Semidiscrete composite solitons in arrays of quadratically nonlinear waveguides

Discrete and Semi-Discrete Multidimensional Solitons and Vortices: Established Results and Novel Findings

This article presents a concise survey of basic discrete and semi-discrete nonlinear models, which produce two- and three-dimensional (2D and 3D) solitons, and a summary of the main theoretical and experimental results obtained for such solitons. The models are based on the discrete nonlinear Schrödinger (DNLS) equations and their generalizations, such as a system of discrete Gross-Pitaevskii (GP) equations with the Lee-Huang-Yang corrections, the 2D Salerno model (SM), DNLS equations with long-range dipole-dipole and quadrupole-quadrupole interactions, a system of coupled discrete equations for the second-harmonic generation with the quadratic (χ(2)) nonlinearity, a 2D DNLS equation with a superlattice modulation opening mini-gaps, a discretized NLS equation with rotation, a DNLS coupler and its PT-symmetric version, a system of DNLS equations for the spin-orbit-coupled (SOC) binary Bose-Einstein condensate, and others. The article presents a review of the basic species of multidimensional discrete modes, including fundamental (zero-vorticity) and vortex solitons, their bound states, gap solitons populating mini-gaps, symmetric and asymmetric solitons in the conservative and PT-symmetric couplers, cuspons in the 2D SM, discrete SOC solitons of the semi-vortex and mixed-mode types, 3D discrete skyrmions, and some others.

Semidiscrete Quantum Droplets and Vortices

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 on-site- and intersite-centered semidiscrete quantum droplets (QDs) emerge in the array, as fundamental ones and self-trapped vortices, with winding numbers, at least, up to five, in both tightly bound and quasicontinuum 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 semidiscrete vortex QDs, including ones with multiple vorticity.

Efficient C-band single-photon upconversion with chip-scale Ti-indiffused pp-LiNbO3 waveguides

Frequency upconversion for single photons at telecom wavelengths is important to simultaneously meet the different wavelength requirements for long-distance communications and quantum memories in a quantum nodal network. It also enables the detection for the telecom "flying qubit" photons with silicon-based efficient single-photon detectors with low dark count (DC) rates. Here, we demonstrate the frequency upconversion of attenuated single photons, using a low-loss titanium-indiffused periodically poled lithium niobate waveguide, pumped with a readily available erbium-doped fiber amplifier in the L-band. Internal and conversion efficiencies up to 84.4% and 49.9% have been achieved, respectively. The DC rates are suppressed down to 44 kHz at 13.9% end-to-end quantum efficiency (including full conversion and detection), enabled by our long-wavelength pump configuration and narrow 3.5-GHz bandpass filtering.

Nonlinearity-induced localization in a periodically driven semidiscrete system

We demonstrate that nonlinearity plays a constructive role in supporting the robustness of dynamical localization in a system which is discrete in one dimension and continuous in the orthogonal one. In the linear regime, time-periodic modulation of the gradient strength along the discrete axis leads to the usual rapid spread of an initially confined wave packet. Addition of the cubic nonlinearity makes the dynamics drastically different, inducing robust localization of moving wave packets. Similar nonlinearity-induced effects are also produced in the presence of a combination of static and oscillating linear potentials. The predicted dynamical localization in the nonlinear medium can be realized in photonic lattices and Bose-Einstein condensates.

Emulation of lossless exciton-polariton condensates by dual-core optical waveguides: stability, collective modes, and dark solitons

We propose a possibility to simulate the exciton-polariton (EP) system in the lossless limit, which is not currently available in semiconductor microcavities, by means of a simple optical dual-core waveguide, with one core carrying the nonlinearity and operating close to the zero-group-velocity-dispersion point, and the other core being linear and dispersive. Both two-dimensional (2D) and one-dimensional (1D) EP systems may be emulated by means of this optical setting. In the framework of this system, we find that, while the uniform state corresponding to the lower branch of the nonlinear dispersion relation is stable against small perturbations, the upper branch is always subject to the modulational instability. The stability and instability are verified by direct simulations too. We analyze collective excitations on top of the stable lower-branch state, which include a Bogoliubov-like gapless mode and a gapped one. Analytical results are obtained for the corresponding sound velocity and energy gap. The effect of a uniform phase gradient (superflow) on the stability is considered too, with a conclusion that the lower-branch state becomes unstable above a critical wave number of the flux. Finally, we demonstrate that the stable 1D state may carry robust dark solitons.

Subwavelength plasmonic lattice solitons in arrays of metallic nanowires

We predict theoretically that stable subwavelength plasmonic lattice solitons (PLSs) are formed in arrays of metallic nanowires embedded in a nonlinear medium. The tight confinement of the guiding modes of the metallic nanowires, combined with the strong nonlinearity induced by the enhanced field at the metal surface, provide the main physical mechanisms for balancing the wave diffraction and the formation of PLSs. As the conditions required for the formation of PLSs are satisfied in a variety of plasmonic systems, we expect these nonlinear modes to have important applications to subwavelength nanophotonics. In particular, we show that the subwavelength PLSs can be used to optically manipulate with nanometer accuracy the power flow in ultracompact photonic systems.

Spatiotemporal dissipative solitons in two-dimensional photonic lattices

We analyze spatiotemporal dissipative solitons in two-dimensional photonic lattices in the presence of gain and loss. In the framework of the continuous-discrete cubic-quintic Ginzburg-Landau model, we demonstrate the existence of novel classes of two-dimensional spatiotemporal dissipative lattice solitons, which also include surface solitons located in the corners or at the edges of the truncated two-dimensional photonic lattice. We find the domains of existence and stability of such spatiotemporal dissipative solitons in the relevant parameter space, for both on-site and intersite lattice solitons. We show that the on-site solitons are stable in the whole domain of their existence, whereas most of the intersite solitons are unstable. We describe the scenarios of the instability-induced dynamics of dissipative solitons in two-dimensional lattices.

Stable discrete surface light bullets

We analyze spatiotemporal light localization near the edge of a semi-infinite array of weakly coupled nonlinear optical waveguides and demonstrate the existence of a novel class of continuous-discrete spatiotemporal solitons, the so-called discrete surface light bullets. We show that their properties are strongly affected by the presence of the surface. To this end the crossover between surface and quasi-bulk bullets is studied by analyzing the families of solitons propagating at different distances from the edge of the waveguide array.