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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 70, Iss. 12 — Dec. 1, 1980
  • pp: 1495–1503

Rigorous theory of scattering by perfectly conducting periodic surfaces with trapezoidal height profile. TE and TM polarization

G. M. Whitman, D. M. Leskiw, and F. Schwering  »View Author Affiliations

JOSA, Vol. 70, Issue 12, pp. 1495-1503 (1980)

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A rigorous method for analyzing plane-wave scattering from perfectly conducting periodic surfaces is examined and applied to trapezoidal profiles. Both TE and TM polarizations of the incident plane wave are considered. An integral equation for the unknown current distribution in the scatter surface is formulated by invoking the extended boundary condition. Upon expressing the current density in terms of its physical optics approximation multiplied by a Fourier series, the integral equation reduces to a linear system of equations. For the case of a piecewise linear surface profile, the coefficient matrix of this system is amenable to efficient computer evaluation, which furnishes the Fourier coefficients of the current distribution. The method is applied to trapezoidal scatterers for which little data is available in the literature, and, by using appropriate limiting procedures, to triangular and rectangular profiles. Scatter fields and surface current densities are calculated. The accuracy of the method, its range, and its limitations, are investigated and comparisons are made with the results of others. The method has given accurate results for surface groove depths of less than half a wavelength and for surface periods of greater than a wavelength at minimal computational cost.

© 1980 Optical Society of America

G. M. Whitman, D. M. Leskiw, and F. Schwering, "Rigorous theory of scattering by perfectly conducting periodic surfaces with trapezoidal height profile. TE and TM polarization," J. Opt. Soc. Am. 70, 1495-1503 (1980)

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  1. K. A. Zaki and A. R. Neureuther, "Scattering from a perfectly conducting surface with sinusoidal height profile, TE polarization," IEEE Trans. Antennas Propag. AP-19, 208–214 (1971).
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  27. In the case of hangars with surface corrugations running in the vertical direction, this indicates the superiority of horizontal over vertical polarization in suppressing undesirable specular reflection.
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  33. Comparison with the power spectrum for θ = 0.1° in Table III indicated that polarization sensitivity near an anomaly is stronger for current than for power, an observation previously noted for sinusoidal profiles.
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