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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 18, Iss. 3 — Mar. 1, 2001
  • pp: 557–564

Synthesis of fiber Bragg gratings for use in transmission

Johannes Skaar  »View Author Affiliations

JOSA A, Vol. 18, Issue 3, pp. 557-564 (2001)

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A method for designing fiber Bragg gratings with desired complex transmission coefficients is proposed. The transmission coefficient of a fiber grating satisfies the minimum-phase condition when the linear phase from the pure propagation is ignored. Therefore only a finite bandwidth is considered for the synthesis. The algorithm is based on a result of Krein and Nudel’man [Prob. Peredachi Inf. 11, 37 (1975)]. A numerical algorithm is developed, and by numerical examples it is demonstrated that it is possible to realize gratings with specified complex transmission responses inside the considered bandwidth. The method is also applicable for thin-film filters.

© 2001 Optical Society of America

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(060.2340) Fiber optics and optical communications : Fiber optics components

Original Manuscript: June 29, 2000
Revised Manuscript: October 10, 2000
Manuscript Accepted: October 10, 2000
Published: March 1, 2001

Johannes Skaar, "Synthesis of fiber Bragg gratings for use in transmission," J. Opt. Soc. Am. A 18, 557-564 (2001)

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  1. K. O. Hill, G. Meltz, “Fiber Bragg grating technology: fundamentals and overview,” J. Lightwave Technol. 15, 1263–1276 (1997). [CrossRef]
  2. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997). [CrossRef]
  3. R. Feced, M. N. Zervas, M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings,” IEEE J. Quantum Electron. 35, 1105–1115 (1999). [CrossRef]
  4. K. Hinton, “Dispersion compensation using apodized Bragg fiber gratings in transmission,” J. Lightwave Technol. 16, 2336–2346 (1998). [CrossRef]
  5. E. Brinkmeyer, “Simple algorithm for reconstructing fiber grating from reflectometric data,” Opt. Lett. 20, 810–812 (1995). [CrossRef] [PubMed]
  6. L. Poladian, “Group-delay reconstruction for fiber Bragg gratings in reflection and transmission,” Opt. Lett. 22, 1571–1573 (1997). [CrossRef]
  7. G. Lenz, B. J. Eggleton, C. R. Giles, C. K. Madsen, R. E. Slusher, “Dispersive properties of optical fibers for WDM systems,” IEEE J. Quantum Electron. 34, 1390–1402 (1998). [CrossRef]
  8. F. Ouellette, “Limits of chirped pulse-compression with an unchirped Bragg grating filter,” Appl. Opt. 29, 4826–4829 (1990). [CrossRef] [PubMed]
  9. B. J. Eggleton, T. Stephens, P. A. Krug, G. Dhosi, Z. Brodzeli, F. Ouellette, “Dispersion compensation using a fibre grating in transmission,” Electron. Lett. 32, 1610–1611 (1996). [CrossRef]
  10. N. M. Litchinitser, B. J. Eggleton, D. B. Patterson, “Fiber Bragg gratings for dispersion compensation in transmission: theoretical model and design criteria for nearly ideal pulse recompression,” J. Lightwave Technol. 15, 1303–1313 (1997). [CrossRef]
  11. J. Skaar, “Synthesis and characterization of fiber Bragg gratings,” Ph.D. dissertation (Norwegian University of Science and Technology, Trondheim, Norway, 2000), available online at http://www.fysel.ntnu.no/Department/Avhandlinger/dring/index.html#2000 .
  12. M. G. Krein, P. Ya. Nudel’man, “On some new problems for Hardy class functions and continuous families of functions with double orthogonality,” Dokl. Akad. Nauk SSSR 206, 537–540 (1973).
  13. M. G. Krein, P. Ya. Nudel’man, “Approximation of functions by minimum-energy transfer functions of linear systems,” Probl. Peredachi Inf. 11, 37–60 (1975).
  14. V. Klibanov, P. E. Sacks, A. V. Tikhonravov, “The phase retrieval problem,” Inverse Probl. 11, 1–28 (1995). [CrossRef]
  15. M. Nussenzveig, Causality and Dispersion Relations (Academic, New York, 1972).
  16. A. Papoulis, The Fourier Integral and Its Applications (McGraw–Hill, New York, 1962), Chap. 10.
  17. L. Aizenberg, Carleman’s Formulas in Complex Analysis (Kluwer Academic, Dordrecht, The Netherlands, 1993).
  18. A. V. Tikhonravov, “Some theoretical aspects of thin-film optics and their applications,” Appl. Opt. 32, 5417–5426 (1993). [CrossRef] [PubMed]
  19. A. M. Bruckstein, B. C. Levy, T. Kailath, “Differential methods in inverse scattering,” SIAM J. Appl. Math. 45, 312–335 (1985). [CrossRef]
  20. N. Young, An Introduction to Hilbert Space (Cambridge U. Press, Cambridge, UK, 1988), Chap. 7.
  21. G. H. Song, “Theory of symmetry in optical filter responses,” J. Opt. Soc. Am. A 11, 2027–2037 (1994). [CrossRef]
  22. N. M. Litchinitser, B. J. Eggleton, G. P. Agrawal, “Dispersion of cascaded fiber gratings in WDM lightwave systems,” J. Lightwave Technol. 16, 1523–1529 (1997). [CrossRef]

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