We introduce novel classes of higher-order spatial optical solitons in analogy with Laguerre-Gaussian and Hermite-Gaussian linear eigenmodes. We reveal that stable higher-order optical solitons can exist in nonlocal nonlinear media in the various forms of soliton necklaces and soliton matrices. Modulational instability can lead to nontrivial transformations between energetically close solitons with different symmetries through the intermediate states resembling generalized Hermite-Laguerre-Gaussian modes.

We reveal that orbital angular momentum can suppress catastrophic self-focusing in nonlinear Kerr media supporting stable spiraling solitons with an elliptic cross section. We discuss the necessary requirements for observation of this effect with coherent optical and matter waves.

We demonstrate the existence of a broad class of higher-order rotating spatial solitons in nonlocal nonlinear media. We employ the generalized Hermite-Laguerre-Gaussian ansatz for constructing multivortex soliton solutions and study numerically their dynamics and stability. We discuss in detail the tripole soliton carrying two spiraling phase dislocations, or self-trapped optical vortices.

No abstract

We study quasi-periodic transformations between nonlocal spatial solitons of different symmetries triggered by modulational instability and resembling a self-induced mode converter. Transformation dynamics of solitons with zero angular momentum, e.g. the quadrupole-type soliton, reveal the equidistant spectrum of spatial field oscillations typical for the breather-type solutions. In contrast, the transformations of nonlocal solitons carrying orbital angular momentum, such as 2x3 soliton matrix, are accompanied by their spiralling and corresponding spectra of field oscillations show mixing of three characteristic spatial frequencies.

We demonstrate the formation of an ultrabroad supercontinuum (SC) generated in short lengths of highly nonlinear tellurite photonic crystal fibers (PCFs) specifically designed for high power picosecond pumping at the thulium wavelength 1930 nm. The fibers exhibit high losses caused by material absorption below ∼500 nm and at long wavelengths >4000 nm by both material and confinement loss. The fibers are endlessly single-mode with a relative hole size of 0.4 and we tune the pitch (Λ) from 3 to 7 μm to achieve zero-dispersion wavelengths both below and above the pump. We show how the SC has a maximum width at an optimum fiber length after which the bandwidth and power decay due to losses. We thus obtain a maximum bandwidth of 4.6 μm for the PCF with the smallest Λ, i.e., 3 μm at an optimum length of only ∼2.8 cm.

We describe theory and simulations of a spinning optical soliton whose propagation spontaneously excites knotted and linked optical vortices. The nonlinear phase of the self-trapped light beam breaks the wave front into a sequence of optical vortex loops around the soliton, which, through the soliton's orbital angular momentum and spatial twist, tangle on propagation to form links and knots. We anticipate similar spontaneous knot topology to be a universal feature of waves whose phase front is twisted and nonlinearly modulated, including superfluids and trapped matter waves.

We study theoretically the propagation of higher-order two-dimensional spatial solitons in optical media with nonlocal thermal nonlinear response. We show that these localized states experience complex dynamics including transformations between solitons of different symmetries which depend strongly on the geometry of a nonlinear sample. Boundaries exert repulsive forces on a soliton and, depending on its initial position relative to the boundaries, we observe transverse motion of a beam as a whole across the sample, effectively facilitating transformations.