Multi-component vortex solutions in symmetric coupled nonlinear Schrödinger equations

Abstract

Abstract. A Hamiltonian system of incoherently coupled nonlinear Schrödinger (NLS) equations is considered in the context of physical experiments in photorefractive crystals and Bose-Einstein condensates. Due to the incoherent coupling, the Hamiltonian system has a group of various symmetries that include symmetries with respect to gauge transformations and polarization rotations. We show that the group of rotational symmetries generates a large family of vortex solutions that generalize scalar vortices, vortex pairs with either double or hidden charge, and coupled states between solitons and vortices. Novel families of vortices with different frequencies and vortices with different charges at the same component are constructed and their linearized stability problem is block-diagonalized for numerical analysis of unstable eigenvalues.

Observation of vector solitons with hidden vorticity

“…Finally, to confirm the conclusions of our experiments, we study numerically the propagation of two-component optical beams in isotropic nonlinear media with a Gaussian nonlocal response. In contrast to the previous results obtained for local media [7,[9][10][11], here we find that when the total power of a vector vortex soliton corresponds to a stable scalar vortex beam [15], both configurations (with explicit and hidden vorticities) become stabilized by strong nonlocal response of the medium, although we notice that the dominating long-lived internal modes are drastically different in those two cases. Here we try to match our experimental conditions better by applying the same initial elliptic deformation to both input vortex components [13].…”

“…Multicomponent spatial vortex solitons can also experience strong instabilities. However, as was shown in several theoretical studies [7,8], the stability of the vector vortex solitons depends on their total orbital angular momentum (OAM), or vorticity [9,10]: when the components have equal topological charges, m 1;2 1 [as shown in Fig. 1(a)], the composite vortex soliton remains unstable, similar to its scalar counterpart.…”

“…However, if the vortices counterrotate, m 1;2 1 [ Fig. 1(b)], and the total OAM vanishes, the theoretical studies suggest that such vector soliton with hidden vorticity may become stable in self-focusing media [10,11], similar to the case of zero charge in both components [12]. However, in spite of many theoretical studies of these types of vector solitons, such composite optical beams have not been observed in experiment.…”

Composite vortices in nonlinear circular waveguide arrays

“…This rotation commutes with operator H L + H N L in the linear stability problem, see (11). Following the result of [46], the stability is consequently independent of ϕ. This result is supported by direct numerical solutions of the linear stability problem.…”

“…This feature can be demonstrated analytically in the framework of the one-dimensional two-component system, in which a counterpart of the HV states is represented by hidden-momentum counter-propagating wave pairs, with equal amplitudes and zero total momentum [44]. In the general case of an arbitrary number of symmetrically interacting components, the stability is determined by the total OAM of the composite beam [45,46]. Vortex solitons of the HV type were recently observed in nematic liquid crystals [47].…”