Abstract

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

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  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).
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  19. Y. Gu, K. S. Chiang, "Effects of average index variation in apodized long-period fiber gratings," Photonic Sensors 3, 102-111 (2013).
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  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).

2013

Y. Gu, K. S. Chiang, "Effects of average index variation in apodized long-period fiber gratings," Photonic Sensors 3, 102-111 (2013).

2011

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).

2009

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).

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).

2007

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).

2006

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).

2005

F. Y. M. Chan, K. S. Chiang, "Analysis of apodized phase-shifted long-period fiber gratings," Opt. Commun. 244, 233-243 (2005).

M. Kulishov, J. Azaña, "Long-period fiber gratings as ultrafast optical differentiators," Opt. Lett. 30, 2700-2702 (2005).

2003

W. J. Stephen, P. T. Ralph, "Optical fibre long-period grating sensors: Characteristics and application," Meas. Sci. Technol. 14, R49 (2003).

J. K. Brenne, J. Skaar, "Design of grating-assisted codirectional couplers with discrete inverse-scattering algorithms," J. Lightw. Technol. 21, 254-263 (2003).

2002

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).

2001

M. Das, K. Thyagarajan, "Dispersion compensation in transmission using uniform long period fiber gratings," Opt. Commun. 190, 159-163 (2001).

2000

D. B. Stegall, T. Erdogan, "Dispersion control with use of long-period fiber gratings," J. Opt. Soc. Amer. A 17, 304-312 (2000).

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).

1999

1998

H. Ke, K. S. Chiang, J. H. Peng, "Analysis of phase-shifted long-period fiber gratings," IEEE Photon. Technol. Lett. 10, 1596-1598 (1998).

1997

L. Poladian, "Group-delay reconstruction for fiber Bragg gratings in reflection and transmission," Opt. Lett. 22, 1571-1573 (1997).

A. Carballar, M. A. Muriel, "Phase reconstruction from reflectivity in fiber Bragg gratings," J. Lightw. Technol. 15, 1314-1322 (1997).

1996

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).

1988

Appl. Spectrosc.

IEEE Photon. J.

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).

IEEE Photon. Technol. Lett.

H. Ke, K. S. Chiang, J. H. Peng, "Analysis of phase-shifted long-period fiber gratings," IEEE Photon. Technol. Lett. 10, 1596-1598 (1998).

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).

J. Lightw. Technol.

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).

J. K. Brenne, J. Skaar, "Design of grating-assisted codirectional couplers with discrete inverse-scattering algorithms," J. Lightw. Technol. 21, 254-263 (2003).

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).

A. Carballar, M. A. Muriel, "Phase reconstruction from reflectivity in fiber Bragg gratings," J. Lightw. Technol. 15, 1314-1322 (1997).

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).

J. Opt. Soc. Amer. A

D. B. Stegall, T. Erdogan, "Dispersion control with use of long-period fiber gratings," J. Opt. Soc. Amer. A 17, 304-312 (2000).

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).

Meas. Sci. Technol.

W. J. Stephen, P. T. Ralph, "Optical fibre long-period grating sensors: Characteristics and application," Meas. Sci. Technol. 14, R49 (2003).

Microwave Opt. Technol. Lett.

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).

Opt. Commun.

F. Y. M. Chan, K. S. Chiang, "Analysis of apodized phase-shifted long-period fiber gratings," Opt. Commun. 244, 233-243 (2005).

M. Das, K. Thyagarajan, "Dispersion compensation in transmission using uniform long period fiber gratings," Opt. Commun. 190, 159-163 (2001).

Opt. Exp.

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).

Opt. Lett.

Photonic Sensors

Y. Gu, K. S. Chiang, "Effects of average index variation in apodized long-period fiber gratings," Photonic Sensors 3, 102-111 (2013).

Other

A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, 1962).

K. S. Chiang, Q. Liu, "Long-period gratings for application in optical communications," Proc. ICOCN/ATFO (2006) pp. 128-133.

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