Abstract

Curvature loss formulas of optical fibers usually ignore the effect of field deformation caused by the curved axis of the fiber. Contrary to naive intuition, this field deformation may substantially decrease the radiation losses of modes with low mode number. Losses of modes with high mode numbers are, however, increased. We present a theoretical evaluation of curvature losses of the modes of a step-index fiber with a bent axis incorporating the influence of field deformation on the loss coefficient. The limitations of the simple loss formula in case of a sharply bent overmoded waveguide are pointed out.

© 1976 Optical Society of America

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  1. M. A. Miller and V. I. Talanov, "Electromagnetic Surface Waves Guided by a Boundary with Small Curvature," Zh. Tekh. Fiz. 26, 2755 (1956).
  2. E. A. J. Marcatili, "Bends in Optical Dielectric Guides," Bell Syst. Tech. J., 48, 2013–2132 (1969).
  3. L. Lewin, "Radiation from Curved Dielectric Slabs and Fibers, "IEEE Trans. Microwave Theory Tech., Vol. MTT-22, No, 7, 718–727 (1974).
  4. J. A. Arnaud, "Transverse Coupling in Fiber Optics Part III: Bending Losses," Bell Syst. Tech. J., 53, 1379–1394 (1974).
  5. A. W. Snyder, I. White, and D. J. Mitchell, "Radiation from Bent Optical Waveguides," Electron. Lett., 11, 332–333 (1975).
  6. V. V. Shevchenko, "Radiation Losses in Bent Waveguides for Surface Waves," Radiophys. Quantum Electron. 14, 607–614 (1973) (Russian original 1971).
  7. D. C. Chang and E. F. Kuester, "General Theory of Surface-Wave Propagation on a Curved Optical Waveguide of Arbitrary Cross Section," Scientific Report No. 11, Electromagnetics Laboratory, Dept. Electr. Eng., University of Colorado, Boulder, Colorado; also IEEE J. Quantum Electron. QE-11, 903–907 (1975).
  8. D. Marcuse, Light Transmission Optics (Van Nostrand, Reinhold, New York, 1972), pp. 398–406.
  9. D. Marcuse, "Curvature Loss Formula for Optical Fibers," J. Opt. Soc. Am. 66, 216–220 (1976).
  10. S. E. Miller, "Directional Control in Lightwave Guidance," Bell Syst. Tech. J., 43, 1727–1739 (1964).
  11. E. A. J. Marcatili and S. E. Miller, "Improved Relations Describing Directional Control in Electromagnetic Wave Guidance," Bell Syst. Tech. J., 48, 2161–2188 (1969).
  12. D. Gloge, "Weakly Guiding Fibers," Appl. Opt., 10, 2252–2258 (1971).
  13. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).
  14. M. Abramovitz and I. A. Stegun, Handbook of Mathematical Functions, Eq. 902.4, p. 364. U. S. Dept. of Commerce, Nati. Bur. Stds., Appl. Math. Ser. Vol. 55 (U. S. GPO, Washington, D. C., 1964).
  15. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1965).
  16. D. Marcuse,"Bent Optical Waveguide with Lossy Jacket," Bell Syst. Tech. J.,53, 1079–1101 (1974).
  17. D. Gloge, "Bending Losses in Multimode Fibers with Graded and Ungraded Core Index," Appl. Opt. 11, 2506–2513 (1972).

1976 (1)

1975 (1)

A. W. Snyder, I. White, and D. J. Mitchell, "Radiation from Bent Optical Waveguides," Electron. Lett., 11, 332–333 (1975).

1974 (3)

L. Lewin, "Radiation from Curved Dielectric Slabs and Fibers, "IEEE Trans. Microwave Theory Tech., Vol. MTT-22, No, 7, 718–727 (1974).

J. A. Arnaud, "Transverse Coupling in Fiber Optics Part III: Bending Losses," Bell Syst. Tech. J., 53, 1379–1394 (1974).

D. Marcuse,"Bent Optical Waveguide with Lossy Jacket," Bell Syst. Tech. J.,53, 1079–1101 (1974).

1973 (1)

V. V. Shevchenko, "Radiation Losses in Bent Waveguides for Surface Waves," Radiophys. Quantum Electron. 14, 607–614 (1973) (Russian original 1971).

1972 (1)

1971 (1)

1969 (2)

E. A. J. Marcatili and S. E. Miller, "Improved Relations Describing Directional Control in Electromagnetic Wave Guidance," Bell Syst. Tech. J., 48, 2161–2188 (1969).

E. A. J. Marcatili, "Bends in Optical Dielectric Guides," Bell Syst. Tech. J., 48, 2013–2132 (1969).

1964 (1)

S. E. Miller, "Directional Control in Lightwave Guidance," Bell Syst. Tech. J., 43, 1727–1739 (1964).

1956 (1)

M. A. Miller and V. I. Talanov, "Electromagnetic Surface Waves Guided by a Boundary with Small Curvature," Zh. Tekh. Fiz. 26, 2755 (1956).

Abramovitz, M.

M. Abramovitz and I. A. Stegun, Handbook of Mathematical Functions, Eq. 902.4, p. 364. U. S. Dept. of Commerce, Nati. Bur. Stds., Appl. Math. Ser. Vol. 55 (U. S. GPO, Washington, D. C., 1964).

Arnaud, J. A.

J. A. Arnaud, "Transverse Coupling in Fiber Optics Part III: Bending Losses," Bell Syst. Tech. J., 53, 1379–1394 (1974).

Chang, D. C.

D. C. Chang and E. F. Kuester, "General Theory of Surface-Wave Propagation on a Curved Optical Waveguide of Arbitrary Cross Section," Scientific Report No. 11, Electromagnetics Laboratory, Dept. Electr. Eng., University of Colorado, Boulder, Colorado; also IEEE J. Quantum Electron. QE-11, 903–907 (1975).

Gloge, D.

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1965).

Kuester, E. F.

D. C. Chang and E. F. Kuester, "General Theory of Surface-Wave Propagation on a Curved Optical Waveguide of Arbitrary Cross Section," Scientific Report No. 11, Electromagnetics Laboratory, Dept. Electr. Eng., University of Colorado, Boulder, Colorado; also IEEE J. Quantum Electron. QE-11, 903–907 (1975).

Lewin, L.

L. Lewin, "Radiation from Curved Dielectric Slabs and Fibers, "IEEE Trans. Microwave Theory Tech., Vol. MTT-22, No, 7, 718–727 (1974).

Marcatili, E. A. J.

E. A. J. Marcatili, "Bends in Optical Dielectric Guides," Bell Syst. Tech. J., 48, 2013–2132 (1969).

E. A. J. Marcatili and S. E. Miller, "Improved Relations Describing Directional Control in Electromagnetic Wave Guidance," Bell Syst. Tech. J., 48, 2161–2188 (1969).

Marcuse, D.

D. Marcuse, "Curvature Loss Formula for Optical Fibers," J. Opt. Soc. Am. 66, 216–220 (1976).

D. Marcuse,"Bent Optical Waveguide with Lossy Jacket," Bell Syst. Tech. J.,53, 1079–1101 (1974).

D. Marcuse, Light Transmission Optics (Van Nostrand, Reinhold, New York, 1972), pp. 398–406.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

Miller, M. A.

M. A. Miller and V. I. Talanov, "Electromagnetic Surface Waves Guided by a Boundary with Small Curvature," Zh. Tekh. Fiz. 26, 2755 (1956).

Miller, S. E.

E. A. J. Marcatili and S. E. Miller, "Improved Relations Describing Directional Control in Electromagnetic Wave Guidance," Bell Syst. Tech. J., 48, 2161–2188 (1969).

S. E. Miller, "Directional Control in Lightwave Guidance," Bell Syst. Tech. J., 43, 1727–1739 (1964).

Mitchell, D. J.

A. W. Snyder, I. White, and D. J. Mitchell, "Radiation from Bent Optical Waveguides," Electron. Lett., 11, 332–333 (1975).

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1965).

Shevchenko, V. V.

V. V. Shevchenko, "Radiation Losses in Bent Waveguides for Surface Waves," Radiophys. Quantum Electron. 14, 607–614 (1973) (Russian original 1971).

Snyder, A. W.

A. W. Snyder, I. White, and D. J. Mitchell, "Radiation from Bent Optical Waveguides," Electron. Lett., 11, 332–333 (1975).

Stegun, I. A.

M. Abramovitz and I. A. Stegun, Handbook of Mathematical Functions, Eq. 902.4, p. 364. U. S. Dept. of Commerce, Nati. Bur. Stds., Appl. Math. Ser. Vol. 55 (U. S. GPO, Washington, D. C., 1964).

Talanov, V. I.

M. A. Miller and V. I. Talanov, "Electromagnetic Surface Waves Guided by a Boundary with Small Curvature," Zh. Tekh. Fiz. 26, 2755 (1956).

White, I.

A. W. Snyder, I. White, and D. J. Mitchell, "Radiation from Bent Optical Waveguides," Electron. Lett., 11, 332–333 (1975).

Appl. Opt. (2)

Bell Syst. Tech. J (1)

E. A. J. Marcatili, "Bends in Optical Dielectric Guides," Bell Syst. Tech. J., 48, 2013–2132 (1969).

Bell Syst. Tech. J. (4)

J. A. Arnaud, "Transverse Coupling in Fiber Optics Part III: Bending Losses," Bell Syst. Tech. J., 53, 1379–1394 (1974).

D. Marcuse,"Bent Optical Waveguide with Lossy Jacket," Bell Syst. Tech. J.,53, 1079–1101 (1974).

S. E. Miller, "Directional Control in Lightwave Guidance," Bell Syst. Tech. J., 43, 1727–1739 (1964).

E. A. J. Marcatili and S. E. Miller, "Improved Relations Describing Directional Control in Electromagnetic Wave Guidance," Bell Syst. Tech. J., 48, 2161–2188 (1969).

Electron. Lett. (1)

A. W. Snyder, I. White, and D. J. Mitchell, "Radiation from Bent Optical Waveguides," Electron. Lett., 11, 332–333 (1975).

IEEE Trans. Microwave Theory Tech. (1)

L. Lewin, "Radiation from Curved Dielectric Slabs and Fibers, "IEEE Trans. Microwave Theory Tech., Vol. MTT-22, No, 7, 718–727 (1974).

J. Opt. Soc. Am. (1)

Radiophys. Quantum Electron. (1)

V. V. Shevchenko, "Radiation Losses in Bent Waveguides for Surface Waves," Radiophys. Quantum Electron. 14, 607–614 (1973) (Russian original 1971).

Zh. Tekh. Fiz. (1)

M. A. Miller and V. I. Talanov, "Electromagnetic Surface Waves Guided by a Boundary with Small Curvature," Zh. Tekh. Fiz. 26, 2755 (1956).

Other (5)

D. C. Chang and E. F. Kuester, "General Theory of Surface-Wave Propagation on a Curved Optical Waveguide of Arbitrary Cross Section," Scientific Report No. 11, Electromagnetics Laboratory, Dept. Electr. Eng., University of Colorado, Boulder, Colorado; also IEEE J. Quantum Electron. QE-11, 903–907 (1975).

D. Marcuse, Light Transmission Optics (Van Nostrand, Reinhold, New York, 1972), pp. 398–406.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

M. Abramovitz and I. A. Stegun, Handbook of Mathematical Functions, Eq. 902.4, p. 364. U. S. Dept. of Commerce, Nati. Bur. Stds., Appl. Math. Ser. Vol. 55 (U. S. GPO, Washington, D. C., 1964).

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1965).

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