Abstract

A full vector complex coupled mode theory (CMT) for the analysis of tilted fiber gratings is presented. With the combination of the perfectly matched layer (PML) and the perfectly reflecting boundary (PRB), the continuous radiation modes are well represented by a set of discrete complex modes. Simulation of coupling to radiation modes is greatly simplified and may be treated in the same fashion as guided modes. Numerical results of the tilted fiber Bragg gratings (TFBGs) with outer-cladding index equal, lower and higher than that of the inner-cladding indicate that the complex coupled mode approach is highly effective in the simulation of couplings to cladding and radiation modes in tilted fiber gratings. The reflective TFBGs are investigated by the proposed approach in detail.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2009

2008

Y.-C. Lu, L. Yang, W.-P. Huang, and S.-S. Jian, "Improved full-vector finite-difference complex mode solver for optical waveguides of circular symmetry," J. Lightwave Technol. 26(13), 1868-1876 (2008).
[CrossRef]

O. Xu, S. Lu, Y. Liu, B. Li, X. Dong, L. Pei, and S. Jian, "Analysis of spectral characteristics for reflective tilted fiber gratings of uniform periods," Opt. Commun. 281(15-16), 3990-3995 (2008).
[CrossRef]

2007

2006

Y. Li, and T. G. Brown, "Radiation modes and tilted fiber gratings," J. Opt. Soc. Am. B 23(8), 1544-1555 (2006).
[CrossRef]

X. Chen, K. Zhou, L. Zhang, and I. Bennion, "In-fiber twist sensor based on a fiber bragg grating with 81° tilted structure," IEEE Photon. Technol. Lett. 18(24), 2596-2598 (2006).
[CrossRef]

2005

2004

2003

K. Feder, P. Westbrook, J. Ging, P. Reyes, and G. Carver, "In-fiber spectrometer using tilted fiber gratings," IEEE Photon. Technol. Lett. 15(7), 933-935 (2003).
[CrossRef]

P. Ivanoff, D. C. Reyes, and P. S. Westbrook, "Tunable pdl of twisted-tilted fiber gratings," IEEE Photon. Technol. Lett. 15(6), 828-830 (2003).
[CrossRef]

Y. Jeong, B. Lee, J. Nilsson, and D. Richardson, "A quasi-mode interpretation of radiation modes in long-period fiber gratings," IEEE J. Quantum Electron. 39(9), 1135-1142 (2003).
[CrossRef]

C. Juregui, and J. M. Lpez-Higuera, "Near-field theoretical model of radiation from a uniform-tilted fiber-bragg grating," Microw. Opt. Technol. Lett. 37(2), 124-127 (2003).
[CrossRef]

C. Juregui, A. Cobo, and J. M. Lpez-Higuera, "3d near-field model for uniform slanted fiber gratings," Microw. Opt. Technol. Lett. 38(5), 428-432 (2003).
[CrossRef]

2002

J. Peupelmann, E. Krause, A. Bandemer, and C. Schaffer, "Fibre-polarimeter based on grating taps," Electron. Lett. 38(21), 1248-1250 (2002).
[CrossRef]

2001

Y. Li, M. Froggatt, and T. Erdogan, "Volume current method for analysis of tilted fiber gratings," J. Lightwave Technol. 19(10), 1580-1591 (2001).
[CrossRef]

Y. Koyamada, "Numerical analysis of core-mode to radiation-mode coupling in long-period fiber gratings," IEEE Photon. Technol. Lett. 13(4), 308-310 (2001).
[CrossRef]

G. Laffont, and P. Ferdinand, "Tilted short-period fibre-bragg-grating-induced coupling to cladding modes for accurate refractometry," Meas. Sci. Technol. 12(7), 765-770 (2001).
[CrossRef]

2000

1999

D. Stegall, and T. Erdogan, "Leaky cladding mode propagation in long-period fiber grating devices," IEEE Photon. Technol. Lett. 11(3), 343-345 (1999).
[CrossRef]

M. Holmes, R. Kashyap, and R. Wyatt, "Physical properties of optical fiber sidetap grating filters: free-space model," IEEE J. Sel. Top. Quantum Electron. 5(5), 1353-1365 (1999).
[CrossRef]

1998

1996

1993

R. Kashyap, R. Wyatt, and R. Campbell, "Wideband gain flattened erbium fibre amplifier using a photosensitive fibre blazed grating," Electron. Lett. 29(2), 154-156 (1993).
[CrossRef]

Albert, J.

Allsop, T.

Bandemer, A.

J. Peupelmann, E. Krause, A. Bandemer, and C. Schaffer, "Fibre-polarimeter based on grating taps," Electron. Lett. 38(21), 1248-1250 (2002).
[CrossRef]

Bennion, I.

T. Allsop, R. Neal, S. Rehman, D. J. Webb, D. Mapps, and I. Bennion, "Generation of infrared surface plasmon resonances with high refractive index sensitivity utilizing tilted fiber Bragg gratings," Appl. Opt. 46(22), 5456-5460 (2007).
[CrossRef] [PubMed]

X. Chen, K. Zhou, L. Zhang, and I. Bennion, "In-fiber twist sensor based on a fiber bragg grating with 81° tilted structure," IEEE Photon. Technol. Lett. 18(24), 2596-2598 (2006).
[CrossRef]

K. Zhou, G. Simpson, X. Chen, L. Zhang, and I. Bennion, "High extinction ratio in-fiber polarizers based on 45 ° tilted fiber Bragg gratings," Opt. Lett. 30(11), 1285-1287 (2005).
[CrossRef] [PubMed]

X. Chen, K. Zhou, L. Zhang, and I. Bennion, "Optical chemsensor based on etched tilted bragg grating structures in multimode fiber," IEEE Photon. Technol. Lett. 17(4), 864-866 (2005).
[CrossRef]

Brown, T. G.

Campbell, R.

R. Kashyap, R. Wyatt, and R. Campbell, "Wideband gain flattened erbium fibre amplifier using a photosensitive fibre blazed grating," Electron. Lett. 29(2), 154-156 (1993).
[CrossRef]

Carver, G.

K. Feder, P. Westbrook, J. Ging, P. Reyes, and G. Carver, "In-fiber spectrometer using tilted fiber gratings," IEEE Photon. Technol. Lett. 15(7), 933-935 (2003).
[CrossRef]

Carver, G. E.

Chan, C.-F.

Chehura, E.

E. Chehura, S. W. James, and R. P. Tatam, "Temperature and strain discrimination using a single tilted fibre bragg grating," Opt. Commun. 275(2), 344-347 (2007).
[CrossRef]

Chen, C.

T. Guo, C. Chen, and J. Albert, "Non-uniform-tilt-modulated fiber bragg grating for temperature-immune microdisplacement measurement," Meas. Sci. Technol. 20(3), 034007 (2009).
[CrossRef]

C.-F. Chan, C. Chen, A. Jafari, A. Laronche, D. J. Thomson, and J. Albert, "Optical fiber refractometer using narrowband cladding-mode resonance shifts," Appl. Opt. 46(7), 1142-1149 (2007).
[CrossRef] [PubMed]

Chen, X.

X. Chen, K. Zhou, L. Zhang, and I. Bennion, "In-fiber twist sensor based on a fiber bragg grating with 81° tilted structure," IEEE Photon. Technol. Lett. 18(24), 2596-2598 (2006).
[CrossRef]

K. Zhou, G. Simpson, X. Chen, L. Zhang, and I. Bennion, "High extinction ratio in-fiber polarizers based on 45 ° tilted fiber Bragg gratings," Opt. Lett. 30(11), 1285-1287 (2005).
[CrossRef] [PubMed]

X. Chen, K. Zhou, L. Zhang, and I. Bennion, "Optical chemsensor based on etched tilted bragg grating structures in multimode fiber," IEEE Photon. Technol. Lett. 17(4), 864-866 (2005).
[CrossRef]

Cobo, A.

C. Juregui, A. Cobo, and J. M. Lpez-Higuera, "3d near-field model for uniform slanted fiber gratings," Microw. Opt. Technol. Lett. 38(5), 428-432 (2003).
[CrossRef]

Dong, L.

Dong, X.

O. Xu, S. Lu, Y. Liu, B. Li, X. Dong, L. Pei, and S. Jian, "Analysis of spectral characteristics for reflective tilted fiber gratings of uniform periods," Opt. Commun. 281(15-16), 3990-3995 (2008).
[CrossRef]

Erdogan, T.

Y. Li, M. Froggatt, and T. Erdogan, "Volume current method for analysis of tilted fiber gratings," J. Lightwave Technol. 19(10), 1580-1591 (2001).
[CrossRef]

K. S. Lee, and T. Erdogan, "Fiber mode coupling in transmissive and reflective tilted fiber gratings," Appl. Opt. 39(9), 1394-1404 (2000).
[CrossRef]

T. Erdogan, T. A. Strasser, and P. S. Westbrook, "In-line polarimeter using blazed fiber gratings," IEEE Photon. Technol. Lett. 12(10), 1352-1354 (2000).
[CrossRef]

D. Stegall, and T. Erdogan, "Leaky cladding mode propagation in long-period fiber grating devices," IEEE Photon. Technol. Lett. 11(3), 343-345 (1999).
[CrossRef]

T. Erdogan, and J. E. Sipe, "Tilted fiber phase gratings," J. Opt. Soc. Am. A 13(2), 296-313 (1996).
[CrossRef]

Feder, K.

K. Feder, P. Westbrook, J. Ging, P. Reyes, and G. Carver, "In-fiber spectrometer using tilted fiber gratings," IEEE Photon. Technol. Lett. 15(7), 933-935 (2003).
[CrossRef]

Feng, S.

Ferdinand, P.

G. Laffont, and P. Ferdinand, "Tilted short-period fibre-bragg-grating-induced coupling to cladding modes for accurate refractometry," Meas. Sci. Technol. 12(7), 765-770 (2001).
[CrossRef]

Froggatt, M.

Ging, J.

K. Feder, P. Westbrook, J. Ging, P. Reyes, and G. Carver, "In-fiber spectrometer using tilted fiber gratings," IEEE Photon. Technol. Lett. 15(7), 933-935 (2003).
[CrossRef]

Grobnic, D.

Guo, T.

T. Guo, H.-Y. Tam, P. A. Krug, and J. Albert, "Reflective tilted fiber Bragg grating refractometer based on strong cladding to core recoupling," Opt. Express 17(7), 5736-5742 (2009).
[CrossRef] [PubMed]

T. Guo, C. Chen, and J. Albert, "Non-uniform-tilt-modulated fiber bragg grating for temperature-immune microdisplacement measurement," Meas. Sci. Technol. 20(3), 034007 (2009).
[CrossRef]

Holmes, M.

M. Holmes, R. Kashyap, and R. Wyatt, "Physical properties of optical fiber sidetap grating filters: free-space model," IEEE J. Sel. Top. Quantum Electron. 5(5), 1353-1365 (1999).
[CrossRef]

Huang, W.-P.

Ivanoff, P.

P. Ivanoff, D. C. Reyes, and P. S. Westbrook, "Tunable pdl of twisted-tilted fiber gratings," IEEE Photon. Technol. Lett. 15(6), 828-830 (2003).
[CrossRef]

Jafari, A.

James, S. W.

E. Chehura, S. W. James, and R. P. Tatam, "Temperature and strain discrimination using a single tilted fibre bragg grating," Opt. Commun. 275(2), 344-347 (2007).
[CrossRef]

Jeong, Y.

Y. Jeong, B. Lee, J. Nilsson, and D. Richardson, "A quasi-mode interpretation of radiation modes in long-period fiber gratings," IEEE J. Quantum Electron. 39(9), 1135-1142 (2003).
[CrossRef]

Jian, S.

S. Lu, O. Xu, S. Feng, and S. Jian, "Analysis of radiation-mode coupling in reflective and transmissive tilted fiber bragg gratings," J. Opt. Soc. Am. A 26(1), 91-98 (2009).
[CrossRef]

O. Xu, S. Lu, Y. Liu, B. Li, X. Dong, L. Pei, and S. Jian, "Analysis of spectral characteristics for reflective tilted fiber gratings of uniform periods," Opt. Commun. 281(15-16), 3990-3995 (2008).
[CrossRef]

Jian, S.-S.

Juregui, C.

C. Juregui, and J. M. Lpez-Higuera, "Near-field theoretical model of radiation from a uniform-tilted fiber-bragg grating," Microw. Opt. Technol. Lett. 37(2), 124-127 (2003).
[CrossRef]

C. Juregui, A. Cobo, and J. M. Lpez-Higuera, "3d near-field model for uniform slanted fiber gratings," Microw. Opt. Technol. Lett. 38(5), 428-432 (2003).
[CrossRef]

Kashyap, R.

M. Holmes, R. Kashyap, and R. Wyatt, "Physical properties of optical fiber sidetap grating filters: free-space model," IEEE J. Sel. Top. Quantum Electron. 5(5), 1353-1365 (1999).
[CrossRef]

R. Kashyap, R. Wyatt, and R. Campbell, "Wideband gain flattened erbium fibre amplifier using a photosensitive fibre blazed grating," Electron. Lett. 29(2), 154-156 (1993).
[CrossRef]

Koyamada, Y.

Y. Koyamada, "Numerical analysis of core-mode to radiation-mode coupling in long-period fiber gratings," IEEE Photon. Technol. Lett. 13(4), 308-310 (2001).
[CrossRef]

Y. Koyamada, "Analysis of core-mode to radiation-mode coupling in fiber Bragg gratings with finite cladding radius," J. Lightwave Technol. 18(9), 1220-1225 (2000).
[CrossRef]

Krause, E.

J. Peupelmann, E. Krause, A. Bandemer, and C. Schaffer, "Fibre-polarimeter based on grating taps," Electron. Lett. 38(21), 1248-1250 (2002).
[CrossRef]

Krug, P. A.

Laffont, G.

G. Laffont, and P. Ferdinand, "Tilted short-period fibre-bragg-grating-induced coupling to cladding modes for accurate refractometry," Meas. Sci. Technol. 12(7), 765-770 (2001).
[CrossRef]

Laronche, A.

Lee, B.

Y. Jeong, B. Lee, J. Nilsson, and D. Richardson, "A quasi-mode interpretation of radiation modes in long-period fiber gratings," IEEE J. Quantum Electron. 39(9), 1135-1142 (2003).
[CrossRef]

Lee, K. S.

Li, B.

O. Xu, S. Lu, Y. Liu, B. Li, X. Dong, L. Pei, and S. Jian, "Analysis of spectral characteristics for reflective tilted fiber gratings of uniform periods," Opt. Commun. 281(15-16), 3990-3995 (2008).
[CrossRef]

Li, Y.

Liu, Y.

O. Xu, S. Lu, Y. Liu, B. Li, X. Dong, L. Pei, and S. Jian, "Analysis of spectral characteristics for reflective tilted fiber gratings of uniform periods," Opt. Commun. 281(15-16), 3990-3995 (2008).
[CrossRef]

Lpez-Higuera, J. M.

C. Juregui, A. Cobo, and J. M. Lpez-Higuera, "3d near-field model for uniform slanted fiber gratings," Microw. Opt. Technol. Lett. 38(5), 428-432 (2003).
[CrossRef]

C. Juregui, and J. M. Lpez-Higuera, "Near-field theoretical model of radiation from a uniform-tilted fiber-bragg grating," Microw. Opt. Technol. Lett. 37(2), 124-127 (2003).
[CrossRef]

Lu, P.

Lu, S.

S. Lu, O. Xu, S. Feng, and S. Jian, "Analysis of radiation-mode coupling in reflective and transmissive tilted fiber bragg gratings," J. Opt. Soc. Am. A 26(1), 91-98 (2009).
[CrossRef]

O. Xu, S. Lu, Y. Liu, B. Li, X. Dong, L. Pei, and S. Jian, "Analysis of spectral characteristics for reflective tilted fiber gratings of uniform periods," Opt. Commun. 281(15-16), 3990-3995 (2008).
[CrossRef]

Lu, Y.-C.

Mapps, D.

Mihailov, S. J.

Mu, J.

Neal, R.

Nilsson, J.

Y. Jeong, B. Lee, J. Nilsson, and D. Richardson, "A quasi-mode interpretation of radiation modes in long-period fiber gratings," IEEE J. Quantum Electron. 39(9), 1135-1142 (2003).
[CrossRef]

Ortega, B.

Pei, L.

O. Xu, S. Lu, Y. Liu, B. Li, X. Dong, L. Pei, and S. Jian, "Analysis of spectral characteristics for reflective tilted fiber gratings of uniform periods," Opt. Commun. 281(15-16), 3990-3995 (2008).
[CrossRef]

Peupelmann, J.

J. Peupelmann, E. Krause, A. Bandemer, and C. Schaffer, "Fibre-polarimeter based on grating taps," Electron. Lett. 38(21), 1248-1250 (2002).
[CrossRef]

Reekie, L.

Rehman, S.

Reyes, D. C.

P. Ivanoff, D. C. Reyes, and P. S. Westbrook, "Tunable pdl of twisted-tilted fiber gratings," IEEE Photon. Technol. Lett. 15(6), 828-830 (2003).
[CrossRef]

Reyes, P.

K. Feder, P. Westbrook, J. Ging, P. Reyes, and G. Carver, "In-fiber spectrometer using tilted fiber gratings," IEEE Photon. Technol. Lett. 15(7), 933-935 (2003).
[CrossRef]

Reyes, P. I.

Richardson, D.

Y. Jeong, B. Lee, J. Nilsson, and D. Richardson, "A quasi-mode interpretation of radiation modes in long-period fiber gratings," IEEE J. Quantum Electron. 39(9), 1135-1142 (2003).
[CrossRef]

Schaffer, C.

J. Peupelmann, E. Krause, A. Bandemer, and C. Schaffer, "Fibre-polarimeter based on grating taps," Electron. Lett. 38(21), 1248-1250 (2002).
[CrossRef]

Shevchenko, Y. Y.

Simpson, G.

Sipe, J. E.

Stegall, D.

D. Stegall, and T. Erdogan, "Leaky cladding mode propagation in long-period fiber grating devices," IEEE Photon. Technol. Lett. 11(3), 343-345 (1999).
[CrossRef]

Strasser, T. A.

T. Erdogan, T. A. Strasser, and P. S. Westbrook, "In-line polarimeter using blazed fiber gratings," IEEE Photon. Technol. Lett. 12(10), 1352-1354 (2000).
[CrossRef]

Tam, H.-Y.

Tatam, R. P.

E. Chehura, S. W. James, and R. P. Tatam, "Temperature and strain discrimination using a single tilted fibre bragg grating," Opt. Commun. 275(2), 344-347 (2007).
[CrossRef]

Thomson, D. J.

Walker, R. B.

Webb, D. J.

Westbrook, P.

K. Feder, P. Westbrook, J. Ging, P. Reyes, and G. Carver, "In-fiber spectrometer using tilted fiber gratings," IEEE Photon. Technol. Lett. 15(7), 933-935 (2003).
[CrossRef]

Westbrook, P. S.

Y. Li, S. Wielandy, G. E. Carver, P. I. Reyes, and P. S. Westbrook, "Scattering from nonuniform tilted fiber gratings," Opt. Lett. 29(12), 1330-1332 (2004).
[CrossRef] [PubMed]

P. Ivanoff, D. C. Reyes, and P. S. Westbrook, "Tunable pdl of twisted-tilted fiber gratings," IEEE Photon. Technol. Lett. 15(6), 828-830 (2003).
[CrossRef]

T. Erdogan, T. A. Strasser, and P. S. Westbrook, "In-line polarimeter using blazed fiber gratings," IEEE Photon. Technol. Lett. 12(10), 1352-1354 (2000).
[CrossRef]

Wielandy, S.

Wyatt, R.

M. Holmes, R. Kashyap, and R. Wyatt, "Physical properties of optical fiber sidetap grating filters: free-space model," IEEE J. Sel. Top. Quantum Electron. 5(5), 1353-1365 (1999).
[CrossRef]

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[CrossRef]

Xu, O.

S. Lu, O. Xu, S. Feng, and S. Jian, "Analysis of radiation-mode coupling in reflective and transmissive tilted fiber bragg gratings," J. Opt. Soc. Am. A 26(1), 91-98 (2009).
[CrossRef]

O. Xu, S. Lu, Y. Liu, B. Li, X. Dong, L. Pei, and S. Jian, "Analysis of spectral characteristics for reflective tilted fiber gratings of uniform periods," Opt. Commun. 281(15-16), 3990-3995 (2008).
[CrossRef]

Yang, L.

Zhang, L.

X. Chen, K. Zhou, L. Zhang, and I. Bennion, "In-fiber twist sensor based on a fiber bragg grating with 81° tilted structure," IEEE Photon. Technol. Lett. 18(24), 2596-2598 (2006).
[CrossRef]

K. Zhou, G. Simpson, X. Chen, L. Zhang, and I. Bennion, "High extinction ratio in-fiber polarizers based on 45 ° tilted fiber Bragg gratings," Opt. Lett. 30(11), 1285-1287 (2005).
[CrossRef] [PubMed]

X. Chen, K. Zhou, L. Zhang, and I. Bennion, "Optical chemsensor based on etched tilted bragg grating structures in multimode fiber," IEEE Photon. Technol. Lett. 17(4), 864-866 (2005).
[CrossRef]

Zhou, K.

X. Chen, K. Zhou, L. Zhang, and I. Bennion, "In-fiber twist sensor based on a fiber bragg grating with 81° tilted structure," IEEE Photon. Technol. Lett. 18(24), 2596-2598 (2006).
[CrossRef]

K. Zhou, G. Simpson, X. Chen, L. Zhang, and I. Bennion, "High extinction ratio in-fiber polarizers based on 45 ° tilted fiber Bragg gratings," Opt. Lett. 30(11), 1285-1287 (2005).
[CrossRef] [PubMed]

X. Chen, K. Zhou, L. Zhang, and I. Bennion, "Optical chemsensor based on etched tilted bragg grating structures in multimode fiber," IEEE Photon. Technol. Lett. 17(4), 864-866 (2005).
[CrossRef]

Appl. Opt.

Electron. Lett.

R. Kashyap, R. Wyatt, and R. Campbell, "Wideband gain flattened erbium fibre amplifier using a photosensitive fibre blazed grating," Electron. Lett. 29(2), 154-156 (1993).
[CrossRef]

J. Peupelmann, E. Krause, A. Bandemer, and C. Schaffer, "Fibre-polarimeter based on grating taps," Electron. Lett. 38(21), 1248-1250 (2002).
[CrossRef]

IEEE J. Quantum Electron.

Y. Jeong, B. Lee, J. Nilsson, and D. Richardson, "A quasi-mode interpretation of radiation modes in long-period fiber gratings," IEEE J. Quantum Electron. 39(9), 1135-1142 (2003).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

M. Holmes, R. Kashyap, and R. Wyatt, "Physical properties of optical fiber sidetap grating filters: free-space model," IEEE J. Sel. Top. Quantum Electron. 5(5), 1353-1365 (1999).
[CrossRef]

IEEE Photon. Technol. Lett.

Y. Koyamada, "Numerical analysis of core-mode to radiation-mode coupling in long-period fiber gratings," IEEE Photon. Technol. Lett. 13(4), 308-310 (2001).
[CrossRef]

D. Stegall, and T. Erdogan, "Leaky cladding mode propagation in long-period fiber grating devices," IEEE Photon. Technol. Lett. 11(3), 343-345 (1999).
[CrossRef]

X. Chen, K. Zhou, L. Zhang, and I. Bennion, "In-fiber twist sensor based on a fiber bragg grating with 81° tilted structure," IEEE Photon. Technol. Lett. 18(24), 2596-2598 (2006).
[CrossRef]

P. Ivanoff, D. C. Reyes, and P. S. Westbrook, "Tunable pdl of twisted-tilted fiber gratings," IEEE Photon. Technol. Lett. 15(6), 828-830 (2003).
[CrossRef]

K. Feder, P. Westbrook, J. Ging, P. Reyes, and G. Carver, "In-fiber spectrometer using tilted fiber gratings," IEEE Photon. Technol. Lett. 15(7), 933-935 (2003).
[CrossRef]

T. Erdogan, T. A. Strasser, and P. S. Westbrook, "In-line polarimeter using blazed fiber gratings," IEEE Photon. Technol. Lett. 12(10), 1352-1354 (2000).
[CrossRef]

X. Chen, K. Zhou, L. Zhang, and I. Bennion, "Optical chemsensor based on etched tilted bragg grating structures in multimode fiber," IEEE Photon. Technol. Lett. 17(4), 864-866 (2005).
[CrossRef]

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J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

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G. Laffont, and P. Ferdinand, "Tilted short-period fibre-bragg-grating-induced coupling to cladding modes for accurate refractometry," Meas. Sci. Technol. 12(7), 765-770 (2001).
[CrossRef]

T. Guo, C. Chen, and J. Albert, "Non-uniform-tilt-modulated fiber bragg grating for temperature-immune microdisplacement measurement," Meas. Sci. Technol. 20(3), 034007 (2009).
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C. Juregui, and J. M. Lpez-Higuera, "Near-field theoretical model of radiation from a uniform-tilted fiber-bragg grating," Microw. Opt. Technol. Lett. 37(2), 124-127 (2003).
[CrossRef]

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[CrossRef]

Opt. Commun.

O. Xu, S. Lu, Y. Liu, B. Li, X. Dong, L. Pei, and S. Jian, "Analysis of spectral characteristics for reflective tilted fiber gratings of uniform periods," Opt. Commun. 281(15-16), 3990-3995 (2008).
[CrossRef]

E. Chehura, S. W. James, and R. P. Tatam, "Temperature and strain discrimination using a single tilted fibre bragg grating," Opt. Commun. 275(2), 344-347 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Other

S. Mihailov, R. Walker, T. Stocki, and D. Johnson, "Fabrication of a tilted fiber-grating polarization-dependent loss equalizer," in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides. Optical Society of America, 2001, p. BFD2.

M. Holmes, R. Kashyap, R. Wyatt, and R. Smith, "Ultra narrow-band optical fibre sidetap filters," in Proc. ECOC'98, vol. 1, Sep 1998, 137-138.

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Figures (10)

Fig. 1.
Fig. 1.

Diagram of a tilted fiber grating written in a three layer optical fiber and the definitions for the analysis.

Fig. 2.
Fig. 2.

Phase matching conditions for TFBGs.

Fig. 3.
Fig. 3.

Mode couplings in TFBGs with different tilted angles. (a) Reflective TFBGs. (c) Transmissive TFBGs.

Fig. 4.
Fig. 4.

(a) The calculated maximum Bragg reflectivity versus tilt angle for TFBGs with different values of index modulation. (b) The calculated reflection spectra for TFBGs with different tilt angle..

Fig. 5.
Fig. 5.

Transmission spectrum evolution of TFBG with the increase of tilt angle, (n cl = n s).

Fig. 6.
Fig. 6.

The minimum transmission and peak wavelength versus tilt angle (n cl = n s).

Fig. 7.
Fig. 7.

Transmission spectrum evolution of TFBG with the increase of tilt angle.(n cl > n s = 1.0)

Fig. 8.
Fig. 8.

The minimum transmission and peak wavelength versus tilt angle (n cl > n s =1.0).

Fig. 9.
Fig. 9.

Transmission spectrum evolution of TFBG with the increase of tilt angle. (n cl < n s = n cl + 0.1)

Fig. 10.
Fig. 10.

The minimum transmission and peak wavelength versus tilt angle. (n cl < n s = n cl + 0.1)

Equations (39)

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K in = K out + K g
λ = 2 n eff Λ cos 2 ( θ )
e rm = e rm ( r ) cos ( μϕ ) , h rm = h rm ( r ) sin ( μϕ )
e ϕm = e ϕm ( r ) sin ( μϕ ) , h ϕm = h ϕm ( r ) cos ( μϕ )
e zm = e zm ( r ) cos ( μϕ ) , h zm = h zm ( r ) sin ( μϕ )
E t ( r t , z ) = p = ± n [ a n p ( z ) + b n p ( z ) ] e n p ( r t )
H t ( r t , z ) = p = ± n [ a n p ( z ) b n p ( z ) ] h n p ( r t )
d a m p d z + j β m p a m p = j p = ± n ( κ mn pq a n q + χ mn pq b n q )
d b m p d z j β m p a m p = + j p = ± n ( κ mn pq b n q + χ mn pq a n q )
κ mn pq ε 0 ω 2 e tm p , h tm p n ̄ ( r ) P ( r ) Δ n ( z ) · ( e tm p · e tn q + e zm p · e zn q ) dS
χ mn pq ε 0 ω 2 e tm p , h tm p n ̄ ( r ) P ( r ) Δ n ( z ) · ( e tm p · e tn q e zm p · e zn q ) dS
Δ n ( z ) = σ ̄ ( z ) + 2 χ ̄ ( z ) cos [ 2 K g z + ϕ ̄ ( z ) ]
n ( z ) = σ ( z ) + 2 χ ( z ) cos [ 2 K ( z + x tan θ ) + ϕ ( z ) ]
{ p q } { κ mn pq 0 , χ mn pq 0 }
κ mn = K ̄ mn σ ( z ) + { K mn + exp [ + j ( 2 Kz + ϕ ( z ) ) ] + K mn exp [ j ( 2 Kz + ϕ ( z ) ) ] } χ ( z )
χ mn = X ̄ mn σ ( z ) + { X mn + exp [ + j ( 2 Kz + ϕ ( z ) ) ] + X mn exp [ j ( 2 Kz + ϕ ( z ) ) ] } χ ( z )
K mn + = ε 0 ω 2 e tm , h tm 0 n ̄ ( r ) P ( r ) r [ ( e ϕm e ϕn ) S ( r ) + ( e rm e rn + e zm e zn ) C ( r ) ] dr
X mn + = ε 0 ω 2 e tm , h tm 0 n ̄ ( r ) P ( r ) r [ ( e ϕm e ϕn ) S ( r ) + ( e rm e rn e zm e zn ) C ( r ) ] dr
K mn = ( 1 ) μ + ν K mn + , X mn = ( 1 ) μ + ν X mn +
K ̄ mn = K mn + θ = 0 = K mn θ = 0 , X ̄ mn = X mn + θ = 0 = X mn θ = 0
C ( r ) = 0 2 π cos ( μϕ ) cos ( νϕ ) · exp ( + 2 jKr tan θ cos ϕ )
S ( r ) = 0 2 π sin ( μϕ ) sin ( νϕ ) · exp ( + 2 jKr tan θ cos ϕ )
u ( z ) = [ a 1 ( z ) exp ( + j β ̄ 1 z ) ] exp [ + ( z ) / 2 ]
v ( z ) = [ b 1 ( z ) exp ( j β ̄ 1 z ) ] exp [ ( z ) / 2 ]
u n ( z ) = [ a n ( z ) exp ( + j β ̄ n z ) ] exp [ + ( z ) / 2 ]
v n ( z ) = [ b n ( z ) exp ( j β ̄ n z ) ] exp [ ( z ) / 2 ]
d u d z = j n 1 X 1 n χ ( z ) v n ( z ) exp [ + j Δ n + z ] j n 1 K 1 n χ ( z ) u n ( z ) exp [ + j Δ n z ]
j κ 1 ( z ) u ( z ) j X 11 χ ( z ) ν ( z ) exp [ + j Δ 1 + z ]
dv d z = + j n 1 X 1 n + χ ( z ) u n ( z ) exp [ j Δ n + z ] + j n 1 K 1 n + χ ( z ) v n ( z ) exp [ j Δ n z ]
+ j κ 1 ( z ) u ( z ) + j X 11 χ ( z ) ν ( z ) exp [ j Δ 1 + z ]
d u n d z = j κ n ( z ) u n ( z ) j X n 1 χ ( z ) v ( z ) exp [ + j Δ n + z ]
j K n 1 + χ ( z ) u ( z ) exp [ j Δ n z ] exp [ + ( z ) ]
d v n d z = + j κ n ( z ) v n ( z ) + j X n 1 + χ ( z ) u ( z ) exp [ j Δ n + z ]
+ j K n 1 χ ( z ) v ( z ) exp [ + j Δ n z ] exp [ ( z ) ]
κ n ( z ) = K ̄ nn σ ( z ) + β n β ̄ n 1 2 d ϕ d z
Δ n ± = β ̄ 1 ± β ̄ 2 2 K
X 11 = X 11 + = X 11
exp ( jϕz ) = { 0 L > ζ · [ 2 π / Re ( ϕ ) ] exp ( jϕz ) otherwise
R = n = 1 N b n ( L / 2 ) / a 1 ( L / 2 ) 2 , T = n = 1 N a n ( + L / 2 ) / a 1 ( L / 2 ) 2 .

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