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Current densities in an illuminated perfectly-conducting sheet

When electromagnetic radiation illuminates a perfectly-conducting metal, it induces a current density on its surface. We consider a thin perfectly-conducting sheet, possibly finite in extent and possibly with apertures in it, so that incident radiation will induce a current density at both sides of the material. The sheet current density is the sum of the current densities at both sides, and this effective current density generates the scattered field. We show that when this sheet current density is known, its splitting in surface current densities at both sides of the sheet is unique, and determined by the incident field in a simple way. A set of two coupled equations for this sheet current density is derived, which holds for any spatial structure of the incident field. This approach to scattering by a sheet is illustrated by considering a plane wave incident on a mirror and on the Sommerfeld half-plane.