Abstract

We demonstrate experimentally, for the first time to our knowledge, a reconstruction of a highly reflecting fiber Bragg grating from its complex reflection spectrum by using a regularization algorithm. The regularization method is based on correcting the measured reflection spectrum at the Bragg zone frequencies and enables the reconstruction of the grating profile using the integral-layer-peeling algorithm. A grating with an approximately uniform profile and with a maximum reflectivity of 99.98% was accurately reconstructed by measuring only its complex reflection spectrum.

© 2007 Optical Society of America

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  1. K. O. Hill and G. Meltz, "Fiber Bragg grating technology fundamentals and overview," J. Lightwave Technol. 15, 1263-1275 (1997).
    [CrossRef]
  2. S. Kieckbusch, F. Knappe, and E. Brinkmeyer, "UV writing of accurately chirped FBGs using in-situ optical frequency domain reflectometry and inverse scattering," in Bragg Gratings, Photosensitivity and Poling in Glass Waveguides (BGPP), Sydney, July 2005, pp. 119-121, http://www.tourhosts.com.au/bgppacoft2005/tprogramlowbarbgpp.asp.
  3. M. J. Ablowitz and H. Segur, Solitons and the Inverse Transform (SIAM, 1981).
    [CrossRef]
  4. J. Skaar and R. Feced, "Reconstruction of gratings from noisy reflection data," J. Opt. Soc. Am. A 19, 2229-2237 (2002).
    [CrossRef]
  5. A. Rosenthal and M. Horowitz, "Reconstruction of a fiber Bragg grating from noisy reflection data," J. Opt. Soc. Am. A 22, 84-92 (2005).
    [CrossRef]
  6. A. Sherman, A. Rosenthal, and M. Horowitz, "Extracting the structure of highly reflecting Fiber Bragg gratings by measuring both the transmission and the reflection spectra," Opt. Lett. 32, 457-459 (2007).
    [CrossRef] [PubMed]
  7. S. Keren, A. Rosenthal, and M. Horowitz, "Measuring the structure of highly reflecting fiber Bragg gratings," IEEE Photon. Technol. Lett. 15, 575-577 (2003).
    [CrossRef]
  8. J. Skaar and O. H. Waagaard, "Design and characterization of finite length fiber gratings," IEEE J. Quantum Electron. 39, 1238-1245 (2003).
    [CrossRef]
  9. A. Rosenthal and M. Horowitz, "Inverse scattering algorithm for reconstructing strongly reflecting fiber Bragg gratings," IEEE J. Quantum Electron. 39, 1018-1026 (2003).
    [CrossRef]
  10. J. Skaar, L. Wang, and T. Erdogan, "On the synthesis of Fiber Bragg gratings by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).
    [CrossRef]

2007 (1)

2005 (1)

2003 (3)

S. Keren, A. Rosenthal, and M. Horowitz, "Measuring the structure of highly reflecting fiber Bragg gratings," IEEE Photon. Technol. Lett. 15, 575-577 (2003).
[CrossRef]

J. Skaar and O. H. Waagaard, "Design and characterization of finite length fiber gratings," IEEE J. Quantum Electron. 39, 1238-1245 (2003).
[CrossRef]

A. Rosenthal and M. Horowitz, "Inverse scattering algorithm for reconstructing strongly reflecting fiber Bragg gratings," IEEE J. Quantum Electron. 39, 1018-1026 (2003).
[CrossRef]

2002 (1)

2001 (1)

J. Skaar, L. Wang, and T. Erdogan, "On the synthesis of Fiber Bragg gratings by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

1997 (1)

K. O. Hill and G. Meltz, "Fiber Bragg grating technology fundamentals and overview," J. Lightwave Technol. 15, 1263-1275 (1997).
[CrossRef]

Ablowitz, M. J.

M. J. Ablowitz and H. Segur, Solitons and the Inverse Transform (SIAM, 1981).
[CrossRef]

Brinkmeyer, E.

S. Kieckbusch, F. Knappe, and E. Brinkmeyer, "UV writing of accurately chirped FBGs using in-situ optical frequency domain reflectometry and inverse scattering," in Bragg Gratings, Photosensitivity and Poling in Glass Waveguides (BGPP), Sydney, July 2005, pp. 119-121, http://www.tourhosts.com.au/bgppacoft2005/tprogramlowbarbgpp.asp.

Erdogan, T.

J. Skaar, L. Wang, and T. Erdogan, "On the synthesis of Fiber Bragg gratings by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

Feced, R.

Hill, K. O.

K. O. Hill and G. Meltz, "Fiber Bragg grating technology fundamentals and overview," J. Lightwave Technol. 15, 1263-1275 (1997).
[CrossRef]

Horowitz, M.

A. Sherman, A. Rosenthal, and M. Horowitz, "Extracting the structure of highly reflecting Fiber Bragg gratings by measuring both the transmission and the reflection spectra," Opt. Lett. 32, 457-459 (2007).
[CrossRef] [PubMed]

A. Rosenthal and M. Horowitz, "Reconstruction of a fiber Bragg grating from noisy reflection data," J. Opt. Soc. Am. A 22, 84-92 (2005).
[CrossRef]

S. Keren, A. Rosenthal, and M. Horowitz, "Measuring the structure of highly reflecting fiber Bragg gratings," IEEE Photon. Technol. Lett. 15, 575-577 (2003).
[CrossRef]

A. Rosenthal and M. Horowitz, "Inverse scattering algorithm for reconstructing strongly reflecting fiber Bragg gratings," IEEE J. Quantum Electron. 39, 1018-1026 (2003).
[CrossRef]

Keren, S.

S. Keren, A. Rosenthal, and M. Horowitz, "Measuring the structure of highly reflecting fiber Bragg gratings," IEEE Photon. Technol. Lett. 15, 575-577 (2003).
[CrossRef]

Kieckbusch, S.

S. Kieckbusch, F. Knappe, and E. Brinkmeyer, "UV writing of accurately chirped FBGs using in-situ optical frequency domain reflectometry and inverse scattering," in Bragg Gratings, Photosensitivity and Poling in Glass Waveguides (BGPP), Sydney, July 2005, pp. 119-121, http://www.tourhosts.com.au/bgppacoft2005/tprogramlowbarbgpp.asp.

Knappe, F.

S. Kieckbusch, F. Knappe, and E. Brinkmeyer, "UV writing of accurately chirped FBGs using in-situ optical frequency domain reflectometry and inverse scattering," in Bragg Gratings, Photosensitivity and Poling in Glass Waveguides (BGPP), Sydney, July 2005, pp. 119-121, http://www.tourhosts.com.au/bgppacoft2005/tprogramlowbarbgpp.asp.

Meltz, G.

K. O. Hill and G. Meltz, "Fiber Bragg grating technology fundamentals and overview," J. Lightwave Technol. 15, 1263-1275 (1997).
[CrossRef]

Rosenthal, A.

A. Sherman, A. Rosenthal, and M. Horowitz, "Extracting the structure of highly reflecting Fiber Bragg gratings by measuring both the transmission and the reflection spectra," Opt. Lett. 32, 457-459 (2007).
[CrossRef] [PubMed]

A. Rosenthal and M. Horowitz, "Reconstruction of a fiber Bragg grating from noisy reflection data," J. Opt. Soc. Am. A 22, 84-92 (2005).
[CrossRef]

S. Keren, A. Rosenthal, and M. Horowitz, "Measuring the structure of highly reflecting fiber Bragg gratings," IEEE Photon. Technol. Lett. 15, 575-577 (2003).
[CrossRef]

A. Rosenthal and M. Horowitz, "Inverse scattering algorithm for reconstructing strongly reflecting fiber Bragg gratings," IEEE J. Quantum Electron. 39, 1018-1026 (2003).
[CrossRef]

Segur, H.

M. J. Ablowitz and H. Segur, Solitons and the Inverse Transform (SIAM, 1981).
[CrossRef]

Sherman, A.

Skaar, J.

J. Skaar and O. H. Waagaard, "Design and characterization of finite length fiber gratings," IEEE J. Quantum Electron. 39, 1238-1245 (2003).
[CrossRef]

J. Skaar and R. Feced, "Reconstruction of gratings from noisy reflection data," J. Opt. Soc. Am. A 19, 2229-2237 (2002).
[CrossRef]

J. Skaar, L. Wang, and T. Erdogan, "On the synthesis of Fiber Bragg gratings by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

Waagaard, O. H.

J. Skaar and O. H. Waagaard, "Design and characterization of finite length fiber gratings," IEEE J. Quantum Electron. 39, 1238-1245 (2003).
[CrossRef]

Wang, L.

J. Skaar, L. Wang, and T. Erdogan, "On the synthesis of Fiber Bragg gratings by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

IEEE J. Quantum Electron. (3)

J. Skaar and O. H. Waagaard, "Design and characterization of finite length fiber gratings," IEEE J. Quantum Electron. 39, 1238-1245 (2003).
[CrossRef]

A. Rosenthal and M. Horowitz, "Inverse scattering algorithm for reconstructing strongly reflecting fiber Bragg gratings," IEEE J. Quantum Electron. 39, 1018-1026 (2003).
[CrossRef]

J. Skaar, L. Wang, and T. Erdogan, "On the synthesis of Fiber Bragg gratings by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

S. Keren, A. Rosenthal, and M. Horowitz, "Measuring the structure of highly reflecting fiber Bragg gratings," IEEE Photon. Technol. Lett. 15, 575-577 (2003).
[CrossRef]

J. Lightwave Technol. (1)

K. O. Hill and G. Meltz, "Fiber Bragg grating technology fundamentals and overview," J. Lightwave Technol. 15, 1263-1275 (1997).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Lett. (1)

Other (2)

S. Kieckbusch, F. Knappe, and E. Brinkmeyer, "UV writing of accurately chirped FBGs using in-situ optical frequency domain reflectometry and inverse scattering," in Bragg Gratings, Photosensitivity and Poling in Glass Waveguides (BGPP), Sydney, July 2005, pp. 119-121, http://www.tourhosts.com.au/bgppacoft2005/tprogramlowbarbgpp.asp.

M. J. Ablowitz and H. Segur, Solitons and the Inverse Transform (SIAM, 1981).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Intensity of the measured complex reflection spectrum.

Fig. 2
Fig. 2

Amplitude of the grating impulse response. The discontinuity at approximately t = 150 ps is caused by a reflection from the grating end.

Fig. 3
Fig. 3

Intensity of the measured complex reflection spectrum after performing spectrum regularization.

Fig. 4
Fig. 4

Amplitude of the reconstructed grating performed from the two grating sides. The solid curve corresponds to the data shown in Figs. 1, 2, whereas the dashed curve corresponds to the reconstruction from the other side of the grating. The figure shows an excellent agreement between the two reconstructions. The maximum difference between the two reconstructed amplitude profiles is equal to 4% of the maximum grating amplitude.

Fig. 5
Fig. 5

Phase of the reconstructed grating performed from the two grating sides. The maximum difference between the two reconstructed phase profiles is 0.03 rad . Curve definitions as in Fig. 4.

Fig. 6
Fig. 6

Grating amplitude, reconstructed from both grating sides when the reflection spectrum is not regularized and the ILP algorithm is used. The figure shows that the grating cannot be reconstructed without regularizing its reflection spectrum. Curve definitions as in Fig. 4.

Fig. 7
Fig. 7

Grating amplitude, reconstructed from both grating sides when the reflection spectrum is regularized, but the DLP algorithm is used instead of the ILP algorithm. The figure shows that the grating cannot be reconstructed using the DLP algorithm. Thus, it is essential that the ILP IS algorithm be used. Curve definitions as in Fig. 4.

Equations (3)

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B ( k ) = r ( k ) 2 1 r ( k ) 2 ,
B ( τ ) = 1 2 π B ( k ) exp ( i k τ ) d τ .
Δ B ( τ ) = 1 N c n exp ( i k n τ ) ,

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