Note on the surface impedance and the transmission of radiation through metal slabs

Abstract

An arbitrary electric field distribution in a metal slab in a uniform magnetic field can be written as a linear combination of four functions each of which satisfies Maxwell's equations for particularly simple boundary conditions. In particular, if the slab is thick compared with the skin depth of the radiation, δ, and if (ω/c)δ « 1, then the reflection and transmission coefficients for the slab are proportional to Gx(0), Gy(0), Gx(d), Gy(d) respectively, where Gx(z), Gy(z) are the electric field distributions generated in a slab bounded by the planes z = 0, z = d by a unit alternating magnetic field applied to the surface z = 0 and directed along y.