Boundary waves on perfect conductors

AbstractThe two classes of maximal, energy-preserving boundary conditions for Maxwell's equations are distinguished by the fact that all self-adjoint operators engendered by conditions of the first class (which includes the classical condition) satisfy a coerciveness inequality, while such an inequality fails to hold for every operator of the second class (J. R. Schulenberger, J. Math. Anal. Appl. 48 (1974)). It is shown that all boundary conditions of the latter class admit surface waves. The principal content of the paper is the representation of the solution u of the Cauchy problem for Maxwell's equations in R+3 with a boundary condition of the second class in terms of two orthogonal parts, u = uσ + uρ, where uρ is a superposition of reflected plane waves and uσ a superposition of surface waves. For comparison, the representation of the solution corresponding to the classical condition (where surface waves are absent) is also given