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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 studied numerically the frequency spectrum of photons in a multilayered microsphere coated by a quasiperiodic (Pascal) dielectric stack. It is found that the transmittancy spectrum of such a stack consists of quasiband gaps and narrow resonances caused by re-relection of optical waves. When the number (Pascal order) of layers increases, the band gaps and resonances split, and the structure of the frequency spectrum acquires a fractal form. Some parts of the spectrum show the self-similarity in the diferent frequency scales. [ABSTRACT FROM AUTHOR]

The paper is devoted to the applications of the time-frequency integrals and the two-dimensional stationary phase method for the problems of waves propagation from moving sources in acoustic dispersive media. Applying the stationary phase method we obtain the effective formula for the acoustic fields in the dispersive media generated by non-uniformly moving modulated source. [ABSTRACT FROM AUTHOR]

We numerically studied the spectrum of Cherenkov optical radiation by a nonrelativistic anisotropic electron bunch crossing 3D dispersive metamaterial. A practically important case when such a medium is described by Drude model is investigated in details. In our theory only parameters of a metamaterial are fixed. The frequency spectrum of internal excitations is left to be defined as a result of the numerical simulation. It is found that a periodic field structure coupled to plasmonic excitations is arisen when the dispersive refractive index of a metamaterial becomes negative. In this case the reversed Cherenkov radiation is observed. [ABSTRACT FROM AUTHOR]

Abstract: We investigated optical transparency in ceramics assisted by disordered porous clusters. The structure and statistical properties of three-dimensional (3D) well porous ceramics is studied. Theoretical model based on the percolation theory and numerical simulations are applied to interpret the observed phase transition from an optically opaque state to a transparent state. The porous ceramic samples were fabricated by the technique of slurry casting. The transmission of optical radiation (optical percolation) over the entire porous samples is observed since the critical concentration of porosity was exceeded. We explain this effect by the rising of the spanning cluster inside of the porous structure that produces a network of porous voids. Our experimental results are in good agreement with the numerical simulations. [Copyright &y& Elsevier]

Abstract: We study transmission of the electromagnetic waves of the near infrared spectral range through the metal–semiconductor spherical stack with a radial dependence of the effective dielectric permittivity of semiconductor layers. Such an inhomogeneity is formed by a high concentration of carriers at the interfaces of thin semiconductor–metal structures and its spatial scale can be of order of a width of narrow metallic layers. Because of complexity of analytical solution, we develop numerical approaches, which allow us to study the features of the electromagnetic wave propagation through such a nonuniform structure. The eigenfrequencies and radial distributions of fields are also discussed. [Copyright &y& Elsevier]

We have studied the effect of external pumping on the dynamics of the entanglement of two two-level atoms interacting with a cavity mode. It is shown that a sequence of well detuned pulses of the classical field leads to the dynamical formation of an extended plateau-like zone of high level atomic entanglement with the duration much longer than the period of Rabi oscillations. The dissipation reduces the amplitude of the entanglement, however practically does not change the width of such zones. [ABSTRACT FROM AUTHOR]

We have numerically studied the transmittance of the metallo-dielectric spherical structure deposited on a microsphere in a frequency range where the dielectric permittivity of metal is negative. We have found an equidistant spectrum of the resonant peaks of almost completely transmittency. The position of the peaks is defined by the thickness of the dielectric layer, and the width of peaks sharply decreases with increases thickness of the metallic layer. We have explored the radial distribution of the electromagnetic field in such a stack and the spectrum of the eigenfrequencies. The amplitude of the field in the dielectric layers may exceed on 1 to 2 orders of magnitude the value of a field in the output of the structure. Such an effect opens the opportunity to use the microspheres coating by metallo-dielectric multilayers for an effective surface harmonic generation in the optical range and for a high-resolution frequency conversion in the bands of such resonances. [Copyright &y& Elsevier]

A nonlinear mechanism of the transformation of low-frequency seismic waves into ultra-low frequency atmospheric acoustic waves is discussed. The spectrum of the seismic waves caused by the earthquake is wide but only ultra-low frequency acoustic waves reach the ionosphere. This process can be amplified due to the nonlinear interaction of low frequency waves and their transformation into ultra-low frequency acoustic wave at the difference frequency. It is shown that thus the efficiency of this transformation is high. [ABSTRACT FROM AUTHOR]

We examine the waveguide properties of a spherical stack∶ a system of optical layers deposited onto the microsphere substrate, with arbitrary ratios between thicknesses of layers and a wavelength of propagating electromagnetic radiation. Frequency dependencies of the reflection coefficient and impedance of the stack are studied. An appropriate matrix formalism is developed to generalize the matrix method well-known for the plane case, into the case of the spherical layer geometry. The material losses and random deviations of thicknesses of layers are taken into account. The quarter-wave length layers are studied in details. Our numerical calculations have revealed the narrow gap of a transparency in a zone of high reflectance of a stack under the suitable parameters. The spectrum of eigenfrequencies of a spherical resonator coating by the dielectric stack has been calculated. It has been found that Q factor electromagnetic oscillations in such a system exponentially grows with increasing number of layers in the stack, but only for eigenfrequencies which are in the zone of high a stack reflection. [ABSTRACT FROM AUTHOR]

Results of experimental and theoretical investigations of dynamic phenomena, which occur under the three-wave resonant interaction of ultrasonic beams in a crystal TeO2, are presented. The interacting waves are fast longitudinal ultrasonic wave (pump, its frequency is 100–1000 MHz) and two slow co- and counter-propagating transverse ones. When the input intensity of the pump wave exceeds ∼5 times the threshold of parametric generation, a complex spatial-temporal dynamics is observed, both regular and chaotic. The resonant three-wave interaction has been simulated by means of solving coupled equations for slowly varying amplitudes of interacting waves, when a transverse inhomogeneity has been taken into account. The spatial-temporal distributions of wave amplitudes within the crystal are complex in all directions and they qualitatively describe the experimental data. [Copyright &y& Elsevier]

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.

We introduce one- and two-dimensional (1D and 2D) models of parity-time (PT)-symmetric couplers with the mutually balanced linear gain and loss applied to the two cores and cubic-quintic (CQ) nonlinearity acting in each one. The 2D and 1D models may be realized in dual-core optical wave guides in the spatiotemporal and spatial domains, respectively. Stationary solutions for PT-symmetric solitons in these systems reduce to their counterparts in the usual coupler. The most essential problem is the stability of the solitons, which become unstable against symmetry breaking with the increase of the energy (norm) and retrieve the stability at still larger energies. The boundary value of the intercore-coupling constant, above which the solitons are completely stable, is found by means of an analytical approximation, based on the cw (zero-dimensional) counterpart of the system. The approximation demonstrates good agreement with numerical findings for the 1D and 2D solitons. Numerical results for the stability limits of the 2D solitons are obtained by means of the computation of eigenvalues for small perturbations, and verified in direct simulations. Although large parts of the soliton families are unstable, the instability is quite weak. Collisions between 2D solitons in the PT-symmetric coupler are studied by means of simulations. Outcomes of the collisions are inelastic but not destructive, as they do not break the PT symmetry.

We report results of systematic numerical studies of two-dimensional matter-wave soliton families supported by an external potential, in a vicinity of the junction between stable and unstable branches of the families, where the norm of the solution attains a minimum, facilitating the creation of the soliton. The model is based on the Gross-Pitaevskii equation for the self-attractive condensate loaded into a quasiperiodic (QP) optical lattice (OL). The same model applies to spatial optical solitons in QP photonic crystals. Dynamical properties and stability of the solitons are analyzed with respect to variations of the depth and wave number of the OL. In particular, it is found that the single-peak solitons are stable or not in exact accordance with the Vakhitov-Kolokolov (VK) criterion, while double-peak solitons, which are found if the OL wave number is small enough, are always unstable against splitting.