Born's rule and the interference of photons with orbital angular momentum by a triangular slit

J. M. Hickmann^a, E. J. S. Fonseca and A. J. Jesus-Silva

Optics and Materials Group - OPTMA, Universidade Federal de Alagoas - Caixa Postal 2051, 57061–970, Maceió, AL, Brazil

^a jmh@optma.org

Received: 10 August 2011
Accepted: 7 November 2011

Abstract

We use photon OAM's two-dimensional properties to extend the double-slit to a two-dimensional triple-slit configuration in the shape of an equilateral triangle, obtaining a bidimensional triangular interference pattern at photon level, whose size depends on the OAM amount. We also show that for this pattern, in contrast with the parallel two- and three-slit cases, the azimuthal phase plays a fundamental role, being undistinguishable from the path phase. Our results confirm that only pairs, here associated to path and azimuthal phases, contribute to the two-dimensional photon detection probability, as established by Born's rule.