Self-trapping of vortex crystals via competing nonlinearities.

We investigate the existence of self-trapped nonlinear waves with multiple phase singularities. Working with the cubic-quintic nonlinear Schrödinger equation, we focus on configurations with an antivortex surrounded by a triangular arrangement of vortices within a hosting soliton. We find stationary patterns that can be interpreted as stable self-trapped vortex crystals, constituting the first example of a configuration of this sort with space-independent potentials. Their stability is linked to their norm, transitioning from unstable to stable as their size increases, with an intermediate region where the structure is marginally unstable, undergoing a remarkable and puzzling self-reconstruction during its evolution.

Polygons of quantized vortices in Bose-Einstein condensates with a circular trap.

We consider a disk-shaped cold atom Bose-Einstein condensate with repulsive atom-atom interactions within a circular trap, described by a two-dimensional time-dependent Gross-Pitaevskii equation with cubic nonlinearity and a circular box potential. In this setup, we discuss the existence of a type of stationary nonlinear waves with propagation-invariant density profiles, consisting of vortices located at the vertices of a regular polygon with or without an antivortex at its center. These polygons rotate around the center of the system and we provide approximate expressions for their angular velocity. For any size of the trap, we find a unique regular polygon solution that is static and is seemingly stable for long evolutions. It consists of a triangle of vortices with unit charge placed around a singly charged antivortex, with the size of the triangle fixed by the cancellation of competing effects on its rotation. There exist other geometries with discrete rotational symmetry that yield static solutions, even if they turn out to be unstable. By numerically integrating in real time the Gross-Pitaevskii equation, we compute the evolution of the vortex structures and discuss their stability and the fate of the instabilities that can unravel the regular polygon configurations. Such instabilities can be driven by the instability of the vortices themselves, by vortex-antivortex annihilation or by the eventual breaking of the symmetry due to the motion of the vortices.

Cityscape LoRa Signal Propagation Predicted and Tested Using Real-World Building-Data Based O-FDTD Simulations and Experimental Characterization.

The age of the Internet of Things (IoT) and smart cities calls for low-power wireless communication networks, for which the Long-Range (LoRa) is a rising star. Efficient network engineering requires the accurate prediction of the Received Signal Strength Indicator (RSSI) spatial distribution. However, the most commonly used models either lack the physical accurateness, resolution, or versatility for cityscape real-world building distribution-based RSSI predictions. For this purpose, we apply the 2D electric field wave-propagation Oscillator Finite-Difference Time-Domain (O-FDTD) method, using the complex dielectric permittivity to model reflection and absorption effects by concrete walls and the receiver sensitivity as the threshold to obtain a simulated coverage area in a 600 × 600 m2 square. Further, we report a simple and low-cost method to experimentally determine the signal coverage area based on mapping communication response-time delays. The simulations show a strong building influence on the RSSI, compared against the Free-Space Path (FSPL) model. We obtain a spatial overlap of 84% between the O-FDTD simulated and experimental signal coverage maps. Our proof-of-concept approach is thoroughly discussed compared to previous works, outlining error sources and possible future improvements. O-FDTD is demonstrated to be most promising for both indoors and outdoors applications and presents a powerful tool for IoT and smart city planners.

Vortex revivals and Fermi-Pasta-Ulam-Tsingou recurrence.

We study the self-trapped vortex-ring eigenstates of the two-dimensional Schrödinger equation with focusing Poisson and cubic nonlinearities. For each value of the topological charge l, there is a family of solutions depending on a parameter that can be understood as the relative importance of the cubic term. We analyze the perturbative stability of the solutions and simulate the fate of the unstable ones. For l=1 and l=2, there is an interval of the family of eigenstates for which the initial profile breaks apart but subsequently reconstructs itself, a process that can be interpreted as a nontrivial nonlinear oscillation between the vortex and an azimuthon. This revival provides a compelling realization of a recurrence of the Fermi-Pasta-Ulam-Tsingou type. Outside this interval, the vortices can be stable (for small cubic terms) or unstable and nonrecurrent (for large cubic terms). We argue that there is a crossover between these regimes that resembles a strong stochasticity threshold. For l≥3, all solutions are unstable and nonrecurrent. Finally, we comment on the possible experimental implementation of this phenomenon in the context of nonlinear laser beam propagation in thermo-optical media.

Dynamics of vortex-antivortex pairs and rarefaction pulses in liquid light.

We present a numerical study of the cubic-quintic nonlinear Schrödinger equation in two transverse dimensions, relevant for the propagation of light in certain exotic media. A well-known feature of the model is the existence of flat-top bright solitons of fixed intensity, whose dynamics resembles the physics of a liquid. They support traveling wave solutions, consisting of rarefaction pulses and vortex-antivortex pairs. In this work, we demonstrate how the vortex-antivortex pairs can be generated in bright soliton collisions displaying destructive interference followed by a snake instability. We then discuss the collisional dynamics of the dark excitations for different initial conditions. We describe a number of distinct phenomena including vortex exchange modes, quasielastic flyby scattering, solitonlike crossing, fully inelastic collisions, and rarefaction pulse merging.

Drag force in bimodal cubic-quintic nonlinear Schrödinger equation.

We consider a system of two cubic-quintic nonlinear Schrödinger equations in two dimensions, coupled by repulsive cubic terms. We analyze situations in which a probe lump of one of the modes is surrounded by a fluid of the other one and analyze their interaction. We find a realization of D'Alembert's paradox for small velocities and nontrivial drag forces for larger ones. We present numerical analysis including the search of static and traveling form-preserving solutions along with simulations of the dynamical evolution in some representative examples.

Coherent cavitation in the liquid of light.

We study the cubic- (focusing-)quintic (defocusing) nonlinear Schrödinger equation in two transverse dimensions. We discuss a family of stationary traveling waves, including rarefaction pulses and vortex-antivortex pairs, in a background of critical amplitude. We show that these rarefaction pulses can be generated inside a flattop soliton when a smaller bright soliton collides with it. The fate of the evolution strongly depends on the relative phase of the solitons. Among several possibilities, we find that the dark pulse can reemerge as a bright soliton.

Fermionic light in common optical media.

Recent experiments have proved that the response to short laser pulses of common optical media, such as air or oxygen, can be described by focusing Kerr and higher order nonlinearities of alternating signs. Such media support the propagation of steady solitary waves. We argue by both numerical and analytical computations that the low-power fundamental bright solitons satisfy an equation of state which is similar to that of a degenerate gas of fermions at zero temperature. Considering, in particular, the propagation in both O2 and air, we also find that the high-power solutions behave like droplets of ordinary liquids. We then show how a grid of the fermionic light bubbles can be generated and forced to merge in a liquid droplet. This leads us to propose a set of experiments aimed at the production of both the fermionic and liquid phases of light, and at the demonstration of the transition from the former to the latter.

Pressure, surface tension, and dripping of self-trapped laser beams.

We show that a laser beam which propagates through an optical medium with Kerr (focusing) and higher order (defocusing) nonlinearities displays pressure and surface-tension properties yielding capillarity and dripping effects totally analogous to usual liquid droplets. The system is reinterpreted in terms of a thermodynamic grand potential, allowing for the computation of the pressure and surface tension beyond the usual hydrodynamical approach based on Madelung transformation and the analogy with the Euler equation. We then show both analytically and numerically that the stationary soliton states of such a light system satisfy the Young-Laplace equation and that the dynamical evolution through a capillary is described by the same law that governs the growth of droplets in an ordinary liquid system.

Supersolitons: solitonic excitations in atomic soliton chains.

We show that, by tuning interactions in nonintegrable vector nonlinear Schrödinger equations modeling Bose-Einstein condensates and other relevant physical systems, it is possible to achieve a regime of elastic particlelike collisions between solitons. This would allow one to construct a Newton's cradle with solitons and supersolitons: localized collective excitations in solitary-wave chains.

Nonlinear phase shift from photon-photon scattering in vacuum.

We show that QED nonlinear effects imply a phase correction to the linear evolution of electromagnetic waves in vacuum. We provide explicit solutions of the modified Maxwell equations for the propagation of a superposition of two plane waves and calculate analytically and numerically the corresponding phase shift. This provides a new framework for the search of all-optical signatures of photon-photon scattering in vacuum. In particular, we propose an experiment for measuring the phase shift in projected high-power laser facilities.

Dynamics of vector solitons and vortices in two-dimensional photonic lattices.

We study discrete vector solitons and vortices in two-dimensional photonic lattices with Kerr nonlinearity and demonstrate novel types of stable, incoherently coupled dipoles and vortex-soliton complexes that can be excited by Gaussian beams. We also discuss what we believe to be novel scenarios of the charge-flipping instability of incoherently coupled discrete vortices.

Turning light into a liquid via atomic coherence.

We study a four-level atomic system with electromagnetically induced transparency with giant chi(3) and chi(5) susceptibilities of opposite signs. This system will allow us to obtain multidimensional solitons and light condensates with surface tension properties analogous to those of usual liquids.

n-body dynamics of stabilized vector solitons.

In this work we study the interactions between stabilized Townes solitons. By means of effective Lagrangian methods, we have found that the interactions between these solitons are governed by central forces, in a first approximation. In our numerical simulations we describe different types of orbits, deflections, trapping, and soliton splitting. Splitting phenomena are also described by finite-dimensional reduced models. All these effects could be used for potential applications of stabilized solitons.

Controllable soliton emission from a Bose-Einstein condensate.

We demonstrate, through numerical simulations, the controllable emission of matter-wave bursts from a Bose-Einstein condensate in a shallow optical dipole trap. The process is triggered by spatial variations of the scattering length along the trapping axis. In our approach, the outcoupling mechanisms are atom-atom interactions and thus, the trap remains unaltered. Once emitted, the matter wave forms a robust soliton. We calculate analytically the parameters for the experimental implementation of these matter-wave bursts of solitons.

Stabilized vortices in layered Kerr media.

In this paper, we demonstrate the possibility of stabilizing beams with angular momentum propagating in Kerr media against filamentation and collapse. Very long propagation distances can be achieved by combining the choice of an appropriate layered medium with alternating focusing and defocusing nonlinearities with the presence of an incoherent guiding beam which is itself stabilized in this medium. The applicability of the results to the field of matter waves is also discussed.

Superfluidlike motion of vortices in light condensates.

We demonstrate, through numerical simulations, the generation of stable vortex lattices in light condensates. This can be achieved by propagating several concentric laser beams with nested vortices of different topological charges in an optical material with a cubic-quintic nonlinearity. We have considered several initial conditions, and in all the cases the net topological charges of the resulting lattice is equal to the topological charge of the initial outer vortex. The lattice exhibits rotation similar to vortex motion in superfluids. These vortex arrays could be used to implement all-optical photonic crystal fibers. Our results also apply to Bose-Einstein condensates in the presence of three-body elastic interactions.

Collisional dynamics of vortices in light condensates.

Through numerical simulation, we have studied the nucleation and annihilation of two-dimensional optical vortex solitons hosted in finite size light beams. Our study covers a wide range of angular momentum l> or =1, also referred to as its topological charge. We demonstrate that surface tension of light beams prevents beam filamentation for a certain range of total reflection angles even if the hosted hole splits and decays into several vortices with lower values of l. We also discuss a mechanism for vortex nucleation starting from Gaussian beams that can be used for experimental purposes. Our work adds extra support to the idea that light beams in cubic-quintic nonlinear materials can undergo a phase transition from a photon gas to a liquid of light.

Stabilized two-dimensional vector solitons.

In this Letter, we introduce the concept of stabilized vector solitons as nonlinear waves constructed by the addition of mutually incoherent fractions of Townes solitons that are stabilized under the effect of a periodic modulation of the nonlinearity. We analyze the stability of these new kinds of structures and describe their behavior and formation in Manakov-like interactions. Potential applications of our results in Bose-Einstein condensation and nonlinear optics are also discussed.

Square vortex solitons with a large angular momentum.

We show the existence of square-shaped optical vortices with a large value of the angular momentum hosted in finite-size laser beams which propagate in nonlinear media with a cubic-quintic nonlinearity. The light profiles take the form of rings with sharp boundaries and variable sizes depending on the power carried. Our stability analysis shows that these light distributions remain stable when they propagate, probably for unlimited values of the angular momentum, provided the hosting beam is wide enough. This happens if the peak amplitude approaches a critical value which only depends on the nonlinear refractive index of the material. A variational approach allows us to calculate the main parameters involved. Our results add extra support to the concept of surface tension of light beams that can be considered as a trace of the existence of a liquid of light.