Abstract

We present a theoretical analysis of light propagation in a four-layer planar waveguide that consists of a long-period grating (LPG) having a period of the order of 100 µm. By means of the coupled-mode theory, we show that such a structure is capable of coupling light from the fundamental guided mode to the cladding modes at specific wavelengths (resonance wavelengths) and thus results in sharp rejection bands in the transmission spectrum of the waveguide. Our numerical results show that the resonance wavelengths as well as the transmission spectrum can be significantly changed with the waveguide and grating parameters. A waveguide-based LPG should provide a useful approach to the design of a wide range of integrated-optic devices, including wavelength-tunable filters, switches, and environmental sensors.

© 2002 Optical Society of America

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  1. A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, P. J. Lamaire, N. S. Bergano, C. R. Davidson, “Long-period fiber-grating-based gain equalizers,” Opt. Lett. 21, 336–338 (1996).
    [CrossRef] [PubMed]
  2. P. F. Wysocki, J. B. Judkins, R. P. Espindola, M. Andrejco, A. M. Vengsarkar, “Broad-band erbium-doped fiber amplifier flattened beyond 40 nm using long-period grating filter,” IEEE Photon. Technol. Lett. 9, 1343–1345 (1997).
    [CrossRef]
  3. J. R. Qian, H. F. Chen, “Gain flattening fibre filters using phase-shifted long period fibre gratings,” Electron. Lett. 34, 1132–1133 (1998).
    [CrossRef]
  4. M. K. Pandit, K. S. Chiang, Z. H. Chen, S. P. Li, “Tunable long-period fiber gratings for EDFA gain and ASE equalization,” Microwave Opt. Technol. Lett. 25, 181–184 (2000).
    [CrossRef]
  5. 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. Lightwave Technol. 14, 58–65 (1996).
    [CrossRef]
  6. B. H. Lee, J. Nishii, “Notch filters based on cascaded multiple long-period fibre gratings,” Electron. Lett. 34, 1872–1873 (1998).
    [CrossRef]
  7. A. A. Abramov, B. J. Eggleton, J. A. Rogers, R. P. Espindola, A. Hale, R. S. Windeler, T. A. Strasser, “Electrically tunable efficient broad-band fiber filter,” IEEE Photon. Technol. Lett. 11, 445–447 (1999).
    [CrossRef]
  8. D. M. Costantini, C. A. P. Muller, S. A. Vasiliev, H. G. Limberger, R. P. Salathe, “Tunable loss filter based on metal-coated long-period fiber grating,” IEEE Photon. Technol. Lett. 11, 1458–1560 (1999).
    [CrossRef]
  9. O. Deparis, R. Kiyan, O. Pottiez, M. Blondel, I. G. Korolev, S. A. Vasiliev, E. M. Dianov, “Bandpass filters based on pi-shifted long-period fiber gratings for actively mode-locked erbium fiber lasers,” Opt. Lett. 26, 1293–1241 (2001).
    [CrossRef]
  10. M. Das, K. Thyagarajan, “Wavelength-division multiplexing isolation filter using concatenated chirped long period gratings,” Opt. Commun. 197, 67–71 (2001).
    [CrossRef]
  11. K. S. Chiang, Y. Liu, M. N. Ng, S. Li, “Coupling between two parallel long-period fibre gratings,” Electron. Lett. 36, 1408–1409 (2000).
    [CrossRef]
  12. D. B. Stegall, T. Erdogan, “Dispersion control with use of long-period fiber gratings,” J. Opt. Soc. Am. A 17, 304–312 (2000).
    [CrossRef]
  13. M. Das, K. Thyagarajan, “Dispersion compensation in transmission using uniform long period fiber gratings,” Opt. Commun. 190, 159–163 (2001).
    [CrossRef]
  14. V. Bhatia, A. M. Vengsarkar, “Optical fiber long-period grating sensors,” Opt. Lett. 21, 692–694 (1996).
    [CrossRef] [PubMed]
  15. V. Bhatia, D. Campbell, R. O. Claus, A. M. Vengsarkar, “Simultaneous strain and temperature measurement with long-period gratings,” Opt. Lett. 22, 648–650 (1997).
    [CrossRef] [PubMed]
  16. V. Grubsky, J. Feinberg, “Long-period fiber gratings with variable coupling for real-time sensing applications,” Opt. Lett. 25, 203–205 (2000).
    [CrossRef]
  17. H. J. Patrick, A. D. Kersey, F. Bucholtz, “Analysis of the response of long-period fiber gratings to the external index of refraction,” J. Lightwave Technol. 16, 1606–1612 (1998).
    [CrossRef]
  18. K. S. Chiang, Y. Liu, M. N. Ng, X. Dong, “Analysis of etched long-period fibre grating and its response to external refractive index,” Electron. Lett. 36, 966–967 (2000).
    [CrossRef]
  19. S. Khaliq, S. W. James, R. P. Tatam, “Fiber-optic liquid-level sensor using a long-period grating,” Opt. Lett. 26, 1224–1226 (2001).
    [CrossRef]
  20. B. H. Lee, Y. Liu, S. B. Lee, S. S. Choi, J. N. Jang, “Displacements of the resonant peaks of a long-period fiber grating induced by a change of ambient refractive index,” Opt. Lett. 22, 1769–1771 (1997).
    [CrossRef]
  21. A. Yariv, Optical Electronics in Modern Communications (Oxford U. Press, New York, 1997).
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  23. X. W. Shu, X. M. Zhu, Q. L. Wang, S. Jiang, W. Shi, Z. J. Huang, D. X. Huang, “Dual resonant peaks of LP015 cladding mode in long-period gratings,” Electron. Lett. 35, 649–651 (1999).
    [CrossRef]
  24. R. S. Moshrefzadeh, M. D. Radcliffe, T. C. Lee, S. K. Mohpatra, “Temperature dependence of index of refraction of polymeric waveguides,” J. Lightwave Technol. 10, 420–425 (1992).
    [CrossRef]
  25. X. W. Shu, X. M. Zhu, S. Jiang, W. Shi, D. X. Huang, “High sensitivity of dual resonant peaks of long-period fiber grating to surrounding refractive index changes,” Electron. Lett. 35, 1580–1581 (1999).
    [CrossRef]
  26. W. P. Wong, K. S. Chiang, “Design of polarization-insensitive Bragg gratings in zero-birefringence ridge waveguides,” IEEE J. Quantum Elect. 37, 1138–1145 (2001).
    [CrossRef]

2001 (5)

O. Deparis, R. Kiyan, O. Pottiez, M. Blondel, I. G. Korolev, S. A. Vasiliev, E. M. Dianov, “Bandpass filters based on pi-shifted long-period fiber gratings for actively mode-locked erbium fiber lasers,” Opt. Lett. 26, 1293–1241 (2001).
[CrossRef]

M. Das, K. Thyagarajan, “Wavelength-division multiplexing isolation filter using concatenated chirped long period gratings,” Opt. Commun. 197, 67–71 (2001).
[CrossRef]

M. Das, K. Thyagarajan, “Dispersion compensation in transmission using uniform long period fiber gratings,” Opt. Commun. 190, 159–163 (2001).
[CrossRef]

S. Khaliq, S. W. James, R. P. Tatam, “Fiber-optic liquid-level sensor using a long-period grating,” Opt. Lett. 26, 1224–1226 (2001).
[CrossRef]

W. P. Wong, K. S. Chiang, “Design of polarization-insensitive Bragg gratings in zero-birefringence ridge waveguides,” IEEE J. Quantum Elect. 37, 1138–1145 (2001).
[CrossRef]

2000 (5)

K. S. Chiang, Y. Liu, M. N. Ng, X. Dong, “Analysis of etched long-period fibre grating and its response to external refractive index,” Electron. Lett. 36, 966–967 (2000).
[CrossRef]

V. Grubsky, J. Feinberg, “Long-period fiber gratings with variable coupling for real-time sensing applications,” Opt. Lett. 25, 203–205 (2000).
[CrossRef]

K. S. Chiang, Y. Liu, M. N. Ng, S. Li, “Coupling between two parallel long-period fibre gratings,” Electron. Lett. 36, 1408–1409 (2000).
[CrossRef]

D. B. Stegall, T. Erdogan, “Dispersion control with use of long-period fiber gratings,” J. Opt. Soc. Am. A 17, 304–312 (2000).
[CrossRef]

M. K. Pandit, K. S. Chiang, Z. H. Chen, S. P. Li, “Tunable long-period fiber gratings for EDFA gain and ASE equalization,” Microwave Opt. Technol. Lett. 25, 181–184 (2000).
[CrossRef]

1999 (4)

A. A. Abramov, B. J. Eggleton, J. A. Rogers, R. P. Espindola, A. Hale, R. S. Windeler, T. A. Strasser, “Electrically tunable efficient broad-band fiber filter,” IEEE Photon. Technol. Lett. 11, 445–447 (1999).
[CrossRef]

D. M. Costantini, C. A. P. Muller, S. A. Vasiliev, H. G. Limberger, R. P. Salathe, “Tunable loss filter based on metal-coated long-period fiber grating,” IEEE Photon. Technol. Lett. 11, 1458–1560 (1999).
[CrossRef]

X. W. Shu, X. M. Zhu, S. Jiang, W. Shi, D. X. Huang, “High sensitivity of dual resonant peaks of long-period fiber grating to surrounding refractive index changes,” Electron. Lett. 35, 1580–1581 (1999).
[CrossRef]

X. W. Shu, X. M. Zhu, Q. L. Wang, S. Jiang, W. Shi, Z. J. Huang, D. X. Huang, “Dual resonant peaks of LP015 cladding mode in long-period gratings,” Electron. Lett. 35, 649–651 (1999).
[CrossRef]

1998 (3)

J. R. Qian, H. F. Chen, “Gain flattening fibre filters using phase-shifted long period fibre gratings,” Electron. Lett. 34, 1132–1133 (1998).
[CrossRef]

B. H. Lee, J. Nishii, “Notch filters based on cascaded multiple long-period fibre gratings,” Electron. Lett. 34, 1872–1873 (1998).
[CrossRef]

H. J. Patrick, A. D. Kersey, F. Bucholtz, “Analysis of the response of long-period fiber gratings to the external index of refraction,” J. Lightwave Technol. 16, 1606–1612 (1998).
[CrossRef]

1997 (3)

1996 (3)

1992 (1)

R. S. Moshrefzadeh, M. D. Radcliffe, T. C. Lee, S. K. Mohpatra, “Temperature dependence of index of refraction of polymeric waveguides,” J. Lightwave Technol. 10, 420–425 (1992).
[CrossRef]

Abramov, A. A.

A. A. Abramov, B. J. Eggleton, J. A. Rogers, R. P. Espindola, A. Hale, R. S. Windeler, T. A. Strasser, “Electrically tunable efficient broad-band fiber filter,” IEEE Photon. Technol. Lett. 11, 445–447 (1999).
[CrossRef]

Adams, M. J.

M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981) Chap. 2, pp. 75–77.

Andrejco, M.

P. F. Wysocki, J. B. Judkins, R. P. Espindola, M. Andrejco, A. M. Vengsarkar, “Broad-band erbium-doped fiber amplifier flattened beyond 40 nm using long-period grating filter,” IEEE Photon. Technol. Lett. 9, 1343–1345 (1997).
[CrossRef]

Bergano, N. S.

Bhatia, V.

Blondel, M.

O. Deparis, R. Kiyan, O. Pottiez, M. Blondel, I. G. Korolev, S. A. Vasiliev, E. M. Dianov, “Bandpass filters based on pi-shifted long-period fiber gratings for actively mode-locked erbium fiber lasers,” Opt. Lett. 26, 1293–1241 (2001).
[CrossRef]

Bucholtz, F.

Campbell, D.

Chen, H. F.

J. R. Qian, H. F. Chen, “Gain flattening fibre filters using phase-shifted long period fibre gratings,” Electron. Lett. 34, 1132–1133 (1998).
[CrossRef]

Chen, Z. H.

M. K. Pandit, K. S. Chiang, Z. H. Chen, S. P. Li, “Tunable long-period fiber gratings for EDFA gain and ASE equalization,” Microwave Opt. Technol. Lett. 25, 181–184 (2000).
[CrossRef]

Chiang, K. S.

W. P. Wong, K. S. Chiang, “Design of polarization-insensitive Bragg gratings in zero-birefringence ridge waveguides,” IEEE J. Quantum Elect. 37, 1138–1145 (2001).
[CrossRef]

M. K. Pandit, K. S. Chiang, Z. H. Chen, S. P. Li, “Tunable long-period fiber gratings for EDFA gain and ASE equalization,” Microwave Opt. Technol. Lett. 25, 181–184 (2000).
[CrossRef]

K. S. Chiang, Y. Liu, M. N. Ng, S. Li, “Coupling between two parallel long-period fibre gratings,” Electron. Lett. 36, 1408–1409 (2000).
[CrossRef]

K. S. Chiang, Y. Liu, M. N. Ng, X. Dong, “Analysis of etched long-period fibre grating and its response to external refractive index,” Electron. Lett. 36, 966–967 (2000).
[CrossRef]

Choi, S. S.

Claus, R. O.

Costantini, D. M.

D. M. Costantini, C. A. P. Muller, S. A. Vasiliev, H. G. Limberger, R. P. Salathe, “Tunable loss filter based on metal-coated long-period fiber grating,” IEEE Photon. Technol. Lett. 11, 1458–1560 (1999).
[CrossRef]

Das, M.

M. Das, K. Thyagarajan, “Dispersion compensation in transmission using uniform long period fiber gratings,” Opt. Commun. 190, 159–163 (2001).
[CrossRef]

M. Das, K. Thyagarajan, “Wavelength-division multiplexing isolation filter using concatenated chirped long period gratings,” Opt. Commun. 197, 67–71 (2001).
[CrossRef]

Davidson, C. R.

Deparis, O.

O. Deparis, R. Kiyan, O. Pottiez, M. Blondel, I. G. Korolev, S. A. Vasiliev, E. M. Dianov, “Bandpass filters based on pi-shifted long-period fiber gratings for actively mode-locked erbium fiber lasers,” Opt. Lett. 26, 1293–1241 (2001).
[CrossRef]

Dianov, E. M.

O. Deparis, R. Kiyan, O. Pottiez, M. Blondel, I. G. Korolev, S. A. Vasiliev, E. M. Dianov, “Bandpass filters based on pi-shifted long-period fiber gratings for actively mode-locked erbium fiber lasers,” Opt. Lett. 26, 1293–1241 (2001).
[CrossRef]

Dong, X.

K. S. Chiang, Y. Liu, M. N. Ng, X. Dong, “Analysis of etched long-period fibre grating and its response to external refractive index,” Electron. Lett. 36, 966–967 (2000).
[CrossRef]

Eggleton, B. J.

A. A. Abramov, B. J. Eggleton, J. A. Rogers, R. P. Espindola, A. Hale, R. S. Windeler, T. A. Strasser, “Electrically tunable efficient broad-band fiber filter,” IEEE Photon. Technol. Lett. 11, 445–447 (1999).
[CrossRef]

Erdogan, T.

D. B. Stegall, T. Erdogan, “Dispersion control with use of long-period fiber gratings,” J. Opt. Soc. Am. A 17, 304–312 (2000).
[CrossRef]

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. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

Espindola, R. P.

A. A. Abramov, B. J. Eggleton, J. A. Rogers, R. P. Espindola, A. Hale, R. S. Windeler, T. A. Strasser, “Electrically tunable efficient broad-band fiber filter,” IEEE Photon. Technol. Lett. 11, 445–447 (1999).
[CrossRef]

P. F. Wysocki, J. B. Judkins, R. P. Espindola, M. Andrejco, A. M. Vengsarkar, “Broad-band erbium-doped fiber amplifier flattened beyond 40 nm using long-period grating filter,” IEEE Photon. Technol. Lett. 9, 1343–1345 (1997).
[CrossRef]

Feinberg, J.

Grubsky, V.

Hale, A.

A. A. Abramov, B. J. Eggleton, J. A. Rogers, R. P. Espindola, A. Hale, R. S. Windeler, T. A. Strasser, “Electrically tunable efficient broad-band fiber filter,” IEEE Photon. Technol. Lett. 11, 445–447 (1999).
[CrossRef]

Huang, D. X.

X. W. Shu, X. M. Zhu, Q. L. Wang, S. Jiang, W. Shi, Z. J. Huang, D. X. Huang, “Dual resonant peaks of LP015 cladding mode in long-period gratings,” Electron. Lett. 35, 649–651 (1999).
[CrossRef]

X. W. Shu, X. M. Zhu, S. Jiang, W. Shi, D. X. Huang, “High sensitivity of dual resonant peaks of long-period fiber grating to surrounding refractive index changes,” Electron. Lett. 35, 1580–1581 (1999).
[CrossRef]

Huang, Z. J.

X. W. Shu, X. M. Zhu, Q. L. Wang, S. Jiang, W. Shi, Z. J. Huang, D. X. Huang, “Dual resonant peaks of LP015 cladding mode in long-period gratings,” Electron. Lett. 35, 649–651 (1999).
[CrossRef]

James, S. W.

Jang, J. N.

Jiang, S.

X. W. Shu, X. M. Zhu, Q. L. Wang, S. Jiang, W. Shi, Z. J. Huang, D. X. Huang, “Dual resonant peaks of LP015 cladding mode in long-period gratings,” Electron. Lett. 35, 649–651 (1999).
[CrossRef]

X. W. Shu, X. M. Zhu, S. Jiang, W. Shi, D. X. Huang, “High sensitivity of dual resonant peaks of long-period fiber grating to surrounding refractive index changes,” Electron. Lett. 35, 1580–1581 (1999).
[CrossRef]

Judkins, J. B.

P. F. Wysocki, J. B. Judkins, R. P. Espindola, M. Andrejco, A. M. Vengsarkar, “Broad-band erbium-doped fiber amplifier flattened beyond 40 nm using long-period grating filter,” IEEE Photon. Technol. Lett. 9, 1343–1345 (1997).
[CrossRef]

A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, P. J. Lamaire, N. S. Bergano, C. R. Davidson, “Long-period fiber-grating-based gain equalizers,” Opt. Lett. 21, 336–338 (1996).
[CrossRef] [PubMed]

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. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

Kersey, A. D.

Khaliq, S.

Kiyan, R.

O. Deparis, R. Kiyan, O. Pottiez, M. Blondel, I. G. Korolev, S. A. Vasiliev, E. M. Dianov, “Bandpass filters based on pi-shifted long-period fiber gratings for actively mode-locked erbium fiber lasers,” Opt. Lett. 26, 1293–1241 (2001).
[CrossRef]

Korolev, I. G.

O. Deparis, R. Kiyan, O. Pottiez, M. Blondel, I. G. Korolev, S. A. Vasiliev, E. M. Dianov, “Bandpass filters based on pi-shifted long-period fiber gratings for actively mode-locked erbium fiber lasers,” Opt. Lett. 26, 1293–1241 (2001).
[CrossRef]

Lamaire, P. J.

Lee, B. H.

Lee, S. B.

Lee, T. C.

R. S. Moshrefzadeh, M. D. Radcliffe, T. C. Lee, S. K. Mohpatra, “Temperature dependence of index of refraction of polymeric waveguides,” J. Lightwave Technol. 10, 420–425 (1992).
[CrossRef]

Lemaire, P. J.

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. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

Li, S.

K. S. Chiang, Y. Liu, M. N. Ng, S. Li, “Coupling between two parallel long-period fibre gratings,” Electron. Lett. 36, 1408–1409 (2000).
[CrossRef]

Li, S. P.

M. K. Pandit, K. S. Chiang, Z. H. Chen, S. P. Li, “Tunable long-period fiber gratings for EDFA gain and ASE equalization,” Microwave Opt. Technol. Lett. 25, 181–184 (2000).
[CrossRef]

Limberger, H. G.

D. M. Costantini, C. A. P. Muller, S. A. Vasiliev, H. G. Limberger, R. P. Salathe, “Tunable loss filter based on metal-coated long-period fiber grating,” IEEE Photon. Technol. Lett. 11, 1458–1560 (1999).
[CrossRef]

Liu, Y.

K. S. Chiang, Y. Liu, M. N. Ng, S. Li, “Coupling between two parallel long-period fibre gratings,” Electron. Lett. 36, 1408–1409 (2000).
[CrossRef]

K. S. Chiang, Y. Liu, M. N. Ng, X. Dong, “Analysis of etched long-period fibre grating and its response to external refractive index,” Electron. Lett. 36, 966–967 (2000).
[CrossRef]

B. H. Lee, Y. Liu, S. B. Lee, S. S. Choi, J. N. Jang, “Displacements of the resonant peaks of a long-period fiber grating induced by a change of ambient refractive index,” Opt. Lett. 22, 1769–1771 (1997).
[CrossRef]

Mohpatra, S. K.

R. S. Moshrefzadeh, M. D. Radcliffe, T. C. Lee, S. K. Mohpatra, “Temperature dependence of index of refraction of polymeric waveguides,” J. Lightwave Technol. 10, 420–425 (1992).
[CrossRef]

Moshrefzadeh, R. S.

R. S. Moshrefzadeh, M. D. Radcliffe, T. C. Lee, S. K. Mohpatra, “Temperature dependence of index of refraction of polymeric waveguides,” J. Lightwave Technol. 10, 420–425 (1992).
[CrossRef]

Muller, C. A. P.

D. M. Costantini, C. A. P. Muller, S. A. Vasiliev, H. G. Limberger, R. P. Salathe, “Tunable loss filter based on metal-coated long-period fiber grating,” IEEE Photon. Technol. Lett. 11, 1458–1560 (1999).
[CrossRef]

Ng, M. N.

K. S. Chiang, Y. Liu, M. N. Ng, X. Dong, “Analysis of etched long-period fibre grating and its response to external refractive index,” Electron. Lett. 36, 966–967 (2000).
[CrossRef]

K. S. Chiang, Y. Liu, M. N. Ng, S. Li, “Coupling between two parallel long-period fibre gratings,” Electron. Lett. 36, 1408–1409 (2000).
[CrossRef]

Nishii, J.

B. H. Lee, J. Nishii, “Notch filters based on cascaded multiple long-period fibre gratings,” Electron. Lett. 34, 1872–1873 (1998).
[CrossRef]

Pandit, M. K.

M. K. Pandit, K. S. Chiang, Z. H. Chen, S. P. Li, “Tunable long-period fiber gratings for EDFA gain and ASE equalization,” Microwave Opt. Technol. Lett. 25, 181–184 (2000).
[CrossRef]

Patrick, H. J.

Pedrazzani, J. R.

Pottiez, O.

O. Deparis, R. Kiyan, O. Pottiez, M. Blondel, I. G. Korolev, S. A. Vasiliev, E. M. Dianov, “Bandpass filters based on pi-shifted long-period fiber gratings for actively mode-locked erbium fiber lasers,” Opt. Lett. 26, 1293–1241 (2001).
[CrossRef]

Qian, J. R.

J. R. Qian, H. F. Chen, “Gain flattening fibre filters using phase-shifted long period fibre gratings,” Electron. Lett. 34, 1132–1133 (1998).
[CrossRef]

Radcliffe, M. D.

R. S. Moshrefzadeh, M. D. Radcliffe, T. C. Lee, S. K. Mohpatra, “Temperature dependence of index of refraction of polymeric waveguides,” J. Lightwave Technol. 10, 420–425 (1992).
[CrossRef]

Rogers, J. A.

A. A. Abramov, B. J. Eggleton, J. A. Rogers, R. P. Espindola, A. Hale, R. S. Windeler, T. A. Strasser, “Electrically tunable efficient broad-band fiber filter,” IEEE Photon. Technol. Lett. 11, 445–447 (1999).
[CrossRef]

Salathe, R. P.

D. M. Costantini, C. A. P. Muller, S. A. Vasiliev, H. G. Limberger, R. P. Salathe, “Tunable loss filter based on metal-coated long-period fiber grating,” IEEE Photon. Technol. Lett. 11, 1458–1560 (1999).
[CrossRef]

Shi, W.

X. W. Shu, X. M. Zhu, Q. L. Wang, S. Jiang, W. Shi, Z. J. Huang, D. X. Huang, “Dual resonant peaks of LP015 cladding mode in long-period gratings,” Electron. Lett. 35, 649–651 (1999).
[CrossRef]

X. W. Shu, X. M. Zhu, S. Jiang, W. Shi, D. X. Huang, “High sensitivity of dual resonant peaks of long-period fiber grating to surrounding refractive index changes,” Electron. Lett. 35, 1580–1581 (1999).
[CrossRef]

Shu, X. W.

X. W. Shu, X. M. Zhu, Q. L. Wang, S. Jiang, W. Shi, Z. J. Huang, D. X. Huang, “Dual resonant peaks of LP015 cladding mode in long-period gratings,” Electron. Lett. 35, 649–651 (1999).
[CrossRef]

X. W. Shu, X. M. Zhu, S. Jiang, W. Shi, D. X. Huang, “High sensitivity of dual resonant peaks of long-period fiber grating to surrounding refractive index changes,” Electron. Lett. 35, 1580–1581 (1999).
[CrossRef]

Sipe, J. E.

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. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

Stegall, D. B.

Strasser, T. A.

A. A. Abramov, B. J. Eggleton, J. A. Rogers, R. P. Espindola, A. Hale, R. S. Windeler, T. A. Strasser, “Electrically tunable efficient broad-band fiber filter,” IEEE Photon. Technol. Lett. 11, 445–447 (1999).
[CrossRef]

Tatam, R. P.

Thyagarajan, K.

M. Das, K. Thyagarajan, “Wavelength-division multiplexing isolation filter using concatenated chirped long period gratings,” Opt. Commun. 197, 67–71 (2001).
[CrossRef]

M. Das, K. Thyagarajan, “Dispersion compensation in transmission using uniform long period fiber gratings,” Opt. Commun. 190, 159–163 (2001).
[CrossRef]

Vasiliev, S. A.

O. Deparis, R. Kiyan, O. Pottiez, M. Blondel, I. G. Korolev, S. A. Vasiliev, E. M. Dianov, “Bandpass filters based on pi-shifted long-period fiber gratings for actively mode-locked erbium fiber lasers,” Opt. Lett. 26, 1293–1241 (2001).
[CrossRef]

D. M. Costantini, C. A. P. Muller, S. A. Vasiliev, H. G. Limberger, R. P. Salathe, “Tunable loss filter based on metal-coated long-period fiber grating,” IEEE Photon. Technol. Lett. 11, 1458–1560 (1999).
[CrossRef]

Vengsarkar, A. M.

P. F. Wysocki, J. B. Judkins, R. P. Espindola, M. Andrejco, A. M. Vengsarkar, “Broad-band erbium-doped fiber amplifier flattened beyond 40 nm using long-period grating filter,” IEEE Photon. Technol. Lett. 9, 1343–1345 (1997).
[CrossRef]

V. Bhatia, D. Campbell, R. O. Claus, A. M. Vengsarkar, “Simultaneous strain and temperature measurement with long-period gratings,” Opt. Lett. 22, 648–650 (1997).
[CrossRef] [PubMed]

V. Bhatia, A. M. Vengsarkar, “Optical fiber long-period grating sensors,” Opt. Lett. 21, 692–694 (1996).
[CrossRef] [PubMed]

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. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, P. J. Lamaire, N. S. Bergano, C. R. Davidson, “Long-period fiber-grating-based gain equalizers,” Opt. Lett. 21, 336–338 (1996).
[CrossRef] [PubMed]

Wang, Q. L.

X. W. Shu, X. M. Zhu, Q. L. Wang, S. Jiang, W. Shi, Z. J. Huang, D. X. Huang, “Dual resonant peaks of LP015 cladding mode in long-period gratings,” Electron. Lett. 35, 649–651 (1999).
[CrossRef]

Windeler, R. S.

A. A. Abramov, B. J. Eggleton, J. A. Rogers, R. P. Espindola, A. Hale, R. S. Windeler, T. A. Strasser, “Electrically tunable efficient broad-band fiber filter,” IEEE Photon. Technol. Lett. 11, 445–447 (1999).
[CrossRef]

Wong, W. P.

W. P. Wong, K. S. Chiang, “Design of polarization-insensitive Bragg gratings in zero-birefringence ridge waveguides,” IEEE J. Quantum Elect. 37, 1138–1145 (2001).
[CrossRef]

Wysocki, P. F.

P. F. Wysocki, J. B. Judkins, R. P. Espindola, M. Andrejco, A. M. Vengsarkar, “Broad-band erbium-doped fiber amplifier flattened beyond 40 nm using long-period grating filter,” IEEE Photon. Technol. Lett. 9, 1343–1345 (1997).
[CrossRef]

Yariv, A.

A. Yariv, Optical Electronics in Modern Communications (Oxford U. Press, New York, 1997).

Zhu, X. M.

X. W. Shu, X. M. Zhu, Q. L. Wang, S. Jiang, W. Shi, Z. J. Huang, D. X. Huang, “Dual resonant peaks of LP015 cladding mode in long-period gratings,” Electron. Lett. 35, 649–651 (1999).
[CrossRef]

X. W. Shu, X. M. Zhu, S. Jiang, W. Shi, D. X. Huang, “High sensitivity of dual resonant peaks of long-period fiber grating to surrounding refractive index changes,” Electron. Lett. 35, 1580–1581 (1999).
[CrossRef]

Electron. Lett. (6)

J. R. Qian, H. F. Chen, “Gain flattening fibre filters using phase-shifted long period fibre gratings,” Electron. Lett. 34, 1132–1133 (1998).
[CrossRef]

B. H. Lee, J. Nishii, “Notch filters based on cascaded multiple long-period fibre gratings,” Electron. Lett. 34, 1872–1873 (1998).
[CrossRef]

K. S. Chiang, Y. Liu, M. N. Ng, S. Li, “Coupling between two parallel long-period fibre gratings,” Electron. Lett. 36, 1408–1409 (2000).
[CrossRef]

K. S. Chiang, Y. Liu, M. N. Ng, X. Dong, “Analysis of etched long-period fibre grating and its response to external refractive index,” Electron. Lett. 36, 966–967 (2000).
[CrossRef]

X. W. Shu, X. M. Zhu, Q. L. Wang, S. Jiang, W. Shi, Z. J. Huang, D. X. Huang, “Dual resonant peaks of LP015 cladding mode in long-period gratings,” Electron. Lett. 35, 649–651 (1999).
[CrossRef]

X. W. Shu, X. M. Zhu, S. Jiang, W. Shi, D. X. Huang, “High sensitivity of dual resonant peaks of long-period fiber grating to surrounding refractive index changes,” Electron. Lett. 35, 1580–1581 (1999).
[CrossRef]

IEEE J. Quantum Elect. (1)

W. P. Wong, K. S. Chiang, “Design of polarization-insensitive Bragg gratings in zero-birefringence ridge waveguides,” IEEE J. Quantum Elect. 37, 1138–1145 (2001).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

A. A. Abramov, B. J. Eggleton, J. A. Rogers, R. P. Espindola, A. Hale, R. S. Windeler, T. A. Strasser, “Electrically tunable efficient broad-band fiber filter,” IEEE Photon. Technol. Lett. 11, 445–447 (1999).
[CrossRef]

D. M. Costantini, C. A. P. Muller, S. A. Vasiliev, H. G. Limberger, R. P. Salathe, “Tunable loss filter based on metal-coated long-period fiber grating,” IEEE Photon. Technol. Lett. 11, 1458–1560 (1999).
[CrossRef]

P. F. Wysocki, J. B. Judkins, R. P. Espindola, M. Andrejco, A. M. Vengsarkar, “Broad-band erbium-doped fiber amplifier flattened beyond 40 nm using long-period grating filter,” IEEE Photon. Technol. Lett. 9, 1343–1345 (1997).
[CrossRef]

J. Lightwave Technol. (3)

H. J. Patrick, A. D. Kersey, F. Bucholtz, “Analysis of the response of long-period fiber gratings to the external index of refraction,” J. Lightwave Technol. 16, 1606–1612 (1998).
[CrossRef]

R. S. Moshrefzadeh, M. D. Radcliffe, T. C. Lee, S. K. Mohpatra, “Temperature dependence of index of refraction of polymeric waveguides,” J. Lightwave Technol. 10, 420–425 (1992).
[CrossRef]

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. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

J. Opt. Soc. Am. A (1)

Microwave Opt. Technol. Lett. (1)

M. K. Pandit, K. S. Chiang, Z. H. Chen, S. P. Li, “Tunable long-period fiber gratings for EDFA gain and ASE equalization,” Microwave Opt. Technol. Lett. 25, 181–184 (2000).
[CrossRef]

Opt. Commun. (2)

M. Das, K. Thyagarajan, “Dispersion compensation in transmission using uniform long period fiber gratings,” Opt. Commun. 190, 159–163 (2001).
[CrossRef]

M. Das, K. Thyagarajan, “Wavelength-division multiplexing isolation filter using concatenated chirped long period gratings,” Opt. Commun. 197, 67–71 (2001).
[CrossRef]

Opt. Lett. (7)

Other (2)

A. Yariv, Optical Electronics in Modern Communications (Oxford U. Press, New York, 1997).

M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981) Chap. 2, pp. 75–77.

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Figures (7)

Fig. 1
Fig. 1

Refractive-index profile of a planar waveguide with a cladding layer, where a long-period grating lies in the region 0 < x < d f .

Fig. 2
Fig. 2

(a) Phase-matching curves for a long-period grating in a planar waveguide with n s = 1.5, n f = 1.52, n cl = 1.51, n ex = 1.0, d f = 2.0 µm, and d cl = 30.0 µm. The dashed vertical line marks the grating period Λ = 290 µm. (b) Transmission spectrum of a grating that is 2.5 cm long and has a period of 290 µm, showing double resonance wavelengths for the coupling to the TE4 mode.

Fig. 3
Fig. 3

Variation of the phase mismatch Δβ between the TE0 and TE1 modes as a function of wavelength for (a) d cl = 4.5 µm, (b) d cl = 5.5 µm, and (c) d cl = 7.5 µm. The dashed straight lines show the values of 2π/Λ and their points of intersection with the curves give the resonance wavelengths.

Fig. 4
Fig. 4

The transmission spectrum of the grating corresponding to Fig. 3(b), showing a rejection band as wide as 345 nm.

Fig. 5
Fig. 5

Variation of the normalized coupled power (to the TE1 mode) with d cl, showing the effect of the cladding thickness on the transmission spectrum.

Fig. 6
Fig. 6

Variation of the normalized coupled power (to the TE1 mode) with n cl, showing the effect of the refractive index of the cladding on the transmission spectrum.

Fig. 7
Fig. 7

Variation of the resonance wavelength (for the coupling to the TE1 mode) as a function of the refractive index of the external medium for (a) the case of a single-resonance wavelength and (b) the case of double-resonance wavelengths.

Equations (6)

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

Ψ=12AzE0xexpiωt-β0z+BzEmxexp[iωt-βmz+cc,
2Ψx2+2Ψz2+k02n2x+Δn2x, zΨ=0,
dAdz=κBexpiΓz,
dBdz=-κAexp-iΓz,
PAz=|Az|2=P01-κ2γ2sin2 γz,
λ0=N0-NmΛ,

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