Array of line sources that produces preselected plane waves

A generalized Poisson summation formula produces an explicit expression for the surface current on a plane that radiates set of preselected waves. Specifically, is expressed as integral in complex function whose poles determine plane-wave directions propagation and residues corresponding amplitudes. When only finite number waves are specified, continuous function. If infinite can degenerate into discrete line sources. In such situations, determines both location strength sources radiate One specify propagating evanescent Explicit formulas derived sets determined by periodic almost-periodic functions. The closed-form expressions be applied directly to problem scattering gratings.