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We demonstrate a possibility of the creation of stable optical solitons combining one continuous and one discrete coordinate, with embedded vorticity, in an array of planar waveguides with intrinsic cubic-quintic nonlinearity. The same system may be realized in terms of the spatiotemporal light propagation in an array of tunnel-coupled optical fibers with the cubic-quintic nonlinearity. In contrast with zero-vorticity states, semidiscrete vortex solitons do not exist without the quintic term in the nonlinearity. Two types of the solitons, emph{viz.}, intersite- and onsite-centered ones (IC and OC, respectively), with even and odd numbers $N$ of actually excited sites in the discrete direction, are identified. We consider the modes carrying the embedded vorticity $S=1$ and $2$. In accordance with their symmetry, the vortex solitons of the OC type exhibit an intrinsic core, while the IC solitons with a small $N$ may have a coreless structure. Facilitating their creation in the experiment, the modes reported in the present work may be much more compact states than their counterparts considered in other systems, and they feature strong anisotropy. They can be set in motion in the discrete direction, provided that the coupling constant exceeds a certain minimum value. Collisions between moving vortex solitons are considered too.
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The properties of vector vortex beams in vertical-cavity-surface emitting lasers with frequency-selective feedback is investigated. They are interpreted as high-order vortex solitons with a spatially non-uniform, but locally linear polarization state. In contrast to most schemes to obtain vector vortex beams relying on imprinting the polarization structure, vector vortex solitons form spontaneously due to the near polarization degeneracy in vertical-cavity devices. We observe radially, hyperbolic and spiral polarization configurations depending on small residual anisotropies in the system and multi-stability between different states. In addition, we demonstrate flip-flop operation of laser solitons via in principle local electronic nonlinearities. Combining the two themes might open up a route for a simple device enabling fast switching between different vector vortex beams for applications. The investigations connect nicely the fields of nonlinear science, singular optics, structured light and semiconductor laser technology.
We consider a binary bosonic condensate with weak mean-field (MF) residual repulsion, loaded in an array of nearly one-dimensional traps coupled by transverse hopping. With the MF force balanced by the effectively one-dimensional attraction, induced in each trap by the Lee-Hung-Yang correction (produced by quantum fluctuations around the MF state), stable onsite-centered and intersite-centered semi-discrete quantum droplets (QDs) emerge in the array, as fundamental ones and self-trapped vortices, with winding numbers, at least, up to 5, in both tightly-bound and quasi-continuum forms. The application of a relatively strong trapping potential leads to squeezing transitions, which increase the number of sites in fundamental QDs, and eventually replace vortex modes by fundamental or dipole ones. The results provide the first realization of stable semi-discrete vortex QDs, including ones with multiple vorticity.
We report results of the investigation of gap solitons (GSs) in the generic model of a periodically modulated Bragg grating (BG), which includes periodic modulation of the BG chirp or local refractive index, and periodic variation of the local reflectivity. We demonstrate that, while the previously studied reflectivity modulation strongly destabilizes all solitons, the periodic chirp modulation, which is a novel feature, stabilizes a new family of double-peak fundamental BGs in the side bandgap at negative frequencies (gap No. -1), and keeps solitons stable in the central bandgap (No. 0). The two soliton families demonstrate bistability, coexisting at equal values of energy. In addition, stable 4-peak bound states are formed by pairs of fundamental GSs in bandgap -1. Self-trapping and mobility of the solitons are studied too.
Soliton solutions are studied for paraxial wave propagation with intensity-dependent dispersion. Although the corresponding Lagrangian density has a singularity, analytical solutions, derived by the pseudo-potential method and the corresponding phase diagram, exhibit one- and two-humped solitons with almost perfect agreement to numerical solutions. The results obtained in this work reveal a hitherto unexplored area of soliton physics associated with nonlinear corrections to wave dispersion.
We examine the evolution of a time-varying perturbation signal pumped into a mono-mode fiber in the anomalous dispersion regime. We analytically establish that the perturbation evolves into a conservative pattern of periodic pulses which structures and profiles share close similarity with the so-called soliton-crystal states recently observed in fiber media [see e.g. A. Haboucha et al., Phys. Rev. Atextbf{78}, 043806 (2008); D. Y. Tang et al., Phys. Rev. Lett. textbf{101}, 153904 (2008); F. Amrani et al., Opt. Express textbf{19}, 13134 (2011)]. We derive mathematically and generate numerically a crystal of solitons using time division multiplexing of identical pulses. We suggest that at very fast pumping rates, the pulse signals overlap and create an unstable signal that is modulated by the fiber nonlinearity to become a periodic lattice of pulse solitons which can be described by elliptic functions. We carry out a linear stability analysis of the soliton-crystal structure and establish that the correlation of centers of mass of interacting pulses broadens their internal-mode spectrum, some modes of which are mutually degenerate. While it has long been known that high-intensity periodic pulse trains in optical fibers are generated from the phenomenon of modulational instability of continuous waves, the present study provides evidence that they can also be generated via temporal multiplexing of an infinitely large number of equal-intensity single pulses to give rise to stable elliptic solitons.
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