The perfectly conducting wire grating: Computation of the diffracted field from Maxwell's equations and Hamilton's canonical system

A theoretical and numerical study of the perfectly conducting wire grating is presented. For both fundamental cases of polarization, we solve the Helmholtz equation rigorously without any physical simplifying assumption. The only approximations are due to the use of numerical techniques in the integration of a differential system. The wire cross section is to a large extent arbitrary. The interest of Hamilton's canonical equations in the numerical treatment of certain practical problems is shown. No doubt, certain ideas contained herein could be adapted for solving many other problems in electromagnetic theory.