Topological reactions of correlation functions in partially coherent electromagnetic beams

Abstract

It was recently shown that so-called coherence vortices, singularities of the two-point correlation function, generally occur in partially coherent electromagnetic beams. We study the three-dimensional structure of these singularities and show that in successive cross sections of a beam a rich variety of topological reactions takes place. These reactions involve, apart from vortices, the creation or annihilation of dipoles, saddles, maxima and minima of the phase of the correlation function. Since these reactions happen generically, i.e., under quite general conditions, these observations have implications for interference experiments with partially coherent, electromagnetic beams.

The subtraction of mutually displaced Gaussian Schell-model beams

“…In classical optics, coherence theory [1][2][3] is a subject that continuously receives innovative contributions from countless authors, both within the scalar [4][5][6][7][8][9][10][11] and vectorial realm [12][13][14][15][16][17][18][19][20][21], including nonstationary states [22][23][24][25][26].…”

Singularities of Partially Polarized Vortex Beams

“…In analogy with the scalar case, we may find eta singularities by fixing one observation point r 1 = r P and looking for singularities with respect to the second point r 2 , i.e., points where η(r P , r 2 ) = 0. As noted by Raghunathan et al [30,31], these singularities behave like scalar coherence vortices, with a discrete topological charge. Eta singularities have been relatively unexplored compared to other classes of singularities, though they have been observed in Mie scattering [32] and in the propagation of partially coherent radially polarized beams [33].…”

Cycle of phase, coherence and polarization singularities in Young’s three-pinhole experiment

“…Singularities of the spectral degree of coherence (called correlation vortices or coherence vortices) have been found in partially coherent scalar wavefields, representing pairs of points where the field is completely uncorrelated [9][10][11]. Generalizing correlation singularities to electromagnetic fields, so-called eta singularities have been introduced [12,13], which represent phase singularities of the electromagnetic correlation function.…”