A formulation of self-similar dielectric wedge diffraction

Robust numerical methods are routinely used for solving Maxwell´s equations in multidimensional dielectric/metallic models. Nonetheless, sharp dielectric edges remains problematic, at least in principle, because no constructive mathematical basis exists for dynamic fields near them. To divine the nature of the edge singularity, previous analytical efforts have assumed separable solutions based on power series expansions. However, this approach is mathematically incomplete since it does not solve the inherently nonseparable initial-boundary value problem. We formulate a provocative mathematical approach exploiting self-similarity of transient fields in a semi-infinite wedge. Self-similarity reduces the number of independent variables by one and follows from the absence of a characteristic length. The only practical limitation is that fields incident on the edge must be plane waves rather than emanating from a proximate source. The analysis leads to a coupled boundary value problem for analytic functions in two complex half planes corresponding to the diffracted wave in each wedge.