Abstract

The interference fringes formed in a long-period fiber grating pair are sensitive to the loss in the cladding mode, which can be induced by bending or by coating on the fiber. Assuming that there is no loss and that both gratings are identical, the interference fringes are shown to have 100% contrast when each grating has 50% transmissivity. By contrast, if the cladding mode is absorbed or scattered the fringe contrast is shown to be degraded. The spectral behaviors of a long-period fiber grating pair with loss is analyzed by the coupled-mode theory and is compared with experimental results.

© 1998 Optical Society of America

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References

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  1. E. M. Dianov, S. A. Vasiliev, A. S. Kurkov, O. I. Medvedkov, and V. N. Protopopov, in Proceedings of European Conference on Optical Communication (Interuniversity Microelectronics Center, Gent, Belgium, 1996), p. 65.
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    [CrossRef]
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    [CrossRef]
  7. P. F. Wysocki, J. Judkins, R. Espindola, M. Andrejco, A. Vengsarkar, and K. Walker, in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. PD2-1.
  8. A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, and P. J. Lemaire, Opt. Lett. 21, 336 (1996).
    [CrossRef] [PubMed]

1998 (1)

B. H. Lee and J. Nishii, Electron. Lett. 34, 1129 (1998).
[CrossRef]

1997 (1)

1996 (1)

Andrejco, M.

P. F. Wysocki, J. Judkins, R. Espindola, M. Andrejco, A. Vengsarkar, and K. Walker, in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. PD2-1.

Boschis, L.

L. Tallone, L. Boschis, L. Cognolato, E. Emelli, E. Riccardi, and O. Rossotto, in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 175.

Cai, J. X.

D. S. Starodubov, V. Grubsky, A. Skorucak, J. Feinberg, J. X. Cai, K.-M. Feng, and A. E. Willner, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. PD8-1.

Choi, S. S.

Cognolato, L.

L. Tallone, L. Boschis, L. Cognolato, E. Emelli, E. Riccardi, and O. Rossotto, in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 175.

Dianov, E. M.

E. M. Dianov, S. A. Vasiliev, A. S. Kurkov, O. I. Medvedkov, and V. N. Protopopov, in Proceedings of European Conference on Optical Communication (Interuniversity Microelectronics Center, Gent, Belgium, 1996), p. 65.

Emelli, E.

L. Tallone, L. Boschis, L. Cognolato, E. Emelli, E. Riccardi, and O. Rossotto, in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 175.

Espindola, R.

P. F. Wysocki, J. Judkins, R. Espindola, M. Andrejco, A. Vengsarkar, and K. Walker, in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. PD2-1.

Feinberg, J.

D. S. Starodubov, V. Grubsky, A. Skorucak, J. Feinberg, J. X. Cai, K.-M. Feng, and A. E. Willner, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. PD8-1.

Feng, K.-M.

D. S. Starodubov, V. Grubsky, A. Skorucak, J. Feinberg, J. X. Cai, K.-M. Feng, and A. E. Willner, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. PD8-1.

Grubsky, V.

D. S. Starodubov, V. Grubsky, A. Skorucak, J. Feinberg, J. X. Cai, K.-M. Feng, and A. E. Willner, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. PD8-1.

Jang, J. N.

Judkins, J.

P. F. Wysocki, J. Judkins, R. Espindola, M. Andrejco, A. Vengsarkar, and K. Walker, in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. PD2-1.

Judkins, J. B.

Kurkov, A. S.

E. M. Dianov, S. A. Vasiliev, A. S. Kurkov, O. I. Medvedkov, and V. N. Protopopov, in Proceedings of European Conference on Optical Communication (Interuniversity Microelectronics Center, Gent, Belgium, 1996), p. 65.

Lee, B. H.

Lee, S. B.

Lemaire, P. J.

Liu, Y.

Medvedkov, O. I.

E. M. Dianov, S. A. Vasiliev, A. S. Kurkov, O. I. Medvedkov, and V. N. Protopopov, in Proceedings of European Conference on Optical Communication (Interuniversity Microelectronics Center, Gent, Belgium, 1996), p. 65.

Nishii, J.

B. H. Lee and J. Nishii, Electron. Lett. 34, 1129 (1998).
[CrossRef]

Pedrazzani, J. R.

Protopopov, V. N.

E. M. Dianov, S. A. Vasiliev, A. S. Kurkov, O. I. Medvedkov, and V. N. Protopopov, in Proceedings of European Conference on Optical Communication (Interuniversity Microelectronics Center, Gent, Belgium, 1996), p. 65.

Riccardi, E.

L. Tallone, L. Boschis, L. Cognolato, E. Emelli, E. Riccardi, and O. Rossotto, in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 175.

Rossotto, O.

L. Tallone, L. Boschis, L. Cognolato, E. Emelli, E. Riccardi, and O. Rossotto, in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 175.

Skorucak, A.

D. S. Starodubov, V. Grubsky, A. Skorucak, J. Feinberg, J. X. Cai, K.-M. Feng, and A. E. Willner, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. PD8-1.

Starodubov, D. S.

D. S. Starodubov, V. Grubsky, A. Skorucak, J. Feinberg, J. X. Cai, K.-M. Feng, and A. E. Willner, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. PD8-1.

Tallone, L.

L. Tallone, L. Boschis, L. Cognolato, E. Emelli, E. Riccardi, and O. Rossotto, in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 175.

Vasiliev, S. A.

E. M. Dianov, S. A. Vasiliev, A. S. Kurkov, O. I. Medvedkov, and V. N. Protopopov, in Proceedings of European Conference on Optical Communication (Interuniversity Microelectronics Center, Gent, Belgium, 1996), p. 65.

Vengsarkar, A.

P. F. Wysocki, J. Judkins, R. Espindola, M. Andrejco, A. Vengsarkar, and K. Walker, in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. PD2-1.

Vengsarkar, A. M.

Walker, K.

P. F. Wysocki, J. Judkins, R. Espindola, M. Andrejco, A. Vengsarkar, and K. Walker, in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. PD2-1.

Willner, A. E.

D. S. Starodubov, V. Grubsky, A. Skorucak, J. Feinberg, J. X. Cai, K.-M. Feng, and A. E. Willner, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. PD8-1.

Wysocki, P. F.

P. F. Wysocki, J. Judkins, R. Espindola, M. Andrejco, A. Vengsarkar, and K. Walker, in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. PD2-1.

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley-Interscience, New York, 1984), pp. 177–185.

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley-Interscience, New York, 1984), pp. 177–185.

Electron. Lett. (1)

B. H. Lee and J. Nishii, Electron. Lett. 34, 1129 (1998).
[CrossRef]

Opt. Lett. (2)

Other (5)

P. F. Wysocki, J. Judkins, R. Espindola, M. Andrejco, A. Vengsarkar, and K. Walker, in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. PD2-1.

E. M. Dianov, S. A. Vasiliev, A. S. Kurkov, O. I. Medvedkov, and V. N. Protopopov, in Proceedings of European Conference on Optical Communication (Interuniversity Microelectronics Center, Gent, Belgium, 1996), p. 65.

L. Tallone, L. Boschis, L. Cognolato, E. Emelli, E. Riccardi, and O. Rossotto, in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 175.

D. S. Starodubov, V. Grubsky, A. Skorucak, J. Feinberg, J. X. Cai, K.-M. Feng, and A. E. Willner, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. PD8-1.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley-Interscience, New York, 1984), pp. 177–185.

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Figures (4)

Fig. 1
Fig. 1

Spectra of a LPG pair with bending in the middle (thick curve) and without bending (thin curve), measured with a 1-nm resolution. The two gratings are separated by 50  cm, and each grating has 400µm periodicity and 20-mm length. The original coating layer, silicon resin, between gratings was not removed.

Fig. 2
Fig. 2

Detailed plot of Fig.  1, measured with a 0.1-nm resolution. The spectrum was measured without bending (thin curve), with small bending (thick curve), and with large bending (dashed–dotted curve). The fringes in the first stop band were overcoupled, and no fringe was observed from the second band.

Fig. 3
Fig. 3

Lower envelope curve of the interference fringes. The thin curve is the same plot as in Fig.  2. The thick curve was calculated from the spectrum of the bent LPG pair (dashed–dotted curve of Fig.  2). Owing to the fine fringe spacing, 0.45  nm, the fringes were smeared out somewhat.

Fig. 4
Fig. 4

Spectra of a weak LPG pair, separated by 30  cm, with bending in the middle (thicker curve, no peaks) and without bending (peaked curve). Each grating has 400µm periodicity and a 20-mm length. The fringe spacing is roughly 0.72  nm.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

AdA0=expiΔβ/2dcos sd-iΔβ2ssin sd,
AL+2dA0=cos sd-iΔβ2ssin sd2×expiΔβd-iβcore-βcladL+d-ακκ*s2sin2 sd,
AL+2dA0=cos2 sd+Δβ2s2 sin2 sdexpiΨ-ακκ*s2sin2 sd,
Ψ=2 tan-1-Δβ2s tan sd+Δβd-βcore-βcladL+d.
Ψ=-βcore-βcladL+d.
Tdoublemin=Tsingle-α1-Tsingle2,
Tdoublemax=Tsingle+α1-Tsingle2,
Tdoublemin=4Tsingle-1/22.
Tdoublemax=Tdoublemin=Tsingle2.

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