OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 27, Iss. 6 — Jun. 1, 2010
  • pp: 1424–1431

More on the iteration of the beam propagation method for analyzing Bragg gratings

Hong Shu  »View Author Affiliations


JOSA A, Vol. 27, Issue 6, pp. 1424-1431 (2010)
http://dx.doi.org/10.1364/JOSAA.27.001424


View Full Text Article

Enhanced HTML    Acrobat PDF (206 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The mathematical foundation of the iteration of the beam propagation method is described in this paper. Detailed analytical analyses are presented. These analyses explain further how the iteration of the beam propagation method works, and provide the reason why it works. Some additional comments are also presented on the formulation and practical implementation in analyzing Bragg gratings in different situations.

© 2010 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(000.4430) General : Numerical approximation and analysis
(050.7330) Diffraction and gratings : Volume gratings
(090.7330) Holography : Volume gratings
(230.7370) Optical devices : Waveguides
(050.1755) Diffraction and gratings : Computational electromagnetic methods

ToC Category:
Diffraction and Gratings

History
Original Manuscript: March 8, 2010
Revised Manuscript: April 16, 2010
Manuscript Accepted: April 17, 2010
Published: May 21, 2010

Citation
Hong Shu, "More on the iteration of the beam propagation method for analyzing Bragg gratings," J. Opt. Soc. Am. A 27, 1424-1431 (2010)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-6-1424


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
  2. J. A. Kong, “Second-order coupled-mode equations for spatially periodic media,” J. Opt. Soc. Am. 67, 825–829 (1977). [CrossRef]
  3. M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Bragg diffraction of finite beams by thick gratings,” J. Opt. Soc. Am. 70, 300–304 (1980). [CrossRef]
  4. T. K. Gaylord and M. G. Moharam, “Analysis and application of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985). [CrossRef]
  5. A. Yariv and M. Nakamura, “Periodic structures for integrated optics,” IEEE J. Quantum Electron. 13, 233–253 (1977). [CrossRef]
  6. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997). [CrossRef]
  7. K. O. Hill, “Aperiodic distributed-parameter waveguides for integrated optics,” Appl. Opt. 13, 1853–1856 (1974). [CrossRef] [PubMed]
  8. H. Kogelnik, “Filter response of nonuniform almost-periodic structures,” Bell Syst. Tech. J. 55, 109–126 (1976).
  9. H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43, 2327–2335 (1972). [CrossRef]
  10. G. P. Agrawal and A. H. Bobeck, “Modeling of distributed feedback semiconductor lasers with axially-varying parameters,” IEEE J. Quantum Electron. 24, 2407–2414 (1988). [CrossRef]
  11. M. Yamada and K. Sakuda, “Analysis of almost-periodic distributed feedback slab waveguides via a fundamental matrix approach,” Appl. Opt. 26, 3474–3478 (1987). [CrossRef] [PubMed]
  12. S. Huang, M. LeBlanc, M. M. Ohn, and R. M. Measures, “Bragg intragrating structural sensing,” Appl. Opt. 34, 5003–5009 (1995). [CrossRef] [PubMed]
  13. J. E. Hellstrom, B. Jacobsson, V. Pasiskevicius, and F. Laurell, “Finite beams in reflective volume Bragg gratings: theory and experiments,” IEEE J. Quantum Electron. 44, 81–89 (2008). [CrossRef]
  14. H. Shu and M. Bass, “Modeling the reflection of a laser beam by a deformed highly reflective volume Bragg grating,” Appl. Opt. 46, 2930–2938 (2007). [CrossRef] [PubMed]
  15. H. Shu, S. Mokhov, B. Y. Zeldovich, and M. Bass, “More on analyzing the reflection of a laser beam by a deformed highly reflective volume Bragg grating using iteration of the beam propagation method,” Appl. Opt. 48, 22–27 (2009). [CrossRef]
  16. H. Shu, “Split step solution in the iteration of the beam propagation method for analyzing Bragg gratings,” Appl. Opt. 48, 4794–4800 (2009). [CrossRef] [PubMed]
  17. H. Shu, “Analytic and numeric modeling of diode laser pumped Yb:YAG laser oscillators and amplifiers,” Ph.D. dissertation (University of Central Florida, 2003).
  18. H. Shu and M. Bass, “Three-dimensional computer model for simulating realistic solid-state lasers,” Appl. Opt. 46, 5687–5697 (2007). [CrossRef] [PubMed]
  19. P. Kaczmarski and P. E. Lagasse, “Bidirectional beam propagation method,” Electron. Lett. 24, 675–676 (1988). [CrossRef]
  20. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1965).
  21. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 5th ed. (Academic, 2001).
  22. G. R. Hadley, “Wide-angle beam propagation using Padé approximant operators,” Opt. Lett. 17, 1426–1428 (1992). [CrossRef] [PubMed]
  23. W. P. Huang and C. L. Xu, “Simulation of three-dimensional optical waveguides by a full-vector beam propagation method,” IEEE J. Quantum Electron. 29, 2639–2649 (1993). [CrossRef]
  24. J. E. Sipe, L. Poladian, and C. M. de Sterke, “Propagation through nonuniform grating structures,” J. Opt. Soc. Am. A 11, 1307–1320 (1994). [CrossRef]
  25. D. I. Kovsh, S. Yang, D. J. Hagan, and E. W. Van Stryland, “Nonlinear optical beam propagation for optical limiting,” Appl. Opt. 38, 5168–5180 (1999). [CrossRef]
  26. W. H. Southwell, “Validity of the Fresnel approximation in the near field,” J. Opt. Soc. Am. 71, 7–14 (1981). [CrossRef]
  27. H. Shu, “Quartic form of the slowly decaying imaginary distance beam propagation method,” Appl. Opt. 48, 4056–4061 (2009). [CrossRef] [PubMed]
  28. S. Jungling and J. C. Chen, “A study and optimization of eigenmode calculations using the imaginary-distance beam-propagation method,” IEEE J. Quantum Electron. 30, 2098–2105 (1994). [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.

Figures

Fig. 1 Fig. 2 Fig. 3
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited