Scattering of partially coherent vortex beams by a $\mathcal {PT}$-symmetric dipole

We investigated the statistical properties of partially coherent optical vortex beams scattered by a $\mathcal {PT}$ dipole, consisting of a pair of point particles having balanced gain and loss. The formalism of second-order classical coherence theory is adopted, together with the first Born approximation, to obtain the cross-spectral density of the scattered field. It is shown that the radiated pattern depends strongly on the coherence properties of the incident beam and on the non-Hermitian properties of the dipole. The spectral density for the scattered radiation is ruled by two terms, one associated to the vortex structure and the other independent of the topological charge, and the competition between these terms dictates the directional properties of the scattered radiation. When they have same order of magnitude, the scattered profile resembles that of an incoherent system, with radiation being emitted in all directions in the three-dimensional space, regardless of the dipole's gain and loss properties. Depending on the gain and loss present in the dipole, the system may scatter light in some preferable directions. All of these effects are accompanied by a change in the spectral degree of coherence of the scattered field.