Abstract

Numerical results are given for the backscattering cross section of a dielectric elliptical cylinder. Computations are carried out using the exact solutions in terms of Mathieu functions. Both polarizations of the incident wave are considered: one with the incident electric vector in the axial direction and the other with the incident magnetic vector in the axial direction. The parameters considered are: <i>K</i><sub>0</sub><sup>2</sup><i>q</i><sup>2</sup>=0.004, 0.4, 4.0, 8.0, 12.0, 16.0, 20.0; 0≤<i>qK</i><sub>0</sub> cosξ<sub>0</sub> <6.5;<<sub>1</sub>/ε<sub>0</sub>=2.0; 0≤θ≤90°. <i>K</i><sub>0</sub> is the free-space wavenumber, <i>q</i> is the semifocal length, <i>q</i> cosξ<sub>0</sub> is the length of the semimajor axis, θ is the angle of incidence with respect to the major axis, and ∊<sub>1</sub>/∊<sub>0</sub> is the relative dielectric constant of the cylinder.

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  1. R. W. P. King and T. T. Wu, The Scattering and Diffraction of Waves (Hartford University Press, Cambridge, Massachusetts, 1959).
  2. C. J. Bouwkamp, Rept. Progr. Phys. 17, 35 (1954).
  3. H. C. van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957).
  4. H. Hönl, A. W. Maue, and K. Westpfahl, "Theorie der Beugung," Handbuch der Physik, edited by S. Flügge (Springer-Verlag, Berlin, 1961), Vol. 25.
  5. C. Yeh, J. Math. Phys. 4, 65 (1963).
  6. For example, in the long-wavelength region, the Rayleigh method [Lord Rayleigh, Phil. Mag. 44, 28 (1897); A. F. Stevenson, J. Appl. Phys. 24, 1134 (1953); V. Twersky, J. Acoust. Soc. Am. 36, 1314 (1964)] is very useful; in the short wavelength region, the approximate treatment of diffraction problems by physical-optics techniques [J. B. Keller, J. Opt. Soc. Am. 52, 102 (1962); Y. M. Chen, J. Math. Phys. 5, 820 (1964)] is very successful.
  7. J. Meixner and F. W. Schäfke, Mathieu-Funktionen und Sphäroid-Funktionen (Springer-Verlag, Berlin, 1954).
  8. N. W. McLachlan, Theory and Application of Mathieu Functions (Oxford University Press, London, 1951).
  9. G. Blanch, J. Math. Phys. 25, 1 (1946).
  10. C. J. Bouwkamp, J. Math Phys. 26, 79 (1947).
  11. National Bureau of Standards, Tables Relating to Mathieu Functions (Columbia University Press, New York, 1951).
  12. G. Blanch and D. S. Clemm, Tables Relating to the Radial Mathieu Functions, Vol. 1, Functions of the First Kind (Aeronautical Research Laboratories, Office of Aerospace Research, U. S. Air Force, 1961).
  13. R. Barakat, A. Houston, and E. Levin, J. Math. Phys. 42, 142 (1963).

Barakat, R.

R. Barakat, A. Houston, and E. Levin, J. Math. Phys. 42, 142 (1963).

Blanch, G.

G. Blanch, J. Math. Phys. 25, 1 (1946).

G. Blanch and D. S. Clemm, Tables Relating to the Radial Mathieu Functions, Vol. 1, Functions of the First Kind (Aeronautical Research Laboratories, Office of Aerospace Research, U. S. Air Force, 1961).

Bouwkamp, C. J.

C. J. Bouwkamp, J. Math Phys. 26, 79 (1947).

C. J. Bouwkamp, Rept. Progr. Phys. 17, 35 (1954).

Clemm, D. S.

G. Blanch and D. S. Clemm, Tables Relating to the Radial Mathieu Functions, Vol. 1, Functions of the First Kind (Aeronautical Research Laboratories, Office of Aerospace Research, U. S. Air Force, 1961).

Hönl, H.

H. Hönl, A. W. Maue, and K. Westpfahl, "Theorie der Beugung," Handbuch der Physik, edited by S. Flügge (Springer-Verlag, Berlin, 1961), Vol. 25.

Houston, A.

R. Barakat, A. Houston, and E. Levin, J. Math. Phys. 42, 142 (1963).

King, R. W. P.

R. W. P. King and T. T. Wu, The Scattering and Diffraction of Waves (Hartford University Press, Cambridge, Massachusetts, 1959).

Levin, E.

R. Barakat, A. Houston, and E. Levin, J. Math. Phys. 42, 142 (1963).

Maue, A. W.

H. Hönl, A. W. Maue, and K. Westpfahl, "Theorie der Beugung," Handbuch der Physik, edited by S. Flügge (Springer-Verlag, Berlin, 1961), Vol. 25.

McLachlan, N. W.

N. W. McLachlan, Theory and Application of Mathieu Functions (Oxford University Press, London, 1951).

Meixner, J.

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

Schäfke, F. W.

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

Stevenson, A. F.

For example, in the long-wavelength region, the Rayleigh method [Lord Rayleigh, Phil. Mag. 44, 28 (1897); A. F. Stevenson, J. Appl. Phys. 24, 1134 (1953); V. Twersky, J. Acoust. Soc. Am. 36, 1314 (1964)] is very useful; in the short wavelength region, the approximate treatment of diffraction problems by physical-optics techniques [J. B. Keller, J. Opt. Soc. Am. 52, 102 (1962); Y. M. Chen, J. Math. Phys. 5, 820 (1964)] is very successful.

van deHulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957).

Westpfahl, K.

H. Hönl, A. W. Maue, and K. Westpfahl, "Theorie der Beugung," Handbuch der Physik, edited by S. Flügge (Springer-Verlag, Berlin, 1961), Vol. 25.

Wu, T. T.

R. W. P. King and T. T. Wu, The Scattering and Diffraction of Waves (Hartford University Press, Cambridge, Massachusetts, 1959).

Yeh, C.

C. Yeh, J. Math. Phys. 4, 65 (1963).

Other (13)

R. W. P. King and T. T. Wu, The Scattering and Diffraction of Waves (Hartford University Press, Cambridge, Massachusetts, 1959).

C. J. Bouwkamp, Rept. Progr. Phys. 17, 35 (1954).

H. C. van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957).

H. Hönl, A. W. Maue, and K. Westpfahl, "Theorie der Beugung," Handbuch der Physik, edited by S. Flügge (Springer-Verlag, Berlin, 1961), Vol. 25.

C. Yeh, J. Math. Phys. 4, 65 (1963).

For example, in the long-wavelength region, the Rayleigh method [Lord Rayleigh, Phil. Mag. 44, 28 (1897); A. F. Stevenson, J. Appl. Phys. 24, 1134 (1953); V. Twersky, J. Acoust. Soc. Am. 36, 1314 (1964)] is very useful; in the short wavelength region, the approximate treatment of diffraction problems by physical-optics techniques [J. B. Keller, J. Opt. Soc. Am. 52, 102 (1962); Y. M. Chen, J. Math. Phys. 5, 820 (1964)] is very successful.

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

N. W. McLachlan, Theory and Application of Mathieu Functions (Oxford University Press, London, 1951).

G. Blanch, J. Math. Phys. 25, 1 (1946).

C. J. Bouwkamp, J. Math Phys. 26, 79 (1947).

National Bureau of Standards, Tables Relating to Mathieu Functions (Columbia University Press, New York, 1951).

G. Blanch and D. S. Clemm, Tables Relating to the Radial Mathieu Functions, Vol. 1, Functions of the First Kind (Aeronautical Research Laboratories, Office of Aerospace Research, U. S. Air Force, 1961).

R. Barakat, A. Houston, and E. Levin, J. Math. Phys. 42, 142 (1963).

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