Multi-Gaussian Schell-model source with a complex coherence state

Abstract

The effects of non-trivial phase of the source degree of coherence on the far-field spectral density for the class of one-dimensional, multi-Gaussian Schell-model beams are explored. While in the absence of the phase, the flat-top spectral density profile with a Gaussian edge drop is symmetrically formed in the far field about the optical axis, various phase functions introduce asymmetric modifications to such distribution. Since the phase of the source degree of coherence must be an odd function, three such examples are considered in detail: linear phase leading to shift, signum phase producing either tilt or split, and cubic phase forming Airy-like radially accelerating profiles. We have established that unless the phase of the source degree of coherence is sufficiently small at all separations, the resulting far-field spectral density profiles are qualitatively very different from those with the trivial phase.