A new type of shape-invariant beams with structured coherence: Laguerre-Christoffel-Darboux beams

Abstract

A new class of sources presenting structured coherence properties is introduced and analyzed. They are obtained as the incoherent superposition of coherent Laguerre-Gaussian modes with suitable coefficients. This ensures that the shape of the intensity profile and the spatial coherence features of the propagated beams are invariant during paraxial approximation. A simple analytical expression is obtained for the cross-spectral density of the sources of this class, regardless of the number of superposed modes. Properties of these sources are analyzed and described by several examples.