Abstract

The problem of scattering of a time-harmonic electromagnetic wave by a perfectly conducting elliptic cylinder embedded in a uniaxially anisotropic medium is being investigated. The optical axis of the medium is assumed perpendicular to the cylinder’s generating line, and the electromagnetic sources are assumed parallel to it, giving rise to a two dimensional problem. Magnetic current line sources radiate E modes, for which a boundary value problem is formulated. A method described by Felsen is utilized to transform this boundary value problem to the familiar Helmholtz equation with a Neumann boundary condition. The solution is found and expanded for the long wave (or small obstacle) range, and interpreted in simple physical terms. The leading terms of the scattered field correspond to radiation by equivalent multipole sources. It is shown that the strength of these sources depends on the orientation of the scatterer with respect to the optical axis, and on the ray refractive index of the medium. If the uniaxial medium represents an ionized gas in a strong magnetic field, some elements of the dielectric tensor may be negative or complex. Our results are shown to remain valid in this case.

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  1. K. G. Budden, Radio Waves in the Ionosphere (Cambridge University Press, 1961), Chapter 3.
  2. L. B. Felsen, Proc. IEE (London) 111, 445 (1964).
  3. Ref. 1, Section 13.19.
  4. J. J. Brandstatter, An Introduction to Waves, Rays and Radiation in Plasma Media (McGraw-Hill Book Company, Newv York, 1963), Chapter VIII.
  5. E. Arbel and L. B. Felsen, "Theory of Radiation from Sources in Anisotropic Media," in Electiromagnetic Waves, edited by E. C. Jordan (Pergamon Press, New York, 1963), pp. 391–459.
  6. B. Rulf, Diffraction and Scattering of Electromagnetic Waves in Anisotropic Media, Ph.D. dissertation, Polytechnic Institute of Brooklyn (1965), Chapters II, III.
  7. J. Meixner and F. W. Shäfke, Mathieusche Funktionen und Sphäroidfunktionen (Springer Verlag, Berlin, 1954).
  8. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill Book Company, New York, 1953), Section 11.2. (There are differences between the definition and notation of Mathieu functions in Ref. (7) and (8). In this study we use the notation of Ref. (7).)
  9. Ref. 7: Sec. 2.2 and 2.7.
  10. Ref. 7: Sec. 2.4 and 9.7.
  11. J. E. Burke and V. Twersky, J. Opt. Soc. Am. 54, 732 (1964).
  12. Ref. 4, Chapter VII.

Arbel, E.

E. Arbel and L. B. Felsen, "Theory of Radiation from Sources in Anisotropic Media," in Electiromagnetic Waves, edited by E. C. Jordan (Pergamon Press, New York, 1963), pp. 391–459.

Brandstatter, J. J.

J. J. Brandstatter, An Introduction to Waves, Rays and Radiation in Plasma Media (McGraw-Hill Book Company, Newv York, 1963), Chapter VIII.

Budden, K. G.

K. G. Budden, Radio Waves in the Ionosphere (Cambridge University Press, 1961), Chapter 3.

Burke, J. E.

J. E. Burke and V. Twersky, J. Opt. Soc. Am. 54, 732 (1964).

Felsen, L. B.

E. Arbel and L. B. Felsen, "Theory of Radiation from Sources in Anisotropic Media," in Electiromagnetic Waves, edited by E. C. Jordan (Pergamon Press, New York, 1963), pp. 391–459.

L. B. Felsen, Proc. IEE (London) 111, 445 (1964).

Feshbach, H.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill Book Company, New York, 1953), Section 11.2. (There are differences between the definition and notation of Mathieu functions in Ref. (7) and (8). In this study we use the notation of Ref. (7).)

Meixner, J.

J. Meixner and F. W. Shäfke, Mathieusche Funktionen und Sphäroidfunktionen (Springer Verlag, Berlin, 1954).

Morse, P. M.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill Book Company, New York, 1953), Section 11.2. (There are differences between the definition and notation of Mathieu functions in Ref. (7) and (8). In this study we use the notation of Ref. (7).)

Rulf, B.

B. Rulf, Diffraction and Scattering of Electromagnetic Waves in Anisotropic Media, Ph.D. dissertation, Polytechnic Institute of Brooklyn (1965), Chapters II, III.

Shäfke, F. W.

J. Meixner and F. W. Shäfke, Mathieusche Funktionen und Sphäroidfunktionen (Springer Verlag, Berlin, 1954).

Twersky, V.

J. E. Burke and V. Twersky, J. Opt. Soc. Am. 54, 732 (1964).

Other (12)

K. G. Budden, Radio Waves in the Ionosphere (Cambridge University Press, 1961), Chapter 3.

L. B. Felsen, Proc. IEE (London) 111, 445 (1964).

Ref. 1, Section 13.19.

J. J. Brandstatter, An Introduction to Waves, Rays and Radiation in Plasma Media (McGraw-Hill Book Company, Newv York, 1963), Chapter VIII.

E. Arbel and L. B. Felsen, "Theory of Radiation from Sources in Anisotropic Media," in Electiromagnetic Waves, edited by E. C. Jordan (Pergamon Press, New York, 1963), pp. 391–459.

B. Rulf, Diffraction and Scattering of Electromagnetic Waves in Anisotropic Media, Ph.D. dissertation, Polytechnic Institute of Brooklyn (1965), Chapters II, III.

J. Meixner and F. W. Shäfke, Mathieusche Funktionen und Sphäroidfunktionen (Springer Verlag, Berlin, 1954).

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill Book Company, New York, 1953), Section 11.2. (There are differences between the definition and notation of Mathieu functions in Ref. (7) and (8). In this study we use the notation of Ref. (7).)

Ref. 7: Sec. 2.2 and 2.7.

Ref. 7: Sec. 2.4 and 9.7.

J. E. Burke and V. Twersky, J. Opt. Soc. Am. 54, 732 (1964).

Ref. 4, Chapter VII.

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