Abstract

An integral-equation approach is developed to compute the propagation coefficients and field distributions of the modes of an open cylindrical waveguide surrounded by a vacuum. The general theory applies to arbitrary graded-index profiles and arbitrarily shaped cross sections. Lossy and uniaxially anisotropic media, with longitudinal extraordinary axis, are included. To investigate the accuracy of the method, we have implemented the integral-equation method for a lossless symmetrical slab waveguide with step- and graded-index profile. Results are given for isotropic and anisotropic waveguides of the indicated kind. The permittivity profiles considered are step-index and two different quadratic profiles.

© 1980 Optical Society of America

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  1. A. W. Snyder, "Asymptotic expressions for eigenfunctions and eigenvalues of a dielectric or optical waveguide," IEEE Trans. Microwave Theory Tech. MTT-17, 1130–1138 (1969).
  2. D. Gloge, "Weakly guiding fibers," Appl. Opt. 10, 2252–2258 (1971).
  3. H.-G. Unger, Planar Optical Waveguides and Fibres (Clarendon, Oxford, 1977), Chap 5.4, pp. 487–500.
  4. A. G. Gronthoud and H. Blok, "The influence of bulk losses and bulk dispersion on the propagation properties of surface waves in a radially inhomogeneous optical waveguide," Opt. Quantum Electron. 10, 95–106 (1978).
  5. C. Yeh, K. Ha, S. B. Dong, and W. P. Brown, "Single mode optical waveguides," Appl. Opt. 18, 1490–1504 (1979).
  6. L. W. Kantorowitsch and W. I. Krylow, Näherungsmethoden der höheren Analysis (VEB Deutscher Verlag der Wissenschaften, Berlin, 1956), Chap. II 4.5, pp. 144–148.
  7. S. R. Norman, D. N. Payne, M. J. Adams, and A. M. Smith, "Analysis and fabrication of single-mode fibers exhibiting extremely low polarization birefringence," Proceedings of the Optical Communication Conference, Amsterdam, 1979, Chaps. 10.1-1–10.1-4 (unpublished).
  8. H.-G. Unger, Planar Optical Waveguides and Fibres (Clarendon, Oxford, 1977), Chap. 2.3, pp. 93–105.
  9. A. T. de Hoop, Modern Topics in Electromagnetics and Antennas, Stevenage, Peter Peregrinus, 1977, PPL Conference Publications 13, Chap. 6, pp. 6.1–6.59.
  10. L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, New York, 1973), Chap. 5.3a,b, pp. 455–462 and Chap. 5.6, p. 549.

1979 (1)

1978 (1)

A. G. Gronthoud and H. Blok, "The influence of bulk losses and bulk dispersion on the propagation properties of surface waves in a radially inhomogeneous optical waveguide," Opt. Quantum Electron. 10, 95–106 (1978).

1971 (1)

1969 (1)

A. W. Snyder, "Asymptotic expressions for eigenfunctions and eigenvalues of a dielectric or optical waveguide," IEEE Trans. Microwave Theory Tech. MTT-17, 1130–1138 (1969).

Adams, M. J.

S. R. Norman, D. N. Payne, M. J. Adams, and A. M. Smith, "Analysis and fabrication of single-mode fibers exhibiting extremely low polarization birefringence," Proceedings of the Optical Communication Conference, Amsterdam, 1979, Chaps. 10.1-1–10.1-4 (unpublished).

Blok, H.

A. G. Gronthoud and H. Blok, "The influence of bulk losses and bulk dispersion on the propagation properties of surface waves in a radially inhomogeneous optical waveguide," Opt. Quantum Electron. 10, 95–106 (1978).

Brown, W. P.

de Hoop, A. T.

A. T. de Hoop, Modern Topics in Electromagnetics and Antennas, Stevenage, Peter Peregrinus, 1977, PPL Conference Publications 13, Chap. 6, pp. 6.1–6.59.

Dong, S. B.

Felsen, L. B.

L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, New York, 1973), Chap. 5.3a,b, pp. 455–462 and Chap. 5.6, p. 549.

Gloge, D.

Gronthoud, A. G.

A. G. Gronthoud and H. Blok, "The influence of bulk losses and bulk dispersion on the propagation properties of surface waves in a radially inhomogeneous optical waveguide," Opt. Quantum Electron. 10, 95–106 (1978).

Ha, K.

Kantorowitsch, L. W.

L. W. Kantorowitsch and W. I. Krylow, Näherungsmethoden der höheren Analysis (VEB Deutscher Verlag der Wissenschaften, Berlin, 1956), Chap. II 4.5, pp. 144–148.

Krylow, W. I.

L. W. Kantorowitsch and W. I. Krylow, Näherungsmethoden der höheren Analysis (VEB Deutscher Verlag der Wissenschaften, Berlin, 1956), Chap. II 4.5, pp. 144–148.

Marcuvitz, N.

L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, New York, 1973), Chap. 5.3a,b, pp. 455–462 and Chap. 5.6, p. 549.

Norman, S. R.

S. R. Norman, D. N. Payne, M. J. Adams, and A. M. Smith, "Analysis and fabrication of single-mode fibers exhibiting extremely low polarization birefringence," Proceedings of the Optical Communication Conference, Amsterdam, 1979, Chaps. 10.1-1–10.1-4 (unpublished).

Payne, D. N.

S. R. Norman, D. N. Payne, M. J. Adams, and A. M. Smith, "Analysis and fabrication of single-mode fibers exhibiting extremely low polarization birefringence," Proceedings of the Optical Communication Conference, Amsterdam, 1979, Chaps. 10.1-1–10.1-4 (unpublished).

Smith, A. M.

S. R. Norman, D. N. Payne, M. J. Adams, and A. M. Smith, "Analysis and fabrication of single-mode fibers exhibiting extremely low polarization birefringence," Proceedings of the Optical Communication Conference, Amsterdam, 1979, Chaps. 10.1-1–10.1-4 (unpublished).

Snyder, A. W.

A. W. Snyder, "Asymptotic expressions for eigenfunctions and eigenvalues of a dielectric or optical waveguide," IEEE Trans. Microwave Theory Tech. MTT-17, 1130–1138 (1969).

Unger, H.-G.

H.-G. Unger, Planar Optical Waveguides and Fibres (Clarendon, Oxford, 1977), Chap. 2.3, pp. 93–105.

H.-G. Unger, Planar Optical Waveguides and Fibres (Clarendon, Oxford, 1977), Chap 5.4, pp. 487–500.

Yeh, C.

Appl. Opt. (2)

IEEE Trans. Microwave Theory Tech. (1)

A. W. Snyder, "Asymptotic expressions for eigenfunctions and eigenvalues of a dielectric or optical waveguide," IEEE Trans. Microwave Theory Tech. MTT-17, 1130–1138 (1969).

Opt. Quantum Electron. (1)

A. G. Gronthoud and H. Blok, "The influence of bulk losses and bulk dispersion on the propagation properties of surface waves in a radially inhomogeneous optical waveguide," Opt. Quantum Electron. 10, 95–106 (1978).

Other (6)

L. W. Kantorowitsch and W. I. Krylow, Näherungsmethoden der höheren Analysis (VEB Deutscher Verlag der Wissenschaften, Berlin, 1956), Chap. II 4.5, pp. 144–148.

S. R. Norman, D. N. Payne, M. J. Adams, and A. M. Smith, "Analysis and fabrication of single-mode fibers exhibiting extremely low polarization birefringence," Proceedings of the Optical Communication Conference, Amsterdam, 1979, Chaps. 10.1-1–10.1-4 (unpublished).

H.-G. Unger, Planar Optical Waveguides and Fibres (Clarendon, Oxford, 1977), Chap. 2.3, pp. 93–105.

A. T. de Hoop, Modern Topics in Electromagnetics and Antennas, Stevenage, Peter Peregrinus, 1977, PPL Conference Publications 13, Chap. 6, pp. 6.1–6.59.

L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, New York, 1973), Chap. 5.3a,b, pp. 455–462 and Chap. 5.6, p. 549.

H.-G. Unger, Planar Optical Waveguides and Fibres (Clarendon, Oxford, 1977), Chap 5.4, pp. 487–500.

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