Singular optics has been associated for decades with the study of phase singularities in fully coherent beams. There are two main types of phase singularities: optical vortices and edge dislocations. Recent research has shown that the correlation functions of partially coherent beams can also exhibit types of phase singularities. This has led to the introduction of a new type of singularity, namely the correlation vortex, which is similar to the optical vortex and is defined as a phase singularity of the two-point cross-spectral density (CSD) function of the fields. While much research has focused on fully coherent beams, partially coherent beams have practical advantages due to their greater resistance to degradation when propagating through random media. In addition to correlation vortices, we propose the existence of another type of correlation singularity: the coherent edge-dislocation. Therefore, we introduce the concept of the coherent edge dislocation carried by the Gaussian Schell-model (GSM) beams, since GSM is a classic example of a partially coherent beam. We then study the interaction of two coherent edge dislocations carried by GSM beams as they propagate through free space and atmospheric turbulence, both theoretically and numerically.

By drawing an analogy with edge dislocations in coherent beams, we show that coherent edge dislocation exists in partially coherent beams. Based on the extended Huygens-Fresnel principle, we derive the analytical expression for the CSD of GSM beams carrying two edge dislocations propagating through atmospheric turbulence. This expression is used to study their interaction in both free space and atmospheric turbulence. The positions of the correlation singularities of partially coherent beams in the z-plane can be determined from the real and imaginary components, as well as from the phase distribution of the spectral degree of coherence of the GSM beams.

The CSD of partially coherent beams has a well-defined phase with respect to two points, and the phase singularities of the CSD are called the correlation singularities. In line with previous research, we propose the existence of another type of correlation singularity: the coherent edge dislocation, which exhibits a π-phase shift along a line in the transverse plane of the correlation function. The refractive index structure constant Cn2=0 leads to an expression for the CSD that degenerates to the CSD formula of GSM beams in free space, allowing us to discuss their interaction in this environment. The two coherent edge dislocations disappear with propagation, while two correlation vortices with opposite topological charges emerge due to their interaction. However, the total topological charge of the correlation vortices is not conserved due to the possible appearance or disappearance of correlation vortices during propagation, unlike the interaction of two edge dislocations, where the total topological charge is zero and conserved during propagation (Fig. 1). The total topological charge is not conserved in the propagation of initial beams with coherence vortices, and off-axis edge dislocation in oceanic turbulence due to the possible appearance or disappearance of correlation vortices. This result is compared with the interaction of a phase vortex and an off-axis edge dislocation in free space, where the total topological charge is conserved. When GSM beams carrying two parallel coherent edge dislocations propagate, the coherent edge dislocations disappear, but no correlation singularities appear in the fields. However, coherent edge dislocations can appear with propagation, which is different from the evolution of two parallel edge dislocations in free space (Fig. 3). The result is compared with the evolution of two parallel edge dislocations in free space, where phase singularities disappear with propagation. When GSM beams carrying two perpendicular coherent edge dislocations propagate, the coherence edge dislocations disappear while perpendicular coherent edge dislocations vanish, with one or two correlation vortices appearing during free space propagation (Fig. 4). This result differs from the interaction of two perpendicular edge dislocations, where no optical vortices appear during propagation. The value of the refractive index structure constant affects the appearance, number, and position of correlation vortices when GSM beams carrying two coherent edge dislocations propagate through atmospheric turbulence (Fig. 5). Correlation singularities may appear, but no coherent edge dislocations are observed with the propagation of GSM beams when the two coherent edge dislocations are parallel in the initial plane, which is different from the free-space case, where coherent edge dislocations may recur, but no correlation singularities appear (Fig. 6). Conversely, coherent edge dislocations may appear but no correlation vortices appear, if the two coherent edge dislocations are perpendicular at the initial plane, which is different from the free space case (Fig. 7).

In addition to correlation vortices, coherent edge dislocations are shown to exist. The CSD of GSM beams carrying two coherent edge dislocations is derived based on the extended Huygens-Fresnel principle. The coherent edge dislocations are generally unstable and disappear, while correlation vortices or edge dislocations may appear during propagation. The number of correlation vortices can change due to the creation or disappearance of these vortices in the fields. A comparison of the interaction of coherent edge dislocations in atmospheric turbulence with that in free space is made.