Beam focusing in reflections from flat subwavelength diffraction gratings

We predict that narrow beams, reflecting from flat subwavelength diffraction gratings, can focus. The effect is shown for the beams of electromagnetic radiation; however, it should be observable for beams of waves of arbitrary nature (microwaves, surface plasmons, and acoustic and mechanical waves). We present analytical estimations of the focusing performance obtained by multiple scattering calculations and demonstrate the focusing effect numerically for an optical system (reflections from an array of dielectric cylinders), using the finite-difference time-domain calculations.