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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: G. I. Stegeman
  • Vol. 23, Iss. 10 — Oct. 1, 2006
  • pp: 2040–2045

Finite Bragg grating synthesis by numerical solution of Hermitian Gel’fand–Levitan–Marchenko equations

Oleg V. Belai, Evgeny V. Podivilov, Osip Ya. Schwarz, David A. Shapiro, and Leonid L. Frumin  »View Author Affiliations


JOSA B, Vol. 23, Issue 10, pp. 2040-2045 (2006)
http://dx.doi.org/10.1364/JOSAB.23.002040


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Abstract

We examine the problem of fiber Bragg grating reconstruction from its reflection coefficient. A direct numerical method of solving the Gel’fand–Levitan–Marchenko integral equations for the problem is developed. The method is based on a bordering procedure, Cholesky decomposition, and piecewise-linear approximation. It is tested using high-reflectance homogeneous and hyperbolic secant profiles. The proposed method is shown to concede the popular discrete layer peeling technique in efficiency but surpasses it in accuracy and stability at high reflectance.

© 2006 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(050.2770) Diffraction and gratings : Gratings
(060.2430) Fiber optics and optical communications : Fibers, single-mode

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: March 22, 2006
Revised Manuscript: June 24, 2006
Manuscript Accepted: June 28, 2006

Citation
Oleg V. Belai, Evgeny V. Podivilov, Osip Ya. Schwarz, David A. Shapiro, and Leonid L. Frumin, "Finite Bragg grating synthesis by numerical solution of Hermitian Gel'fand-Levitan-Marchenko equations," J. Opt. Soc. Am. B 23, 2040-2045 (2006)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-23-10-2040


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References

  1. G. P. Agrawal, Fiber-Optic Communication Systems (Wiley, 2002). [CrossRef]
  2. R. Kashyap, Fiber Bragg Gratings (Academic, 1999).
  3. M. Sumetsky and B. J. Eggleton, "Fiber Bragg gratings for dispersion compensation in optical communication systems," J. Opt. Fiber. Commun. Rep. 2, 256-278 (2005). [CrossRef]
  4. V. E. Zakharov and A. B. Shabat, "Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media," Zh. Eksp. Teor. Fiz. 61, 118-134 (1971).
  5. L. Poladian, "Simple grating synthesis algorithm," Opt. Lett. 25, 787-789 (2000). [CrossRef]
  6. L. Poladian, "Simple grating synthesis algorithm," Opt. Lett. 25, 1400 (2000), errata. [CrossRef]
  7. J. Skaar, L. Wang, and T. Erdogan, "On the synthesis of fiber Bragg gratings by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001). [CrossRef]
  8. P. Frangos and D. Jaggard, "A numerical solution to the Zakharov-Shabat inverse scattering problem," IEEE Trans. Antennas Propag. 39, 74-79 (1991). [CrossRef]
  9. C. Papachristos and P. Frangos, "Design of corrugated optical waveguide filters through a direct numerical solution of the coupled Gel'fand-Levitan-Marchenko integral equations," J. Opt. Soc. Am. A 19, 1005-1012 (2002). [CrossRef]
  10. C. Papachristos and P. Frangos, "Synthesis of single- and multi-mode planar optical waveguides by a direct numerical solution of the Gel'fand-Levitan-Marchenko integral equations," Opt. Commun. 203, 27-37 (2002). [CrossRef]
  11. G. B. Xiao and K. Yashiro, "An efficient algorithm for solving Zakharov-Shabat inverse scattering problem," IEEE Trans. Antennas Propag. 50, 807-811 (2002). [CrossRef]
  12. P. V. Frangos and D. L. Jaggard, "The reconstruction of stratified dielectric profiles using successive approximations," IEEE Trans. Antennas Propag. 35, 1267-1272 (1987). [CrossRef]
  13. J. Skaar and R. Feced, "Reconstruction of gratings from noisy reflection data," J. Opt. Soc. Am. A 19, 2229-2237 (2002). [CrossRef]
  14. J. Capmany and J. Marti, "Design of fibre grating dispersion compensators using a novel iterative solution of the Gel'fand-Levitan-Marchenko coupled equations," Electron. Lett. 32, 918-919 (1996). [CrossRef]
  15. E. Peral, J. Capmany, and J. Marti, "Iterative solution to the Gel'fand-Levitan-Marchenko coupled equations and application to synthesis of fiber gratings," IEEE J. Quantum Electron. 32, 2078-2084 (1996). [CrossRef]
  16. L. Poladian, "Iterative and noniterative design algorithms for Bragg gratings," Opt. Laser Technol. 5, 215-222 (1999).
  17. P. V. Frangos and D. L. Jaggard, "Inverse scattering: solution of coupled Gelfand-Levitan-Marchenko integral equations using successive kernel approximations," IEEE Trans. Antennas Propag. 43, 547-552 (1995). [CrossRef]
  18. G. H. Song and S. Y. Shin, "Design of corrugated waveguide filters by the Gel'fand-Levitan-Marchenko inverse-scattering method," J. Opt. Soc. Am. A 2, 1905-1915 (1985). [CrossRef]
  19. F. Ahmad and M. Razzagh, "A numerical solution to the Gel'fand-Levitan-Marchenko equation," Appl. Math. Comput. 89, 31-39 (1998). [CrossRef]
  20. A. Rosenthal and M. Horowitz, "Inverse scattering algorithm for reconstructing strongly reflecting fiber Bragg gratings," IEEE J. Quantum Electron. 39, 1018-1026 (2003). [CrossRef]
  21. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in Fortran (Cambridge U. Press, 1992).
  22. H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969).
  23. H. Bateman and A. Erdelyi, Higher Transcendental Functions (McGraw-Hill, 1953), Vol. 2.
  24. D. A. Shapiro, "Family of exact solutions for reflection spectrum of Bragg grating," Opt. Commun. 215, 295-301 (2003). [CrossRef]
  25. J. Skaar and O. H. Waagaard, "Design and characterization of finite-length fiber grating," IEEE J. Quantum Electron. 39, 1238-1245 (2003). [CrossRef]

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