On the Nonspecular Reflection of Electromagnetic Waves

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Abstract
The nonspecular reflection of plane electromagnetic waves of arbitrary polarization by certain perfectly conducting surfaces composed of either semicylindrical or hemispherical bosses on an infinite plane is analyzed. Solutions for the problem of the single boss on an infinite plane and a plane wave at an arbitrary angle of incidence are given and extended subject to the single‐scattering hypothesis to obtain the far field solutions for certain small finite patterned distributions and both small finite and infinite uniform random distributions of bosses small compared with the wavelength. The results for the various cases are then compared in the plane of incidence and similarities between the analogous expressions for the distributions of semi‐cylinders and hemispheres are noted. Expressions are obtained for the ratios of the components of the reflected intensity and radial energy flux polarized parallel and perpendicular to the plane of incidence as well as for the total intensity and radial energy flux for the case where the incident wave is unpolarized. It is found that for certain values of the parameters the reflected radiation may consist only of either the specular or the scattered contributions, while for other values one of the scattered contributions, either the parallel or perpendicular component, may vanish. The results also indicate the occurrence of an extremum in the reflected radiation in the vicinity of the specular angle of reflection, which for certain ranges of the parameters for the small finite distributions may be a minimum rather than a maximum. For these cases there is also some critical angle of incidence (not necessarily π/2 or grazing incidence) for which the reflection at the specular angle is completely specular. The analogous distributions of cylinders and spheres are also considered.