Abstract

The influence of the stimulated Raman scattering in the four-wave mixing process in high birefringent fibers is theoretically analyzed. We consider the dual pump configuration in both co-polarized and orthogonal polarization schemes and treat simultaneously the stimulated Raman scattering and the four-wave mixing processes. The obtained results are valid even when the shift between the pumps and signal lies inside the Raman band. Results show that when the phase-matching condition is achieved the generation of the idler wave is mostly dependent on the real part of the fiber nonlinear response function, whereas the amplification of the signal wave is mostly dependent on the imaginary part. Results also show that when the phase-matching condition is satisfied the optical power evolution of the signal and idler waves for small frequency detunings are mostly described by the anisotropic Raman response of the fiber, whereas for high frequency detunings the isotropic response dominates. Our analysis also shows that the stimulated Raman scattering can increase the efficiency of the four-wave mixing process, for certain frequency detunings.

© 2009 IEEE

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  2. N. Bloembergen, Y. R. Shen, "Coupling between vibrations and light waves in Raman laser media," Physical Review Letters 12, 504-507 (1964).
  3. R. H. Stolen, J. E. Bjorkholm, "Parametric amplication and frequency conversion in optical fibers," IEEE J. Quantum Electron. 18, 1062-1072 (1982).
  4. J. Hanstyd, P. A. Andrekson, M. Westlund, J. Li, P. Hedekvist, "Fiber-based optical parametric amplifiers and their applications," IEEE J. Sel. Topics Quantum Electron. 8, 506-520 (2002).
  5. K. Inoue, H. Toba, "Wavelength conversion experiment using fiber four-wave mixing," IEEE Photon. Technol. Lett. 4, 69-72 (1992).
  6. P. Antunes, P. S. André, A. N. Pinto, "Single-photon source by means of four-wave mixing inside a dispersion-shifted optical fiber," FIO'06—Frontiers in Optics (2006).
  7. H. Takesue, K. Inoue, "Generation of polarization-entangled photon pairs and violation of Bell's inequality using spontaneous four-wave mixing in a fiber loop," Physical Review A 70, 031802- (2004).
  8. M. C. Fugihara, A. N. Pinto, "Low-cost Raman amplifer for CWDM systems," Microwave and Optical Technology Letters 50, 297-301 (2008).
  9. S. Cui, J. Liu, X. Ma, "A novel effcient optimal design method for gain-flattened multiwavelength pumped fiber Raman amplifier," IEEE Photon. Technol. Lett. 16, 2451-2453 (2004).
  10. P.-G. Yan, S.-C. Ruan, C.-Y. Guo, Y.-Q. Yu, L. Li, "Effcient, tunable photonic crystal fiber Raman laser," Microwave and Optical Technology Letters 49, 395-397 (2007).
  11. D. I. Chang, D. S. Lim, M. Y. Jeon, H. K. Lee, K. H. Kim, T. Park, "Dual-wavelength cascaded Raman fibre laser," Electronics Letters 36, 1356-1358 (2000).
  12. F. Vanholsbeeck, P. Emplit, S. Coen, "Complete experimental characterization of the influence of parametric four-wave mixing on stimulated Raman gain," Optics Letters 28, 1960-1962 (2003).
  13. S. Trillo, S. Wabnitz, "Parametric and Raman amplification in birefringent fibers," J. Opt. Soc. Am. B 9, 1061-1082 (1992).
  14. A. S. Y. Hsieh, G. K. L. Wong, S. G. Murdoch, S. Coen, F. Vanhols-beeck, R. Leonhardt, J. D. Harvey, "Combined effect of Raman and parametric gain on single-pump parametric amplifiers," Optics Express 15, 8104-8114 (2007).
  15. A. S. Y. Hsieh, S. G. Murdoch, S. Coen, R. Leonhardt, J. D. Harvey, "Influence of Raman susceptibility on optical parametric amplification in optical fibers," Optics Letters 32, 521-523 (2007).
  16. K. Washio, K. Inoue, S. Kishida, "Effcient large-frequency-shifted three-wave mixing in low dispersion wavelength region in single-mode optical fiber," Electronic Letters 16, 658-660 (1980).
  17. C. Lin, W. A. Reed, A. D. Pearson, H. T. Shang, "Phase matching in the minimum-chromatic-dispersion region of single-mode fibers for stimulated four-photon mixing," Optics Letters 6, 493-495 (1981).
  18. K. P. Hansen, J. R. Jensen, C. Jacobsen, H. R. Simonsen, J. Broeng, P. M. W. Skovgaard, A. Petersson, "Highly nonlinear photonic crystal fiber with zero-dispersion at 1.55 $\mu$m," Conference on Optical Fiber Communication OFC (2002).
  19. J. Hansryd, P. A. Andrekson, "Broad-band continuous-wave-pumped fiber optical parametric amplifier with 49-dB gain and wavelength- conversion efficiency," IEEE Photon. Technol. Lett. 13, 194-196 (2001).
  20. A. Ferrando, M. Zacarés, P. F. de Córdoba, D. Binosi, J. A. Monsoriu, "Spatial soliton formation in photonic crystal fibers," Optics Express 11, 452-459 (2003).
  21. P. A. Andersen, C. Peucheret, K. M. Hilligsøe, K. S. Berg, K. P. Hansen, P. Jeppesen, "Supercontinuum generation in a photonic crystal fiber using picosecond pulses at 1550 nm," 5th International Conference on Transparent Optical Networks: ICTON (2003) pp. 66-69.
  22. A. I. Siahlo, L. K. Oxenløwe, K. S. Berg, A. T. Clausen, P. A. Andersen, C. Peucheret, A. Tersigni, P. Jeppesen, K. P. Hansen, J. R. Folkenberg, "A high-speed demultiplexer based on a nonlinear optical loop mirror with a photonic crystal fiber," IEEE Photon. Technol. Lett. 15, 1147-1149 (2003).
  23. M. Bottacini, F. P. A. Cuciotta, S. Selleri, "Modeling of photonic crystal fiber Raman amplifiers," J. Lightw. Technol. 22, 1707-1713 (2004).
  24. J. E. Sharping, M. Fiorentino, A. Coker, P. Kumar, "Four-wave mixing in a microstructure fiber," Optics Letters 26, 1048-1050 (2001).
  25. F. Biancalana, D. V. Skryabin, P. S. J. Russell, "Four-wave mixing instabilities in photonic-crystal and tapered fibers," Physical Review E 68, 046603- (2003).
  26. K. J. Blow, D. Wood, "Theoretical description of transient stimulated Raman scattering in optical fibers," IEEE J. Quantum Electron. 25, 2665-2673 (1989).
  27. Y. Chen, "Combined processess of stimulated Raman scattering and four-wave mixing in optical fibers," J. Opt. Soc. Am. B 7, 43-52 (1990).
  28. E. A. Golovchenko, A. N. Pilipetskii, "Undified analysis of four-photon mixing, modulational instability, and stimulated Raman scattering under various polarization conditions in fibers," J. Opt. Soc. Am. B 11, 92-101 (1994).
  29. E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, E. M. Dianov, "Mutual influence of the parametric effects and stimulated scattering in optical fibers," IEEE J. Quantum Electron. 26, 1815-1820 (1990).
  30. P. V. Mamyshev, S. V. Chernikov, "Ultrashort-pulse propagation in optical fibers," Optics Letters 15, 1076-1078 (1990).
  31. R. W. Hellwarth, "Third-order optical susceptibilities of liquids and solids," Prog. Quant. Electron. 5, 1-68 (1977).
  32. Q. Lin, F. Yaman, G. P. Agrawal, "Photon-pair generation in optical fibers through four-wave mixing: Role of Raman scattering and pump polarization," Physical Review A 75, 023803- (2007).
  33. Q. Lin, G. P. Agrawal, "Raman response function for silica fibers," Optics Letters 31, 2086-3088 (2006).
  34. C. Headley, G. P. Agrawal, Raman Amplification in Fiber Optical Communication Systems (Academic Press, 2005).
  35. Q. Lin, 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).
  36. J. R. Thompson, R. Roy, "Multiple four-wave mixing process in an optical fiber," Optics Letters 16, 557-559 (1991).
  37. J. R. Thompson, R. Roy, "Nonlinear dynamics of multiple four-wave mixing processes in a single-mode fiber," Physical Review A 43, 4987-4996 (1991).
  38. X. M. Liu, "Theory and experiments for multiple four-wave-mixing processes with multifrequency pumps in optical fibers," Physical Review A 77, 043818- (2008).
  39. Q. Lin, F. Yaman, G. P. Agrawal, "Photon-pair generation by four-wave mixing in optical fibers," Optics Letters 31, 1286-1288 (2006).
  40. R. H. Stolen, M. A. Bösch, C. Lin, "Phase matching in birefringent fibers," Optics Letters 6, 213-215 (1981).
  41. E. Lantz, D. Gindre, H. Maillotte, J. Monneret, "Phase matching for parametric amplification in a single mode birefringent fiber: Influence of non-phase-matched waves," J. Opt. Soc. Am. B 14, 116-125 (1997).

2008 (2)

M. C. Fugihara, A. N. Pinto, "Low-cost Raman amplifer for CWDM systems," Microwave and Optical Technology Letters 50, 297-301 (2008).

X. M. Liu, "Theory and experiments for multiple four-wave-mixing processes with multifrequency pumps in optical fibers," Physical Review A 77, 043818- (2008).

2007 (4)

Q. Lin, F. Yaman, G. P. Agrawal, "Photon-pair generation in optical fibers through four-wave mixing: Role of Raman scattering and pump polarization," Physical Review A 75, 023803- (2007).

P.-G. Yan, S.-C. Ruan, C.-Y. Guo, Y.-Q. Yu, L. Li, "Effcient, tunable photonic crystal fiber Raman laser," Microwave and Optical Technology Letters 49, 395-397 (2007).

A. S. Y. Hsieh, G. K. L. Wong, S. G. Murdoch, S. Coen, F. Vanhols-beeck, R. Leonhardt, J. D. Harvey, "Combined effect of Raman and parametric gain on single-pump parametric amplifiers," Optics Express 15, 8104-8114 (2007).

A. S. Y. Hsieh, S. G. Murdoch, S. Coen, R. Leonhardt, J. D. Harvey, "Influence of Raman susceptibility on optical parametric amplification in optical fibers," Optics Letters 32, 521-523 (2007).

2006 (2)

Q. Lin, G. P. Agrawal, "Raman response function for silica fibers," Optics Letters 31, 2086-3088 (2006).

Q. Lin, F. Yaman, G. P. Agrawal, "Photon-pair generation by four-wave mixing in optical fibers," Optics Letters 31, 1286-1288 (2006).

2004 (4)

Q. Lin, 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).

M. Bottacini, F. P. A. Cuciotta, S. Selleri, "Modeling of photonic crystal fiber Raman amplifiers," J. Lightw. Technol. 22, 1707-1713 (2004).

H. Takesue, K. Inoue, "Generation of polarization-entangled photon pairs and violation of Bell's inequality using spontaneous four-wave mixing in a fiber loop," Physical Review A 70, 031802- (2004).

S. Cui, J. Liu, X. Ma, "A novel effcient optimal design method for gain-flattened multiwavelength pumped fiber Raman amplifier," IEEE Photon. Technol. Lett. 16, 2451-2453 (2004).

2003 (4)

A. Ferrando, M. Zacarés, P. F. de Córdoba, D. Binosi, J. A. Monsoriu, "Spatial soliton formation in photonic crystal fibers," Optics Express 11, 452-459 (2003).

A. I. Siahlo, L. K. Oxenløwe, K. S. Berg, A. T. Clausen, P. A. Andersen, C. Peucheret, A. Tersigni, P. Jeppesen, K. P. Hansen, J. R. Folkenberg, "A high-speed demultiplexer based on a nonlinear optical loop mirror with a photonic crystal fiber," IEEE Photon. Technol. Lett. 15, 1147-1149 (2003).

F. Vanholsbeeck, P. Emplit, S. Coen, "Complete experimental characterization of the influence of parametric four-wave mixing on stimulated Raman gain," Optics Letters 28, 1960-1962 (2003).

F. Biancalana, D. V. Skryabin, P. S. J. Russell, "Four-wave mixing instabilities in photonic-crystal and tapered fibers," Physical Review E 68, 046603- (2003).

2002 (1)

J. Hanstyd, P. A. Andrekson, M. Westlund, J. Li, P. Hedekvist, "Fiber-based optical parametric amplifiers and their applications," IEEE J. Sel. Topics Quantum Electron. 8, 506-520 (2002).

2001 (2)

J. E. Sharping, M. Fiorentino, A. Coker, P. Kumar, "Four-wave mixing in a microstructure fiber," Optics Letters 26, 1048-1050 (2001).

J. Hansryd, P. A. Andrekson, "Broad-band continuous-wave-pumped fiber optical parametric amplifier with 49-dB gain and wavelength- conversion efficiency," IEEE Photon. Technol. Lett. 13, 194-196 (2001).

2000 (1)

D. I. Chang, D. S. Lim, M. Y. Jeon, H. K. Lee, K. H. Kim, T. Park, "Dual-wavelength cascaded Raman fibre laser," Electronics Letters 36, 1356-1358 (2000).

1997 (1)

1994 (1)

1992 (2)

K. Inoue, H. Toba, "Wavelength conversion experiment using fiber four-wave mixing," IEEE Photon. Technol. Lett. 4, 69-72 (1992).

S. Trillo, S. Wabnitz, "Parametric and Raman amplification in birefringent fibers," J. Opt. Soc. Am. B 9, 1061-1082 (1992).

1991 (2)

J. R. Thompson, R. Roy, "Multiple four-wave mixing process in an optical fiber," Optics Letters 16, 557-559 (1991).

J. R. Thompson, R. Roy, "Nonlinear dynamics of multiple four-wave mixing processes in a single-mode fiber," Physical Review A 43, 4987-4996 (1991).

1990 (3)

Y. Chen, "Combined processess of stimulated Raman scattering and four-wave mixing in optical fibers," J. Opt. Soc. Am. B 7, 43-52 (1990).

E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, E. M. Dianov, "Mutual influence of the parametric effects and stimulated scattering in optical fibers," IEEE J. Quantum Electron. 26, 1815-1820 (1990).

P. V. Mamyshev, S. V. Chernikov, "Ultrashort-pulse propagation in optical fibers," Optics Letters 15, 1076-1078 (1990).

1989 (1)

K. J. Blow, D. Wood, "Theoretical description of transient stimulated Raman scattering in optical fibers," IEEE J. Quantum Electron. 25, 2665-2673 (1989).

1982 (1)

R. H. Stolen, J. E. Bjorkholm, "Parametric amplication and frequency conversion in optical fibers," IEEE J. Quantum Electron. 18, 1062-1072 (1982).

1981 (2)

C. Lin, W. A. Reed, A. D. Pearson, H. T. Shang, "Phase matching in the minimum-chromatic-dispersion region of single-mode fibers for stimulated four-photon mixing," Optics Letters 6, 493-495 (1981).

R. H. Stolen, M. A. Bösch, C. Lin, "Phase matching in birefringent fibers," Optics Letters 6, 213-215 (1981).

1980 (1)

K. Washio, K. Inoue, S. Kishida, "Effcient large-frequency-shifted three-wave mixing in low dispersion wavelength region in single-mode optical fiber," Electronic Letters 16, 658-660 (1980).

1977 (1)

R. W. Hellwarth, "Third-order optical susceptibilities of liquids and solids," Prog. Quant. Electron. 5, 1-68 (1977).

1964 (1)

N. Bloembergen, Y. R. Shen, "Coupling between vibrations and light waves in Raman laser media," Physical Review Letters 12, 504-507 (1964).

Electronic Letters (1)

K. Washio, K. Inoue, S. Kishida, "Effcient large-frequency-shifted three-wave mixing in low dispersion wavelength region in single-mode optical fiber," Electronic Letters 16, 658-660 (1980).

Electronics Letters (1)

D. I. Chang, D. S. Lim, M. Y. Jeon, H. K. Lee, K. H. Kim, T. Park, "Dual-wavelength cascaded Raman fibre laser," Electronics Letters 36, 1356-1358 (2000).

IEEE J. Quantum Electron. (3)

R. H. Stolen, J. E. Bjorkholm, "Parametric amplication and frequency conversion in optical fibers," IEEE J. Quantum Electron. 18, 1062-1072 (1982).

K. J. Blow, D. Wood, "Theoretical description of transient stimulated Raman scattering in optical fibers," IEEE J. Quantum Electron. 25, 2665-2673 (1989).

E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, E. M. Dianov, "Mutual influence of the parametric effects and stimulated scattering in optical fibers," IEEE J. Quantum Electron. 26, 1815-1820 (1990).

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

J. Hanstyd, P. A. Andrekson, M. Westlund, J. Li, P. Hedekvist, "Fiber-based optical parametric amplifiers and their applications," IEEE J. Sel. Topics Quantum Electron. 8, 506-520 (2002).

IEEE Photon. Technol. Lett. (4)

K. Inoue, H. Toba, "Wavelength conversion experiment using fiber four-wave mixing," IEEE Photon. Technol. Lett. 4, 69-72 (1992).

S. Cui, J. Liu, X. Ma, "A novel effcient optimal design method for gain-flattened multiwavelength pumped fiber Raman amplifier," IEEE Photon. Technol. Lett. 16, 2451-2453 (2004).

J. Hansryd, P. A. Andrekson, "Broad-band continuous-wave-pumped fiber optical parametric amplifier with 49-dB gain and wavelength- conversion efficiency," IEEE Photon. Technol. Lett. 13, 194-196 (2001).

A. I. Siahlo, L. K. Oxenløwe, K. S. Berg, A. T. Clausen, P. A. Andersen, C. Peucheret, A. Tersigni, P. Jeppesen, K. P. Hansen, J. R. Folkenberg, "A high-speed demultiplexer based on a nonlinear optical loop mirror with a photonic crystal fiber," IEEE Photon. Technol. Lett. 15, 1147-1149 (2003).

J. Lightw. Technol. (1)

M. Bottacini, F. P. A. Cuciotta, S. Selleri, "Modeling of photonic crystal fiber Raman amplifiers," J. Lightw. Technol. 22, 1707-1713 (2004).

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

Microwave and Optical Technology Letters (2)

P.-G. Yan, S.-C. Ruan, C.-Y. Guo, Y.-Q. Yu, L. Li, "Effcient, tunable photonic crystal fiber Raman laser," Microwave and Optical Technology Letters 49, 395-397 (2007).

M. C. Fugihara, A. N. Pinto, "Low-cost Raman amplifer for CWDM systems," Microwave and Optical Technology Letters 50, 297-301 (2008).

Optics Express (2)

A. S. Y. Hsieh, G. K. L. Wong, S. G. Murdoch, S. Coen, F. Vanhols-beeck, R. Leonhardt, J. D. Harvey, "Combined effect of Raman and parametric gain on single-pump parametric amplifiers," Optics Express 15, 8104-8114 (2007).

A. Ferrando, M. Zacarés, P. F. de Córdoba, D. Binosi, J. A. Monsoriu, "Spatial soliton formation in photonic crystal fibers," Optics Express 11, 452-459 (2003).

Optics Letters (9)

J. E. Sharping, M. Fiorentino, A. Coker, P. Kumar, "Four-wave mixing in a microstructure fiber," Optics Letters 26, 1048-1050 (2001).

J. R. Thompson, R. Roy, "Multiple four-wave mixing process in an optical fiber," Optics Letters 16, 557-559 (1991).

P. V. Mamyshev, S. V. Chernikov, "Ultrashort-pulse propagation in optical fibers," Optics Letters 15, 1076-1078 (1990).

Q. Lin, G. P. Agrawal, "Raman response function for silica fibers," Optics Letters 31, 2086-3088 (2006).

A. S. Y. Hsieh, S. G. Murdoch, S. Coen, R. Leonhardt, J. D. Harvey, "Influence of Raman susceptibility on optical parametric amplification in optical fibers," Optics Letters 32, 521-523 (2007).

C. Lin, W. A. Reed, A. D. Pearson, H. T. Shang, "Phase matching in the minimum-chromatic-dispersion region of single-mode fibers for stimulated four-photon mixing," Optics Letters 6, 493-495 (1981).

F. Vanholsbeeck, P. Emplit, S. Coen, "Complete experimental characterization of the influence of parametric four-wave mixing on stimulated Raman gain," Optics Letters 28, 1960-1962 (2003).

Q. Lin, F. Yaman, G. P. Agrawal, "Photon-pair generation by four-wave mixing in optical fibers," Optics Letters 31, 1286-1288 (2006).

R. H. Stolen, M. A. Bösch, C. Lin, "Phase matching in birefringent fibers," Optics Letters 6, 213-215 (1981).

Physical Review A (4)

Q. Lin, F. Yaman, G. P. Agrawal, "Photon-pair generation in optical fibers through four-wave mixing: Role of Raman scattering and pump polarization," Physical Review A 75, 023803- (2007).

H. Takesue, K. Inoue, "Generation of polarization-entangled photon pairs and violation of Bell's inequality using spontaneous four-wave mixing in a fiber loop," Physical Review A 70, 031802- (2004).

J. R. Thompson, R. Roy, "Nonlinear dynamics of multiple four-wave mixing processes in a single-mode fiber," Physical Review A 43, 4987-4996 (1991).

X. M. Liu, "Theory and experiments for multiple four-wave-mixing processes with multifrequency pumps in optical fibers," Physical Review A 77, 043818- (2008).

Physical Review E (1)

F. Biancalana, D. V. Skryabin, P. S. J. Russell, "Four-wave mixing instabilities in photonic-crystal and tapered fibers," Physical Review E 68, 046603- (2003).

Physical Review Letters (1)

N. Bloembergen, Y. R. Shen, "Coupling between vibrations and light waves in Raman laser media," Physical Review Letters 12, 504-507 (1964).

Prog. Quant. Electron. (1)

R. W. Hellwarth, "Third-order optical susceptibilities of liquids and solids," Prog. Quant. Electron. 5, 1-68 (1977).

Other (5)

C. Headley, G. P. Agrawal, Raman Amplification in Fiber Optical Communication Systems (Academic Press, 2005).

P. A. Andersen, C. Peucheret, K. M. Hilligsøe, K. S. Berg, K. P. Hansen, P. Jeppesen, "Supercontinuum generation in a photonic crystal fiber using picosecond pulses at 1550 nm," 5th International Conference on Transparent Optical Networks: ICTON (2003) pp. 66-69.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001).

P. Antunes, P. S. André, A. N. Pinto, "Single-photon source by means of four-wave mixing inside a dispersion-shifted optical fiber," FIO'06—Frontiers in Optics (2006).

K. P. Hansen, J. R. Jensen, C. Jacobsen, H. R. Simonsen, J. Broeng, P. M. W. Skovgaard, A. Petersson, "Highly nonlinear photonic crystal fiber with zero-dispersion at 1.55 $\mu$m," Conference on Optical Fiber Communication OFC (2002).

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