Hypersingularity, electromagnetic edge condition, and an analytic hyperbolic wedge model.
It is insufficient to consider that hypersingularity is unphysical solely based on energy considerations. With a proper combination of the two degenerate hypersingular modes, the energy-flux edge condition is satisfied. A hyperbolic wedge model is presented that is much simpler than the previous model for the purpose of studying singular characteristics of the edge fields. This model not only reproduces the sharp edge model as the wedge becomes infinitely sharp but also naturally shows how the two degenerate hypersingular modes of the sharp edge model should be combined. In an incidental study of the effect of rounding edges on numerical computation, I show that the converged results for rounded edges do not converge to a fixed value when the radius of curvature tends to zero, if the corresponding sharp edge supports hypersingularity. I also prove that introducing a small amount of absorption loss for the purpose of improving numerical convergence is effective only when the ratio of the real parts of the permittivities of the two media forming the wedge is close to -1. Finally I remark on the possible illposedness of the hypersingularity problem without imposition of the edge condition.
Lifeng
L
Li