Abstract

Over the past several years polarization-sensitive mode-coupling characteristics of tilted fiber Bragg gratings have been exploited for the development of a number of useful devices, including fiber polarimeters, gain flattening filters, spectrum analyzers, and polarization-dependent-loss compensators. Although a variety of tools are available to model blazed grating responses, to our knowledge a simplified explanation of the parametric dependencies and potential behavior has never been fully presented, making the optimization of these components difficult and elusive at times. We provide a thorough, intuitive discussion of these trends and possibilities as observed through an extensive theoretical and numerical analysis rooted in the volume current method. In addition to a review of the potential limitations and shortcomings of this formulation, some rough guidelines for the manufacture of various devices are also disclosed.

© 2005 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  32. R. Jordan and D. G. Hall, "Radiation from concentric-circle grating, surface-emitting planar waveguides: the volume current method," Appl. Phys. Lett. 64, 3077-3079 (1994).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  35. Y. Li, M. Froggatt, and T. Erdogan, "Volume current method for analysis of tilted fiber gratings," J. Lightwave Technol. 19, 1580-1591 (2001).
    [CrossRef]
  36. R. Kashyap, Fiber Bragg Gratings (Academic, New York, 1999), p. 128.
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2004

2003

K. Zhou, A. G. Simpson, L. Zhang, and I. Bennion, "Side detection of strong radiation-mode out-coupling from blazed FBGs in single-mode and multimode fibers," IEEE Photonics Technol. Lett. 15, 936-938 (2003).
[CrossRef]

2002

K. S. Lee and J. Y. Cho, "Polarization-mode coupling in birefringent fiber gratings," J. Opt. Soc. Am. A 19, 1621-1631 (2002).
[CrossRef]

J. M. Battiato and R. K. Kostuk, "45° slanted fibre Bragg grating design with prism coupled holographic exposure," Electron. Lett. 38, 1323-1324 (2002).
[CrossRef]

S. J. Mihailov, R. B. Walker, P. Lu, H. Ding, X. Dai, C. Smelser, and L. Chen, "UV-induced polarisation-dependent loss (PDL) in tilted fibre Bragg gratings: application of a PDL equaliser," IEE Proc.: Optoelectron. 149, 211-216 (2002).

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

2001

2000

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

1999

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

1997

P.-Y. Fonjallaz, H. G. Limberger, and R. P. Salathé, "Bragg gratings with efficient and wavelength-selective fiber out-coupling," J. Lightwave Technol. 15, 371-376 (1997).
[CrossRef]

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, "Fiber grating sensors," J. Lightwave Technol. 15, 1442-1463 (1997).
[CrossRef]

1996

1995

F. Bilodeau, D. C. Johnson, S. Theriault, B. Malo, J. Albert, and K. O. Hill, "All-fiber dense-wavelength-division multiplexer/demultiplexer using photoimprinted Bragg gratings," IEEE Photonics Technol. Lett. 7, 388-390 (1995).
[CrossRef]

1994

R. Jordan and D. G. Hall, "Radiation from concentric-circle grating, surface-emitting planar waveguides: the volume current method," Appl. Phys. Lett. 64, 3077-3079 (1994).
[CrossRef]

1993

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, "Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask," Appl. Phys. Lett. 62, 1035-1037 (1993).
[CrossRef]

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

1991

F. Ouellette, "All-fiber filter for efficient dispersion compensation," Opt. Lett. 16, 303-305 (1991).
[CrossRef] [PubMed]

P. St. J. Russell, "Bloch wave analysis of dispersion and pulse propagation in pure distributed feedback structures," J. Mod. Opt. 38, 1599-1619 (1991).
[CrossRef]

1990

K.O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, "Efficient mode conversion in telecommunication fibre using externally written gratings," Electron. Lett. 26, 1270-1272 (1990).
[CrossRef]

1989

1985

P. C. Kendall, P. N. Robson, and J. E. Sitch, "Rib waveguide curvature loss: the scalar problem," IEE Proc.-J: Optoelectron. 132, 140-145 (1985).

M. Kuznetsov, "Radiation loss in dielectric waveguide Y-branch structures," J. Lightwave Technol. LT-3, 674-677 (1985).
[CrossRef]

1983

M. Kuznetsov and H. A. Haus, "Radiation loss in dielectric waveguide structures by the volume current method," IEEE J. Quantum Electron. QE-19, 1505-1514 (1983).
[CrossRef]

1978

K. O. Hill, Y. Fujji, D. C. Johnson, and B. S. Kawasaki, "Photosensitivity in optical waveguides: application to reflection filter fabrication," Appl. Phys. Lett. 32, 647-649 (1978).
[CrossRef]

1975

A. W. Snyder, I. White, and D. J. Mitchell, "Radiation from bent optical waveguides," Electron. Lett. 38, 332-333 (1975).
[CrossRef]

1974

1970

A. W. Snyder, "Radiation losses due to variations of radius on dielectric or optical fibers," IEEE Trans. Microwave Theory Tech. MTT-18, 608-615 (1970).
[CrossRef]

Albert, J.

F. Bilodeau, D. C. Johnson, S. Theriault, B. Malo, J. Albert, and K. O. Hill, "All-fiber dense-wavelength-division multiplexer/demultiplexer using photoimprinted Bragg gratings," IEEE Photonics Technol. Lett. 7, 388-390 (1995).
[CrossRef]

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, "Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask," Appl. Phys. Lett. 62, 1035-1037 (1993).
[CrossRef]

Askins, C. G.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, "Fiber grating sensors," J. Lightwave Technol. 15, 1442-1463 (1997).
[CrossRef]

Bandemer, A.

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

Battiato, J. M.

J. M. Battiato and R. K. Kostuk, "45° slanted fibre Bragg grating design with prism coupled holographic exposure," Electron. Lett. 38, 1323-1324 (2002).
[CrossRef]

Bennion, I.

K. Zhou, A. G. Simpson, L. Zhang, and I. Bennion, "Side detection of strong radiation-mode out-coupling from blazed FBGs in single-mode and multimode fibers," IEEE Photonics Technol. Lett. 15, 936-938 (2003).
[CrossRef]

Bilodeau, F.

F. Bilodeau, D. C. Johnson, S. Theriault, B. Malo, J. Albert, and K. O. Hill, "All-fiber dense-wavelength-division multiplexer/demultiplexer using photoimprinted Bragg gratings," IEEE Photonics Technol. Lett. 7, 388-390 (1995).
[CrossRef]

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, "Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask," Appl. Phys. Lett. 62, 1035-1037 (1993).
[CrossRef]

K.O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, "Efficient mode conversion in telecommunication fibre using externally written gratings," Electron. Lett. 26, 1270-1272 (1990).
[CrossRef]

Campbell, R. J.

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

Carver, G. E.

Chauve, J.

L. Kotacka, J. Chauve, and R. Kashyap, "Angular and azimuthal distribution of side scattered light from fiber Bragg gratings," paper 5577-34 presented at Photonics North 2004, Ottawa, Ontario, Canada, 27-29 September 2004.

Chen, L.

S. J. Mihailov, R. B. Walker, P. Lu, H. Ding, X. Dai, C. Smelser, and L. Chen, "UV-induced polarisation-dependent loss (PDL) in tilted fibre Bragg gratings: application of a PDL equaliser," IEE Proc.: Optoelectron. 149, 211-216 (2002).

Cho, J. Y.

Chu, S. T.

Dai, X.

S. J. Mihailov, R. B. Walker, P. Lu, H. Ding, X. Dai, C. Smelser, and L. Chen, "UV-induced polarisation-dependent loss (PDL) in tilted fibre Bragg gratings: application of a PDL equaliser," IEE Proc.: Optoelectron. 149, 211-216 (2002).

Davis, M. A.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, "Fiber grating sensors," J. Lightwave Technol. 15, 1442-1463 (1997).
[CrossRef]

DeMarco, J.

J. L. Wagener, T. A. Strasser, J. R. Pedrazzani, J. DeMarco, and D. J. DiGiovanni, "Fibre grating optical spectrum analyzer tap," in 23rd European Conference on Optical Communications, IEE Conference Publication 448/5(Institution of Electrical Engineers, Stevenage, England, 1997), pp. 65-68.

DiGiovanni, D. J.

J. L. Wagener, T. A. Strasser, J. R. Pedrazzani, J. DeMarco, and D. J. DiGiovanni, "Fibre grating optical spectrum analyzer tap," in 23rd European Conference on Optical Communications, IEE Conference Publication 448/5(Institution of Electrical Engineers, Stevenage, England, 1997), pp. 65-68.

Ding, H.

S. J. Mihailov, R. B. Walker, P. Lu, H. Ding, X. Dai, C. Smelser, and L. Chen, "UV-induced polarisation-dependent loss (PDL) in tilted fibre Bragg gratings: application of a PDL equaliser," IEE Proc.: Optoelectron. 149, 211-216 (2002).

Durko, H. L.

Erdogan, T.

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

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

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

P. S. Westbrook, T. A. Strasser, and T. Erdogan, "Compact, in-line, all-fiber polarimeter using fiber gratings," in Optical Fiber Communications Conference, Postconference Digest, Vol. 37 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2000), PD22, pp. 233-235.

Fonjallaz, P.-Y.

P.-Y. Fonjallaz, H. G. Limberger, and R. P. Salathé, "Bragg gratings with efficient and wavelength-selective fiber out-coupling," J. Lightwave Technol. 15, 371-376 (1997).
[CrossRef]

Friebele, E. J.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, "Fiber grating sensors," J. Lightwave Technol. 15, 1442-1463 (1997).
[CrossRef]

Froggatt, M.

Fujji, Y.

K. O. Hill, Y. Fujji, D. C. Johnson, and B. S. Kawasaki, "Photosensitivity in optical waveguides: application to reflection filter fabrication," Appl. Phys. Lett. 32, 647-649 (1978).
[CrossRef]

Glenn, W. H.

G. Meltz, W. W. Morey, and W. H. Glenn, "Formation of Bragg gratings in optical fibers by a transverse holographic method," Opt. Lett. 14, 823-825 (1989).
[CrossRef] [PubMed]

G. Meltz, W. W. Morey, and W. H. Glenn, "In-fiber Bragg grating tap," in Optical Fiber Communications, Vol. 1 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 24.

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Rhyzhik, Table of Integrals, Series, and Products, 6th ed. (Academic, New York, 2000), pp. 909-910, Equation Set 8.451.

Grobnic, D.

R. B. Walker, S. J. Mihailov, P. Lu, and D. Grobnic, "Optimizing grating based devices with the volume current method," paper 5577-35 presented at Photonics North 2004, Ottawa, Ontario, Canada, 27-29 September 2004.

Hall, D. G.

R. Jordan and D. G. Hall, "Radiation from concentric-circle grating, surface-emitting planar waveguides: the volume current method," Appl. Phys. Lett. 64, 3077-3079 (1994).
[CrossRef]

Haus, H. A.

M. Kuznetsov and H. A. Haus, "Radiation loss in dielectric waveguide structures by the volume current method," IEEE J. Quantum Electron. QE-19, 1505-1514 (1983).
[CrossRef]

Hill, K. O.

F. Bilodeau, D. C. Johnson, S. Theriault, B. Malo, J. Albert, and K. O. Hill, "All-fiber dense-wavelength-division multiplexer/demultiplexer using photoimprinted Bragg gratings," IEEE Photonics Technol. Lett. 7, 388-390 (1995).
[CrossRef]

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, "Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask," Appl. Phys. Lett. 62, 1035-1037 (1993).
[CrossRef]

K.O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, "Efficient mode conversion in telecommunication fibre using externally written gratings," Electron. Lett. 26, 1270-1272 (1990).
[CrossRef]

K. O. Hill, Y. Fujji, D. C. Johnson, and B. S. Kawasaki, "Photosensitivity in optical waveguides: application to reflection filter fabrication," Appl. Phys. Lett. 32, 647-649 (1978).
[CrossRef]

Holmes, M. J.

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

Johnson, D. C.

F. Bilodeau, D. C. Johnson, S. Theriault, B. Malo, J. Albert, and K. O. Hill, "All-fiber dense-wavelength-division multiplexer/demultiplexer using photoimprinted Bragg gratings," IEEE Photonics Technol. Lett. 7, 388-390 (1995).
[CrossRef]

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, "Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask," Appl. Phys. Lett. 62, 1035-1037 (1993).
[CrossRef]

K.O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, "Efficient mode conversion in telecommunication fibre using externally written gratings," Electron. Lett. 26, 1270-1272 (1990).
[CrossRef]

K. O. Hill, Y. Fujji, D. C. Johnson, and B. S. Kawasaki, "Photosensitivity in optical waveguides: application to reflection filter fabrication," Appl. Phys. Lett. 32, 647-649 (1978).
[CrossRef]

Jordan, R.

R. Jordan and D. G. Hall, "Radiation from concentric-circle grating, surface-emitting planar waveguides: the volume current method," Appl. Phys. Lett. 64, 3077-3079 (1994).
[CrossRef]

Kashyap, R.

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

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

L. Kotacka, J. Chauve, and R. Kashyap, "Angular and azimuthal distribution of side scattered light from fiber Bragg gratings," paper 5577-34 presented at Photonics North 2004, Ottawa, Ontario, Canada, 27-29 September 2004.

R. Kashyap, Fiber Bragg Gratings (Academic, New York, 1999), p. 128.

Kawasaki, B. S.

K. O. Hill, Y. Fujji, D. C. Johnson, and B. S. Kawasaki, "Photosensitivity in optical waveguides: application to reflection filter fabrication," Appl. Phys. Lett. 32, 647-649 (1978).
[CrossRef]

Kendall, P. C.

P. C. Kendall, P. N. Robson, and J. E. Sitch, "Rib waveguide curvature loss: the scalar problem," IEE Proc.-J: Optoelectron. 132, 140-145 (1985).

Kersey, A. D.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, "Fiber grating sensors," J. Lightwave Technol. 15, 1442-1463 (1997).
[CrossRef]

Kittel, C.

C. Kittel, Introduction to Solid State Physics, 6th ed. (Wiley, Toronto, 1996), p. 29.

Koo, K. P.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, "Fiber grating sensors," J. Lightwave Technol. 15, 1442-1463 (1997).
[CrossRef]

Kostuk, R. K.

J. M. Battiato and R. K. Kostuk, "45° slanted fibre Bragg grating design with prism coupled holographic exposure," Electron. Lett. 38, 1323-1324 (2002).
[CrossRef]

Kotacka, L.

L. Kotacka, J. Chauve, and R. Kashyap, "Angular and azimuthal distribution of side scattered light from fiber Bragg gratings," paper 5577-34 presented at Photonics North 2004, Ottawa, Ontario, Canada, 27-29 September 2004.

Krause, E.

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

Kuznetsov, M.

M. Kuznetsov, "Radiation loss in dielectric waveguide Y-branch structures," J. Lightwave Technol. LT-3, 674-677 (1985).
[CrossRef]

M. Kuznetsov and H. A. Haus, "Radiation loss in dielectric waveguide structures by the volume current method," IEEE J. Quantum Electron. QE-19, 1505-1514 (1983).
[CrossRef]

LeBlanc, M.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, "Fiber grating sensors," J. Lightwave Technol. 15, 1442-1463 (1997).
[CrossRef]

Lee, K. S.

Li, Y.

Limberger, H. G.

P.-Y. Fonjallaz, H. G. Limberger, and R. P. Salathé, "Bragg gratings with efficient and wavelength-selective fiber out-coupling," J. Lightwave Technol. 15, 371-376 (1997).
[CrossRef]

Little, B. E.

Lu, P.

S. J. Mihailov, R. B. Walker, P. Lu, H. Ding, X. Dai, C. Smelser, and L. Chen, "UV-induced polarisation-dependent loss (PDL) in tilted fibre Bragg gratings: application of a PDL equaliser," IEE Proc.: Optoelectron. 149, 211-216 (2002).

R. B. Walker, S. J. Mihailov, P. Lu, and D. Grobnic, "Optimizing grating based devices with the volume current method," paper 5577-35 presented at Photonics North 2004, Ottawa, Ontario, Canada, 27-29 September 2004.

Malo, B.

F. Bilodeau, D. C. Johnson, S. Theriault, B. Malo, J. Albert, and K. O. Hill, "All-fiber dense-wavelength-division multiplexer/demultiplexer using photoimprinted Bragg gratings," IEEE Photonics Technol. Lett. 7, 388-390 (1995).
[CrossRef]

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, "Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask," Appl. Phys. Lett. 62, 1035-1037 (1993).
[CrossRef]

K.O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, "Efficient mode conversion in telecommunication fibre using externally written gratings," Electron. Lett. 26, 1270-1272 (1990).
[CrossRef]

Meltz, G.

G. Meltz, W. W. Morey, and W. H. Glenn, "Formation of Bragg gratings in optical fibers by a transverse holographic method," Opt. Lett. 14, 823-825 (1989).
[CrossRef] [PubMed]

G. Meltz and W. W. Morey, "Design and performance of bidirectional fiber Bragg grating taps," Optical Fiber Communication, Vol. 4 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 44.

G. Meltz, W. W. Morey, and W. H. Glenn, "In-fiber Bragg grating tap," in Optical Fiber Communications, Vol. 1 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 24.

Mihailov, S. J.

S. J. Mihailov, R. B. Walker, P. Lu, H. Ding, X. Dai, C. Smelser, and L. Chen, "UV-induced polarisation-dependent loss (PDL) in tilted fibre Bragg gratings: application of a PDL equaliser," IEE Proc.: Optoelectron. 149, 211-216 (2002).

R. B. Walker, S. J. Mihailov, P. Lu, and D. Grobnic, "Optimizing grating based devices with the volume current method," paper 5577-35 presented at Photonics North 2004, Ottawa, Ontario, Canada, 27-29 September 2004.

Mitchell, D. J.

A. W. Snyder, I. White, and D. J. Mitchell, "Radiation from bent optical waveguides," Electron. Lett. 38, 332-333 (1975).
[CrossRef]

Morey, W. W.

G. Meltz, W. W. Morey, and W. H. Glenn, "Formation of Bragg gratings in optical fibers by a transverse holographic method," Opt. Lett. 14, 823-825 (1989).
[CrossRef] [PubMed]

G. Meltz and W. W. Morey, "Design and performance of bidirectional fiber Bragg grating taps," Optical Fiber Communication, Vol. 4 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 44.

G. Meltz, W. W. Morey, and W. H. Glenn, "In-fiber Bragg grating tap," in Optical Fiber Communications, Vol. 1 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 24.

Ouellette, F.

Patrick, H. J.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, "Fiber grating sensors," J. Lightwave Technol. 15, 1442-1463 (1997).
[CrossRef]

Pedrazzani, J. R.

J. L. Wagener, T. A. Strasser, J. R. Pedrazzani, J. DeMarco, and D. J. DiGiovanni, "Fibre grating optical spectrum analyzer tap," in 23rd European Conference on Optical Communications, IEE Conference Publication 448/5(Institution of Electrical Engineers, Stevenage, England, 1997), pp. 65-68.

Peupelmann, J.

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

Putnam, M. A.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, "Fiber grating sensors," J. Lightwave Technol. 15, 1442-1463 (1997).
[CrossRef]

Rawson, E. G.

Rhyzhik, I. M.

I. S. Gradshteyn and I. M. Rhyzhik, Table of Integrals, Series, and Products, 6th ed. (Academic, New York, 2000), pp. 909-910, Equation Set 8.451.

Robson, P. N.

P. C. Kendall, P. N. Robson, and J. E. Sitch, "Rib waveguide curvature loss: the scalar problem," IEE Proc.-J: Optoelectron. 132, 140-145 (1985).

Russell, P. St. J.

P. St. J. Russell, "Bloch wave analysis of dispersion and pulse propagation in pure distributed feedback structures," J. Mod. Opt. 38, 1599-1619 (1991).
[CrossRef]

Salathé, R. P.

P.-Y. Fonjallaz, H. G. Limberger, and R. P. Salathé, "Bragg gratings with efficient and wavelength-selective fiber out-coupling," J. Lightwave Technol. 15, 371-376 (1997).
[CrossRef]

Schäffer, C.

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

Simpson, A. G.

K. Zhou, A. G. Simpson, L. Zhang, and I. Bennion, "Side detection of strong radiation-mode out-coupling from blazed FBGs in single-mode and multimode fibers," IEEE Photonics Technol. Lett. 15, 936-938 (2003).
[CrossRef]

Sipe, J. E.

Sitch, J. E.

P. C. Kendall, P. N. Robson, and J. E. Sitch, "Rib waveguide curvature loss: the scalar problem," IEE Proc.-J: Optoelectron. 132, 140-145 (1985).

Skaar, J.

Skinner, I.

K.O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, "Efficient mode conversion in telecommunication fibre using externally written gratings," Electron. Lett. 26, 1270-1272 (1990).
[CrossRef]

Smelser, C.

S. J. Mihailov, R. B. Walker, P. Lu, H. Ding, X. Dai, C. Smelser, and L. Chen, "UV-induced polarisation-dependent loss (PDL) in tilted fibre Bragg gratings: application of a PDL equaliser," IEE Proc.: Optoelectron. 149, 211-216 (2002).

Snyder, A. W.

A. W. Snyder, I. White, and D. J. Mitchell, "Radiation from bent optical waveguides," Electron. Lett. 38, 332-333 (1975).
[CrossRef]

A. W. Snyder, "Radiation losses due to variations of radius on dielectric or optical fibers," IEEE Trans. Microwave Theory Tech. MTT-18, 608-615 (1970).
[CrossRef]

Strasser, T. A.

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

P. S. Westbrook, T. A. Strasser, and T. Erdogan, "Compact, in-line, all-fiber polarimeter using fiber gratings," in Optical Fiber Communications Conference, Postconference Digest, Vol. 37 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2000), PD22, pp. 233-235.

J. L. Wagener, T. A. Strasser, J. R. Pedrazzani, J. DeMarco, and D. J. DiGiovanni, "Fibre grating optical spectrum analyzer tap," in 23rd European Conference on Optical Communications, IEE Conference Publication 448/5(Institution of Electrical Engineers, Stevenage, England, 1997), pp. 65-68.

Theriault, S.

F. Bilodeau, D. C. Johnson, S. Theriault, B. Malo, J. Albert, and K. O. Hill, "All-fiber dense-wavelength-division multiplexer/demultiplexer using photoimprinted Bragg gratings," IEEE Photonics Technol. Lett. 7, 388-390 (1995).
[CrossRef]

Vineberg, K. A.

K.O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, "Efficient mode conversion in telecommunication fibre using externally written gratings," Electron. Lett. 26, 1270-1272 (1990).
[CrossRef]

Waagaard, O. H.

Wagener, J. L.

J. L. Wagener, T. A. Strasser, J. R. Pedrazzani, J. DeMarco, and D. J. DiGiovanni, "Fibre grating optical spectrum analyzer tap," in 23rd European Conference on Optical Communications, IEE Conference Publication 448/5(Institution of Electrical Engineers, Stevenage, England, 1997), pp. 65-68.

Walker, R. B.

S. J. Mihailov, R. B. Walker, P. Lu, H. Ding, X. Dai, C. Smelser, and L. Chen, "UV-induced polarisation-dependent loss (PDL) in tilted fibre Bragg gratings: application of a PDL equaliser," IEE Proc.: Optoelectron. 149, 211-216 (2002).

R. B. Walker, S. J. Mihailov, P. Lu, and D. Grobnic, "Optimizing grating based devices with the volume current method," paper 5577-35 presented at Photonics North 2004, Ottawa, Ontario, Canada, 27-29 September 2004.

Westbrook, P. S.

Y. Li, S. Wielandy, G. E. Carver, H. L. Durko, and P. S. Westbrook, "Influence of the longitudinal mode field in grating scattering from weakly guided optical fiber waveguides," Opt. Lett. 29, 691-693 (2004).
[CrossRef] [PubMed]

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

P. S. Westbrook, T. A. Strasser, and T. Erdogan, "Compact, in-line, all-fiber polarimeter using fiber gratings," in Optical Fiber Communications Conference, Postconference Digest, Vol. 37 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2000), PD22, pp. 233-235.

White, I.

A. W. Snyder, I. White, and D. J. Mitchell, "Radiation from bent optical waveguides," Electron. Lett. 38, 332-333 (1975).
[CrossRef]

Wielandy, S.

Wyatt, R.

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

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

Zhang, L.

K. Zhou, A. G. Simpson, L. Zhang, and I. Bennion, "Side detection of strong radiation-mode out-coupling from blazed FBGs in single-mode and multimode fibers," IEEE Photonics Technol. Lett. 15, 936-938 (2003).
[CrossRef]

Zhou, K.

K. Zhou, A. G. Simpson, L. Zhang, and I. Bennion, "Side detection of strong radiation-mode out-coupling from blazed FBGs in single-mode and multimode fibers," IEEE Photonics Technol. Lett. 15, 936-938 (2003).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

R. Jordan and D. G. Hall, "Radiation from concentric-circle grating, surface-emitting planar waveguides: the volume current method," Appl. Phys. Lett. 64, 3077-3079 (1994).
[CrossRef]

K. O. Hill, Y. Fujji, D. C. Johnson, and B. S. Kawasaki, "Photosensitivity in optical waveguides: application to reflection filter fabrication," Appl. Phys. Lett. 32, 647-649 (1978).
[CrossRef]

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, "Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask," Appl. Phys. Lett. 62, 1035-1037 (1993).
[CrossRef]

Electron. Lett.

K.O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, "Efficient mode conversion in telecommunication fibre using externally written gratings," Electron. Lett. 26, 1270-1272 (1990).
[CrossRef]

J. M. Battiato and R. K. Kostuk, "45° slanted fibre Bragg grating design with prism coupled holographic exposure," Electron. Lett. 38, 1323-1324 (2002).
[CrossRef]

A. W. Snyder, I. White, and D. J. Mitchell, "Radiation from bent optical waveguides," Electron. Lett. 38, 332-333 (1975).
[CrossRef]

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

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

IEE Proc.-J: Optoelectron.

P. C. Kendall, P. N. Robson, and J. E. Sitch, "Rib waveguide curvature loss: the scalar problem," IEE Proc.-J: Optoelectron. 132, 140-145 (1985).

IEE Proc.: Optoelectron.

S. J. Mihailov, R. B. Walker, P. Lu, H. Ding, X. Dai, C. Smelser, and L. Chen, "UV-induced polarisation-dependent loss (PDL) in tilted fibre Bragg gratings: application of a PDL equaliser," IEE Proc.: Optoelectron. 149, 211-216 (2002).

IEEE J. Quantum Electron.

M. Kuznetsov and H. A. Haus, "Radiation loss in dielectric waveguide structures by the volume current method," IEEE J. Quantum Electron. QE-19, 1505-1514 (1983).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

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

IEEE Photonics Technol. Lett.

K. Zhou, A. G. Simpson, L. Zhang, and I. Bennion, "Side detection of strong radiation-mode out-coupling from blazed FBGs in single-mode and multimode fibers," IEEE Photonics Technol. Lett. 15, 936-938 (2003).
[CrossRef]

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

F. Bilodeau, D. C. Johnson, S. Theriault, B. Malo, J. Albert, and K. O. Hill, "All-fiber dense-wavelength-division multiplexer/demultiplexer using photoimprinted Bragg gratings," IEEE Photonics Technol. Lett. 7, 388-390 (1995).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

A. W. Snyder, "Radiation losses due to variations of radius on dielectric or optical fibers," IEEE Trans. Microwave Theory Tech. MTT-18, 608-615 (1970).
[CrossRef]

J. Lightwave Technol.

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

M. Kuznetsov, "Radiation loss in dielectric waveguide Y-branch structures," J. Lightwave Technol. LT-3, 674-677 (1985).
[CrossRef]

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, "Fiber grating sensors," J. Lightwave Technol. 15, 1442-1463 (1997).
[CrossRef]

P.-Y. Fonjallaz, H. G. Limberger, and R. P. Salathé, "Bragg gratings with efficient and wavelength-selective fiber out-coupling," J. Lightwave Technol. 15, 371-376 (1997).
[CrossRef]

J. Mod. Opt.

P. St. J. Russell, "Bloch wave analysis of dispersion and pulse propagation in pure distributed feedback structures," J. Mod. Opt. 38, 1599-1619 (1991).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Lett.

Other

I. S. Gradshteyn and I. M. Rhyzhik, Table of Integrals, Series, and Products, 6th ed. (Academic, New York, 2000), pp. 909-910, Equation Set 8.451.

R. Kashyap, Fiber Bragg Gratings (Academic, New York, 1999), p. 128.

J. L. Wagener, T. A. Strasser, J. R. Pedrazzani, J. DeMarco, and D. J. DiGiovanni, "Fibre grating optical spectrum analyzer tap," in 23rd European Conference on Optical Communications, IEE Conference Publication 448/5(Institution of Electrical Engineers, Stevenage, England, 1997), pp. 65-68.

G. Meltz, W. W. Morey, and W. H. Glenn, "In-fiber Bragg grating tap," in Optical Fiber Communications, Vol. 1 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 24.

L. Kotacka, J. Chauve, and R. Kashyap, "Angular and azimuthal distribution of side scattered light from fiber Bragg gratings," paper 5577-34 presented at Photonics North 2004, Ottawa, Ontario, Canada, 27-29 September 2004.

R. B. Walker, S. J. Mihailov, P. Lu, and D. Grobnic, "Optimizing grating based devices with the volume current method," paper 5577-35 presented at Photonics North 2004, Ottawa, Ontario, Canada, 27-29 September 2004.

C. Kittel, Introduction to Solid State Physics, 6th ed. (Wiley, Toronto, 1996), p. 29.

P. S. Westbrook, T. A. Strasser, and T. Erdogan, "Compact, in-line, all-fiber polarimeter using fiber gratings," in Optical Fiber Communications Conference, Postconference Digest, Vol. 37 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2000), PD22, pp. 233-235.

G. Meltz and W. W. Morey, "Design and performance of bidirectional fiber Bragg grating taps," Optical Fiber Communication, Vol. 4 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 44.

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Figures (13)

Fig. 1
Fig. 1

Schematic of selected grating parameters. r and ϕ represent polar coordinates about the fiber axis. k i ( k i = 2 π n eff λ ) is the incident guided mode wave vector with effective index n eff and free-space wavelength λ. k t and Δ symbolize the transverse and longitudinal components of the radiation wave vector k out ( k out 2 π n 0 λ ) where n 0 is the core refractive index. K t ( K t = 2 π sin ξ Λ ) is the transverse component of the grating vector K ( K = 2 π Λ ) where Λ is the grating period and ξ is the blaze angle. K new is the detuning vector (phase mismatch) and ξ out is the longitudinal tap angle of the radiated mode.

Fig. 2
Fig. 2

Normalized grating response for a nonpolarized guided mode.

Fig. 3
Fig. 3

Normalized grating response to a polarized guided mode.

Fig. 4
Fig. 4

Behavioral regime A: variation of f 2 norm azimuthal distribution with K t k t ( a u = 1.5 , k t u = 8 ) .

Fig. 5
Fig. 5

Behavioral regime B: variation of f 2 norm azimuthal distribution with K t k t ( a u = 1.5 , k t u = 8 ) .

Fig. 6
Fig. 6

General classification of f 2 ( norm ) ’s response types ( a u = 1.6 , k t u = 12.5 ) .

Fig. 7
Fig. 7

Typical example of VCM data and empirical fits: split response type.

Fig. 8
Fig. 8

Physical significance of i ( a u = 1.5 , k t u = 8 ) .

Fig. 9
Fig. 9

Typical example of VCM data and empirical fits: split response angular spread.

Fig. 10
Fig. 10

Typical example of VCM data and empirical fits: peak coupling efficiency.

Fig. 11
Fig. 11

Constants dependent on a u : split response.

Fig. 12
Fig. 12

Dependencies of K t k t and Δ ϕ on k t u : split response.

Fig. 13
Fig. 13

Combinations of K t k t and k t u yielding a split response and 25° azimuthal spread ( a u = 1.6 ) .

Tables (3)

Tables Icon

Table 1 Empirical Recipe Coefficients for Various Response Types

Tables Icon

Table 2 Empirical Angular Spread Coefficients for Split and Mixed Response Types

Tables Icon

Table 3 Empirical Coefficients for Peak Coupling Efficiency of all Response Types

Equations (55)

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

r k t ( 9 128 ) 1 2 ,
S ( π k 0 c κ 2 E 0 2 4 ϵ r f 1 f 2 ) ( r ̂ + Δ k t z ̂ ) ,
κ = ϵ 0 n 0 δ n ; k t = ( k 0 2 n 0 2 Δ 2 ) 1 2 ;
Δ = k 0 n eff K g ; K g = 2 π Λ cos ξ .
f 1 = Δ 2 + k t 2 sin 2 ( δ ϕ ) ,
K new = ( K t 2 + k t 2 2 K t k t sin ϕ ) 1 2 ,
f 2 = [ K new a J 0 ( u a ) J 1 ( K new a ) u a J 1 ( u a ) J 0 ( K new a ) K new 2 u 2 ] 2 ,
u = k 0 ( n 0 2 n eff 2 ) 1 2 ; K t = 2 π Λ sin ξ .
f 2 norm = f 2 a 2 = [ C J 1 ( C ) J 0 ( D ) D J 1 ( D ) J 0 ( C ) C 2 D 2 ] 2 ,
C = K new a = a u ( k t u ) [ 1 2 ( K t k t ) sin ϕ + ( K t k t ) 2 ] 1 2 ,
D = a u .
0 a u V 2.4 .
k t min = 100 r max ( 9 128 ) 1 2 = 75 2 2 ( 1 a clad ) ,
( k t u ) min = a k t min a u 26.517 a u ( 1 a clad ) .
( k t u ) max = k t max k 0 ( n 0 2 n eff 2 ) 1 2 = 1 ( n 0 2 n eff 2 ) 1 2 .
26.517 a u ( a a clad ) k t u 1 ( n 0 2 n eff 2 ) 1 2 .
0 K t k t .
K t k t = 1 ± ψ k t u ,
ψ = χ i a u ,
ψ = exp [ φ 1 i ( a u ) 2 + φ 2 i ( a u ) + φ 3 i ] ,
χ i = C 1 ( i ) + C 2 ,
φ 1 i = C 3 ( i ) + C 4 ,
φ 2 i = C 5 ( i ) + C 6 ,
φ 3 i = C 7 ( i ) C 8 ,
Δ ϕ = Ψ 1 ( k t u ) Ψ 2 ,
Ψ 1 = κ 1 i ( a u ) κ 2 i ,
Ψ 2 = γ 1 i ( a u ) + γ 2 i ,
κ 1 i = D 1 ( i ) 2 + D 2 ( i ) + D 3 ,
κ 2 i = D 4 ( i ) + D 5 ,
γ 1 i = D 6 ( i ) + D 7 ,
γ 2 i = D 8 ( i ) + D 9 ,
f 2 ( peak ) = a 2 exp [ Ω 1 ( a u ) 4 + Ω 2 ( a u ) 3 + Ω 3 ( a u ) 2 + Ω 4 ( a u ) + Ω 5 ] ,
Ω 1 = G 1 i 2 + G 2 i + G 3 ,
Ω 2 = G 4 i 2 + G 5 i + G 6 ,
Ω 3 = G 7 i 2 + G 8 i + G 9 ,
Ω 4 = G 10 i 3 + G 11 i 2 + G 12 i + G 13 ,
Ω 5 = G 14 i 3 + G 15 i 2 + G 16 i + G 17 ,
ξ = arctan ( K t k t ( k t u ) [ 1 ( n eff n 0 ) 2 ] 1 2 ( n eff n 0 ) { 1 ( k t u ) 2 [ 1 ( n eff n 0 ) 2 ] } 1 2 ) ,
Λ = λ n 0 [ ( K t k t ) 2 ( k t u ) 2 [ 1 ( n eff n 0 ) 2 ] + ( ( n eff n 0 ) { 1 ( k t u ) 2 [ 1 ( n eff n 0 ) 2 ] } 2 ) ] 1 2 .
Term n = 1 R 1
( 1 ) k Γ ( ν + 2 k + 1 2 ) ( 2 z ) 2 k ( 2 k ) ! Γ ( ν 2 k + 1 2 ) , Γ ( ν + 2 n + 1 2 ) ( 2 z ) 2 n ( 2 n ) ! Γ ( ν 2 n + 1 2 ) ,
1 Γ ( 1 2 + 2 ) 2 ( 2 k t r ) 2 Γ ( 1 2 2 )
r k t Γ ( 1 2 + 2 ) 8 Γ ( 1 2 2 ) 1 2
r k t ( 9 128 ) 1 2 .
cos ξ Λ λ [ n eff ( n 0 2 5625 λ 2 32 π 2 r 2 ) 1 2 ] ,
f 1 nonpolarized ( ϕ ) = 1 π 0 π f 1 ( δ , ϕ ) d δ = 1 π 0 π [ Δ 2 + k t 2 sin 2 ( δ ϕ ) ] d δ = Δ 2 + k t 2 2 .
k t u = ( k 0 2 n 0 2 Δ 2 ) 1 2 k 0 ( n 0 2 n eff 2 ) 1 2 ,
( k t u ) 2 ( n 0 2 n eff 2 ) = n 0 2 [ n eff ( λ Λ ) cos ξ ] 2 ,
λ Λ = n eff [ n 0 2 ( k t u ) 2 ( n 0 2 n eff 2 ) ] 1 2 cos ξ .
K t k t = 2 π sin ξ Λ ( k 0 2 n 0 2 Δ 2 ) 1 2 = 2 π sin ξ Λ k 0 [ n 0 2 ( n eff K g k 0 ) 2 ] 1 2 = ( λ Λ ) sin ξ { n 0 2 [ n eff ( λ Λ ) cos ξ ] 2 } 1 2 .
K t k t = { n eff [ n 0 2 ( k t u ) 2 ( n 0 2 n eff 2 ) ] 1 2 } tan ξ [ n 0 2 ( n eff { n eff [ n 0 2 ( k t u ) 2 ( n 0 2 n eff 2 ) ] 1 2 } ) 2 ] 1 2
ξ = arctan ( K t k t ( k t u ) [ 1 ( n eff n 0 ) 2 ] 1 2 ( n eff n 0 ) { 1 ( k t u ) 2 [ 1 ( n eff n 0 ) 2 ] } 1 2 ) .
( k t u ) K t k t = [ 2 π sin ξ Λ ( k 0 2 n 0 2 Δ 2 ) 1 2 ] [ ( k 0 2 n 0 2 Δ 2 ) 1 2 k 0 ( n 0 2 n eff 2 ) 1 2 ] 1 2 ,
Λ = λ ( k t u ) K t k t { n 0 [ 1 ( n eff n 0 ) 2 ] 1 2 } sin ξ .
Λ = λ n 0 [ ( K t k t ) 2 ( k t u ) 2 [ 1 ( n eff n 0 ) 2 ] + ( ( n eff n 0 ) { 1 ( k t u ) 2 [ 1 ( n eff n 0 ) 2 ] } 1 2 ) 2 ] .

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