OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 21, Iss. 4 — Apr. 1, 2004
  • pp: 552–560

Inverse scattering algorithm for reconstructing lossy fiber Bragg gratings

Amir Rosenthal and Moshe Horowitz  »View Author Affiliations

JOSA A, Vol. 21, Issue 4, pp. 552-560 (2004)

View Full Text Article

Enhanced HTML    Acrobat PDF (179 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We demonstrate an inverse scattering algorithm for reconstructing the structure of lossy fiber Bragg gratings. The algorithm enables us to extract the profiles of the refractive index and the loss coefficient along the grating from the grating transmission spectrum and from the reflection spectra, measured from both sides of the grating. Such an algorithm can be used to develop novel distributed evanescent-wave fiber Bragg sensors that measure the change in both the refractive index and the attenuation coefficient of the medium surrounding the grating. The algorithm can also be used to analyze and to design fiber Bragg gratings written in fiber amplifiers. A novel method to overcome instability problems in extracting the parameters of the lossy grating is introduced. The new method also makes it possible to reduce the spectral resolution needed to accurately extract the grating parameters.

© 2004 Optical Society of America

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(060.2370) Fiber optics and optical communications : Fiber optics sensors

Original Manuscript: July 10, 2003
Revised Manuscript: December 4, 2003
Manuscript Accepted: December 5, 2003
Published: April 1, 2004

Amir Rosenthal and Moshe Horowitz, "Inverse scattering algorithm for reconstructing lossy fiber Bragg gratings," J. Opt. Soc. Am. A 21, 552-560 (2004)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. A. D. Kersey, “A Review of recent developments in fiber optic sensors technology,” Opt. Fiber Technol. 2, 291–317 (1996). [CrossRef]
  2. V. Goloborodko, S. Keren, A. Rosenthal, B. Levit, M. Horowitz, “Measuring temperature profiles in high-power optical components,” Appl. Opt. 42, 2284–2288 (2003). [CrossRef] [PubMed]
  3. S. Huang, M. M. Ohn, M. LeBlanc, R. M. Measures, “Continuous arbitrary strain profile measurements with fiber Bragg gratings,” Smart Mater. Struct. 7, 248–256 (1998). [CrossRef]
  4. M. Volanthen, H. Geiger, M. J. Cole, J. P. Dakin, “Measurement of arbitrary strain profiles within fibre gratings,” Electron. Lett. 32, 1028–1029 (1996). [CrossRef]
  5. P. H. Paul, G. Kychakoff, “Fiber-optic evanescent field absorption sensor,” Appl. Phys. Lett. 51, 12–14 (1987). [CrossRef]
  6. H. Tai, H. Tanaka, T. Yoshino, “Fiber-optic evanescent-wave methane-gas sensor using optical absorption for the 3.392-µm line of a He–Ne laser,” Opt. Lett. 12, 437–439 (1987). [CrossRef] [PubMed]
  7. V. Ruddy, B. D. MacCraith, J. A. Murphy, “Evanescent wave absorption spectroscopy using multimode fibers,” J. Appl. Phys. 67, 6070–6074 (1990). [CrossRef]
  8. G. P. Anderson, J. P. Golden, L. K. Cao, D. Wijesuriya, L. C. Shriver-Lake, F. S. Ligler, “Development of an evanescent wave fiber optic biosensor,” IEEE Eng. Med. Biol. Mag. 13, 358–363 (1994). [CrossRef]
  9. A. Messica, A. Greenstein, A. Katzir, “Theory of fiber-optic, evanescent-wave spectroscopy and sensors,” Appl. Opt. 35, 2274–2284 (1996). [CrossRef] [PubMed]
  10. S. K. Khijwania, B. D. Gupta, “Fiber optic evanscent field absorption sensor: effect of fiber parameters and geometry of the probe,” Opt. Quantum Electron. 31, 625–636 (1999). [CrossRef]
  11. P. K. Choudhury, T. Yoshino, “On the optical sensing means for the study of chemical kinetics,” Meas. Sci. Technol. 13, 1793–1797 (2002). [CrossRef]
  12. K. Schroeder, W. Ecke, R. Mueller, R. Willsch, A. Andreev, “A fibre Bragg grating refractometer,” Meas. Sci. Technol. 12, 757–764 (2001). [CrossRef]
  13. J. Dubendorfer, R. E. Kunz, G. Jobst, I. Moser, G. Urban, “Integrated optical pH sensor using replicated chirped grating coupler sensor chips,” Sens. Actuators B 50, 210–219 (1998). [CrossRef]
  14. S. Keren, M. Horowitz, “Distributed three-dimensional fiber Bragg grating refractometer for biochemical sensing,” Opt. Lett. 28, 2037–2039 (2003). [CrossRef] [PubMed]
  15. S. Keren, M. Horowitz, “Interrogation of fiber gratings by use of low-coherence spectral interferometry of noiselike pulses,” Opt. Lett. 26, 328–330 (2001). [CrossRef]
  16. 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]
  17. J. Skaar, L. Wang, T. Erdogan, “On the synthesis of fiber Bragg gratings by layer peeling,” J. Lightwave Technol. 37, 165–173 (2001).
  18. A. Rosenthal, M. Horowitz, “Inverse scattering algorithm for reconstructing strongly reflecting fiber Bragg gratings,” IEEE J. Quantum Electron. 39, 1018–1026 (2003). [CrossRef]
  19. A. M. Bruckstein, B. C. Levy, T. Kailath, “Differential methods in inverse scattering,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 45, 312–335 (1985). [CrossRef]
  20. J. Frolik, A. E. Yagle, “Forward and inverse scattering for discrete layered lossy and absorbing media,” IEEE Trans. Circuits Syst. 44, 710–722 (1997). [CrossRef]
  21. W. H. Loh, R. I. Laming, “1.55 µm phase-shifted distributed feedback fibre laser,” Electron. Lett. 31, 1440–1442 (1995). [CrossRef]
  22. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969). [CrossRef]
  23. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997). [CrossRef]
  24. M. J. Ablowitz, H. Segur, Solitons and the Inverse Scattering Transform (Society for Applied Mathematics, Philadelphia, Pa., 1981).
  25. S. Keren, A. Rosenthal, M. Horowitz, “Measuring the structure of highly reflecting fiber Bragg gratings,” IEEE Photon. Technol. Lett. 15, 575–577 (2003). [CrossRef]
  26. A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, New York, 1962).
  27. J. G. Proakis, D. G. Manolakis, Digital Signal Processing: Principles, Algorithms, and Applications, 3rd ed. (Prentice-Hall International, London, 1996).

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.


Fig. 1 Fig. 2 Fig. 3
Fig. 4

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited