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Optics Letters

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  • Editor: Alan E. Willner
  • Vol. 35, Iss. 24 — Dec. 15, 2010
  • pp: 4148–4150

Iterative nonlinear beam propagation using Hamiltonian ray tracing and Wigner distribution function

Hanhong Gao, Lei Tian, Baile Zhang, and George Barbastathis  »View Author Affiliations


Optics Letters, Vol. 35, Issue 24, pp. 4148-4150 (2010)
http://dx.doi.org/10.1364/OL.35.004148


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Abstract

We present an iterative method for simulating beam propagation in nonlinear media using Hamiltonian ray tracing. The Wigner distribution function of the input beam is computed at the entrance plane and is used as the initial condition for solving the Hamiltonian equations. Examples are given for the study of periodic self-focusing, spatial solitons, and Gaussian–Schell model in Kerr-effect media. Simulation results show good agreement with the split-step beam propagation method. The main advantage of ray tracing, even in the nonlinear case, is that ray diagrams are intuitive and easy to interpret in terms of traditional optical engineering terms, such as aberrations, ray-intercept plots, etc.

© 2010 Optical Society of America

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(190.3270) Nonlinear optics : Kerr effect
(080.5692) Geometric optics : Ray trajectories in inhomogeneous media

ToC Category:
Nonlinear Optics

History
Original Manuscript: September 30, 2010
Revised Manuscript: November 11, 2010
Manuscript Accepted: November 12, 2010
Published: December 10, 2010

Citation
Hanhong Gao, Lei Tian, Baile Zhang, and George Barbastathis, "Iterative nonlinear beam propagation using Hamiltonian ray tracing and Wigner distribution function," Opt. Lett. 35, 4148-4150 (2010)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-35-24-4148


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References

  1. G. Agrawal, Nonlinear Fiber Optics, 3rd ed.(Academic, 2001).
  2. H. J. W. M. Hoekstra, Opt. Quantum Electron. 29, 157 (1997). [CrossRef]
  3. M. Soljačić, C. Luo, J. Joannopoulos, and S. Fan, Opt. Lett. 28, 637 (2003). [CrossRef] [PubMed]
  4. J. Bravo-Abad, S. Fan, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, J. Lightwave Technol. 25, 2539 (2007). [CrossRef]
  5. M. Tsang, D. Psaltis, and F. G. Omenetto, Opt. Lett. 28, 1873 (2003). [CrossRef] [PubMed]
  6. O. V. Sinkin, R. Holzlöhner, J. Zweck, and C. R. Menyuk, J. Lightwave Technol. 21, 61 (2003). [CrossRef]
  7. V. V. Shkunov and D. Z. Anderson, Phys. Rev. Lett. 81, 2683 (1998). [CrossRef]
  8. M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Phys. Rev. Lett. 79, 4990 (1997). [CrossRef]
  9. D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997). [CrossRef]
  10. D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, Phys. Rev. E 63, 35601 (2001). [CrossRef]
  11. D. Dragoman, Appl. Opt. 35, 4142 (1996). [CrossRef] [PubMed]
  12. B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, Phys. Rev. E 65, 035602 (2002). [CrossRef]
  13. K. B. Wolf, Geometric Optics on Phase Space (Springer, 2004).
  14. A. Walther, J. Opt. Soc. Am. 58, 1256 (1968). [CrossRef]
  15. E. Wolf, J. Opt. Soc. Am. 68, 6 (1978). [CrossRef]
  16. M. J. Bastiaans, Opt. Acta 26, 1265 (1979). [CrossRef]
  17. M. Alonso, J. Opt. Soc. Am. A 18, 902 (2001). [CrossRef]
  18. M. J. Bastiaans, J. Opt. Soc. Am. A 3, 1227 (1986). [CrossRef]
  19. C. Sun, D. V. Dylov, and J. W. Fleischer, Opt. Lett. 34, 3003 (2009). [CrossRef] [PubMed]
  20. H. Gao, S. Takahashi, L. Tian, and G. Barbastathis, in Optical MEMS and Nanophotonics 2010, Paper Th1-2, pp. 179–180.
  21. Y. Jiao, S. Fan, and D. A. B. Miller, Phys. Rev. E 70, 036612 (2004). [CrossRef]
  22. P. S. J. Russel and T. A. Birks, J. Lightwave Technol. 17, 1982 (1999). [CrossRef]
  23. R. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).
  24. R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964). [CrossRef]
  25. P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965). [CrossRef]
  26. Y. Kivshar and G. Agrawal, Optical Solitons (Academic, 2003).

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