Fano-shape grating resonances of 3D infinite double-periodic grating of thin dielectric bricks

We study the plane wave scattering from double periodic dielectric layer located in free space and illuminated by a linearly polarized plane wave. For the problem solution, we use the method of integral functional based on the vector volume integral-differential equations for the equivalent electric and magnetic polarization currents of the assumed periodic medium. Reflectance and transmittance as a function of the normalized wavelength and the grating parameters are analyzed. Extraordinary sharp grating-type resonances are revealed in the TM- and TE-polarized wave scattering near but not equal to the Rayleigh wavelengths of non-zero diffraction orders.