Coherence singularities: birth, evolution, possible applications

Abstract

Coherent singular beams, in particular optical vortices, are attractive for different applications: free-space optical communication, imaging, particle manipulation, etc. However, their deformation during propagation through random media and speckle noise forced to look to their partially coherent analogues. The singularities of partially coherent beams associated with zero points of the cross-correlation function have been theoretically predicted and experimentally demonstrated for some particular cases of Laguerre-Gaussian (LG) and Hermite-Gaussian (HG) Schell-model beams (SMBs). Here we establish a theoretical background for explanation of these singularities evolution during propagation of the SMBs associated with structurally stable Hermite-Laguerre-Gaussian modes, which include as a particular case the LG and HG ones. The derived a closed-form expression for the evolution of the mutual intensity of such beams allows easily calculating the intensity distribution and cross-correlation function at every plane of paraxial optical system. The birth and evolution of the cross- correlation singularities is analyzed. Their structure in far field serves as a fingerprint of the associated mode while the intensity distribution may not resemble the mode shape. The robustness of these singularities can be exploited for information encoding and random medium monitoring.