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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Liquid light condensates.

We show that a laser beam which propagates through a cubic-quintic nonlinear optical material may reach, for a given power, a condensed state with a collisional dynamics resembling a liquid drop. We qualitatively describe the analogies between this system and the usual fluids and show them by simulating numerically total reflections of these beams with planar boundaries and localized defects. We use the analogy "liquid light" to stress the connections with the dynamics of quantum fluids, including Bose-Einstein condensates.

Temporal modulation of spatial optical solitons.

A variational method is used to investigate temporal effects that are experimentally observed in the propagation of spatial solitons in planar systems. These effects appear when the laser beam used to reach the soliton propagation regime is pulsed. In the absence of dispersion, the three-dimensional equation of propagation, including two space and one time variable, becomes a two-dimensional spatial equation.