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Diffraction of a plane electromagnetic wave by a perfectly conducting elliptic cylinder

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Abstract

The scattering of a plane electromagnetic wave by a perfectly conducting elliptic cylinder is investigated theoretically. The calculations are based upon the expansion of the scattered wave functions in terms of Mathieu functions. Both E- and H-polarized waves are considered. Numerical results, in particular for the scattering cross-section, are presented for cylinders the cross-sectional dimensions of which are up to many wavelengths (e.g. distance between the focal lines up to 20 wavelengths).

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Abbreviations

E :

electric field vector

c :

parameter pertaining to the cross-section of the elliptic cylinder (c=2hπ/λ)

ce n :

Matthieu function of first kind and order n

h :

half the focal distance

H :

magnetic field vector

i x, y, z, η, ξ :

unit vector in x, y, z, η, ξ-direction, respectively

k :

wave number (k=ω(ε 0 μ 0)1/2)

Mc (j) n :

modified Mathieu function of kind j and order n

Ms (j) n :

modified Mathieu function of kind j and order n

q :

parameter pertaining to the cross-section of the elliptic cylinder (q=k 2 h 2/4)

se n :

Mathieu function of first kind and order n

t :

time

U :

scalar wave function defined by (2.1)

x, y, z :

Cartesian coordinates

Z :

wave impedance (Z=(μ 0/ε 0)1/2)

ε 0 :

permittivity of vacuum

η :

angular elliptic coordinate

θ :

angle between x-axis and direction of propagation of incident wave

λ :

wavelength in free space

μ 0 :

permeability of vacuum

ξ :

radial elliptic coordinate

ξ 0 :

value of ξ on the boundary of elliptic cylinder

σ s :

scattering cross-section

ω :

angular frequency

∂ x, y, η, ξ :

partial differentiation with respect to x, y, η, ξ

References

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Authors and Affiliations

  1. Department of Electrical Engineering, Division of Electromagnetic Research, Delft University of Technology, Delft, The Netherlands

    P. M. van den Berg & H. J. van Schaik

Authors
  1. P. M. van den Berg
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  2. H. J. van Schaik
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van den Berg, P.M., van Schaik, H.J. Diffraction of a plane electromagnetic wave by a perfectly conducting elliptic cylinder. Appl. Sci. Res. 28, 145–157 (1973). https://doi.org/10.1007/BF00413063

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