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.

中文翻译：

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部分相干涡旋光束被a散射 $ \数学{PT} $不对称偶极子

我们研究了由\\数学{PT} $散射的部分相干光学涡旋光束的统计特性偶极子，由一对具有平衡增益和损耗的点粒子组成。将二阶经典相干理论的形式主义与第一波恩近似一起采用，以获得散射场的跨谱密度。结果表明，辐射方向图很大程度上取决于入射光束的相干特性和偶极子的非赫米特特性。散射辐射的光谱密度由两个术语决定，一个与涡旋结构相关，另一个与拓扑电荷无关，这些术语之间的竞争决定了散射辐射的方向特性。当它们具有相同的数量级时，散射轮廓类似于非相干系统的散射轮廓，其中辐射在三维空间的所有方向上发射，不管偶极子的增益和损耗特性如何。根据偶极子中存在的增益和损耗，系统可能会将光散射到一些优选的方向上。所有这些效应都伴随着散射场的光谱相干度变化。