Structure transitions in arrays of point-vortices upon free space propagation

Abstract

Abstract We study the free space propagation of arrays of N × N point vortices with equal unitary topological charge embedded in a Gaussian beam, initially distributed into either a square lattice or a disordered array with the same mean vortex density and separation. The far-field patterns and the near-field evolution are analyzed as a function of different control parameters, such as the size of the carrier beam, the number of vortices, the mean separation distance among them P, and a geometrical parameter S p , defined as the ratio of the size of the array to the size of the host beam. The value of S p turns out to be determinant for the final spatial distribution of the optical vortices in the far-field pattern and also plays a very relevant role in the near-field evolution. While the initial array structure is basically preserved, rotated and scaled up when S p > ∼ 0.75 , the vortices redistribute forming a circumference around the propagation axis for S p < ∼ 0.5 , depleting most of the central intensity, even if the vortex density is far lower than the previously predicted limit for depletion. In the near field, we find an expression for the rotation angle of the whole structure when preserved, as a function of the propagation distance, which depends on P, but it is around eight-fold larger than the Gouy phase shift of the host. Also, we observe the formation of a high intensity ring pattern, whose radius is independent of the size of the carrier and the initial distribution of vortices, but it is only determined by the number of vortices. We verified our numerical results with experiments, finding a very good agreement between them.