The rich physics exhibited by random optical wave fields permitted Hanbury Brown and Twiss to unveil fundamental aspects of light. Furthermore, it has been recognized that optical vortices are ubiquitous in random light and that the phase distribution around these optical singularities imprints a spectrum of orbital angular momentum onto a light field. We demonstrate that random fluctuations of intensity give rise to the formation of correlations in the orbital angular momentum components and angular positions of pseudothermal light. The presence of these correlations is manifested through distinct interference structures in the orbital angular momentum-mode distribution of random light. These novel forms of interference correspond to the azimuthal analog of the Hanbury Brown and Twiss effect. This family of effects can be of fundamental importance in applications where entanglement is not required and where correlations in angular position and orbital angular momentum suffice. We also suggest that the azimuthal Hanbury Brown and Twiss effect can be useful in the exploration of novel phenomena in other branches of physics and astrophysics.
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