Diffraction from phase modulated apertures

We apply the Rayleigh-Sommerfeld diffraction integral to solve the diffracted fields of periodically phase-modulated apertures. We show that the diffraction of small phase modulated apertures (with few refractive index modulation periods) behaves as for phase gratings, but the sharp diffraction peaks may already appear in the Fresnel region behind the aperture. Thus, these components may serve as lensless miniature interconnection gratings in micro-optics.