TY - JOUR

T1 - Scattering by Periodic Metal Surfaces with Sinusoidal Height Profiles—A Theoretical Approach

AU - Whitman, Gerald

AU - Schwering, Felix

PY - 1977/11

Y1 - 1977/11

N2 - A theory of scattering by periodic metal surfaces is presented that utilizes the physical optics approximation to determine the current distribution in the metal surface to first order, but modifies this approximate distribution by multiplication with a Fourier series whose fundamental period is that of the surface profile (Floquet's theorem). The coefficients of the Fourier series are determined from the condition that the field radiated by the current distribution into the lower (shielded) half-space must cancel the primary plane wave in this space range. The theory reduces the scatter problem to the familiar task of solving a linear system. For certain basic types of surface profiles, including the sinusoidal profile considered here, the coefficients of the linear system are obtained as closed form expressions in well-known functions (Bessel functions for sinusoidal profiles and exponential functions for piecewise linear profiles). The theory is thus amenable to efficient computer evaluation. Comparison of numerical results based on this theory with data obtained by recent numerical schemes shows that for depths of surface grooves less than a wavelength and for unrestricted groove widths, reliable and comparable, if not more accurate, data is obtained, in many cases at considerably cheaper computational cost.

AB - A theory of scattering by periodic metal surfaces is presented that utilizes the physical optics approximation to determine the current distribution in the metal surface to first order, but modifies this approximate distribution by multiplication with a Fourier series whose fundamental period is that of the surface profile (Floquet's theorem). The coefficients of the Fourier series are determined from the condition that the field radiated by the current distribution into the lower (shielded) half-space must cancel the primary plane wave in this space range. The theory reduces the scatter problem to the familiar task of solving a linear system. For certain basic types of surface profiles, including the sinusoidal profile considered here, the coefficients of the linear system are obtained as closed form expressions in well-known functions (Bessel functions for sinusoidal profiles and exponential functions for piecewise linear profiles). The theory is thus amenable to efficient computer evaluation. Comparison of numerical results based on this theory with data obtained by recent numerical schemes shows that for depths of surface grooves less than a wavelength and for unrestricted groove widths, reliable and comparable, if not more accurate, data is obtained, in many cases at considerably cheaper computational cost.

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U2 - 10.1109/TAP.1977.1141682

DO - 10.1109/TAP.1977.1141682

M3 - Article

AN - SCOPUS:0017556303

SN - 0018-926X

VL - 25

SP - 869

EP - 876

JO - IEEE Transactions on Antennas and Propagation

JF - IEEE Transactions on Antennas and Propagation

IS - 6

ER -