OSA's Digital Library

Journal of Lightwave Technology

Journal of Lightwave Technology


  • Vol. 31, Iss. 13 — Jul. 1, 2013
  • pp: 2223–2229

Phase Retrieval From Transmission Spectrum for Long-Period Fiber Gratings

Bing Zou and Kin Seng Chiang

Journal of Lightwave Technology, Vol. 31, Issue 13, pp. 2223-2229 (2013)

View Full Text Article

Acrobat PDF (1165 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

  • Export Citation/Save Click for help


We demonstrate a method to retrieve the phase spectrum of a long-period fiber grating (LPFG) from its transmission spectrum. The method is based on the Hilbert transform that relates the minimum phase and the amplitude spectrum of a linear system, and is applicable to under-coupled LPFGs with arbitrary grating profiles. We verify the method with numerical examples and experiments. The method provides a simple and effective way to obtain the phase characteristics of LPFGs and thus complement the measured transmission spectra of the gratings.

© 2013 IEEE

Bing Zou and Kin Seng Chiang, "Phase Retrieval From Transmission Spectrum for Long-Period Fiber Gratings," J. Lightwave Technol. 31, 2223-2229 (2013)

Sort:  Year  |  Journal  |  Reset


  1. A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, "Long-period fiber gratings as band-rejection filters," J. Lightw. Technol. 14, 58-65 (1996).
  2. K. S. Chiang, Q. Liu, "Long-period gratings for application in optical communications," Proc. ICOCN/ATFO (2006) pp. 128-133.
  3. W. J. Stephen, P. T. Ralph, "Optical fibre long-period grating sensors: Characteristics and application," Meas. Sci. Technol. 14, R49 (2003).
  4. D. B. Stegall, T. Erdogan, "Dispersion control with use of long-period fiber gratings," J. Opt. Soc. Amer. A 17, 304-312 (2000).
  5. M. Das, K. Thyagarajan, "Dispersion compensation in transmission using uniform long period fiber gratings," Opt. Commun. 190, 159-163 (2001).
  6. M. Kulishov, J. Azaña, "Long-period fiber gratings as ultrafast optical differentiators," Opt. Lett. 30, 2700-2702 (2005).
  7. R. Ashrafi, M. H. Asghari, J. Azana, "Ultrafast Optical arbitrary-order differentiators based on apodized long-period gratings," IEEE Photon. J. 3, 353-364 (2011).
  8. Y. Park, M. Kulishov, R. Slavík, J. Azaña, "Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber gratings," Opt. Exp. 14, 12670-12678 (2006).
  9. A. Carballar, M. A. Muriel, "Phase reconstruction from reflectivity in fiber Bragg gratings," J. Lightw. Technol. 15, 1314-1322 (1997).
  10. L. Poladian, "Group-delay reconstruction for fiber Bragg gratings in reflection and transmission," Opt. Lett. 22, 1571-1573 (1997).
  11. J. Skaar, H. E. Engan, "Phase reconstruction from reflectivity in fiber Bragg gratings," Opt. Lett. 24, 136-138 (1999).
  12. R. Feced, M. N. Zervas, "Efficient inverse scattering algorithm for the design of grating-assisted codirectional mode couplers," J. Opt. Soc. Amer. A 17, 1573-1582 (2000).
  13. J. K. Brenne, J. Skaar, "Design of grating-assisted codirectional couplers with discrete inverse-scattering algorithms," J. Lightw. Technol. 21, 254-263 (2003).
  14. A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, 1962).
  15. K. Ohta, H. Ishida, "Comparison among several numerical integration methods for Kramers-Kronig transformation," Appl. Spectrosc. 42, 952-957 (1988).
  16. H. Ke, K. S. Chiang, J. H. Peng, "Analysis of phase-shifted long-period fiber gratings," IEEE Photon. Technol. Lett. 10, 1596-1598 (1998).
  17. F. Y. M. Chan, K. S. Chiang, "Analysis of apodized phase-shifted long-period fiber gratings," Opt. Commun. 244, 233-243 (2005).
  18. X. Yang, X. Guo, C. Lu, C. T. Hiang, "Apodized long-period grating with low insertion loss," Microwave Opt. Technol. Lett. 35, 283-286 (2002).
  19. Y. Gu, K. S. Chiang, "Effects of average index variation in apodized long-period fiber gratings," Photonic Sensors 3, 102-111 (2013).
  20. Y. Liu, H. W. Lee, K. S. Chiang, T. Zhu, Y. J. Rao, "Glass structure changes in CO2-laser writing of long-period fiber gratings in boron-doped single-mode fibers," J. Lightw. Technol. 27, 857-863 (2009).
  21. Y. Gu, K. S. Chiang, Y. J. Rao, "Writing of apodized phase-shifted long-period fiber gratings with a computer-controlled CO2 laser," IEEE Photon. Technol. Lett. 21, 657-659 (2009).
  22. Q. Liu, K. S. Chiang, Y. Liu, "Characterization of single-mode fiber with fiber Bragg gratings for the design of long-period gratings," J. Lightw. Technol. 25, 2129-2134 (2007).

Cited By

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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited