Abstract

The diffraction of plane electromagnetic waves by a slit in an infinitely thin, perfectly conducting screen between two media with different dielectric constants is studied using rigorous diffraction theory. Both the case where the electric vector is parallel to slit and the case where the magnetic vector is parallel to slit are examined. The problem is formulated in elliptic cylinder coordinates and solved in terms of Mathieu functions. The explicit determination of the diffracted wave-expansion coefficients leads to solving infinite systems of complex linear equations. The long-wave (Rayleigh scattering) region is studied in detail. The scattered intensity at infinity, transmission coefficient, and backscatter coefficient are evaluated. Finally, numerical results are presented for some special cases.

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  1. M. Fizeau, Ann. Chim. 63, 385 (1861).
  2. Lord Rayleigh, Phil. Mag. 43, 259 (1897).
  3. Lord Rayleigh, Phil. Mag. 14, 350 (1907).
  4. Lord Rayleigh, Proc. Roy. Soc. (London) A89 194 (1913).
  5. P. M. Morse and P. J. Rubenstein, Phys. Rev. 54, 895 (1938).
  6. H. Hönl, A. W. Maue, and K. Westpfahl, "Theorie der Beugung," in Encyclopedia of Physics, edited by S. Flügge (Springer-Verlag, Berlin, 1961), Vol. XXV/1, pp. 418–453.
  7. J. Meixner, New York University Institute of Mathematical Sciences, Division of Electromagnetic Research, Research Report EM-68, 1954.
  8. J. Meixner and F. W. Schäfke, Mathieusche Funktionen und Sphäroidfunktionen (Springer-Verlag, Berlin, 1954).
  9. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill Book Company, Inc., New York, 1953), Part II.
  10. L. D. Landau and E. M. Liftshitz, Electrodynamics of Continuous Media (Pergamon Press, Ltd., London, 1961).
  11. C. J. Bouwkamp, Physica 12, 467 (1946).
  12. J. Meixner, Ann. Physik 6, 2 (1949).
  13. Methods similar to this have been employed by the author in various water wave problems. See, for example, R. Barakat, J. Fluid. Mech. 13, 540 (1962).
  14. Reference 9, p 1430.
  15. R. Barakat, A. Houston, and E. Levin, J. Math. and Phys. (to he published).

Barakat, R.

Methods similar to this have been employed by the author in various water wave problems. See, for example, R. Barakat, J. Fluid. Mech. 13, 540 (1962).

R. Barakat, A. Houston, and E. Levin, J. Math. and Phys. (to he published).

Bouwkamp, C. J.

C. J. Bouwkamp, Physica 12, 467 (1946).

Feshbach, H.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill Book Company, Inc., New York, 1953), Part II.

Fizeau, M.

M. Fizeau, Ann. Chim. 63, 385 (1861).

Hönl, H.

H. Hönl, A. W. Maue, and K. Westpfahl, "Theorie der Beugung," in Encyclopedia of Physics, edited by S. Flügge (Springer-Verlag, Berlin, 1961), Vol. XXV/1, pp. 418–453.

Houston, A.

R. Barakat, A. Houston, and E. Levin, J. Math. and Phys. (to he published).

Landau, L. D.

L. D. Landau and E. M. Liftshitz, Electrodynamics of Continuous Media (Pergamon Press, Ltd., London, 1961).

Levin, E.

R. Barakat, A. Houston, and E. Levin, J. Math. and Phys. (to he published).

Liftshitz, E. M.

L. D. Landau and E. M. Liftshitz, Electrodynamics of Continuous Media (Pergamon Press, Ltd., London, 1961).

Maue, A. W.

H. Hönl, A. W. Maue, and K. Westpfahl, "Theorie der Beugung," in Encyclopedia of Physics, edited by S. Flügge (Springer-Verlag, Berlin, 1961), Vol. XXV/1, pp. 418–453.

Meixner, J.

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

J. Meixner, Ann. Physik 6, 2 (1949).

J. Meixner, New York University Institute of Mathematical Sciences, Division of Electromagnetic Research, Research Report EM-68, 1954.

Morse, P. M.

P. M. Morse and P. J. Rubenstein, Phys. Rev. 54, 895 (1938).

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill Book Company, Inc., New York, 1953), Part II.

Rayleigh, Lord

Lord Rayleigh, Proc. Roy. Soc. (London) A89 194 (1913).

Lord Rayleigh, Phil. Mag. 43, 259 (1897).

Lord Rayleigh, Phil. Mag. 14, 350 (1907).

Rubenstein, P. J.

P. M. Morse and P. J. Rubenstein, Phys. Rev. 54, 895 (1938).

Schäfke, F. W.

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

Westpfahl, K.

H. Hönl, A. W. Maue, and K. Westpfahl, "Theorie der Beugung," in Encyclopedia of Physics, edited by S. Flügge (Springer-Verlag, Berlin, 1961), Vol. XXV/1, pp. 418–453.

Other (15)

M. Fizeau, Ann. Chim. 63, 385 (1861).

Lord Rayleigh, Phil. Mag. 43, 259 (1897).

Lord Rayleigh, Phil. Mag. 14, 350 (1907).

Lord Rayleigh, Proc. Roy. Soc. (London) A89 194 (1913).

P. M. Morse and P. J. Rubenstein, Phys. Rev. 54, 895 (1938).

H. Hönl, A. W. Maue, and K. Westpfahl, "Theorie der Beugung," in Encyclopedia of Physics, edited by S. Flügge (Springer-Verlag, Berlin, 1961), Vol. XXV/1, pp. 418–453.

J. Meixner, New York University Institute of Mathematical Sciences, Division of Electromagnetic Research, Research Report EM-68, 1954.

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

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill Book Company, Inc., New York, 1953), Part II.

L. D. Landau and E. M. Liftshitz, Electrodynamics of Continuous Media (Pergamon Press, Ltd., London, 1961).

C. J. Bouwkamp, Physica 12, 467 (1946).

J. Meixner, Ann. Physik 6, 2 (1949).

Methods similar to this have been employed by the author in various water wave problems. See, for example, R. Barakat, J. Fluid. Mech. 13, 540 (1962).

Reference 9, p 1430.

R. Barakat, A. Houston, and E. Levin, J. Math. and Phys. (to he published).

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