Diffractive multifocal focusing of de Broglie matter

Diffraction of a de Broglie matter wave by a system of two pinholes on an optical axis exhibits the multifocal focusing effect of matter waves in the near-field (Fresnel zone). The focusing, defocusing and refocusing phenomenon results from periodic phase changes at singular points, which are observed for the even Fresnel numbers, where the intensity is zero and the phase is undefined. As an on-axis observation point passes through a singular point, the nature of the wave in the neighborhood of the axis changes from that of a diverging wave to that of a converging wave, i.e., the wave refocuses. The amplitudes of the oscillations in the intensity and phase of the de Broglie wave depend on the ratio of the radii of the two apertures in the system. This effect of diffractive multifocal focusing of de Broglie waves can be used for designing a diffractive lens for matter-wave beams.