Singular integral equations in diffraction problem by an infinite periodic strip grating with one strip removed: E-polarization case

The E- polarized plane wave diffraction by the infinite periodic grating with removed strip is considered. The scattered field is represented as a sum of the field of the infinite periodic grating and the field of the correction currents excited due to extraction of a single strip. The problem is reduced to the dual integral equations relatively unknown spectral function of the correction field. After differentiation of these equations the singular integral equation with additional conditions with respect to the correction current density is obtained. For comparison, the single mode current approximation model is also presented. The currents on the strips and far-field distribution of correction current are analyzed.