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A transverse magnetic surface wave is normally incident upon an infinitely long elliptic cylinder which may be a perfect conductor or a dielectric. The possibility of zero reflexion is investigated by the method of matched asymptotic expansions when the width of the cylinder is small compared with the other length scales of the problem. The radiated wave and the reflected and transmitted surface waves are calculated for various combinations of geometrical and material properties.doi:10.1098/rspa.1977.0021 fatcat:vkbfdw5cdfgcpl2d6uni6gko4i