Abstract

The radiated power emanating from a bent single-mode fiber is computed for various radii of curvature by a full-vectorial analysis. The only approximation is the truncation of a spectral series, the accuracy of which can be controlled. Hence, the complex propagation coefficient of the fundamental mode approaches the exact value and consequently, the bending loss does as well. Two widely accepted bending-loss formulas, based on asymptotic approximations to scalar-field theory, are compared with our full-vectorial results. Both have a limited region of validity. For simplicity, the comparison is performed on a step-index fiber with a cladding of infinite extent. However, the full-wave method is capable of dealing with arbitrary index profiles.

© 2007 Optical Society of America

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  1. L. Faustini and G. Martini, "Bend loss in single-mode fibers," J. Lightwave Technol. 15, 671-679 (1997).
    [CrossRef]
  2. D. Marcuse, "Curvature loss formula for optical fibers," J. Opt. Soc. Am. 66, 216-220 (1976).
  3. H. Renner, "Bending losses of coated single-mode fibers: A simple approach," J. Lightwave Technol. 10, 544-551 (1992).
    [CrossRef]
  4. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).
  5. L. Lewin, D. C. Chang, and E. F. Kuester, Electromagnetic Waves and Curved Structures (Peter Peregrinus Ltd., 1977).
  6. I. A. White, "Radiation from bends in optical waveguides: The volume-current method," IEE J. Microwaves, Opt. Acoust. 3, 186-188 (1979).
  7. C. Vassallo, Optical Waveguide Concepts (Elsevier Science, 1991).
  8. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1965).
  9. C. Vassallo, "Scalar-field theory and 2-D ray theory for bent single-mode weakly guiding optical fibers," J. Lightwave Technol. LT-3, 416-423 (1985).
  10. W. H. Press, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in Fortran 77: The Art of Scientific Computing (Cambridge U. Press, 1973).
  11. J. G. Dil and H. Blok, "Propagation of electromagnetic surface waves in a radially inhomogeneous optical waveguide," Opt. Quantum Electron. 5, 415-428 (1973).
    [CrossRef]
  12. B. P. de Hon and M. Bingle, "A model impedance-angle formalism: schemes for accurate graded-index bent-slab calculations and optical fiber mode counting," Radio Sci. 38, 13-1 (2003), doi: 10.1029/2001RS002570.
  13. D. I. Kaklamani and H. T. Anastassiu, "Aspects of the method of auxiliarly sources (MAS) in computational electromagnetics," IEEE Antennas Propag. Mag. 44, 48-64 (2002).
    [CrossRef]
  14. J. L. Synge and A. Schild, Tensor Calculus (U. of Toronto Press, 1956).
  15. A. T. de Hoop, Handbook of Radiation and Scattering of Waves: Acoustic Waves in Fluids, Elastic Waves in Solids, Electromagnetic Waves (Academic, 1995).
  16. Y. Leviatan and A. Boag, "Analysis of electromagnetic scattering from dielectric cylinders using a multifilament current model," IEEE Trans. Antennas Propag. 35, 1119-1127 (1987).
    [CrossRef]

2003 (1)

B. P. de Hon and M. Bingle, "A model impedance-angle formalism: schemes for accurate graded-index bent-slab calculations and optical fiber mode counting," Radio Sci. 38, 13-1 (2003), doi: 10.1029/2001RS002570.

2002 (1)

D. I. Kaklamani and H. T. Anastassiu, "Aspects of the method of auxiliarly sources (MAS) in computational electromagnetics," IEEE Antennas Propag. Mag. 44, 48-64 (2002).
[CrossRef]

1997 (1)

L. Faustini and G. Martini, "Bend loss in single-mode fibers," J. Lightwave Technol. 15, 671-679 (1997).
[CrossRef]

1992 (1)

H. Renner, "Bending losses of coated single-mode fibers: A simple approach," J. Lightwave Technol. 10, 544-551 (1992).
[CrossRef]

1987 (1)

Y. Leviatan and A. Boag, "Analysis of electromagnetic scattering from dielectric cylinders using a multifilament current model," IEEE Trans. Antennas Propag. 35, 1119-1127 (1987).
[CrossRef]

1985 (1)

C. Vassallo, "Scalar-field theory and 2-D ray theory for bent single-mode weakly guiding optical fibers," J. Lightwave Technol. LT-3, 416-423 (1985).

1979 (1)

I. A. White, "Radiation from bends in optical waveguides: The volume-current method," IEE J. Microwaves, Opt. Acoust. 3, 186-188 (1979).

1976 (1)

1973 (1)

J. G. Dil and H. Blok, "Propagation of electromagnetic surface waves in a radially inhomogeneous optical waveguide," Opt. Quantum Electron. 5, 415-428 (1973).
[CrossRef]

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1965).

Anastassiu, H. T.

D. I. Kaklamani and H. T. Anastassiu, "Aspects of the method of auxiliarly sources (MAS) in computational electromagnetics," IEEE Antennas Propag. Mag. 44, 48-64 (2002).
[CrossRef]

Bingle, M.

B. P. de Hon and M. Bingle, "A model impedance-angle formalism: schemes for accurate graded-index bent-slab calculations and optical fiber mode counting," Radio Sci. 38, 13-1 (2003), doi: 10.1029/2001RS002570.

Blok, H.

J. G. Dil and H. Blok, "Propagation of electromagnetic surface waves in a radially inhomogeneous optical waveguide," Opt. Quantum Electron. 5, 415-428 (1973).
[CrossRef]

Boag, A.

Y. Leviatan and A. Boag, "Analysis of electromagnetic scattering from dielectric cylinders using a multifilament current model," IEEE Trans. Antennas Propag. 35, 1119-1127 (1987).
[CrossRef]

Chang, D. C.

L. Lewin, D. C. Chang, and E. F. Kuester, Electromagnetic Waves and Curved Structures (Peter Peregrinus Ltd., 1977).

de Hon, B. P.

B. P. de Hon and M. Bingle, "A model impedance-angle formalism: schemes for accurate graded-index bent-slab calculations and optical fiber mode counting," Radio Sci. 38, 13-1 (2003), doi: 10.1029/2001RS002570.

de Hoop, A. T.

A. T. de Hoop, Handbook of Radiation and Scattering of Waves: Acoustic Waves in Fluids, Elastic Waves in Solids, Electromagnetic Waves (Academic, 1995).

Dil, J. G.

J. G. Dil and H. Blok, "Propagation of electromagnetic surface waves in a radially inhomogeneous optical waveguide," Opt. Quantum Electron. 5, 415-428 (1973).
[CrossRef]

Faustini, L.

L. Faustini and G. Martini, "Bend loss in single-mode fibers," J. Lightwave Technol. 15, 671-679 (1997).
[CrossRef]

Kaklamani, D. I.

D. I. Kaklamani and H. T. Anastassiu, "Aspects of the method of auxiliarly sources (MAS) in computational electromagnetics," IEEE Antennas Propag. Mag. 44, 48-64 (2002).
[CrossRef]

Kuester, E. F.

L. Lewin, D. C. Chang, and E. F. Kuester, Electromagnetic Waves and Curved Structures (Peter Peregrinus Ltd., 1977).

Leviatan, Y.

Y. Leviatan and A. Boag, "Analysis of electromagnetic scattering from dielectric cylinders using a multifilament current model," IEEE Trans. Antennas Propag. 35, 1119-1127 (1987).
[CrossRef]

Lewin, L.

L. Lewin, D. C. Chang, and E. F. Kuester, Electromagnetic Waves and Curved Structures (Peter Peregrinus Ltd., 1977).

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

Marcuse, D.

Martini, G.

L. Faustini and G. Martini, "Bend loss in single-mode fibers," J. Lightwave Technol. 15, 671-679 (1997).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in Fortran 77: The Art of Scientific Computing (Cambridge U. Press, 1973).

Renner, H.

H. Renner, "Bending losses of coated single-mode fibers: A simple approach," J. Lightwave Technol. 10, 544-551 (1992).
[CrossRef]

Schild, A.

J. L. Synge and A. Schild, Tensor Calculus (U. of Toronto Press, 1956).

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1965).

Synge, J. L.

J. L. Synge and A. Schild, Tensor Calculus (U. of Toronto Press, 1956).

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in Fortran 77: The Art of Scientific Computing (Cambridge U. Press, 1973).

Vassallo, C.

C. Vassallo, "Scalar-field theory and 2-D ray theory for bent single-mode weakly guiding optical fibers," J. Lightwave Technol. LT-3, 416-423 (1985).

C. Vassallo, Optical Waveguide Concepts (Elsevier Science, 1991).

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in Fortran 77: The Art of Scientific Computing (Cambridge U. Press, 1973).

White, I. A.

I. A. White, "Radiation from bends in optical waveguides: The volume-current method," IEE J. Microwaves, Opt. Acoust. 3, 186-188 (1979).

IEE J. Microwaves, Opt. Acoust. (1)

I. A. White, "Radiation from bends in optical waveguides: The volume-current method," IEE J. Microwaves, Opt. Acoust. 3, 186-188 (1979).

IEEE Antennas Propag. Mag. (1)

D. I. Kaklamani and H. T. Anastassiu, "Aspects of the method of auxiliarly sources (MAS) in computational electromagnetics," IEEE Antennas Propag. Mag. 44, 48-64 (2002).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

Y. Leviatan and A. Boag, "Analysis of electromagnetic scattering from dielectric cylinders using a multifilament current model," IEEE Trans. Antennas Propag. 35, 1119-1127 (1987).
[CrossRef]

J. Lightwave Technol. (3)

C. Vassallo, "Scalar-field theory and 2-D ray theory for bent single-mode weakly guiding optical fibers," J. Lightwave Technol. LT-3, 416-423 (1985).

L. Faustini and G. Martini, "Bend loss in single-mode fibers," J. Lightwave Technol. 15, 671-679 (1997).
[CrossRef]

H. Renner, "Bending losses of coated single-mode fibers: A simple approach," J. Lightwave Technol. 10, 544-551 (1992).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Quantum Electron. (1)

J. G. Dil and H. Blok, "Propagation of electromagnetic surface waves in a radially inhomogeneous optical waveguide," Opt. Quantum Electron. 5, 415-428 (1973).
[CrossRef]

Radio Sci. (1)

B. P. de Hon and M. Bingle, "A model impedance-angle formalism: schemes for accurate graded-index bent-slab calculations and optical fiber mode counting," Radio Sci. 38, 13-1 (2003), doi: 10.1029/2001RS002570.

Other (7)

J. L. Synge and A. Schild, Tensor Calculus (U. of Toronto Press, 1956).

A. T. de Hoop, Handbook of Radiation and Scattering of Waves: Acoustic Waves in Fluids, Elastic Waves in Solids, Electromagnetic Waves (Academic, 1995).

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

L. Lewin, D. C. Chang, and E. F. Kuester, Electromagnetic Waves and Curved Structures (Peter Peregrinus Ltd., 1977).

W. H. Press, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in Fortran 77: The Art of Scientific Computing (Cambridge U. Press, 1973).

C. Vassallo, Optical Waveguide Concepts (Elsevier Science, 1991).

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1965).

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