Born's rule and single-photon diffraction by a triangular slit

The double-slit at single photon or electron level is the ubiqutous quantum interference experiment with the path phase playing a key role. On the other hand, photon's orbital angular momentum (OAM) brings a new dimension to interference problems with the spiral phase degree of freedom. In this work, we use OAM's two dimensional properties to extended the double-slit to a triple-slit configuration in the shape of an equilateral triangle, obtaining a triangular latticed single-photon counting interference pattern. In order to understand this interference pattern in terms of wave-particle duality, we have to take into account that, in contrast with the parallel double and triple slit cases, the azimuthal phase also plays a fundamental role, being undistinguishable from path phase.