Guiding of electromagnetic waves by uniformly rough surfaces : Part I

A simple derivation is given for the reflection of electromagnetic waves from a perfectly-conducting plane surface which has a uniform distribution of hemispherical bosses whose electrical constants are arbitrary. The spacing between the centers of the bosses is taken to be small, which is the justification for neglecting the incoherent radiation. An approximate boundary condition is developed which must be satisfied in an average sense by the tangential fields on the reference plane. The excitation of surface waves on the rough surface is then discussed. It is indicated that to a first order, a rough surface of the kind described here possesses an inductive surface reactance and will support a trapped wave. The effect of finite conductivity of the bosses is to damp exponentially this trapped wave.