On z-coherence in self-focusing

TL;DR

This paper derives analytical expressions for intensity and z-coherence in self-focusing of circularly coherent light, confirming previous numerical results and revealing new complex features with a pseudo-modal interpretation.

Contribution

It provides the first closed-form analytical expressions for z-coherence in self-focusing, enhancing understanding of the phenomenon.

Findings

Analytical formulas for intensity distribution and z-coherence.

Confirmation of previous numerical results.

Discovery of new complex features in z-coherence.

Abstract

Both the intensity distribution and the degree of coherence between pairs of points along the propagation axis (z-coherence) are derived in closed form for a phenomenon of self-focusing produced by circularly coherent light. The first confirms results previously obtained numerically, while the second exhibits new complex features. The physical interpretation is obtained by a suitable pseudo-modal expansion that suggests an analogy with a simple two-mode structure.