Spectral theory of EM wave scattering by periodic strips

A new method is proposed for analyzing electromagnetic (EM) wave scattering and waveguiding by a planar periodic system of thin and perfectly conducting strips. The method exploits some known properties of Fourier series with coefficients expressed by Legendre polynomials. The method can be used to solve problems associated with EM wave propagation and polarization having an arbitrary angle with respect to strips in arbitrary anisotropic media, multiperiodic systems of strips, and layered systems of skewed periodic strips. In the paper the method is presented by an example, namely the scattering of EM waves from a grating consisting of perfectly conducting strips in vacuum. Numerical calculations show that the method converges much faster than do alternative methods