Near and far fields of high-quality resonances of an infinite grating of sub-wavelength wires

An infinite grating of identical dielectric cylinders placed periodically in free space and illuminated by a plane wave is investigated. Numerical and analytical solutions are derived for the E and H-polarisation cases. The study is focused on the ultra high-Q resonances at the frequencies close to the Rayleigh “anomalies” where the Floquet harmonics “pass over horizon.” The in-resonance near field patterns for the scattering problem are demonstrated and compared to the natural mode fields. They reveal that, near the grating, the dominant contribution comes from two Floquet harmonics propagating along the plane of grating however evanescent in the normal direction. As a result, a powerful standing wave is formed along the grating, with the amplitude proportional to the natural mode Q-factor.