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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry Van Driel
  • Vol. 26, Iss. 12 — Dec. 1, 2009
  • pp: 2290–2300

Operating regimes, split-step modeling, and the Haus master mode-locking model

Edwin Ding and J. Nathan Kutz  »View Author Affiliations


JOSA B, Vol. 26, Issue 12, pp. 2290-2300 (2009)
http://dx.doi.org/10.1364/JOSAB.26.002290


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Abstract

We develop an iterative (averaging) method to characterize the mode-locking dynamics in a laser cavity mode locked with a combination of wave plates and a passive polarizer. The model explicitly accounts for the effects of self- and cross-phase modulation, an arbitrary alignment of the fast- and slow-axes of the fiber with the wave plates and polarizer, fiber birefringence, saturable gain, and chromatic dispersion. The general averaging scheme results in the cubic-quintic Ginzburg–Landau equation at the leading order and the Swift–Hohenberg equation at the next order. An extensive comparison between the full model and the averaged equations shows a quantitative agreement that allows for characterizing the stability and operating regimes of the laser cavity.

© 2009 Optical Society of America

OCIS Codes
(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons
(140.4050) Lasers and laser optics : Mode-locked lasers

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: June 10, 2009
Revised Manuscript: September 7, 2009
Manuscript Accepted: October 9, 2009
Published: November 11, 2009

Citation
Edwin Ding and J. Nathan Kutz, "Operating regimes, split-step modeling, and the Haus master mode-locking model," J. Opt. Soc. Am. B 26, 2290-2300 (2009)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-26-12-2290


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References

  1. H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron. 6, 1173-1185 (2000). [CrossRef]
  2. J. N. Kutz, “Mode-locked soliton lasers,” SIAM Rev. 48, 629-678 (2006). [CrossRef]
  3. K. Tamura, H. A. Haus, and E. P. Ippen, “Self-starting additive pulse mode-locked erbium fiber ring laser,” Electron. Lett. 28, 2226-2228 (1992). [CrossRef]
  4. H. A. Haus, E. P. Ippen, and K. Tamura, “Additive-pulse mode-locking in fiber lasers,” IEEE J. Quantum Electron. 30, 200-208 (1994). [CrossRef]
  5. M. E. Fermann, M. J. Andrejco, Y. Silberberg, and M. L. Stock, “Passive mode-locking by using nonlinear polarization evolution in a polarizing-maintaining erbium-doped fiber laser,” Opt. Lett. 29, 447-449 (1993).
  6. M. Hofer, M. E. Fermann, F. Haberl, M. H. Ober, and A. J. Schmidt, “Mode locking with cross-phase and self-phase modulation,” Opt. Lett. 16, 502-504 (1991). [CrossRef] [PubMed]
  7. M. Hofer, M. H. Ober, F. Haberl, and M. E. Fermann, “Characterization of ultrashort pulse formation in passively mode-locked fiber lasers,” IEEE J. Quantum Electron. 28, 720-728 (1992). [CrossRef]
  8. H. Leblond, M. Salhi, A. Hideur, T. Chartier, M. Brunel, and F. Sanchez, “Experimental and theoretical study of the passively mode-locked ytterbium-doped double-clad fiber lasers,” Phys. Rev. A 65, 063811 (2002). [CrossRef]
  9. A. Komarov, H. Leblond, and F. Sanchez, “Multistability and hysteresis phenomena in passively mode-locked fiber lasers,” Phys. Rev. A 71, 053809 (2005). [CrossRef]
  10. A. Komarov, H. Leblond, and F. Sanchez, “Quintic complex Ginzburg-Landau model for ring fiber lasers,” Phys. Rev. E 72, 025604 (2005). [CrossRef]
  11. A. Haboucha, H. Leblond, M. Salhi, A. Komarov, and F. Sanchez, “Coherent soliton pattern formation in a fiber laser,” Opt. Lett. 33, 524-526 (2008). [CrossRef] [PubMed]
  12. B. C. Collings, S. T. Cundiff, N. Akhmediev, J. M. Soto-Crespo, K. Bergman, and W. H. Knox, “Polarization locked temporal vector solitons in a fiber laser: experiment,” J. Opt. Soc. Am. B 17, 354-365 (2000). [CrossRef]
  13. D. Y. Tang, W. S. Man, and H. Y. Tam, “Stimulated soliton pulse formation and its mechanism in a passively mode-locked fiber soliton laser,” Opt. Commun. 165, 189-194 (1999). [CrossRef]
  14. D. Y. Tang, L. M. Zhao, B. Zhao, and A. Q. Liu, “Mechanism of multi-soliton formation and soliton energy quantization in passively mode-locked fibre lasers,” Phys. Rev. A 72, 043816 (2005). [CrossRef]
  15. D. Y. Tang, W. S. Man, H. Y. Tam, and P. Drummond, “Observation of bound states of solitons in a passively mode-locked fibre soliton laser,” Phys. Rev. A 64, 033814 (2001). [CrossRef]
  16. A. Chong, J. Buckley, W. Renninger, and F. Wise, “All-normal-dispersion femtosecond fiber laser,” Opt. Express 14, 10095-10100 (2006). [CrossRef] [PubMed]
  17. A. Chong, J. Buckley, W. Renninger, and F. Wise, “Properties of normal-dispersion femtosecond fiber laser,” J. Opt. Soc. Am. B 25, 140-148 (2008). [CrossRef]
  18. W. Renninger, A. Chong, and F. Wise, “Dissipative solitons in normal-dispersion fiber lasers,” Phys. Rev. A 77, 023814 (2008). [CrossRef]
  19. P. E. Langridgea, G. S. McDonald, W. J. Firth, and S. Wabnitz, “Self-sustained mode locking using induced nonlinear birefringence in optical fiber,” Opt. Commun. 97, 178-182 (1993). [CrossRef]
  20. A. Kim, J. N. Kutz, and D. Muraki, “Pulse-train uniformity in optical fiber lasers passively mode-locked by nonlinear polarization rotation,” IEEE J. Quantum Electron. 36, 465-471 (2000). [CrossRef]
  21. K. Spaulding, D. Yong, A. Kim, and J. N. Kutz, “Nonlinear dynamics of mode-locking optical fiber ring lasers,” J. Opt. Soc. Am. B 19, 1045-1054 (2002). [CrossRef]
  22. E. Ding and J. N. Kutz, “Stability analysis of the mode-locking dynamics in a laser cavity with a passive polarizer,” J. Opt. Soc. Am. B 26, 1400-1411 (2009). [CrossRef]
  23. B. Bale, J. N. Kutz, A. Chong, W. Renninger, and F. Wise, “Spectral filtering for ultrafast mode locking in the normal dispersive regime,” Opt. Lett. 33, 941-943 (2008). [CrossRef] [PubMed]
  24. B. Bale, J. N. Kutz, A. Chong, W. Renninger, and F. Wise, “Spectral filtering for high-energy mode locking in normal dispersion fiber lasers,” J. Opt. Soc. Am. B 25, 1763-1770 (2008). [CrossRef]
  25. T. Kapitula, J. N. Kutz, and B. Sandstede, “Stability of pulses in the master-mode locking equation,” J. Opt. Soc. Am. B 19, 740-746 (2002). [CrossRef]
  26. T. Kapitula, J. N. Kutz, and B. Sandstede, “The Evans function for nonlocal equations,” Indiana Univ. Math. J. 53, 1095-1126 (2004). [CrossRef]
  27. G. Strang, “On the construction and comparison of difference schemes,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 5, 506-517 (1968).
  28. N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locking lasers: complex Ginzburg-Landau equation approach,” Phys. Rev. E 63, 056602 (2001). [CrossRef]
  29. J. M. Soto-Crespo and N. Akhmediev, “Composite solitons and two-pulse generation in passively mode-locked lasers modeled by the complex quintic Swift-Hohenberg equation,” Phys. Rev. E 66, 066610 (2002). [CrossRef]
  30. J. M. Soto-Crespo, N. Akhmediev, and K. S. Chiang, “Simultaneous existence of a multiplicity of a stable and unstable solitons in dissipative systems,” Phys. Lett. A 291, 115-123 (2001). [CrossRef]
  31. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic Press, 2001).
  32. C. R. Menyuk, “Pulse propagation in an elliptically birefringent Kerr media,” IEEE J. Quantum Electron. 25, 2674-2682 (1989). [CrossRef]
  33. C. R. Menyuk, “Nonlinear pulse propagation in birefringent optical fibers,” IEEE J. Quantum Electron. 23, 174-176 (1987). [CrossRef]
  34. E. Farnum and J. N. Kutz, “Multi-frequency mode-locked lasers,” J. Opt. Soc. Am. B 25, 1002-1010 (2008). [CrossRef]
  35. A. Gerrard and J. M. Burch, Introduction to Matrix Methods in Optics (Dover, 1994).
  36. B. Bale and J. N. Kutz, “Variational method for mode-locked lasers,” J. Opt. Soc. Am. B 25, 1193-1202 (2008). [CrossRef]
  37. J. M. Soto-Crespo, N. N. Akhmediev, V. V. Afanasjev, and S. Wabnitz, “Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion,” Phys. Rev. E 55, 4783-4796 (1997). [CrossRef]
  38. D. Anderson, M. Lisak, and A. Berntson, “A variational approach to nonlinear evolution equations in optics,” Pramana, J. Phys. 57, 917-936 (2001). [CrossRef]

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