Abstract

We present long-period-grating in a planar optical waveguide that contains a low-index trench in the cladding region. The effect of the trench on transmission spectrum of the grating has been studied. The waveguide structure has been analyzed by the transfer matrix method and the output spectrum of the grating has been calculated by the coupled mode theory. Our numerical results show that position, strength, and width of the trench significantly affect the transmission spectrum of the grating. In particular, we show the appearance of triple resonance between a set of coupled modes and obtain an ultrawide band rejection in the output spectrum. We numerically demonstrate applications of the proposed structure in wideband rejection filters, refractive index sensors, and gain equalization of erbium-doped waveguide amplifiers.

© 2013 Optical Society of America

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  1. A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, P. J. Lamaire, N. S. Bergano, and C. R. Davidson, “Long-period fiber-grating-based gain equalizers,” Opt. Lett. 21, 336–338 (1996).
    [CrossRef]
  2. P. F. Wysocki, J. B. Judkins, R. P. Espindola, M. Andrejco, and 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. A. M. Vengsarkar, P. J. Lamaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band rejection filters,” J. Lightwave Technol. 14, 58–65(1996).
    [CrossRef]
  4. D. M. Constantini, C. A. P. Muller, S. A. Vasiliev, H. G. Limberger, and R. P. Salathe, “Tunable loss filter based on metal coated long-period fiber grating,” IEEE Photon. Technol. Lett. 11, 1458–1560 (1999).
    [CrossRef]
  5. K. S. Chiang, Y. Liu, M. N. Ng, and S. Li, “Coupling between two parallel long period fiber gratings,” Electron. Lett. 36, 1408–1409 (2000).
    [CrossRef]
  6. D. B. Stegall and T. Erdogan, “Dispersion control with use of long-period fiber gratings,” J. Opt. Soc. Am. A 17, 304–312 (2000).
    [CrossRef]
  7. M. Das and K. Thyagarajan, “Dispersion compensation in transmission using uniform long period fiber gratings,” Opt. Commun. 190, 159–163 (2001).
    [CrossRef]
  8. Y. Han, C. S. Kim, U. C. Paek, and Y. Chung, “Performance enhancement of long period fiber gratings for strain and temperature sensing,” IEICE Trans. Electron. E83-C, 282–286 (2000).
  9. V. Bhatia and A. M. Vengsarkar, “Optical fiber long-period grating sensors,” Opt. Lett. 21, 692–694 (1996).
    [CrossRef]
  10. H. J. Patrick, A. D. Kersey, and 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]
  11. A. S. Kurkov, M. Douay, O. Duhem, B. Leleu, J. F. Heninot, J. F. Bayon, and L. Rivoallan, “Long-period fiber grating as a wavelength selective polarization element,” Electron. Lett. 33, 616–617 (1997).
    [CrossRef]
  12. V. Rastogi and K. S. Chiang, “Long-period gratings in planar optical waveguides,” Appl. Opt. 41, 6351–6355(2002).
    [CrossRef]
  13. K. S. Chiang, K. P. Lor, Q. Liu, C. K. Chow, Y. M. Chu, and H. P. Chan, “Long-period waveguide gratings,” Jpn. J. Appl. Phys. 43.8B, 5690–5696 (2004).
    [CrossRef]
  14. K. S. Chiang, K. P. Lor, C. K. Chow, H. P. Chan, V. Rastogi, and Y. M. Chu, “Widely tunable long-period gratings fabricated in polymer-clad ion-exchanged glass waveguides,” IEEE Photon. Technol. Lett. 15, 1094–1096 (2003).
    [CrossRef]
  15. K. P. Lor, Q. Liu, and K. S. Chiang, “UV-written long-period gratings on polymer waveguides,” IEEE Photon. Technol. Lett. 17, 594–596 (2005).
    [CrossRef]
  16. Y. M. Chu, K. S. Chiang, and Q. Liu, “Widely tunable optical bandpass filter by use of polymer long-period waveguide gratings,” Appl. Opt. 45, 2755–2760 (2006).
    [CrossRef]
  17. Y. Bai, Q. Liu, K. P. Lor, and K. S. Chiang, “Widely tunable long-period waveguide grating couplers,” Opt. Express 14, 12644–12654 (2006).
    [CrossRef]
  18. Y. Zhang, D.-L. Zhang, and E. Y.-B. Pun, “Analysis of temperature/pressure sensitivity of the resonant wavelength of long period channel waveguide gratings,” J. Opt. Soc. Am. A 25, 2776–2783 (2008).
    [CrossRef]
  19. M. R. Ramadas, E. Garmire, A. K. Ghatak, K. Thyagarajan, and M. R. Shenoy, “Analysis of absorbing and leaky planar waveguides: a novel method,” Opt. Lett. 14, 376–378 (1989).
    [CrossRef]
  20. M. R. Ramadas, R. K. Varshney, K. Thyagarajan, and A. K. Ghatak, “A matrix approach to study the propagation characteristics of a general nonlinear planar waveguide,” J. Lightwave Technol. 7, 1901–1905 (1989).
    [CrossRef]
  21. A. Yariv, Optical Electronics in Modern Communications(Oxford, 1997).
  22. H. J. Patrick, A. D. Kersey, and F. Bucholtz, “Analysis of the response of long period fiber gratings to external index of refraction,” J. Lightwave Technol. 16, 1606–1612 (1998).
    [CrossRef]
  23. J. L. Philipsen, C. L. Thomsen, L. Leick, Y. Shen, P. C. Nielsen, C. Laurent-Laud, M. G. Dyndgaard, and T. Feuchter, “Erbium-doped waveguide amplifier technology and components,” in Proceedings of European Conference on Optical Communication (IEEE, 2003), pp. 420–421.
  24. H. Chen, “Design and simulation of broad band IR integrated waveguide amplifiers with long period waveguide grating filter,” J. Infrared Millim. Terahz. Waves 31, 24–30 (2010).
    [CrossRef]
  25. H. Chen, D. Jizhi, and L. Yongzhi, “Thin film filter for broadband IR integrated waveguide amplifier,” Int. J. Infrared Millim. Waves 26, 297–305 (2005).
    [CrossRef]

2010

H. Chen, “Design and simulation of broad band IR integrated waveguide amplifiers with long period waveguide grating filter,” J. Infrared Millim. Terahz. Waves 31, 24–30 (2010).
[CrossRef]

2008

2006

2005

K. P. Lor, Q. Liu, and K. S. Chiang, “UV-written long-period gratings on polymer waveguides,” IEEE Photon. Technol. Lett. 17, 594–596 (2005).
[CrossRef]

H. Chen, D. Jizhi, and L. Yongzhi, “Thin film filter for broadband IR integrated waveguide amplifier,” Int. J. Infrared Millim. Waves 26, 297–305 (2005).
[CrossRef]

2004

K. S. Chiang, K. P. Lor, Q. Liu, C. K. Chow, Y. M. Chu, and H. P. Chan, “Long-period waveguide gratings,” Jpn. J. Appl. Phys. 43.8B, 5690–5696 (2004).
[CrossRef]

2003

K. S. Chiang, K. P. Lor, C. K. Chow, H. P. Chan, V. Rastogi, and Y. M. Chu, “Widely tunable long-period gratings fabricated in polymer-clad ion-exchanged glass waveguides,” IEEE Photon. Technol. Lett. 15, 1094–1096 (2003).
[CrossRef]

2002

2001

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

2000

Y. Han, C. S. Kim, U. C. Paek, and Y. Chung, “Performance enhancement of long period fiber gratings for strain and temperature sensing,” IEICE Trans. Electron. E83-C, 282–286 (2000).

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

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

1999

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

1998

1997

A. S. Kurkov, M. Douay, O. Duhem, B. Leleu, J. F. Heninot, J. F. Bayon, and L. Rivoallan, “Long-period fiber grating as a wavelength selective polarization element,” Electron. Lett. 33, 616–617 (1997).
[CrossRef]

P. F. Wysocki, J. B. Judkins, R. P. Espindola, M. Andrejco, and 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]

1996

1989

M. R. Ramadas, E. Garmire, A. K. Ghatak, K. Thyagarajan, and M. R. Shenoy, “Analysis of absorbing and leaky planar waveguides: a novel method,” Opt. Lett. 14, 376–378 (1989).
[CrossRef]

M. R. Ramadas, R. K. Varshney, K. Thyagarajan, and A. K. Ghatak, “A matrix approach to study the propagation characteristics of a general nonlinear planar waveguide,” J. Lightwave Technol. 7, 1901–1905 (1989).
[CrossRef]

Andrejco, M.

P. F. Wysocki, J. B. Judkins, R. P. Espindola, M. Andrejco, and 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]

Bai, Y.

Bayon, J. F.

A. S. Kurkov, M. Douay, O. Duhem, B. Leleu, J. F. Heninot, J. F. Bayon, and L. Rivoallan, “Long-period fiber grating as a wavelength selective polarization element,” Electron. Lett. 33, 616–617 (1997).
[CrossRef]

Bergano, N. S.

Bhatia, V.

A. M. Vengsarkar, P. J. Lamaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band rejection filters,” J. Lightwave Technol. 14, 58–65(1996).
[CrossRef]

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

Bucholtz, F.

Chan, H. P.

K. S. Chiang, K. P. Lor, Q. Liu, C. K. Chow, Y. M. Chu, and H. P. Chan, “Long-period waveguide gratings,” Jpn. J. Appl. Phys. 43.8B, 5690–5696 (2004).
[CrossRef]

K. S. Chiang, K. P. Lor, C. K. Chow, H. P. Chan, V. Rastogi, and Y. M. Chu, “Widely tunable long-period gratings fabricated in polymer-clad ion-exchanged glass waveguides,” IEEE Photon. Technol. Lett. 15, 1094–1096 (2003).
[CrossRef]

Chen, H.

H. Chen, “Design and simulation of broad band IR integrated waveguide amplifiers with long period waveguide grating filter,” J. Infrared Millim. Terahz. Waves 31, 24–30 (2010).
[CrossRef]

H. Chen, D. Jizhi, and L. Yongzhi, “Thin film filter for broadband IR integrated waveguide amplifier,” Int. J. Infrared Millim. Waves 26, 297–305 (2005).
[CrossRef]

Chiang, K. S.

Y. M. Chu, K. S. Chiang, and Q. Liu, “Widely tunable optical bandpass filter by use of polymer long-period waveguide gratings,” Appl. Opt. 45, 2755–2760 (2006).
[CrossRef]

Y. Bai, Q. Liu, K. P. Lor, and K. S. Chiang, “Widely tunable long-period waveguide grating couplers,” Opt. Express 14, 12644–12654 (2006).
[CrossRef]

K. P. Lor, Q. Liu, and K. S. Chiang, “UV-written long-period gratings on polymer waveguides,” IEEE Photon. Technol. Lett. 17, 594–596 (2005).
[CrossRef]

K. S. Chiang, K. P. Lor, Q. Liu, C. K. Chow, Y. M. Chu, and H. P. Chan, “Long-period waveguide gratings,” Jpn. J. Appl. Phys. 43.8B, 5690–5696 (2004).
[CrossRef]

K. S. Chiang, K. P. Lor, C. K. Chow, H. P. Chan, V. Rastogi, and Y. M. Chu, “Widely tunable long-period gratings fabricated in polymer-clad ion-exchanged glass waveguides,” IEEE Photon. Technol. Lett. 15, 1094–1096 (2003).
[CrossRef]

V. Rastogi and K. S. Chiang, “Long-period gratings in planar optical waveguides,” Appl. Opt. 41, 6351–6355(2002).
[CrossRef]

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

Chow, C. K.

K. S. Chiang, K. P. Lor, Q. Liu, C. K. Chow, Y. M. Chu, and H. P. Chan, “Long-period waveguide gratings,” Jpn. J. Appl. Phys. 43.8B, 5690–5696 (2004).
[CrossRef]

K. S. Chiang, K. P. Lor, C. K. Chow, H. P. Chan, V. Rastogi, and Y. M. Chu, “Widely tunable long-period gratings fabricated in polymer-clad ion-exchanged glass waveguides,” IEEE Photon. Technol. Lett. 15, 1094–1096 (2003).
[CrossRef]

Chu, Y. M.

Y. M. Chu, K. S. Chiang, and Q. Liu, “Widely tunable optical bandpass filter by use of polymer long-period waveguide gratings,” Appl. Opt. 45, 2755–2760 (2006).
[CrossRef]

K. S. Chiang, K. P. Lor, Q. Liu, C. K. Chow, Y. M. Chu, and H. P. Chan, “Long-period waveguide gratings,” Jpn. J. Appl. Phys. 43.8B, 5690–5696 (2004).
[CrossRef]

K. S. Chiang, K. P. Lor, C. K. Chow, H. P. Chan, V. Rastogi, and Y. M. Chu, “Widely tunable long-period gratings fabricated in polymer-clad ion-exchanged glass waveguides,” IEEE Photon. Technol. Lett. 15, 1094–1096 (2003).
[CrossRef]

Chung, Y.

Y. Han, C. S. Kim, U. C. Paek, and Y. Chung, “Performance enhancement of long period fiber gratings for strain and temperature sensing,” IEICE Trans. Electron. E83-C, 282–286 (2000).

Constantini, D. M.

D. M. Constantini, C. A. P. Muller, S. A. Vasiliev, H. G. Limberger, and 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 and K. Thyagarajan, “Dispersion compensation in transmission using uniform long period fiber gratings,” Opt. Commun. 190, 159–163 (2001).
[CrossRef]

Davidson, C. R.

Douay, M.

A. S. Kurkov, M. Douay, O. Duhem, B. Leleu, J. F. Heninot, J. F. Bayon, and L. Rivoallan, “Long-period fiber grating as a wavelength selective polarization element,” Electron. Lett. 33, 616–617 (1997).
[CrossRef]

Duhem, O.

A. S. Kurkov, M. Douay, O. Duhem, B. Leleu, J. F. Heninot, J. F. Bayon, and L. Rivoallan, “Long-period fiber grating as a wavelength selective polarization element,” Electron. Lett. 33, 616–617 (1997).
[CrossRef]

Dyndgaard, M. G.

J. L. Philipsen, C. L. Thomsen, L. Leick, Y. Shen, P. C. Nielsen, C. Laurent-Laud, M. G. Dyndgaard, and T. Feuchter, “Erbium-doped waveguide amplifier technology and components,” in Proceedings of European Conference on Optical Communication (IEEE, 2003), pp. 420–421.

Erdogan, T.

D. B. Stegall and 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. Lamaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band rejection filters,” J. Lightwave Technol. 14, 58–65(1996).
[CrossRef]

Espindola, R. P.

P. F. Wysocki, J. B. Judkins, R. P. Espindola, M. Andrejco, and 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]

Feuchter, T.

J. L. Philipsen, C. L. Thomsen, L. Leick, Y. Shen, P. C. Nielsen, C. Laurent-Laud, M. G. Dyndgaard, and T. Feuchter, “Erbium-doped waveguide amplifier technology and components,” in Proceedings of European Conference on Optical Communication (IEEE, 2003), pp. 420–421.

Garmire, E.

Ghatak, A. K.

M. R. Ramadas, E. Garmire, A. K. Ghatak, K. Thyagarajan, and M. R. Shenoy, “Analysis of absorbing and leaky planar waveguides: a novel method,” Opt. Lett. 14, 376–378 (1989).
[CrossRef]

M. R. Ramadas, R. K. Varshney, K. Thyagarajan, and A. K. Ghatak, “A matrix approach to study the propagation characteristics of a general nonlinear planar waveguide,” J. Lightwave Technol. 7, 1901–1905 (1989).
[CrossRef]

Han, Y.

Y. Han, C. S. Kim, U. C. Paek, and Y. Chung, “Performance enhancement of long period fiber gratings for strain and temperature sensing,” IEICE Trans. Electron. E83-C, 282–286 (2000).

Heninot, J. F.

A. S. Kurkov, M. Douay, O. Duhem, B. Leleu, J. F. Heninot, J. F. Bayon, and L. Rivoallan, “Long-period fiber grating as a wavelength selective polarization element,” Electron. Lett. 33, 616–617 (1997).
[CrossRef]

Jizhi, D.

H. Chen, D. Jizhi, and L. Yongzhi, “Thin film filter for broadband IR integrated waveguide amplifier,” Int. J. Infrared Millim. Waves 26, 297–305 (2005).
[CrossRef]

Judkins, J. B.

P. F. Wysocki, J. B. Judkins, R. P. Espindola, M. Andrejco, and 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, and C. R. Davidson, “Long-period fiber-grating-based gain equalizers,” Opt. Lett. 21, 336–338 (1996).
[CrossRef]

A. M. Vengsarkar, P. J. Lamaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band rejection filters,” J. Lightwave Technol. 14, 58–65(1996).
[CrossRef]

Kersey, A. D.

Kim, C. S.

Y. Han, C. S. Kim, U. C. Paek, and Y. Chung, “Performance enhancement of long period fiber gratings for strain and temperature sensing,” IEICE Trans. Electron. E83-C, 282–286 (2000).

Kurkov, A. S.

A. S. Kurkov, M. Douay, O. Duhem, B. Leleu, J. F. Heninot, J. F. Bayon, and L. Rivoallan, “Long-period fiber grating as a wavelength selective polarization element,” Electron. Lett. 33, 616–617 (1997).
[CrossRef]

Lamaire, P. J.

A. M. Vengsarkar, P. J. Lamaire, J. B. Judkins, V. Bhatia, T. Erdogan, and 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, and C. R. Davidson, “Long-period fiber-grating-based gain equalizers,” Opt. Lett. 21, 336–338 (1996).
[CrossRef]

Laurent-Laud, C.

J. L. Philipsen, C. L. Thomsen, L. Leick, Y. Shen, P. C. Nielsen, C. Laurent-Laud, M. G. Dyndgaard, and T. Feuchter, “Erbium-doped waveguide amplifier technology and components,” in Proceedings of European Conference on Optical Communication (IEEE, 2003), pp. 420–421.

Leick, L.

J. L. Philipsen, C. L. Thomsen, L. Leick, Y. Shen, P. C. Nielsen, C. Laurent-Laud, M. G. Dyndgaard, and T. Feuchter, “Erbium-doped waveguide amplifier technology and components,” in Proceedings of European Conference on Optical Communication (IEEE, 2003), pp. 420–421.

Leleu, B.

A. S. Kurkov, M. Douay, O. Duhem, B. Leleu, J. F. Heninot, J. F. Bayon, and L. Rivoallan, “Long-period fiber grating as a wavelength selective polarization element,” Electron. Lett. 33, 616–617 (1997).
[CrossRef]

Li, S.

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

Limberger, H. G.

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

Liu, Q.

Y. M. Chu, K. S. Chiang, and Q. Liu, “Widely tunable optical bandpass filter by use of polymer long-period waveguide gratings,” Appl. Opt. 45, 2755–2760 (2006).
[CrossRef]

Y. Bai, Q. Liu, K. P. Lor, and K. S. Chiang, “Widely tunable long-period waveguide grating couplers,” Opt. Express 14, 12644–12654 (2006).
[CrossRef]

K. P. Lor, Q. Liu, and K. S. Chiang, “UV-written long-period gratings on polymer waveguides,” IEEE Photon. Technol. Lett. 17, 594–596 (2005).
[CrossRef]

K. S. Chiang, K. P. Lor, Q. Liu, C. K. Chow, Y. M. Chu, and H. P. Chan, “Long-period waveguide gratings,” Jpn. J. Appl. Phys. 43.8B, 5690–5696 (2004).
[CrossRef]

Liu, Y.

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

Lor, K. P.

Y. Bai, Q. Liu, K. P. Lor, and K. S. Chiang, “Widely tunable long-period waveguide grating couplers,” Opt. Express 14, 12644–12654 (2006).
[CrossRef]

K. P. Lor, Q. Liu, and K. S. Chiang, “UV-written long-period gratings on polymer waveguides,” IEEE Photon. Technol. Lett. 17, 594–596 (2005).
[CrossRef]

K. S. Chiang, K. P. Lor, Q. Liu, C. K. Chow, Y. M. Chu, and H. P. Chan, “Long-period waveguide gratings,” Jpn. J. Appl. Phys. 43.8B, 5690–5696 (2004).
[CrossRef]

K. S. Chiang, K. P. Lor, C. K. Chow, H. P. Chan, V. Rastogi, and Y. M. Chu, “Widely tunable long-period gratings fabricated in polymer-clad ion-exchanged glass waveguides,” IEEE Photon. Technol. Lett. 15, 1094–1096 (2003).
[CrossRef]

Muller, C. A. P.

D. M. Constantini, C. A. P. Muller, S. A. Vasiliev, H. G. Limberger, and 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, and S. Li, “Coupling between two parallel long period fiber gratings,” Electron. Lett. 36, 1408–1409 (2000).
[CrossRef]

Nielsen, P. C.

J. L. Philipsen, C. L. Thomsen, L. Leick, Y. Shen, P. C. Nielsen, C. Laurent-Laud, M. G. Dyndgaard, and T. Feuchter, “Erbium-doped waveguide amplifier technology and components,” in Proceedings of European Conference on Optical Communication (IEEE, 2003), pp. 420–421.

Paek, U. C.

Y. Han, C. S. Kim, U. C. Paek, and Y. Chung, “Performance enhancement of long period fiber gratings for strain and temperature sensing,” IEICE Trans. Electron. E83-C, 282–286 (2000).

Patrick, H. J.

Pedrazzani, J. R.

Philipsen, J. L.

J. L. Philipsen, C. L. Thomsen, L. Leick, Y. Shen, P. C. Nielsen, C. Laurent-Laud, M. G. Dyndgaard, and T. Feuchter, “Erbium-doped waveguide amplifier technology and components,” in Proceedings of European Conference on Optical Communication (IEEE, 2003), pp. 420–421.

Pun, E. Y.-B.

Ramadas, M. R.

M. R. Ramadas, E. Garmire, A. K. Ghatak, K. Thyagarajan, and M. R. Shenoy, “Analysis of absorbing and leaky planar waveguides: a novel method,” Opt. Lett. 14, 376–378 (1989).
[CrossRef]

M. R. Ramadas, R. K. Varshney, K. Thyagarajan, and A. K. Ghatak, “A matrix approach to study the propagation characteristics of a general nonlinear planar waveguide,” J. Lightwave Technol. 7, 1901–1905 (1989).
[CrossRef]

Rastogi, V.

K. S. Chiang, K. P. Lor, C. K. Chow, H. P. Chan, V. Rastogi, and Y. M. Chu, “Widely tunable long-period gratings fabricated in polymer-clad ion-exchanged glass waveguides,” IEEE Photon. Technol. Lett. 15, 1094–1096 (2003).
[CrossRef]

V. Rastogi and K. S. Chiang, “Long-period gratings in planar optical waveguides,” Appl. Opt. 41, 6351–6355(2002).
[CrossRef]

Rivoallan, L.

A. S. Kurkov, M. Douay, O. Duhem, B. Leleu, J. F. Heninot, J. F. Bayon, and L. Rivoallan, “Long-period fiber grating as a wavelength selective polarization element,” Electron. Lett. 33, 616–617 (1997).
[CrossRef]

Salathe, R. P.

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

Shen, Y.

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A. M. Vengsarkar, P. J. Lamaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band rejection filters,” J. Lightwave Technol. 14, 58–65(1996).
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D. M. Constantini, C. A. P. Muller, S. A. Vasiliev, H. G. Limberger, and R. P. Salathe, “Tunable loss filter based on metal coated long-period fiber grating,” IEEE Photon. Technol. Lett. 11, 1458–1560 (1999).
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[CrossRef]

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A. Yariv, Optical Electronics in Modern Communications(Oxford, 1997).

J. L. Philipsen, C. L. Thomsen, L. Leick, Y. Shen, P. C. Nielsen, C. Laurent-Laud, M. G. Dyndgaard, and T. Feuchter, “Erbium-doped waveguide amplifier technology and components,” in Proceedings of European Conference on Optical Communication (IEEE, 2003), pp. 420–421.

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Figures (13)

Fig. 1.
Fig. 1.

RI profile of the proposed planar waveguide structure employing LPG. The grating lies in the layer 0<x<df.

Fig. 2.
Fig. 2.

Phase matching curves of LPWG, for (a) TE0-TE1 mode coupling and (b) TE0-TE2 mode coupling. The vertical line marks the grating period.

Fig. 3.
Fig. 3.

Variation of phase matching curves for different values of ntr with ns=1.50, nf=1.52, ncl=1.511, df=2.0μm, dcl=9.5μm, and dtr=11μm.

Fig. 4.
Fig. 4.

Variation of the phase mismatch Δβ between TE0 and TE2 modes as a function of wavelength for (a) ntr=1.498, (b) ntr=1.50, and (c) ntr=1.502 with dtr=11μm and the other parameters defined by Eq. (8). The dashed line shows the values of 2π/Λ and their points of intersection with the curves give the resonant wavelengths.

Fig. 5.
Fig. 5.

Transmission spectrum of the grating for (a) ntr=1.498, (b) ntr=1.50, and (c) ntr=1.502.

Fig. 6.
Fig. 6.

Variation of the phase mismatch Δβ between TE0 and TE2 modes as a function of wavelength for (a) dcl=9μm, (b) dcl=9.5μm, and (c) dcl=10μm with ntr=1.50, dtr=11μm and the other parameters defined by Eq. (8). The dashed line shows the values of 2π/Λ and their points of intersection with the curves give the resonant wavelengths.

Fig. 7.
Fig. 7.

Transmission spectrum of the grating for (a) dcl=9μm, (b) dcl=9.5μm, and (c) dcl=10μm.

Fig. 8.
Fig. 8.

Variation of the phase mismatch Δβ between TE0 and TE2 modes as a function of wavelength for (a) dtr=7μm, (b) dtr=9μm, and (c) dtr=11μm with ntr=1.50 and the other parameters defined by Eq. (8). The dashed line shows the values of 2π/Λ and their points of intersection with the curves give the resonant wavelengths.

Fig. 9.
Fig. 9.

Spectral variation of the transmission spectrum for (a) dtr=7μm, (b) dtr=9μm, and (c) dtr=11μm.

Fig. 10.
Fig. 10.

Transmission spectrum of the grating for (a) ncl=1.51, (b) ncl=1.511, and (c) ncl=1.512 with ntr=1.50, dcl=9.5μm, dtr=7μm and the other parameters defined by Eq. (8).

Fig. 11.
Fig. 11.

(a) Variation of the transmission spectrum with nex and (b) variation of resonance wavelength as a function of external RI.

Fig. 12.
Fig. 12.

(a) Variation of the transmission spectrum with external RI. (b) Variation of Δλ0 and resonance wavelength of the second dip as a function of external RI.

Fig. 13.
Fig. 13.

Flattening of the EDWA gain spectrum in the C-band using LPWG.

Equations (8)

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ET=12[A(z)E0(x)exp[i(ωtβ0z)]+B(z)Em(x)exp[i(ωtβmz)]+cc],
2ETx2+2ETz2+k02[n2(x)+Δn2(x,z)]ET=0,
dAdz=κBe(iΓz),
dBdz=κAe(iΓz)+αBB2,
Γ=Δβ2πΛ,
Δβ=β0βm,
κ=k0Δn028cμ0η,η=0dfE0Emdx.
ns=1.50,nf=1.52,ncl=1.511,df=2.0μm,dcl=9.5μm.

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