Measuring the topological charge of coherence vortices through the geometry of the far-field cross-correlation function

Abstract

Determination of orbital angular momentum of optical vortex beams has attracted the attention of many researchers over the last few years. For some applications, it is convenient to use a partially coherent vortex beam because of its robustness. In this work, we developed a method to measure the topological charge of a partially coherent vortex beam. Our method relies simply in the measurement of the minimum radius of a zero contour of the modulus of the cross-correlation function and in the measurement of the full width at half maximum of its central spot.

Optical phase singularities: Physical nature, manifestations and applications

“…Very interesting possibilities arise from the ideas of "coherence vortices" (CV)-"hidden" phase singularities which exist in the correlation function rather than in the immediately observable field distribution (1) [164][165][166][167][168][169][170][171][172][173][174][175][176][177][178][179][180][181][182][183]. Generally, usual partially-coherent paraxial fields are spatially inhomogeneous and are characterized by the two-point correlation function…”

“…Usual OV beams can evolve into CVs when the degree of coherence falls down (ρ c → 0): according to the conservation laws, the TC, associated with the phase singularity, "moves" from the field to the coherence function, as well as the OAM does. When the projection 2) is used, the correlation function (25) F(r 2 , −r 2 ) contains annular ring-like edge phase dislocations [9] with the configurations depending on the input partiallycoherent LG p l beam characteristics [176][177][178][179]. The singularity of the function F(r 2 , −r 2 ) may exist even in a non-vortex beam (l = 0) due to the non-zero radial index [178].…”

“…Besides the beam-wander conditions, the CVs can be generated when an OV beam passes a random scatterer (e.g., rotating ground-glass disc) [179,180], or due to special randomization of multiple partially-coherent "source" beams regularly arranged over the input plane [181]. In the arrangement of [179], the "regular" large-scale singularity is "hidden" inside the visually chaotic speckle structure but can be recovered via the correlation analysis.…”

“…Besides the beam-wander conditions, the CVs can be generated when an OV beam passes a random scatterer (e.g., rotating ground-glass disc) [179,180], or due to special randomization of multiple partially-coherent "source" beams regularly arranged over the input plane [181]. In the arrangement of [179], the "regular" large-scale singularity is "hidden" inside the visually chaotic speckle structure but can be recovered via the correlation analysis. Notably, such CV structures are "robust": After the beam passes through an obstacle which apparently blocks a noticeable part of the beam profile, its coherence function experiences essential changes but with further beam propagation, these changes disappear and the CV is restored [179,180].…”

“…In the arrangement of [179], the "regular" large-scale singularity is "hidden" inside the visually chaotic speckle structure but can be recovered via the correlation analysis. Notably, such CV structures are "robust": After the beam passes through an obstacle which apparently blocks a noticeable part of the beam profile, its coherence function experiences essential changes but with further beam propagation, these changes disappear and the CV is restored [179,180]. Together with the self-healing properties mentioned in the above paragraph [183], this fact is illustration of the important general feature of the CV structures: their high stability and low sensitivity to external perturbations, even when compared with the usual OVs.…”