Linear focusing by a plane grating with curved grooves

We study the field diffracted by a plane grating with curved (parabolic) grooves. We will demonstrate that when a monochromatic plane wave is incident on a grating with parabolic grooves the diffracted field has a focal line whose position depends on the curvature radius of the parabolas and the incidence angle of the light onto the grating. The effect described has potential applications in grating-based devices for focusing light without requiring any additional optics.