An inherent limitation of the Luneburg-Kline representation for the current on a conducting body

An attempt is made to determine fundamental limitations, e.g. limitations not imposed by an inability to perform integrals, of a Luneburg-Kline (L-K) representation for the surface current induced on a conducting surface by a plane wave. By expanding the current, normalized by the incident field phase factor, in an L-K series and substituting this result in the magnetic-field integral equation, it is found that all the coefficients in the expansion are identically zero in the shadow region of the scatterer. This limitation is explained in terms of the inability of the L-K series to adequately represent the creeping-wave nature of the current in the transition/shadow region. These results raise the question of the physical source of previously derived higher-order L-K terms