Diffraction of TM-polarized plane electromagnetic wave by multielement grating in a half-space

The problem of electromagnetic plane wave diffraction by a multielement grating which is imbedded in a half-space is considered in the case of TM-polarization. A system of singular integral equations is derived by satisfying the necessary boundary conditions. A system of linear algebraic equations is obtained through the application of specially constructed quadrature formulae and an appropriate Green´s function calculation. Numerical results describing the resonance characteristics of the cascaded grating are presented.