Diffraction by a perfectly conducting strip grating

The problem of scattering of an s-polarised wave by a periodic grating of thin ideally conducting strips at normal incidence is solved. The Riemann–Hilbert method is used to obtain an infinite system of equations for the Fourier coefficients of the electric and magnetic fields. The truncated system is solved numerically and fast convergence to the exact solution is shown. The transmission coefficients are calculated depending on two dimensionless parameters: the ratio of the grating period to the wavelength of light and the coefficient of filling the grating area with a conductor. The distribution of the local field is found and the data on the transmission coefficient known from the literature are refined.