Variational principle in three-dimensional problem of diffraction by impedance screen

Problems of the diffraction of electromagnetic waves on conducting screens of finite sizes are reduced, as a rule, to the Fredholm integral equations for the current density at both the perfect and impedance surfaces. For a perfectly conducting screen it has been shown that the scattered field can be presented by a stationary functional with respect to the surface current density. It provides a method for an approximate consideration of the problem eliminating the stage of direct solution of equations. The validity of the variational approach for the case of an impedance screen is shown. The stationary expression for the diffraction field is derived