OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 12, Iss. 10 — May. 17, 2004
  • pp: 2033–2055

Four-wave mixing in fibers with random birefringence

C. J. McKinstrie, H. Kogelnik, R. M. Jopson, S. Radic, and A. V. Kanaev  »View Author Affiliations


Optics Express, Vol. 12, Issue 10, pp. 2033-2055 (2004)
http://dx.doi.org/10.1364/OPEX.12.002033


View Full Text Article

Enhanced HTML    Acrobat PDF (252 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Parametric amplification is made possible by four-wave mixing. In low-birefringence fibers the birefringence axes and strength vary randomly with distance. Light-wave propagation in such fibers is governed by the Manakov equation. In this paper the Manakov equation is used to study degenerate and nondegenerate four-wave mixing. The effects of linear and nonlinear wavenumber mismatches, and nonlinear polarization rotation, are included in the analysis. Formulas are derived for the initial quadratic growth of the idler power, and the subsequent exponential growth of the signal and idler powers (which continues until pump depletion occurs). These formulas are valid for arbitrary pump and signal polarizations.

© 2004 Optical Society of America

OCIS Codes
(060.2320) Fiber optics and optical communications : Fiber optics amplifiers and oscillators
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.5040) Nonlinear optics : Phase conjugation

ToC Category:
Research Papers

History
Original Manuscript: February 13, 2004
Revised Manuscript: April 28, 2004
Published: May 17, 2004

Citation
C. McKinstrie, H. Kogelnik, R. Jopson, S. Radic, and A. Kanaev, "Four-wave mixing in fibers with random birefringence," Opt. Express 12, 2033-2055 (2004)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-10-2033


Sort:  Journal  |  Reset  

References

  1. K. O. Hill, D. C. Johnson, B. S. Kawasaki and R. I. MacDonald, �??CW three-wave mixing in single-mode optical fibers,�?? J. Appl. Phys. 49, 5098�??5106 (1978). [CrossRef]
  2. R. H. Stolen and J. E. Bjorkholm, �??Parametric amplification and frequency conversion in optical fibers,�?? IEEE J. Quantum Electron. 18, 1062�??1072 (1982). [CrossRef]
  3. J. Hansryd and P. A. Andrekson, �??Broadband continuous-wave pumped fiber optical parametric amplifier with 49-dB gain and wavelength-conversion efficiency,�?? IEEE Photon. Technol. Lett. 13, 194�??196 (2001). [CrossRef]
  4. S. Radic, C. J.McKinstrie, A. R. Chraplyvy, G. Raybon, J. C. Centanni, C. G. Jorgensen, K. Brar and C. Headley, �??Continuous-wave parametric-gain synthesis using nondegenerate-pump four-wave mixing,�?? IEEE Photon. Technol. Lett. 14, 1406�??1408 (2002). [CrossRef]
  5. 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, 506�??520 (2002) and references therein. [CrossRef]
  6. C. J. McKinstrie, S. Radic and A. R. Chraplyvy, �??Parametric amplifiers driven by two pump waves,�?? IEEE J. Sel. Top. Quantum Electron. 8, 538�??547 and 956 (2002) and references therein. [CrossRef]
  7. C. J. McKinstrie, S. Radic and C. Xie, �??Parametric instabilities driven by orthogonal pump waves in birefringent fibers,�?? Opt. Express. 11, 2619�??2633 (2003) and references therein [CrossRef] [PubMed]
  8. C. J. McKinstrie, S. Radic and C. Xie, �??Phase conjugation driven by orthogonal pump waves in birefringent fibers,�?? J. Opt. Soc. Am. B 20, 1437�??1446 (2003). [CrossRef]
  9. K. Inoue, �??Polarization effect on four-wave mixing efficiency in a single-mode fiber,�?? IEEE J. Quantum Electron. 28, 883�??894 (1992). [CrossRef]
  10. R.M. Jopson and R. E. Tench, �??Polarisation-independent phase conjugation of lightwave signals,�?? Electron. Lett. 29, 2216�??2217 (1993). [CrossRef]
  11. K. Inoue, �??Polarization independent wavelength conversion using fiber four-wave mixing with two orthogonal pump lights of different frequencies,�?? J. Lightwave Technol. 12, 1916�??1920 (1994). [CrossRef]
  12. K. K. Y. Wong, M. E. Marhic, K. Uesaka and L. G. Kazovsky, �??Polarization-independent two-pump fiber optical parametric amplifier,�?? IEEE Photon. Technol. Lett. 14, 911�??913 (2002). [CrossRef]
  13. S. Radic, C. J. McKinstrie, R. M. Jopson, Q. Lin and G. P. Agrawal, �??Record performance of a parametric amplifier constructed with highly-nonlinear fiber,�?? Electron. Lett. 39, 838�??839 (2003). [CrossRef]
  14. T. Tanemura and K. Kikuchi, �??Polarization-independent broad-band wavelength conversion using two-pump fiber optical parametric amplification without idler spectral broadening,�?? IEEE Photon. Technol. Lett. 15, 1573�??1575 (2003). [CrossRef]
  15. S. Radic, C. J. McKinstrie, R. Jopson, C. Jorgensen, K. Brar and C. Headley, �??Polarization-dependent parametric gain in amplifiers with orthogonally multiplexed pumps, Optical Fiber Communication conference, Atlanta, Georgia, 23�??28 March 2003, paper ThK3.
  16. S. V. Manakov, �??On the theory of two-dimensional stationary self-focusing of electromagnetic waves,�?? Sov. Phys. JETP 38, 248�??253 (1974).
  17. C. R. Menyuk, �??Nonlinear pulse propagation in birefringent optical fibers,�?? IEEE J. Quantum Electron. 23, 174�??176 (1987). [CrossRef]
  18. P. K. A. Wai, C. R. Menyuk and H. H. Chen, �??Stability of solitons in randomly varying birefringent fibers,�?? Opt. Lett. 16, 1231�??1233 (1991). [CrossRef] [PubMed]
  19. S. G. Evanglides, L. F. Mollenauer, J. P. Gordon and N. S. Bergano, �??Polarization multiplexing with solitons,�?? J. Lightwave Technol., 10, 28�??35 (1992). [CrossRef]
  20. 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]
  21. T. I. Lakoba, �??Concerning the equations governing nonlinear pulse propagation in randomly birefringent fibers,�?? J. Opt. Soc. Am. B 13, 2006�??2011 (1996). [CrossRef]
  22. H. Kogelnik, R. M. Jopson and L. E. Nelson, �??Polarization-mode dispersion,�?? in Optical Fiber Telecommunications IVB, edited by I. P. Kaminow and T. Li (Academic, San Diego, 2002), pp. 725�??861.
  23. M. Karlsson, J. Brentel and P. A. Andrekson, �??Long-term measurement of PMD and polarization drift in installed fibers,�?? J. Lightwave Technol. 18, 941�??951 (2000). [CrossRef]
  24. J. P. Gordon and H. Kogelnik, �??PMD fundamentals: Polarization mode dispersion in optical fibers,�?? Proc. Nat. Acad. Sci. 97, 4541�??4550 (2000). [CrossRef] [PubMed]
  25. L. F. Mollenauer, J. P. Gordon and F. Heismann, �??Polarization scattering by soliton�??soliton collisions,�?? Opt. Lett. 20, 2060�??2062 (1995). [CrossRef] [PubMed]
  26. D. Wang and C. R. Menyuk, �??Reduced model of the evolution of the polarization states in wavelength-division-multiplexed channels,�?? Opt. Lett. 23, 1677�??1679 (1998). [CrossRef]
  27. R. W. Boyd, Nonlinear Optics (Academic, San Diego, 1992), Sections 1.4, 2.3 and 6.5.
  28. J.M.Manley and H. E. Rowe, �??Some general properties of nonlinear elements�??Part I. General energy relations,�?? Proc. IRE 44, 904�??913 (1956). [CrossRef]
  29. M. T. Weiss, �??Quantum derivation of energy relations analogous to those for nonlinear reactances,�?? Proc. IRE 45, 1012�??1013 (1957).
  30. M. Yu, C. J. McKinstrie and G. P. Agrawal, �??Instability due to cross-phase modulation in the normal dispersion regime,�?? Phys. Rev. E 48, 2178�??2186 (1993). [CrossRef]
  31. C. J. McKinstrie, X. D. Cao and J. S. Li, �??Nonlinear detuning of four-wave interactions,�?? J. Opt. Soc. Am. B 10, 1856�??1869 (1993) and references therein. [CrossRef]
  32. A. Carena, V. Curri, R. Gaudino, P. Poggiolini and S. Benedetto, �??On the joint effects of fiber parametric gain and birefringence and their influence on ASE noise,�?? J. Lightwave Technol. 16, 1149�??1157 (1998). [CrossRef]
  33. Q. Lin and G. P. Agrawal, �??Effects of polarization-mode dispersion on fiber-based parametric amplification and wavelength conversion,�?? Annual Meeting of the Optical Society of America, Tucson, Arizona, 5�??9 October 2003, paper TuP3.
  34. K. Inoue, �??Tunable and selective wavelength conversion using fiber four-wave mixing with two pump lights,�?? IEEE Photon. Technol. Lett. 6, 1451�??1453 (1994). [CrossRef]
  35. T. Tanemura, C. S. Goh, K. Kikuchi and S. Y. Set, �??Widely tunable wavelength conversion using nondegenerate fiber four-wave mixing driven by co-modulated pump waves,�?? European Conference on Optical Communications, Rimini, Italy, 21�??25 September 2003, paper We3.7.3.
  36. G. G. Luther and C. J. McKinstrie, �??Transverse modulational instability of counterpropagating waves,�?? J. Opt.Soc. Am. B 9, 1047�??1061 (1992). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited