Abstract
We present a review of new results which suggest the existence of fully stable spinning
solitons (self-supporting localised objects with an internal vorticity) in optical fibres with selffocusing
Kerr (cubic) nonlinearity, and in bulk media featuring a combination of the cubic selfdefocusing
and quadratic nonlinearities. Their distinctive difference from other optical solitons with
an internal vorticity, which were recently studied in various optical media, theoretically and also
experimentally, is that all the spinning solitons considered thus far have been found to be unstable
against azimuthal perturbations.
In the first part of the paper, we consider solitons in a nonlinear optical fibre in a region of parameters
where the fibre carries exactly two distinct modes, viz., the fundamental one and the first-order
helical mode. From the viewpoint of application to communication systems, this opens the way
to doubling the number of channels carried by a fibre. Besides that, these solitons are objects of
fundamental interest. To fully examine their stability, it is crucially important to consider collisions
between them, and their collisions with fundamental solitons, in (ordinary or hollow) optical fibres.
We introduce a system of coupled nonlinear Schr¨ odinger equations for the fundamental and helical
modes with nonstandard values of the cross-phase-modulation coupling constants, and show, in
analytical and numerical forms, results of collisions between solitons carried by the two modes.
In the second part of the paper, we demonstrate that the interaction of the fundamental beam with
its second harmonic in bulk media, in the presence of self-defocusing Kerr nonlinearity, gives rise to
the first ever example of completely stable spatial ring-shaped solitons with intrinsic vorticity. The
stability is demonstrated both by direct simulations and by analysis of linearized equations.