Abstract

The attenuation of rays within lossless dielectric structures is determined by two in-principle-exact methods: (a) solution of the appropriate eigenvalue equation, and (b) Poynting’s vector theorem. The methods are applied to cylinders and spheres. There are no trapped rays within the circle or sphere, or any finite structure; however, many rays are only very weakly attenuated.

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  1. A. W. Snyder and D. J. Mitchell, J. Opt. Soc. Am. 64, 599 (1974).
  2. Lord Rayleigh, Phil. Mag. 27, 100 (1914).
  3. F. G. Reich, Appl. Opt. 4, 1395 (1965).
  4. J. R. Wait, Radio Sci. 2 (New Series), 10005 (1967).
  5. D. S. Jones, The Theory of Electromagnetism (Pergamon, New York, 1964), pp. 562–564.
  6. A. W. Snyder, IEEE Trans. Microwave Theory Tech. 17, 1130 (1969).
  7. A. W. Snyder, D. J. Mitchell, and C. Pask, J. Opt. Soc. Am. 64, 608 (1974).
  8. A. W. Snyder and D. J. Mitchell, Electron. Lett. 10 (2), 16 (1974).
  9. N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, New York, 1972), p. 293.
  10. J. A. Stratton, Electromnagnetic Theory (McGraw-Hill, New York, 1941), pp. 556–557.
  11. Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun, Natl. Bur. Stand. (U. S.) Appl. Math. Ser. 55 (U. S. Government Printing Office, Washington, D. C., 1964; Dover, New York, 1965).

Burke, J. J.

N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, New York, 1972), p. 293.

Jones, D. S.

D. S. Jones, The Theory of Electromagnetism (Pergamon, New York, 1964), pp. 562–564.

Kapany, N. S.

N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, New York, 1972), p. 293.

Mitchell, D. J.

A. W. Snyder and D. J. Mitchell, Electron. Lett. 10 (2), 16 (1974).

A. W. Snyder and D. J. Mitchell, J. Opt. Soc. Am. 64, 599 (1974).

A. W. Snyder, D. J. Mitchell, and C. Pask, J. Opt. Soc. Am. 64, 608 (1974).

Pask, C.

A. W. Snyder, D. J. Mitchell, and C. Pask, J. Opt. Soc. Am. 64, 608 (1974).

Rayleigh, Lord

Lord Rayleigh, Phil. Mag. 27, 100 (1914).

Reich, F. G.

F. G. Reich, Appl. Opt. 4, 1395 (1965).

Snyder, A. W.

A. W. Snyder, IEEE Trans. Microwave Theory Tech. 17, 1130 (1969).

A. W. Snyder, D. J. Mitchell, and C. Pask, J. Opt. Soc. Am. 64, 608 (1974).

A. W. Snyder and D. J. Mitchell, J. Opt. Soc. Am. 64, 599 (1974).

A. W. Snyder and D. J. Mitchell, Electron. Lett. 10 (2), 16 (1974).

Stratton, J. A.

J. A. Stratton, Electromnagnetic Theory (McGraw-Hill, New York, 1941), pp. 556–557.

Wait, J. R.

J. R. Wait, Radio Sci. 2 (New Series), 10005 (1967).

Other (11)

A. W. Snyder and D. J. Mitchell, J. Opt. Soc. Am. 64, 599 (1974).

Lord Rayleigh, Phil. Mag. 27, 100 (1914).

F. G. Reich, Appl. Opt. 4, 1395 (1965).

J. R. Wait, Radio Sci. 2 (New Series), 10005 (1967).

D. S. Jones, The Theory of Electromagnetism (Pergamon, New York, 1964), pp. 562–564.

A. W. Snyder, IEEE Trans. Microwave Theory Tech. 17, 1130 (1969).

A. W. Snyder, D. J. Mitchell, and C. Pask, J. Opt. Soc. Am. 64, 608 (1974).

A. W. Snyder and D. J. Mitchell, Electron. Lett. 10 (2), 16 (1974).

N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, New York, 1972), p. 293.

J. A. Stratton, Electromnagnetic Theory (McGraw-Hill, New York, 1941), pp. 556–557.

Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun, Natl. Bur. Stand. (U. S.) Appl. Math. Ser. 55 (U. S. Government Printing Office, Washington, D. C., 1964; Dover, New York, 1965).

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