935–1937 (1995).
    [Crossref]
  3. M. E. Marhic, N. Kagi, T.-K. Chiang, and L. G. Kazovsky, “Broadband fiber optical parametric amplifiers,” Opt. Lett. 21, 573–575 (1996).
    [Crossref] [PubMed]
  4. M. E. Marhic, Y. Park, F. S. Yang, and L. G. Kazovsky, “Broadband fiber optical parametric amplifiers and wavelength converters with low-ripple Chebyshev gain spectra,” Opt. Lett. 21, 1354–1356 (1996).
    [Crossref] [PubMed]
  5. P. A. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, and M. Haner, “16 Gbit/s all-optical demultiplexing using four-wave mixing,” Electron. Lett. 27, 922–924 (1992).
    [Crossref]
  6. P. O. Hedekvist and P. A. Andrekson, “Demonstration of fiber four-wave mixing optical demultiplexing with 19 dB parametric amplification,” Electron. Lett. 32, 830–831 (1996).
    [Crossref]
  7. P. O. Hedekvist, M. Karlsson, and P. A. Andrekson, “Fiber four-wave mixing demultiplexing with inherent parametric amplification,” J. Lightwave Technol. 15, 2051–2058 (1997).
    [Crossref]
  8. T. Morioka, H. Takara, S. Kawanishi, T. Kitoh, and M. Saruwatari, “Error-free 500 Gbit/s all optical demultiplexing using low-noise, low-jitter supercontinuum short pulses,” Electron. Lett. 32, 833–834 (1996).
    [Crossref]
  9. T. Morioka, S. Kawanishi, K. Uchiyama, H. Takara, and M. Saruwatari, “Polarization independent 100 Gbit/s all-optical demultiplexer using four-wave mixing in a polarization maintaining fiber loop,” Electron. Lett. 30, 591–592 (1994).
    [Crossref]
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    [Crossref]
  12. A. Hasegawa, “Generation of a train of soliton pulses by induced modulational instability in optical fibers,” Opt. Lett. 9, 288–290 (1984).
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  13. M. N. Islam, S. P. Dijaili, and J. P. Gordon, “Modulation-instability-based fiber interferometer switch near 1.5 μm,” Opt. Lett. 13, 518–520 (1988).
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  14. M. E. Marhic, Y. Park, F. S. Yang, and L. G. Kazovsky, “Widely tunable spectrum translation and wavelength exchange by four-wave mixing in optical fibers,” Opt. Lett. 21, 1354–1356 (1996).
    [Crossref] [PubMed]
  15. I. Bar-Joseph, A. A. Friesem, R. G. Waarts, and H. H. Yaffe, “Parametric interaction of a modulated wave in a single-mode fiber,” Opt. Lett. 11, 534–536 (1986).
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    [Crossref]
  17. R.-D. Li, P. Kumar, and W. L. Kath, “Dispersion compensation with phase-sensitive amplifiers,” J. Lightwave Technol. 12, 541–549 (1994).
    [Crossref]
  18. C. G. Goedde, W. L. Kath, and P. Kumar, “Compensation of the soliton self-frequency shift with phase-sensitive amplifiers,” Opt. Lett. 19, 2077–2079 (1994).
    [Crossref] [PubMed]
  19. J. N. Kutz, W. L. Kath, R.-D. Li, and P. Kumar, “Long-distance pulse propagation in nonlinear optical fibers by using periodically spaced parametric amplifiers,” Opt. Lett. 18, 802–804 (1993).
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    [Crossref]
  22. W. Imajuku and A. Takada, “Optical phase-sensitive amplification using two phase-locked light sources,” Electron. Lett. 33, 1403–1404 (1997).
    [Crossref]
  23. K. Inoue, “Four-wave mixing in an optical fiber in the zero-dispersion wavelength region,” J. Lightwave Technol. 10, 1553–1561 (1992).
    [Crossref]
  24. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995), Chap. 10.
  25. L. B. Jeunhomme, Single-Mode Fiber Optics, Principles and Applications, 2nd ed. (Marcel Dekker, New York, 1990), Chap. 4.3.
  26. N. Kuwaki and M. Ohashi, “Evaluation of longitudinal chromatic dispersion,” J. Lightwave Technol. 8, 1476–1481 (1990).
    [Crossref]
  27. S. Nishi and M. Saruwatari, “Technique for measuring the distributed zero dispersion wavelength of optical fibers using pulse amplification caused by modulation instability,” Electron. Lett. 31, 225–226 (1995).
    [Crossref]
  28. H. Onaka, K. Otsuka, H. Miyata, and T. Chikama, “Measuring the longitudinal distribution of four-wave mixing efficiency in dispersion shifted fibers,” IEEE Photonics Technol. Lett. 6, 1454–1456 (1994).
    [Crossref]
  29. R. M. Jopson, M. Eiselt, R. H. Stolen, R. M. Derosier, A. M. Vengsarkar, and U. Koren, “Nondestructive dispersion-zero measurements along an optical fiber,” Electron. Lett. 31, 2115–2117 (1995).
    [Crossref]
  30. L. F. Mollenauer, P. V. Mamyshev, and M. J. Neubelt, “Method for facile and accurate measurement of optical fiber dispersion maps,” Opt. Lett. 21, 1724–1726 (1996).
    [Crossref] [PubMed]
  31. K. Nakajima, M. Ohashi, and M. Tateda, “Chromatic dispersion distribution along a single-mode optical fiber,” J. Lightwave Technol. 15, 1095–1101 (1997).
    [Crossref]
  32. M. Karlsson, “Modulational instability in lossy optical fibers,” J. Opt. Soc. Am. B 12, 2071–2077 (1995).
  33. K. Kikuchi and C. Lorattanasane, “Design of highly efficient four-wave mixing devices using optical fibers,” IEEE Photonics Technol. Lett. 6, 992–994 (1994).
    [Crossref]
  34. S. Wabnitz, “Nonlinear enhancement and optimization of phase-conjugation efficiency in optical fibers,” IEEE Photonics Technol. Lett. 7, 652–654 (1995).
    [Crossref]
  35. The effective length is defined as zeff=Lloss[1- exp(-z/Lloss)], where z is the propagation distance and Lloss is the loss length (a fiber loss of 0.2 dB/km corresponds to Lloss=21 km).
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    [Crossref]
  37. G. Laval, R. Pellat, and D. Pesme, “Absolute parametric excitation by an imperfect pump or by turbulence in an inhomogeneous plasma,” Phys. Rev. Lett. 36, 192–196 (1976).
    [Crossref]
  38. F. Kh. Abdullaev, S. A. Darmanyan, A. Kobyakov, and F. Lederer, “Modulational instability in optical fibers with variable dispersion,” Phys. Lett. A 220, 213–218 (1996).
    [Crossref]
  39. 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]
  40. C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D 26, 1817–1839 (1982).
    [Crossref]
  41. C. M. Caves and D. D. Crouch, “Quantum wideband traveling-wave analysis of a degenerate parametric amplifier,” J. Opt. Soc. Am. B 4, 1535–1545 (1987).
    [Crossref]
  42. A. Papoulis, Probability, Random Variables and Stochastic Processes, 3rd ed. (McGraw-Hill, New York, 1991), Chap. 11-3.
  43. S. Karlin and H. M. Taylor, A Second Course in Stochastic Processes (Academic, New York, 1981), Chap. 15.14.
  44. G. J. Foschini and C. D. Poole, “Statistical theory of polarization mode dispersion in single mode fibers,” J. Lightwave Technol. 9, 1439–1456 (1991).
    [Crossref]
  45. P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).
    [Crossref]
  46. A. Einstein, “On the theory of Brownian movement,” Ann. Phys. (Leipzig) 19, 371–381 (1906) (in German), reprinted in English in A. Einstein, Investigations on the Theory of the Brownian Movement (Dover, New York, 1956).
    [Crossref]

1997 (3)

P. O. Hedekvist, M. Karlsson, and P. A. Andrekson, “Fiber four-wave mixing demultiplexing with inherent parametric amplification,” J. Lightwave Technol. 15, 2051–2058 (1997).
[Crossref]

W. Imajuku and A. Takada, “Optical phase-sensitive amplification using two phase-locked light sources,” Electron. Lett. 33, 1403–1404 (1997).
[Crossref]

K. Nakajima, M. Ohashi, and M. Tateda, “Chromatic dispersion distribution along a single-mode optical fiber,” J. Lightwave Technol. 15, 1095–1101 (1997).
[Crossref]

1996 (9)

T. Morioka, H. Takara, S. Kawanishi, T. Kitoh, and M. Saruwatari, “Error-free 500 Gbit/s all optical demultiplexing using low-noise, low-jitter supercontinuum short pulses,” Electron. Lett. 32, 833–834 (1996).
[Crossref]

P. O. Hedekvist, M. Karlsson, and P. A. Andrekson, “Polarization dependence and efficiency in a fiber four-wave mixing phase conjugator with orthogonal pump waves,” IEEE Photonics Technol. Lett. 8, 776–778 (1996).
[Crossref]

P. O. Hedekvist and P. A. Andrekson, “Demonstration of fiber four-wave mixing optical demultiplexing with 19 dB parametric amplification,” Electron. Lett. 32, 830–831 (1996).
[Crossref]

F. Kh. Abdullaev, S. A. Darmanyan, A. Kobyakov, and F. Lederer, “Modulational instability in optical fibers with variable dispersion,” Phys. Lett. A 220, 213–218 (1996).
[Crossref]

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).
[Crossref]

M. E. Marhic, N. Kagi, T.-K. Chiang, and L. G. Kazovsky, “Broadband fiber optical parametric amplifiers,” Opt. Lett. 21, 573–575 (1996).
[Crossref] [PubMed]

M. E. Marhic, Y. Park, F. S. Yang, and L. G. Kazovsky, “Broadband fiber optical parametric amplifiers and wavelength converters with low-ripple Chebyshev gain spectra,” Opt. Lett. 21, 1354–1356 (1996).
[Crossref] [PubMed]

M. E. Marhic, Y. Park, F. S. Yang, and L. G. Kazovsky, “Widely tunable spectrum translation and wavelength exchange by four-wave mixing in optical fibers,” Opt. Lett. 21, 1354–1356 (1996).
[Crossref] [PubMed]

L. F. Mollenauer, P. V. Mamyshev, and M. J. Neubelt, “Method for facile and accurate measurement of optical fiber dispersion maps,” Opt. Lett. 21, 1724–1726 (1996).
[Crossref] [PubMed]

1995 (5)

M. Karlsson, “Modulational instability in lossy optical fibers,” J. Opt. Soc. Am. B 12, 2071–2077 (1995).

R. M. Jopson, M. Eiselt, R. H. Stolen, R. M. Derosier, A. M. Vengsarkar, and U. Koren, “Nondestructive dispersion-zero measurements along an optical fiber,” Electron. Lett. 31, 2115–2117 (1995).
[Crossref]

N. Kagi, T.-K. Chiang, M. E. Marhic, and L. G. Kazovsky, “Fiber optical parametric amplifier operating near zero-dispersion wavelength,” Electron. Lett. 31, 1935–1937 (1995).
[Crossref]

S. Wabnitz, “Nonlinear enhancement and optimization of phase-conjugation efficiency in optical fibers,” IEEE Photonics Technol. Lett. 7, 652–654 (1995).
[Crossref]

S. Nishi and M. Saruwatari, “Technique for measuring the distributed zero dispersion wavelength of optical fibers using pulse amplification caused by modulation instability,” Electron. Lett. 31, 225–226 (1995).
[Crossref]

1994 (7)

H. Onaka, K. Otsuka, H. Miyata, and T. Chikama, “Measuring the longitudinal distribution of four-wave mixing efficiency in dispersion shifted fibers,” IEEE Photonics Technol. Lett. 6, 1454–1456 (1994).
[Crossref]

K. Kikuchi and C. Lorattanasane, “Design of highly efficient four-wave mixing devices using optical fibers,” IEEE Photonics Technol. Lett. 6, 992–994 (1994).
[Crossref]

R.-D. Li, P. Kumar, and W. L. Kath, “Dispersion compensation with phase-sensitive amplifiers,” J. Lightwave Technol. 12, 541–549 (1994).
[Crossref]

T. Morioka, S. Kawanishi, K. Uchiyama, H. Takara, and M. Saruwatari, “Polarization independent 100 Gbit/s all-optical demultiplexer using four-wave mixing in a polarization maintaining fiber loop,” Electron. Lett. 30, 591–592 (1994).
[Crossref]

I. H. Deutsch and I. Abram, “Reduction of quantum noise in soliton propagation by phase-sensitive amplification,” J. Opt. Soc. Am. B 11, 2303–2313 (1994).
[Crossref]

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]

C. G. Goedde, W. L. Kath, and P. Kumar, “Compensation of the soliton self-frequency shift with phase-sensitive amplifiers,” Opt. Lett. 19, 2077–2079 (1994).
[Crossref] [PubMed]

1993 (2)

1992 (2)

P. A. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, and M. Haner, “16 Gbit/s all-optical demultiplexing using four-wave mixing,” Electron. Lett. 27, 922–924 (1992).
[Crossref]

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

1991 (2)

G. J. Foschini and C. D. Poole, “Statistical theory of polarization mode dispersion in single mode fibers,” J. Lightwave Technol. 9, 1439–1456 (1991).
[Crossref]

G. Cappellini and S. Trillo, “Third-order three-wave mixing in single-mode fibers: exact solutions and spatial instability effects,” J. Opt. Soc. Am. B 8, 824–838 (1991).
[Crossref]

1990 (1)

N. Kuwaki and M. Ohashi, “Evaluation of longitudinal chromatic dispersion,” J. Lightwave Technol. 8, 1476–1481 (1990).
[Crossref]

1988 (1)

1987 (1)

1986 (1)

1984 (1)

1982 (2)

C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D 26, 1817–1839 (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]

1979 (1)

1976 (2)

D. Anderson and A. Bondeson, “Parametric wave interactions in random media,” Phys. Scr. 14, 324–328 (1976);“Influence of random inhomogeneities on parametric interactions,” Phys. Scr. 15, 56–58 (1977).
[Crossref]

G. Laval, R. Pellat, and D. Pesme, “Absolute parametric excitation by an imperfect pump or by turbulence in an inhomogeneous plasma,” Phys. Rev. Lett. 36, 192–196 (1976).
[Crossref]

1906 (1)

A. Einstein, “On the theory of Brownian movement,” Ann. Phys. (Leipzig) 19, 371–381 (1906) (in German), reprinted in English in A. Einstein, Investigations on the Theory of the Brownian Movement (Dover, New York, 1956).
[Crossref]

Abdullaev, F. Kh.

F. Kh. Abdullaev, S. A. Darmanyan, A. Kobyakov, and F. Lederer, “Modulational instability in optical fibers with variable dispersion,” Phys. Lett. A 220, 213–218 (1996).
[Crossref]

Abraham, I.

Abram, I.

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995), Chap. 10.

Anderson, D.

D. Anderson and A. Bondeson, “Parametric wave interactions in random media,” Phys. Scr. 14, 324–328 (1976);“Influence of random inhomogeneities on parametric interactions,” Phys. Scr. 15, 56–58 (1977).
[Crossref]

Andrekson, P. A.

P. O. Hedekvist, M. Karlsson, and P. A. Andrekson, “Fiber four-wave mixing demultiplexing with inherent parametric amplification,” J. Lightwave Technol. 15, 2051–2058 (1997).
[Crossref]

P. O. Hedekvist and P. A. Andrekson, “Demonstration of fiber four-wave mixing optical demultiplexing with 19 dB parametric amplification,” Electron. Lett. 32, 830–831 (1996).
[Crossref]

P. O. Hedekvist, M. Karlsson, and P. A. Andrekson, “Polarization dependence and efficiency in a fiber four-wave mixing phase conjugator with orthogonal pump waves,” IEEE Photonics Technol. Lett. 8, 776–778 (1996).
[Crossref]

P. A. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, and M. Haner, “16 Gbit/s all-optical demultiplexing using four-wave mixing,” Electron. Lett. 27, 922–924 (1992).
[Crossref]

Bar-Joseph, I.

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]

Bondeson, A.

D. Anderson and A. Bondeson, “Parametric wave interactions in random media,” Phys. Scr. 14, 324–328 (1976);“Influence of random inhomogeneities on parametric interactions,” Phys. Scr. 15, 56–58 (1977).
[Crossref]

Cappellini, G.

Caves, C. M.

Chiang, T.-K.

M. E. Marhic, N. Kagi, T.-K. Chiang, and L. G. Kazovsky, “Broadband fiber optical parametric amplifiers,” Opt. Lett. 21, 573–575 (1996).
[Crossref] [PubMed]

N. Kagi, T.-K. Chiang, M. E. Marhic, and L. G. Kazovsky, “Fiber optical parametric amplifier operating near zero-dispersion wavelength,” Electron. Lett. 31, 1935–1937 (1995).
[Crossref]

Chikama, T.

H. Onaka, K. Otsuka, H. Miyata, and T. Chikama, “Measuring the longitudinal distribution of four-wave mixing efficiency in dispersion shifted fibers,” IEEE Photonics Technol. Lett. 6, 1454–1456 (1994).
[Crossref]

Crouch, D. D.

Darmanyan, S. A.

F. Kh. Abdullaev, S. A. Darmanyan, A. Kobyakov, and F. Lederer, “Modulational instability in optical fibers with variable dispersion,” Phys. Lett. A 220, 213–218 (1996).
[Crossref]

Derosier, R. M.

R. M. Jopson, M. Eiselt, R. H. Stolen, R. M. Derosier, A. M. Vengsarkar, and U. Koren, “Nondestructive dispersion-zero measurements along an optical fiber,” Electron. Lett. 31, 2115–2117 (1995).
[Crossref]

Deutsch, I. H.

Dijaili, S. P.

Einstein, A.

A. Einstein, “On the theory of Brownian movement,” Ann. Phys. (Leipzig) 19, 371–381 (1906) (in German), reprinted in English in A. Einstein, Investigations on the Theory of the Brownian Movement (Dover, New York, 1956).
[Crossref]

Eiselt, M.

R. M. Jopson, M. Eiselt, R. H. Stolen, R. M. Derosier, A. M. Vengsarkar, and U. Koren, “Nondestructive dispersion-zero measurements along an optical fiber,” Electron. Lett. 31, 2115–2117 (1995).
[Crossref]

Fekete, D.

Foschini, G. J.

G. J. Foschini and C. D. Poole, “Statistical theory of polarization mode dispersion in single mode fibers,” J. Lightwave Technol. 9, 1439–1456 (1991).
[Crossref]

Friesem, A. A.

Goedde, C. G.

Gordon, J. P.

Grangier, Ph.

Haner, M.

P. A. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, and M. Haner, “16 Gbit/s all-optical demultiplexing using four-wave mixing,” Electron. Lett. 27, 922–924 (1992).
[Crossref]

Hasegawa, A.

Hedekvist, P. O.

P. O. Hedekvist, M. Karlsson, and P. A. Andrekson, “Fiber four-wave mixing demultiplexing with inherent parametric amplification,” J. Lightwave Technol. 15, 2051–2058 (1997).
[Crossref]

P. O. Hedekvist and P. A. Andrekson, “Demonstration of fiber four-wave mixing optical demultiplexing with 19 dB parametric amplification,” Electron. Lett. 32, 830–831 (1996).
[Crossref]

P. O. Hedekvist, M. Karlsson, and P. A. Andrekson, “Polarization dependence and efficiency in a fiber four-wave mixing phase conjugator with orthogonal pump waves,” IEEE Photonics Technol. Lett. 8, 776–778 (1996).
[Crossref]

Imajuku, W.

W. Imajuku and A. Takada, “Optical phase-sensitive amplification using two phase-locked light sources,” Electron. Lett. 33, 1403–1404 (1997).
[Crossref]

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]

Islam, M. N.

Jeunhomme, L. B.

L. B. Jeunhomme, Single-Mode Fiber Optics, Principles and Applications, 2nd ed. (Marcel Dekker, New York, 1990), Chap. 4.3.

Jopson, R. M.

R. M. Jopson, M. Eiselt, R. H. Stolen, R. M. Derosier, A. M. Vengsarkar, and U. Koren, “Nondestructive dispersion-zero measurements along an optical fiber,” Electron. Lett. 31, 2115–2117 (1995).
[Crossref]

Kagi, N.

M. E. Marhic, N. Kagi, T.-K. Chiang, and L. G. Kazovsky, “Broadband fiber optical parametric amplifiers,” Opt. Lett. 21, 573–575 (1996).
[Crossref] [PubMed]

N. Kagi, T.-K. Chiang, M. E. Marhic, and L. G. Kazovsky, “Fiber optical parametric amplifier operating near zero-dispersion wavelength,” Electron. Lett. 31, 1935–1937 (1995).
[Crossref]

Karlin, S.

S. Karlin and H. M. Taylor, A Second Course in Stochastic Processes (Academic, New York, 1981), Chap. 15.14.

Karlsson, M.

P. O. Hedekvist, M. Karlsson, and P. A. Andrekson, “Fiber four-wave mixing demultiplexing with inherent parametric amplification,” J. Lightwave Technol. 15, 2051–2058 (1997).
[Crossref]

P. O. Hedekvist, M. Karlsson, and P. A. Andrekson, “Polarization dependence and efficiency in a fiber four-wave mixing phase conjugator with orthogonal pump waves,” IEEE Photonics Technol. Lett. 8, 776–778 (1996).
[Crossref]

M. Karlsson, “Modulational instability in lossy optical fibers,” J. Opt. Soc. Am. B 12, 2071–2077 (1995).

Kath, W. L.

Kawanishi, S.

T. Morioka, H. Takara, S. Kawanishi, T. Kitoh, and M. Saruwatari, “Error-free 500 Gbit/s all optical demultiplexing using low-noise, low-jitter supercontinuum short pulses,” Electron. Lett. 32, 833–834 (1996).
[Crossref]

T. Morioka, S. Kawanishi, K. Uchiyama, H. Takara, and M. Saruwatari, “Polarization independent 100 Gbit/s all-optical demultiplexer using four-wave mixing in a polarization maintaining fiber loop,” Electron. Lett. 30, 591–592 (1994).
[Crossref]

Kazovsky, L. G.

Kikuchi, K.

K. Kikuchi and C. Lorattanasane, “Design of highly efficient four-wave mixing devices using optical fibers,” IEEE Photonics Technol. Lett. 6, 992–994 (1994).
[Crossref]

Kitoh, T.

T. Morioka, H. Takara, S. Kawanishi, T. Kitoh, and M. Saruwatari, “Error-free 500 Gbit/s all optical demultiplexing using low-noise, low-jitter supercontinuum short pulses,” Electron. Lett. 32, 833–834 (1996).
[Crossref]

Kobyakov, A.

F. Kh. Abdullaev, S. A. Darmanyan, A. Kobyakov, and F. Lederer, “Modulational instability in optical fibers with variable dispersion,” Phys. Lett. A 220, 213–218 (1996).
[Crossref]

Koren, U.

R. M. Jopson, M. Eiselt, R. H. Stolen, R. M. Derosier, A. M. Vengsarkar, and U. Koren, “Nondestructive dispersion-zero measurements along an optical fiber,” Electron. Lett. 31, 2115–2117 (1995).
[Crossref]

Kumar, P.

Kutz, J. N.

Kuwaki, N.

N. Kuwaki and M. Ohashi, “Evaluation of longitudinal chromatic dispersion,” J. Lightwave Technol. 8, 1476–1481 (1990).
[Crossref]

Laval, G.

G. Laval, R. Pellat, and D. Pesme, “Absolute parametric excitation by an imperfect pump or by turbulence in an inhomogeneous plasma,” Phys. Rev. Lett. 36, 192–196 (1976).
[Crossref]

Lederer, F.

F. Kh. Abdullaev, S. A. Darmanyan, A. Kobyakov, and F. Lederer, “Modulational instability in optical fibers with variable dispersion,” Phys. Lett. A 220, 213–218 (1996).
[Crossref]

Levenson, J. A.

Li, R.-D.

Logan, R. A.

P. A. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, and M. Haner, “16 Gbit/s all-optical demultiplexing using four-wave mixing,” Electron. Lett. 27, 922–924 (1992).
[Crossref]

Lorattanasane, C.

K. Kikuchi and C. Lorattanasane, “Design of highly efficient four-wave mixing devices using optical fibers,” IEEE Photonics Technol. Lett. 6, 992–994 (1994).
[Crossref]

Mamyshev, P. V.

Marhic, M. E.

Menyuk, C. R.

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).
[Crossref]

Miyata, H.

H. Onaka, K. Otsuka, H. Miyata, and T. Chikama, “Measuring the longitudinal distribution of four-wave mixing efficiency in dispersion shifted fibers,” IEEE Photonics Technol. Lett. 6, 1454–1456 (1994).
[Crossref]

Mollenauer, L. F.

Morioka, T.

T. Morioka, H. Takara, S. Kawanishi, T. Kitoh, and M. Saruwatari, “Error-free 500 Gbit/s all optical demultiplexing using low-noise, low-jitter supercontinuum short pulses,” Electron. Lett. 32, 833–834 (1996).
[Crossref]

T. Morioka, S. Kawanishi, K. Uchiyama, H. Takara, and M. Saruwatari, “Polarization independent 100 Gbit/s all-optical demultiplexer using four-wave mixing in a polarization maintaining fiber loop,” Electron. Lett. 30, 591–592 (1994).
[Crossref]

Nakajima, K.

K. Nakajima, M. Ohashi, and M. Tateda, “Chromatic dispersion distribution along a single-mode optical fiber,” J. Lightwave Technol. 15, 1095–1101 (1997).
[Crossref]

Neubelt, M. J.

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S. Nishi and M. Saruwatari, “Technique for measuring the distributed zero dispersion wavelength of optical fibers using pulse amplification caused by modulation instability,” Electron. Lett. 31, 225–226 (1995).
[Crossref]

Ohashi, M.

K. Nakajima, M. Ohashi, and M. Tateda, “Chromatic dispersion distribution along a single-mode optical fiber,” J. Lightwave Technol. 15, 1095–1101 (1997).
[Crossref]

N. Kuwaki and M. Ohashi, “Evaluation of longitudinal chromatic dispersion,” J. Lightwave Technol. 8, 1476–1481 (1990).
[Crossref]

Olsson, N. A.

P. A. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, and M. Haner, “16 Gbit/s all-optical demultiplexing using four-wave mixing,” Electron. Lett. 27, 922–924 (1992).
[Crossref]

Onaka, H.

H. Onaka, K. Otsuka, H. Miyata, and T. Chikama, “Measuring the longitudinal distribution of four-wave mixing efficiency in dispersion shifted fibers,” IEEE Photonics Technol. Lett. 6, 1454–1456 (1994).
[Crossref]

Otsuka, K.

H. Onaka, K. Otsuka, H. Miyata, and T. Chikama, “Measuring the longitudinal distribution of four-wave mixing efficiency in dispersion shifted fibers,” IEEE Photonics Technol. Lett. 6, 1454–1456 (1994).
[Crossref]

Papoulis, A.

A. Papoulis, Probability, Random Variables and Stochastic Processes, 3rd ed. (McGraw-Hill, New York, 1991), Chap. 11-3.

Park, Y.

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G. Laval, R. Pellat, and D. Pesme, “Absolute parametric excitation by an imperfect pump or by turbulence in an inhomogeneous plasma,” Phys. Rev. Lett. 36, 192–196 (1976).
[Crossref]

Pepper, D. M.

Pesme, D.

G. Laval, R. Pellat, and D. Pesme, “Absolute parametric excitation by an imperfect pump or by turbulence in an inhomogeneous plasma,” Phys. Rev. Lett. 36, 192–196 (1976).
[Crossref]

Poole, C. D.

G. J. Foschini and C. D. Poole, “Statistical theory of polarization mode dispersion in single mode fibers,” J. Lightwave Technol. 9, 1439–1456 (1991).
[Crossref]

Rivera, Th.

Saruwatari, M.

T. Morioka, H. Takara, S. Kawanishi, T. Kitoh, and M. Saruwatari, “Error-free 500 Gbit/s all optical demultiplexing using low-noise, low-jitter supercontinuum short pulses,” Electron. Lett. 32, 833–834 (1996).
[Crossref]

S. Nishi and M. Saruwatari, “Technique for measuring the distributed zero dispersion wavelength of optical fibers using pulse amplification caused by modulation instability,” Electron. Lett. 31, 225–226 (1995).
[Crossref]

T. Morioka, S. Kawanishi, K. Uchiyama, H. Takara, and M. Saruwatari, “Polarization independent 100 Gbit/s all-optical demultiplexer using four-wave mixing in a polarization maintaining fiber loop,” Electron. Lett. 30, 591–592 (1994).
[Crossref]

Simpson, J. R.

P. A. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, and M. Haner, “16 Gbit/s all-optical demultiplexing using four-wave mixing,” Electron. Lett. 27, 922–924 (1992).
[Crossref]

Stolen, R. H.

R. M. Jopson, M. Eiselt, R. H. Stolen, R. M. Derosier, A. M. Vengsarkar, and U. Koren, “Nondestructive dispersion-zero measurements along an optical fiber,” Electron. Lett. 31, 2115–2117 (1995).
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W. Imajuku and A. Takada, “Optical phase-sensitive amplification using two phase-locked light sources,” Electron. Lett. 33, 1403–1404 (1997).
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T. Morioka, H. Takara, S. Kawanishi, T. Kitoh, and M. Saruwatari, “Error-free 500 Gbit/s all optical demultiplexing using low-noise, low-jitter supercontinuum short pulses,” Electron. Lett. 32, 833–834 (1996).
[Crossref]

T. Morioka, S. Kawanishi, K. Uchiyama, H. Takara, and M. Saruwatari, “Polarization independent 100 Gbit/s all-optical demultiplexer using four-wave mixing in a polarization maintaining fiber loop,” Electron. Lett. 30, 591–592 (1994).
[Crossref]

Tanbun-Ek, T.

P. A. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, and M. Haner, “16 Gbit/s all-optical demultiplexing using four-wave mixing,” Electron. Lett. 27, 922–924 (1992).
[Crossref]

Tateda, M.

K. Nakajima, M. Ohashi, and M. Tateda, “Chromatic dispersion distribution along a single-mode optical fiber,” J. Lightwave Technol. 15, 1095–1101 (1997).
[Crossref]

Taylor, H. M.

S. Karlin and H. M. Taylor, A Second Course in Stochastic Processes (Academic, New York, 1981), Chap. 15.14.

Trillo, S.

Uchiyama, K.

T. Morioka, S. Kawanishi, K. Uchiyama, H. Takara, and M. Saruwatari, “Polarization independent 100 Gbit/s all-optical demultiplexer using four-wave mixing in a polarization maintaining fiber loop,” Electron. Lett. 30, 591–592 (1994).
[Crossref]

Vengsarkar, A. M.

R. M. Jopson, M. Eiselt, R. H. Stolen, R. M. Derosier, A. M. Vengsarkar, and U. Koren, “Nondestructive dispersion-zero measurements along an optical fiber,” Electron. Lett. 31, 2115–2117 (1995).
[Crossref]

Waarts, R. G.

Wabnitz, S.

S. Wabnitz, “Nonlinear enhancement and optimization of phase-conjugation efficiency in optical fibers,” IEEE Photonics Technol. Lett. 7, 652–654 (1995).
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Wai, P. K. A.

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).
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Yaffe, H. H.

Yang, F. S.

Yariv, A.

Ann. Phys. (Leipzig) (1)

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Electron. Lett. (8)

N. Kagi, T.-K. Chiang, M. E. Marhic, and L. G. Kazovsky, “Fiber optical parametric amplifier operating near zero-dispersion wavelength,” Electron. Lett. 31, 1935–1937 (1995).
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P. A. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, and M. Haner, “16 Gbit/s all-optical demultiplexing using four-wave mixing,” Electron. Lett. 27, 922–924 (1992).
[Crossref]

P. O. Hedekvist and P. A. Andrekson, “Demonstration of fiber four-wave mixing optical demultiplexing with 19 dB parametric amplification,” Electron. Lett. 32, 830–831 (1996).
[Crossref]

T. Morioka, H. Takara, S. Kawanishi, T. Kitoh, and M. Saruwatari, “Error-free 500 Gbit/s all optical demultiplexing using low-noise, low-jitter supercontinuum short pulses,” Electron. Lett. 32, 833–834 (1996).
[Crossref]

T. Morioka, S. Kawanishi, K. Uchiyama, H. Takara, and M. Saruwatari, “Polarization independent 100 Gbit/s all-optical demultiplexer using four-wave mixing in a polarization maintaining fiber loop,” Electron. Lett. 30, 591–592 (1994).
[Crossref]

W. Imajuku and A. Takada, “Optical phase-sensitive amplification using two phase-locked light sources,” Electron. Lett. 33, 1403–1404 (1997).
[Crossref]

S. Nishi and M. Saruwatari, “Technique for measuring the distributed zero dispersion wavelength of optical fibers using pulse amplification caused by modulation instability,” Electron. Lett. 31, 225–226 (1995).
[Crossref]

R. M. Jopson, M. Eiselt, R. H. Stolen, R. M. Derosier, A. M. Vengsarkar, and U. Koren, “Nondestructive dispersion-zero measurements along an optical fiber,” Electron. Lett. 31, 2115–2117 (1995).
[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, 1062–1072 (1982).
[Crossref]

IEEE Photonics Technol. Lett. (4)

P. O. Hedekvist, M. Karlsson, and P. A. Andrekson, “Polarization dependence and efficiency in a fiber four-wave mixing phase conjugator with orthogonal pump waves,” IEEE Photonics Technol. Lett. 8, 776–778 (1996).
[Crossref]

H. Onaka, K. Otsuka, H. Miyata, and T. Chikama, “Measuring the longitudinal distribution of four-wave mixing efficiency in dispersion shifted fibers,” IEEE Photonics Technol. Lett. 6, 1454–1456 (1994).
[Crossref]

K. Kikuchi and C. Lorattanasane, “Design of highly efficient four-wave mixing devices using optical fibers,” IEEE Photonics Technol. Lett. 6, 992–994 (1994).
[Crossref]

S. Wabnitz, “Nonlinear enhancement and optimization of phase-conjugation efficiency in optical fibers,” IEEE Photonics Technol. Lett. 7, 652–654 (1995).
[Crossref]

J. Lightwave Technol. (7)

K. Nakajima, M. Ohashi, and M. Tateda, “Chromatic dispersion distribution along a single-mode optical fiber,” J. Lightwave Technol. 15, 1095–1101 (1997).
[Crossref]

N. Kuwaki and M. Ohashi, “Evaluation of longitudinal chromatic dispersion,” J. Lightwave Technol. 8, 1476–1481 (1990).
[Crossref]

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

P. O. Hedekvist, M. Karlsson, and P. A. Andrekson, “Fiber four-wave mixing demultiplexing with inherent parametric amplification,” J. Lightwave Technol. 15, 2051–2058 (1997).
[Crossref]

R.-D. Li, P. Kumar, and W. L. Kath, “Dispersion compensation with phase-sensitive amplifiers,” J. Lightwave Technol. 12, 541–549 (1994).
[Crossref]

G. J. Foschini and C. D. Poole, “Statistical theory of polarization mode dispersion in single mode fibers,” J. Lightwave Technol. 9, 1439–1456 (1991).
[Crossref]

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).
[Crossref]

J. Opt. Soc. Am. B (5)

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Phys. Lett. A (1)

F. Kh. Abdullaev, S. A. Darmanyan, A. Kobyakov, and F. Lederer, “Modulational instability in optical fibers with variable dispersion,” Phys. Lett. A 220, 213–218 (1996).
[Crossref]

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C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D 26, 1817–1839 (1982).
[Crossref]

Phys. Rev. Lett. (1)

G. Laval, R. Pellat, and D. Pesme, “Absolute parametric excitation by an imperfect pump or by turbulence in an inhomogeneous plasma,” Phys. Rev. Lett. 36, 192–196 (1976).
[Crossref]

Phys. Scr. (1)

D. Anderson and A. Bondeson, “Parametric wave interactions in random media,” Phys. Scr. 14, 324–328 (1976);“Influence of random inhomogeneities on parametric interactions,” Phys. Scr. 15, 56–58 (1977).
[Crossref]

Other (5)

The effective length is defined as zeff=Lloss[1- exp(-z/Lloss)], where z is the propagation distance and Lloss is the loss length (a fiber loss of 0.2 dB/km corresponds to Lloss=21 km).

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995), Chap. 10.

L. B. Jeunhomme, Single-Mode Fiber Optics, Principles and Applications, 2nd ed. (Marcel Dekker, New York, 1990), Chap. 4.3.

A. Papoulis, Probability, Random Variables and Stochastic Processes, 3rd ed. (McGraw-Hill, New York, 1991), Chap. 11-3.

S. Karlin and H. M. Taylor, A Second Course in Stochastic Processes (Academic, New York, 1981), Chap. 15.14.

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Figures (1)

Fig. 1
Fig. 1

3-dB bandwidth of the parametric gain plotted as a function of propagation distance normalized to the correlation length. Each curve corresponds to a certain value of the variance of the λ0 variation times the correlation length squared, Rλ(0)Lc2, in units of nm2 km2.

Equations (25)

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Δβ=-β3(ωp-ω0)+β42 (ωp-ω0)2+16 (ωp-ωs)2(ωp-ωs)2,
Δβ=κ(λp-λ0)(λs-λp)2,
λ0(z)=λ0con+λ0ran(z),
λ0ran(z)λ0ran(z+ζ)=Rλ(ζ).
Lc=0Rλ(ζ) dζRλ(0),
i ddz Ap+γPpAp=0,
i ddz As+2γPpAs+γAp2Ac* expiΔβdz=0,
i ddz Ac+2γPpAc+γAp2As* expiΔβdz=0.
i ddz As=Δk(z)2 As-γPpAc*,
i ddz Ac=Δk(z)2 Ac-γPpAs*.
dAdz=[G+HW(z)]E,
G=-iΔiγPp-iγPpiΔH=-i00i.
A(z)=exp[Gz+12 H2f(z)]A(0),
f(z)=2 Lc2Ld2 exp-zLc-1+zLc,
A=As0 exp-f(z)2 cosh(zα)-i Δα sinh(zα)-i γPpα sinh(zα),
G=12 1+cosh[g(z)]+f(z)g(z) sinh[g(z)]exp[-f(z)],
Ld22Lc2exp-zLc-1+zLc.
dAsdz=-i[Δ+W(z)]As+i2γAp1Ap2As*,
As=As0 exp-f(z)2[cosh(2γPz)+exp(iϕ)sinh(2γPz)],
G(z, ϕ)=Ps(z)Ps0=exp[-f(z)]cosh[g(z)]+f(z)+4γPz cos(ϕ)g(z) sinh[g(z)],
dudz=[G+HW(z)]u,
Lc=0RW(ζ)dζ/RW(0).
u(z)=exp[Gz+HB(z)]u0,
u(z)=expGz+H22 B2u0.
B2=0zW(z1)dz10zW(z2)dz2=20z(z-ζ)RW(ζ)dζ.

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