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We apply the complex two-dimensional stationary-phase method for problems of electromagnetic waves radiation from the moving modulated sources in dispersive and lossy medium. The explicit formulas for fields generated by a moving source, the Doppler effect, and the retarded time are obtained. We apply the developed approach to numerical study of the Cherenkov radiation in a dispersive medium (Drude model). Our simulations have shown that in double negative dispersive metamaterials, the Cherenkov cone splits in two branches. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We investigate the plasmon-mediated nonlinear dynamics and the optics of a laser emission of random nanoemitters (NEs) embedded in a two-dimensional (2D) lattice of conducting nanorings (NRs) enhanced by plasmon-polariton (PP) excitations. The interaction of quantum NEs with the PP field in the NRs perturbs the dynamics of the electronic populations in NEs, leading to a significant dependence of laser generation (dynamics) on the plasma frequency ωp of PP. This results in a strong coupling of NE field emission with the PP field and sharp variations of the average current in the NR lattice. The phase transition in the system was found when the macroscopic structures of PP fields are excited simultaneously in different regions of the system if ωp (control parameter) reaches critical value ωc. We have established the analytical dependence of the PP current I = I(ωp/ωc) on the plasma frequency, which is in excellent agreement with the results of numerical simulations. This effect may allow the design of new types of PP active devices with the use of conducting NRs in modern nanoelectronics., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

We systematically study the percolation phase transition at the change of concentration of the chaotic defects (pores) in an extended system where the disordered defects additionally have a variable random radius, using the methods of a neural network (NN). Two important parameters appear in such a material: the average value and the variance of the random pore radius, which leads to significant change in the properties of the phase transition compared with conventional percolation. To train a network, we use the spatial structure of a disordered environment (feature class), and the output (label class) indicates the state of the percolation transition. We found high accuracy of the transition prediction (except the narrow threshold area) by the trained network already in the two-dimensional case. We have also employed such a technique for the extended three-dimensional (3D) percolation system. Our simulations showed the high accuracy of prediction in the percolation transition in 3D case too. The considered approach opens up interesting perspectives for using NN to identify the phase transitions in real percolating nanomaterials with a complex cluster structure.

We report results of a systematic numerical analysis of interactions between three-dimensional (3D) fundamental solitons, performed in the framework of the nonlinear Schrödinger equation (NLSE) with the cubic-quintic (CQ) nonlinearity, combining the self-focusing and defocusing terms. The 3D NLSE with the CQ terms may be realized in terms of spatiotemporal propagation of light in nonlinear optical media, and in Bose-Einstein condensates, provided that losses may be neglected. The first part of the work addresses interactions between identical fundamental solitons, with phase shift φ between them, separated by a finite distance in the free space. The outcome strongly changes with the variation of φ: in-phase solitons with φ = 0, or with sufficiently small φ, merge into a single fundamental soliton, with weak residual oscillations in it (in contrast to the merger into a strongly oscillating breather, which is exhibited by the 1D version of the same setting), while the choice of φ = π leads to fast separation between mutually repelling solitons. At intermediate values of φ, such as φ = π/2, the interaction is repulsive too, breaking the symmetry between the initially identical fundamental solitons, there appearing two solitons with different total energies (norms). The symmetry-breaking effect is qualitatively explained, similar to how it was done previously for 1D solitons. In the second part of the work, a pair of fundamental solitons trapped in a 2D potential is considered. It is demonstrated that they may form a slowly rotating robust "molecule," if initial kicks are applied to them in opposite directions, perpendicular to the line connecting their centers.

We introduce a one-dimensional model of the parity-time ( PT)-symmetric coupler, with mutually balanced linear gain and loss acting in the two cores, and nonlinearity represented by the combination of self-focusing cubic and defocusing quintic terms in each core. The system may be realized in optical waveguides, in the spatial and temporal domains alike. Stationary solutions for PT-symmetric solitons in the systems are tantamount to their counterparts in the ordinary coupler with the cubic-quintic nonlinearity, where the spontaneous symmetry breaking of solitons is accounted for by bifurcation loops. A novel problem is stability of the PT-symmetric solitons, which is affected by the competition of the PT symmetry, linear coupling, cubic self-focusing, and quintic defocusing. As a result, the solitons become unstable against symmetry breaking with the increase of the energy (alias integral power, in terms of the spatial-domain realization), and they retrieve the stability at still larger energies. Above a certain value of the strength of the quintic self-defocusing, the PT symmetry of the solitons becomes unbreakable. In the same system, PT-antisymmetric solitons are entirely unstable. We identify basic scenarios of the evolution of unstable solitons, which may lead to generation of additional ones, while stronger instability creates expanding quasi-turbulent patterns with limited amplitudes. Collisions between stable solitons are demonstrated to be quasi-elastic.