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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 22, Iss. 1 — Jan. 1, 2005
  • pp: 84–92

Reconstruction of a fiber Bragg grating from noisy reflection data

Amir Rosenthal and Moshe Horowitz  »View Author Affiliations


JOSA A, Vol. 22, Issue 1, pp. 84-92 (2005)
http://dx.doi.org/10.1364/JOSAA.22.000084


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Abstract

We develop a novel method that enables one to reconstruct the structure of highly reflecting fiber Bragg gratings from noisy reflection spectra. When the reflection spectrum is noisy and the grating reflectivity is high, noise in the Bragg zone of the reflection spectrum is amplified by the inverse scattering algorithms and prevents the reconstruction of the grating. Our method is based on regularizing the reflection spectrum in frequencies inside the Bragg zone by using the data on the grating spectrum outside the Bragg zone. The regularized reflection spectrum is used to reconstruct the grating structure by means of inverse scattering. Our method enables one to analyze gratings with a high reflectivity from a spectrum that contains a high level of noise. Such gratings could not be analyzed by using methods described in previous work [IEEE J. Quantum Electron. 39, 1238 (2003)].

© 2005 Optical Society of America

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(290.3200) Scattering : Inverse scattering

History
Original Manuscript: June 8, 2004
Revised Manuscript: August 8, 2004
Published: January 1, 2005

Citation
Amir Rosenthal and Moshe Horowitz, "Reconstruction of a fiber Bragg grating from noisy reflection data," J. Opt. Soc. Am. A 22, 84-92 (2005)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-22-1-84


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References

  1. E. Peral, J. Capmany, J. Marti, “Iterative solution to the Gel’fan-Levitan-Marchenko coupled equations,” IEEE J. Quantum Electron. 32, 2078–2084 (1996). [CrossRef]
  2. 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]
  3. L. Poladian, “Simple grating synthesis algorithm,” Opt. Lett. 25, 787–789 (2000). [CrossRef]
  4. J. Skaar, L. Wang, T. Erdogan, “On the synthesis of fiber Bragg gratings by layer peeling,” J. Lightwave Technol. 37, 165–173 (2001).
  5. A. Rosenthal, M. Horowitz, “Inverse scattering algorithm for reconstructing strongly reflecting fiber Bragg gratings,” IEEE J. Quantum Electron. 39, 1018–1026 (2003). [CrossRef]
  6. S. Keren, A. Rosenthal, M. Horowitz, “Measuring the structure of highly reflecting fiber Bragg gratings,” IEEE Photonics Technol. Lett. 15, 575–577 (2003). [CrossRef]
  7. A. M. Bruckstein, I. Koltracht, T. Kailath, “Inverse scattering with noisy data,” SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 7, 1331–1349 (1986). [CrossRef]
  8. J. Skaar, R. Feced, “Reconstruction of gratings from noisy reflection data,” J. Opt. Soc. Am. A 19, 2229–2237 (2002). [CrossRef]
  9. J. Skaar, O. H. Waagaard, “Design and characterization of finite length fiber gratings,” IEEE J. Quantum Electron. 39, 1238–1245 (2003). [CrossRef]
  10. A. Rosenthal, M. Horowitz, “New technique to accurately interpolate the complex reflection spectrum of fiber Bragg gratings,” IEEE J. Quantum Electron. 40, 1099–1104 (2004). [CrossRef]
  11. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997). [CrossRef]
  12. L. Poladian, “Group-delay reconstruction for fiber Bragg gratings in reflection and transmission,” Opt. Lett. 22, 1571–1573 (1997). [CrossRef]
  13. A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, New York, 1962).
  14. M. J. Ablowitz, A. S. Fokas, Complex Variables (Cambridge U. Press, Cambridge, UK, 1997).
  15. L. Debnath, P. Mikusiéski, Introduction to Hilbert Spaces with Applications (Academic, San Diego, Calif., 1990).
  16. G. H. Golub, C. F. Van Ioan, Matrix Computations (The Johns Hopkins U. Press, Baltimore, Md., 1996).
  17. B. Porat, Digital Processing of Random Signals: Theory and Methods (Prentice Hall, Englewood Cliffs, N.J., 1994).
  18. R. Courant, D. Hilbert, Methods of Mathematical Physics (Interscience, New York, 1966).
  19. M. J. Ablowitz, H. Segur, Solitons and the Inverse Scattering Transform (Society for Applied Mathematics, Philadelphia, Pa., 1981).
  20. L. Poladian, “Graphical and WKB analysis of nonuniform Bragg gratings,” Phys. Rev. E 48, 4758–4767 (1993). [CrossRef]
  21. T. Kailath, Linear Systems (Prentice Hall, Englewood Cliffs, N.J., 1980).

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