Stable multipole solitons in defocusing saturable media with an annular trapping potential

We systematically investigate the existence, stability, and propagation dynamics of multipole-mode (necklace-shaped) solitons in the two-dimensional model of an optical medium with the defocusing saturable nonlinearity and an annular potential trough. Various families of stable multipole solitons trapped in the trough, from dipole, quadrupole, and octupole ones to multi-lobe complexes, are found. The existence domain remains invariant with the increase of the potential's depth. Solitons with a large number N of lobes are stable in a wide parameter region, up to N = 48 and even farther. Actually, stable multipole solitons of an arbitrarily high order N can be found, provided that the trough's radius is big enough. The power of stable multipoles is essentially larger in comparison to previously studied models. It is demonstrated analytically and numerically that the application of a phase torque initiates stable rotation of the multipole complexes. Thus, we put forward an effective scheme for the stabilization of multipole solitons with an arbitrary high number of lobes, including rotating ones, which offers new possibilities for manipulating complex light beams.