OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 11, Iss. 18 — Sep. 8, 2003
  • pp: 2163–2176

A fast and stable method for Raman amplifier propagation equations

Xueming Liu and Byoungho Lee  »View Author Affiliations


Optics Express, Vol. 11, Issue 18, pp. 2163-2176 (2003)
http://dx.doi.org/10.1364/OE.11.002163


View Full Text Article

Enhanced HTML    Acrobat PDF (394 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A novel predictor-corrector method for the coupled equations for ultrabroad-band Raman amplifiers with multiple pumps is proposed and derived, for the first time, based on the Adams formula. The proposed algorithm is effective in solving Raman amplifier equations that include pumps, signals, noises, and their backscattering waves. The detail procedure is given, and proves the excellence of our algorithm. Simulation results show that, in designing the Raman amplifier, our multistep method can effectively improve the accuracy and stability compared with the one-step method and explicit multistep method. The numerical results show that the power of backscattering pumps and signals is lower by ~30 dB and 20 dB than their original power, respectively, and the power of forward and backward noises is less than that of input signals by ~30 dB under our simulation conditions.

© 2003 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(000.4430) General : Numerical approximation and analysis
(060.2320) Fiber optics and optical communications : Fiber optics amplifiers and oscillators

ToC Category:
Research Papers

History
Original Manuscript: July 22, 2003
Revised Manuscript: August 20, 2003
Published: September 8, 2003

Citation
Xueming Liu and Byoungho Lee, "A fast and stable method for Raman amplifier propagation equations," Opt. Express 11, 2163-2176 (2003)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-18-2163


Sort:  Journal  |  Reset  

References

  1. M. N. Islam, �??Raman amplifiers for telecommunications,�?? IEEE J. Sel. Top. Quantum Electron. 8, 548-559 (2002) [CrossRef]
  2. E. M. Dianov, �??Advances in Raman fibers,�?? J. Lightwave Technol. 20, 1457�??1462 (2002) [CrossRef]
  3. M. Karásek and M. Menif, �??Channel addition/removal response in Raman fiber amplifiers: modeling and experimentation,�?? J. Lightwave Technol. 20, 1680�??1687 (2002) [CrossRef]
  4. A. Carena, V. Curri, and P. Poggiolini, �??On the optimization of hybrid Raman/erbium-doped fiber amplifiers,�?? IEEE Photon. Technol. Lett. 13, 1170-1172 (2001) [CrossRef]
  5. N. Kikuchi, K. K. Wong, K. Uesaka, K. Shimizu, S. Yam, E. S. Hu, M. Marhic, and L. G. Kazovsky, �??Novel in-service wavelength-band upgrade scheme for fiber Raman amplifier,�?? IEEE Photon. Technol. Lett. 15, 27�??29 (2003) [CrossRef]
  6. K. Suto, T. Saito, T. Kimura, J. I. Nishizawa, T. Tanabe, �??Semiconductor Raman amplifier for terahertz bandwidth optical communication,�?? J. Lightwave Technol. 20, 705-711 (2002) [CrossRef]
  7. H. S. Seo, K. Oh, U. C. Paek, �??Gain optimization of germanosilicate fiber Raman amplifier and its applications in the compensation of Raman-induced crosstalk among wavelength division multiplexing channels,�?? IEEE J. Quantum Electron. 37, 1110-1116 (2001). [CrossRef]
  8. B. Cuenot, �??Comparison of engineering scenarios for N x 160 Gb/s WDM transmission systems,�?? IEEE Photon. Technol. Lett. 15, 864-866 (2003). [CrossRef]
  9. A. Pizzinat, M. Santagiustina, C. Schivo, �??Impact of hybrid EDFA-distributed Raman amplification on a 4 x 40-Gb/s WDM optical communication system,�?? IEEE Photon. Technol. Lett. 15, 341-343 (2003). [CrossRef]
  10. V. E. Perlin and H. G. Winful, �??Optimizing the noise performance of broad-band WDM systems with distributed Raman amplification,�?? IEEE Photon. Technol. Lett. 14, 1199-1201 (2002). [CrossRef]
  11. E. Poutrina, G. P. Agrawal, �??Timing jitter in dispersion-managed soliton systems with distributed, lumped, and hybrid amplification,�?? J. Lightwave Technol. 20, 762-769 (2002). [CrossRef]
  12. D. Dahan, G. Eisenstein, �??Numerical comparison between distributed and discrete amplification in a point-to-point 40-gb/s 40-WDM-based transmission system with three different modulation formats,�?? J. Lightwave Technol. 20, 379-388 (2002). [CrossRef]
  13. S. Radic, S. Chandrasekhar, P. Bernasconi, J. Centanni, C. Abraham, N. Copner, K. Tan, �??Feasibility of hybrid Raman/EDFA amplification in bidirectional optical transmission,�?? IEEE Photon. Technol. Lett. 14, 221-223 (2002). [CrossRef]
  14. A. G. Okhrimchuk, G. Onishchukov, E. Lederer, �??Long-haul soliton transmission at 1.3 µm using distributed Raman amplification,�?? J. Lightwave Technol. 19, 837-841 (2001). [CrossRef]
  15. N. Takachio, H. Suzuki, �??Application of Raman-distributed amplification to WDM transmission systems using 1.55-µm dispersion-shifted fiber,�?? J. Lightwave Technol. 19, 60-69 (2001). [CrossRef]
  16. X. Zhou, M. Birk, S. Woodward, �??Pump-noise induced FWM effect and its reduction in a distributed Raman fiber amplifier,�?? IEEE Photon. Technol. Lett. 14,1686-1688 (2002). [CrossRef]
  17. B. Min, P. Kim, N. Park, �??Flat amplitude equal spacing 798-channel Rayleigh-assisted Brillouin/Raman multiwavelength comb generation in dispersion compensating fiber,�?? IEEE Photon. Technol. Lett. 13, 1352-1354 (2001). [CrossRef]
  18. T. Okuno, T. Tsuzaki, M. Nishimura, �??Novel optical hybrid line configuration for quasi-lossless transmission by distributed Raman amplification,�?? IEEE Photon. Technol. Lett. 13, 806-808 (2001). [CrossRef]
  19. L. D. Garrett, M. Eiselt, R. W. Tkach, V. Dominic, R. Waarts, D. Giltner, D. Mehuys, �??Field demonstration of distributed Raman amplification with 3.8-dB Q-improvement for 5 x 120-km transmission,�?? IEEE Photon. Technol. Lett. 13, 157-159 (2001). [CrossRef]
  20. W. S. Wong, C. J. Chen, M. C. Ho, H. K. Lee, �??Phase-matched four-wave mixing between pumps and signals in a copumped Raman amplifier,�?? IEEE Photon. Technol. Lett. 15, 209-211 (2003). [CrossRef]
  21. K. Song, S. D. Dods, �??Cross modulation of pump-signals in distributed Raman amplifiers, theory and experiment,�?? IEEE Photon. Technol. Lett. 13, 1173-1175 (2001). [CrossRef]
  22. H. Kim, R. J. Essiambre, �??Transmission of 8 x 20 Gb/s DQPSK signals over 310-km SMF with 0.8-b/s/Hz spectral efficiency,�?? IEEE Photon. Technol. Lett. 15, 769-771 (2003) . [CrossRef]
  23. K. Toge, K. Hogari, T. Horiguchi, �??Measurement of Raman gain distribution in optical fibers,�?? IEEE Photon. Technol. Lett. 14, 974-976 (2002). [CrossRef]
  24. P. B. Hansen, L. Eskildsen, S. G. Grubb, A. J. Stentz, T. A. Strasser, J. Judkins, J. J. DeMarco, R. Pedrazzani, and D. J. DiGiovanni, �??Capacity upgrades of transmission systems by Raman amplification,�?? IEEE Photon. Technol. Lett. 9, 262�??264 (1997). [CrossRef]
  25. H. Kidorf, K. Rottwitt, M. Nissov, M. Ma, and E. Rabarijaona, �??Pump interactions in a 100-nm bandwidth Raman amplifier,�?? IEEE Photon. Technol. Lett. 11, 530-532 (1999) . [CrossRef]
  26. M. Achtenhagen, G. G. Change, B. Nyman, and A. Hardy, �??Analysis of a multiple-pump Raman amplifier,�?? Appl. Phys. Lett. 78, 1322-1324 (2001). [CrossRef]
  27. X. Zhou, C. Lu, P. Shum, and T. H. Cheng, �??A simplified model and optimal design of a multiwavelength backward-pumped Raman amplifier,�?? IEEE Photon. Technol. Lett. 13, 945�??947 (2001). [CrossRef]
  28. P. C Xiao, Q. J zeng, J. Huang, and J. M. Liu, �??A new optimal algorithm for multipump sources of distributed fiber Raman amplifier,�?? IEEE Photon. Technol. Lett. 15, 206-208 (2003). [CrossRef]
  29. L. Helczynski and A. Berntson, �??Comparison of EDFA and bidirectionally pumped Raman amplifier in a 40-Gb/s Rz transmission system,�?? IEEE Photon. Technol. Lett. 13, 669-671 (2001). [CrossRef]
  30. P. M. Krummrich, R. E. Neuhauser, and C. Glingener, �??Bandwidth limitations of broadband distributed Raman fiber amplifiers for WDM systems,�?? in Optical Fiber Communications Conference 2001, MI3-1, 2001.
  31. Z. M. Liao and G. P. Agrawal, �??Role of distributed amplification in designing high-capacity soliton systems.�?? Opt. Express 9, 66-71 (2001), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-2-66">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-2-66</a>. [CrossRef] [PubMed]
  32. C. Finot, G. Millot, C. Billet, and J. M. Dudley, �??Experimental generation of parabolic pulses via Raman amplification in optical fiber,�?? Opt. Express 11, 1547-1552 (2003), <a href=http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1547>http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1547</a>. [CrossRef] [PubMed]
  33. T. E. Murphy, �??10-GHz 1.3-ps pulse generation using chirped soliton compression in a Raman gain medium,�?? IEEE Photon. Technol. Lett. 14, 1424-1426 (2002). [CrossRef]
  34. M. Nakazawa, �??Rayleigh backscattering theory for single-mode optical fibers,�?? J. Opt. Soc. Amer. 73, 1175-1181 (1983). [CrossRef]
  35. P. B. Hansen, L. Eskildsen, A. J. Stentz, T. A. Strasser, J. Judkins, J. J. DeMarco, R. Pedrazzani, and D. J. DiGiovanni, �??Rayleigh scattering limitations in distributed Raman pre-amplifiers,�?? IEEE Photon. Technol. Lett. 10, 159-161 (1998). [CrossRef]
  36. D. N. Christodoulides and R. B. Jander, �??Evolution of stimulated Raman crosstalk in wavelength division multiplexed systems,�?? IEEE Photon. Technol. Lett. 8, 1722�??1724 (1996). [CrossRef]
  37. C. M. McIntosh, A. G. Grandpierre, D. N. Christodoulides, J. Toulouse and J. M. P. Delavaux, �??Eliminating SRS channel depletion in massive WDM systems via optical filtering techniques,�?? IEEE Photon. Technol. Lett. 13, 302�??304 (2001). [CrossRef]
  38. V. E. Perlin and H. G. Winful, �??Optimal design of flat-gain wide-band fiber Raman amplifiers,�?? J. Lightwave Technol. 20, 250�??254 (2002) . [CrossRef]
  39. X. M Liu, H. Y zhang and Y. L Guo, �??A novel method for Raman amplifier propagation equations,�?? IEEE Photon. Technol. Lett. 15, 392-394 (2003). [CrossRef]
  40. B. Min, W. J. Lee and N. Park, �??Efficient formulation of Raman amplifier propagation equations with average power analysis,�?? IEEE Photon. Technol. Lett. 12, 1486�??1488 (2000). [CrossRef]
  41. X. M Liu and B Lee, �??Effective shooting algorithm and its application to fiber amplifiers,�?? Opt. Express 11, 1452-1461 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-12-1452">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-12-1452</a>. [CrossRef] [PubMed]
  42. P. Kim, J. Park, H. Yoon, J. Park, N. Park, �??In situ design method for multichannel gain of a distributed Raman amplifier with multiwave OTDR,�?? IEEE Photon. Technol. Lett. 14, 1683-1685 (2002). [CrossRef]
  43. M. E. Marhic and D. E. Nikonov, �??Low third-order glass-host nonlinearities in erbium-doped waveguide amplifiers,�?? Proceedings of SPIE, vol. 4645, pp. 193 (2002). [CrossRef]
  44. A. Quarteroni, R. Sacco, and F. Saleri, Numerical Mathematics (Springer-Verlag, New York, 2000).
  45. B. F. Plybon, An Introduction to Applied Numerical Analysis (PWS-KENT Publishing Company, Boston, 1992), pp. 428-441.
  46. J. H. Mathews, Numerical Methods for Mathematics, Science, and Engineering (Second edition, Prentice Hall, New Jersey, 1992), pp. 464-475.
  47. J. D. Faires, R. L. Burden, Numerical method. Boston (PWS-KENT Publishing Company, Boston, 1992), pp. 168-179.
  48. <a href="http://www.nr.com">http://www.nr.com</a>.

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