# 2021

Phase transitions in a quasi-one-dimensional system of interacting spinless electrons were determined and it was established that, for certain system parameters, the less probable ordering of the unit cell with period 3 has a lower ground state energy than ordering with period 2. Graphs of the dependences of the energy of the system on the asymmetry of the external potential of various parameters of the problem are plotted (the interaction potential, jumping over, distance between channels, number of nodes in a channel). **Rokhmanova** **T****.****N****., ****Ovcharenko** **G****.****V****.**

Analytical expressions for the thermal Coulomb resistance in a system of two quantum wires containing one-dimensional electronic crystals were obtained, and their dependences on the parameters of the system were analyzed. In particular, characteristic temperatures that determine the shape of the temperature dependence of the Coulomb resistance were revealed. **Apostolov** **S****.****S****., ****Mazanov** **M****.****V**.

An original method has been developed for the theoretical description of the propagation of surface electromagnetic waves and for calculating the leakage (radiation) field arising from scattering by random impedance inhomogeneities. Using the developed method, the directional diagram of the leakage field was calculated and it was shown that, in the model of a nondisipative metal, the incident plasmon-polariton is completely reflected from the disturbed surface area in the opposite direction, regardless of the presence of conditions for anderson localization on it. **Tarasov** **Yu****.****V****., ****Kadygrob** **D****.****V****., ****Kvitka** **N****.****M****.**

The influence of the random component on the properties of p-polarized inhomogeneous electromagnetic waves, which propagate along the layers in a randomly modulated dielectric and are localized in the perpendicular direction, is established. It is shown that for inhomogeneous waves with fixed values of frequency and wave number, a random inhomogeneity leads to a weakening of localization. For Plasmon-polaritons, Anderson’s localization changes the dispersion law, as a result of which the depth of localization changes in different ways, depending on which of the parameters, frequency or wavenumber, is fixed. **Ak. NAS of Ukraine V.M. Yakovenko, Corresponding Member NAS of Ukraine Yampolskiy V.A., Maizelis Z.A.**

# 2020

In the study of symbolic and numerical random sequences within the framework of a high-order additive Markov chain, a connection between correlation functions and conditional entropies of sequences was established. An expression for the entropy was obtained using two-point probability distribution functions, and then, for a numerical random chain, the entropy was estimated in terms of the correlation function. The conditional entropy of the additive Markov chain was also derived as the sum of mutual Kullbeck-Leibler informations. **O****.****V****. ****Usatenko****, ****S****.****S****. ****Melnik****, ****G****.****M****. ****Pritula**

A new method for calculating the natural frequencies of non-uniformly filled spherical resonators has been developed. The spectrum was determined by introducing effective “dynamic” potentials encoding the filling inhomogeneity. Angularly symmetric cavities, cavities with violation of polar symmetry, and cavities with no angular symmetry have been investigated. The method is quite effective for computational complex algorithms for solving various spectral problems, including for studying the chaotic properties of the spectra of systems. **Z****.****E****. ****Eremenko****, ****Yu****.****V****. ****Tarasov****, ****I****.****M****. ****Volovichev**

Stationary stochastic processes in systems with nonlocal memory are studied and new solutions of the Mori-Zwanzig equation describing non-Markov systems are obtained. The dynamics of the system is analyzed depending on the amplitudes of local and nonlocal memory, and attention is drawn to the transition boundary between asymptotically stationary and non-stationary behavior of the process. It is shown that there are two types of boundaries with fundamentally different dynamics of the system. Diffusion processes with memory occur at the boundaries of the first type, while the phenomenon of stochastic resonance occurs at the boundaries of the second type. **S.S. Melnik, O.V. Usatenko, Corresponding Member NAS of Ukraine Yampolskiy V.A.**

# 2019

Localized waves propagating along a plate of finite thickness, which is made of a layered superconductor with layers perpendicular to the surface of the plate, are theoretically investigated. Due to the strong anisotropy of a layered superconductor, the electromagnetic field of a mode is a superposition of ordinary and unusual waves, which in the general case cannot be separated from each other. The dispersion law is obtained for an arbitrary direction of propagation of such localized modes relative to the layers. It is shown that dispersion curves can be both monotonic and non-monotonically growing, that is, contain areas with anomalous dispersion. Frequencies are determined depending on the angle of propagation at which anomalous dispersion can be observed. The dependence of the frequency on both the modulus of the longitudinal wave vector and its projections is analyzed, which can be important for practical use in electronics in the terahertz range. **Apostolov S.S., Maizelis Z.A., Shimkiv D.V., Shmatko A.A., Corresponding Member NAS of Ukraine Yampolskiy V.A.**

The properties of magnetotransport in two-dimensional electron double layers filled with a strongly correlated electron liquid are studied. For sufficiently pure samples and at a sufficiently high temperature, transport in these systems can be described using a hydrodynamic model. The main attention is focused on the influence of a constant magnetic field on the longitudinal interlayer resistance, which arises due to Coulomb scattering, and the identification of several transport mechanisms caused by the viscosity of an electron liquid, magnetoplasmonic resonance, and dissipative heat fluxes. In particular, it was established how the Hall viscosity falls into the Coulomb resistance and affects its temperature dependence in a magnetic field. **Apostolov S.S., Levchenko A., Pesin D.**

Electron transport in one-dimensional quantum systems and the formation of zig-zag ordering in quantum wires at a certain electron density are studied theoretically. The Hartree-Fock method was used to optimize the program and simulate a sufficiently large system with long-range interaction. Phase transitions in such quasi-two-dimensional quantum systems are investigated and a comparison is made with the classical regime. **Rokhmanova T.N.**

For the first time, a new method has been developed for calculating the eigenfrequencies of a spherical resonator with inhomogeneous dielectric filling in terms of only two unrelated Helmholtz equations for scalar Hertz functions, in which the spatial inhomogeneity of the system can be described in terms of effective potentials. The method was used to obtain and study the spectrum of symmetric and asymmetric layered spherical resonators. It is shown that even without the presence of absorption, when an inhomogeneity arises in the filling, its resonance lines noticeably broaden, which indicates the presence of wave chaos. **Eremenko** **Z****.****E****., ****Tarasov** **Yu****.****V****., ****Volovichev** **I****.****N****.**

A mathematical model has been built and software has been created for numerical simulation of the formation of photo- and thermo-EMF in thin-film semiconductor structures under the influence of periodic external disturbances, taking into account the role of near-contact space charge layers. **Volovichev I.N.**

Non-Markov random continuous processes described by the Mori-Zwanzig equation are studied. As a starting point, we use the Ornstein-Uhlenbeck Markov process and introduce into the expression for the higher-order transition probability function and to the stochastic differential equation an integral memory term, which depends on the past process. An equation is obtained connecting the memory function (the kernel of the integral term) and the two-point correlation function. The conditions for the stationarity of the process are established. A method for generating stationary continuous stochastic processes with a given pair correlation function is proposed. As an illustration, several examples of numerical modeling of processes with non-local memory are given. **Melnik S.S., Usatenko O.V., Corresponding Member NAS of Ukraine Yampolskiy V.A.**

A family of explicit solutions of equations describing the nonlinear classical vector model with anisotropic Heisenberg interaction on a triangular lattice is obtained. It is shown that there are a number of nonlinear structures due to the relationship between the interaction anisotropy and the specific geometry of the lattice. The method, which was developed to obtain a solution to this problem, expands the field of application of the approaches of the theory of solitons in the case of lattices that differ from rectangular, which makes it possible to investigate the possibility of the formation of specific nonlinear structures (solitons, kinks, etc.) **Vekslerchik V.E.**

The correlation properties of random sequences with an additive linear conditional probability distribution function have been studied and a reliable tool for generating sequences has been created. The state space of the sequence under investigation is considered to belong to a finite set of real numbers. The conditional probability distribution function is assumed to be additive and linear with respect to the values of the random variable. In the paper, equations are derived that connect the correlation functions with the coefficients of the memory function, which in turn are determined by the conditional probability function of the N-th order Markov sequence. The obtained analytical solutions of these equations are compared with the results of numerical simulation. Examples of possible correlation scenarios in additive linear high-order Markov chains are given. **Vekslerchik V.E., Pritula G.M., Melnik S.S., Usatenko O.V.**

# 2018

Nonlinear localized electromagnetic modes in a plate of a layered superconductor are studied theoretically. It is assumed that the plate is in a uniform dielectric environment, the superconducting layers are perpendicular to the plate surface, and the modes propagate across the layers. It is found that, despite the symmetry of the system, both symmetric and antisymmetric localized modes can exist in the plate, which is associated with the nonlinearity of the Josephson plasma. It is shown that under certain conditions the dispersion of localized modes can turn out to be anomalous, and the group velocity can vanish. Due to nonlinearity, dispersion relations contain the amplitude of localized modes, which opens up the possibility of observing the phenomenon of stopping light of localized modes in a layered superconductor plate. **Apostolov S.S., Kadigrob D.V., Maizelis Z.A., Nikolaenko O.O., Corresponding Member NAS of Ukraine Yampolskiy V.A.**

The reflection of electromagnetic radiation from the surface of a neutron star is theoretically investigated. Such radiation arises due to relativistic positrons flying from the magnetosphere to the star in the electric field of the polar gap. This study explained both the displacement of the interpulse in the Crab pulsar (specular reflection in the presence of an oblique magnetic field) and the appearance of additional high-frequency components (diffraction by the periodic structure created by incident radiation), revealed by Moffett and Hankins. Since high-frequency components arise at the same frequencies at which the interpulse shift is observed, they are considered to be a consequence of the same physical process. This process is the reflection from the surface of a neutron star of the radiation of reverse positrons. The appearance of high-frequency components is considered as a manifestation of stimulated scattering by surface waves. For comparison, the data of laboratory experiments on the diffraction of laser radiation by a metal diffraction grating are presented, demonstrating the appearance of a near-surface wave under resonance conditions, which can serve as an analogue of the high-frequency component in the Crab pulsar. In the formation of high-frequency components, phenomena such as Wood’s anomalies are important, which lead to a significant increase in the stimulated scattering growth rate at resonance with a surface electromagnetic wave. **Gavrikov V.K., Kontorovich V.M., Spevak I.S.**

# 2017

The spectral properties of linear and weakly nonlinear terahertz localized modes in a plate of a layered superconductor are studied theoretically. It is assumed that the plate is in a uniform dielectric environment, the superconducting layers are perpendicular to the surface of the plate, and the modes of transverse magnetic polarization propagate across the layers. Dispersion relations are obtained for modes symmetric and antisymmetric with respect to the magnetic field. It is shown that in a certain range of frequencies and wavenumbers the dispersion of such modes turns out to be anomalous and the group velocity can vanish. This opens up the possibility of observing such unusual physical phenomena as “negative refraction” and “stopping light” for localized modes in layered superconductors. **Gavrilenko V.I., Apostolov S.S., Maizelis Z.A., Corresponding Member NAS of Ukraine Yampolskiy V.A.**

The transmission of a terahertz electromagnetic wave of transverse magnetic polarization through a one-dimensional photonic crystal of finite thickness containing a defect in the form of a plate of a layered superconductor, the superconducting layers of which are orthogonal to the layers of the photonic crystal, is theoretically investigated. An analytical expression for the transmission coefficient is obtained and it is shown that the transparency in the band gap of a photonic crystal can be significantly enhanced due to the resonant excitation of modes localized at the defect. **Apostolov S.S., Makarov N.M., Corresponding Member NAS of Ukraine Yampolskiy V.A.**

The theory of the dynamic thermoelectric effect is developed. The influence of boundary conditions is investigated both for a simplified analytical mathematical model of the effect and for numerical modeling of a physically realistic model. A method has been found for determining the optimal parameters of a semiconductor at which the investigated effect is most pronounced. The optimal spatial period and speed of movement of the temperature distribution have been established, which provide in this structure the greatest value of the generated thermoelectric EMF and the greatest electrical power that can be transferred to the load. It is proved that, in contrast to the classical thermoelectric effect, in the dynamic mode, the presence of minority carriers with a lower Seebeck coefficient does not reduce the value of the thermoelectric emf, but can significantly increase it. The conditions for the generation of EMF in a monopolar multi-valley semiconductor due to inter-valley transitions are established, analytical expressions for the value of the EMF are obtained, and the previously obtained results are confirmed by numerical simulation. **Volovichev I.N.**

# 2016

The reflection of waves of transverse electric and transverse magnetic polarizations from the surface of a semi-infinite layered superconductor in the presence of an external constant magnetic field is studied theoretically. The superconducting layers are assumed to be perpendicular to the sample. Due to the strong anisotropy of the limits of the superconductor of the irradiated, the transformation of the polarization of the wave occurs during its reflection. It is shown that, although a constant magnetic field penetrates into the sample to a relatively shallow depth, it qualitatively affects the distribution of the electromagnetic wave field and, for this reason, the reflection and transformation coefficients. Thus, an external magnetic field can serve as a convenient tool for controlling the transformation of wave polarization. Analytical expressions for the reflection and transformation coefficients are obtained, and the parameters are determined at which the most effective transformation of transverse electric waves into transverse magnetic waves and vice versa occurs. **Apostolov S.S., Maizelis Z.A., Rokhmanova T.N., Corresponding Member NAS of Ukraine Yampolskiy V.A.**

A new nonlinear electrodynamic phenomenon arising in a plate of a layered superconductor upon its one-sided irradiation by a plane electromagnetic wave of the terahertz range is predicted and theoretically investigated. It is shown that the surface reactance of the sample and the reflection coefficient of the wave behave in a hysteresis manner when the amplitude of the incident wave changes. An analogy between the electrodynamic problem of the distribution of the electromagnetic field in a superconductor and the problem of the mechanical motion of a particle in a central field is discussed. **Apostolov S.S., Bozhko A.A., Maizelis Z.A., Sorokina M.A., Corresponding Member NAS of Ukraine Yampolskiy V.A.**

The amplitude-phase dynamics of an ensemble of globally coupled oscillators with a Van der Pol type of nonlinearity is studied analytically in the self-consistent field approximation. The main result of the work is the exact analytical solution of nonlinear equations for the order parameters obtained as a result of the orthogonal reduction procedure, which distinguishes the class of integrable equations. A complete classification of modes and bifurcations has been carried out. An exact expression for the invariant manifold (in particular, the limit cycle) is obtained and analytical solutions are found for arbitrary initial conditions and various modes of the dynamics of order parameters. The results of this work can be important for the development of beamforming mechanisms in active phased antennas, as well as for the construction of nonlinear antennas. **G. M. Pritula, V. I. Pritula, O. V. Usatenko **

The influence of nonequilibrium current carriers on transport processes in semiconductors was theoretically investigated, which made it possible to predict a number of new effects. The possibility of the appearance of an EMF in a semiconductor with a uniform concentration of current carriers due to the inhomogeneity of their mobility (including self-induced by light), as well as when the electron gas is heated by incident radiation with photon energy, is shown, which is insufficient for the appearance of traditional photoeffects. The revealed regularities can be important in the design of photoconverters and sensors based on polycrystalline and porous semiconductors when optimizing the grain size and the degree of doping. **Volovichev I.N.**

# 2015

The transmission of terahertz electromagnetic waves through plates of layered superconductors in the presence of an external constant magnetic field is studied theoretically. It is shown that an external magnetic field actually transforms Josephson plasmas into an inhomogeneous medium with a spatially and frequency dependent dielectric constant. Even a relatively weak magnetic field has a significant effect on the transparency of a layered superconductor. Moreover, with the help of a magnetic field, it is possible to achieve almost complete transmission of terahertz waves through a superconductor. It is shown that the magnetic field significantly changes the dependence of the transmission coefficient on the plate thickness, frequency and angle of incidence of the wave. Thus, it has been proved that the magnetic field can be used as a convenient tool for controlling the transparency of layered superconductors. **Apostolov S.S., Maizelis Z.A., Makarov N.M., Perez Rodriguez F., Rokhmanova T.N., Corresponding Member. ****NAS of Ukraine Yampolskiy V.A.**

Surface electromagnetic states (SEMS) in the terahertz frequency range in graphene with a linear dispersion law of current carriers, placed in an antiferromagnetic photonic crystal, have been studied theoretically. A relationship has been obtained linking the frequency of the PEMS with the parameters of the structure. The problem of excitation of PEMS by an external electromagnetic wave is solved and the dependence of the transmission coefficient on the external magnetic field and the concentration of current carriers is found. It is found that the analysis of the position of the maxima of the transmission coefficient is associated with the resonant excitation of the PEMS, which makes it possible to establish the character of the dispersion law of current carriers in a two-dimensional electron gas. **Averkov Yu.O., Tarapov S.I., Yakovenko V.M., Corresponding Member NAS of Ukraine Yampolskiy V.A.**

The scattering of surface and bulk electromagnetic waves by statistical inhomogeneities of metal surfaces is studied under conditions of strong and weak fluctuations of the surface impedance. The wave scattering indicatrix is calculated, expressed in terms of the correlation function of the surface impedance and the size of the fluctuation region of the surface. **Yu.V. Tarasov, O.V. Usatenko**

The diffraction anomaly is investigated – the quasi-resonant enhancement of the energy flux during the diffraction of a plane monochromatic electromagnetic wave, which is carried away from the surface of the periodic metal / dielectric interface, in the diffraction order that corresponds to propagation at a certain grazing angle. The quasi-resonant dependence of the energy flux on the angle of incidence and wavelength is calculated. The energy that is carried away by this creeping wave can make up a significant fraction of the incident wave energy; therefore, the specified quasi-resonant amplification is accompanied by a corresponding decrease in the energy of the specularly reflected wave. The calculations were performed on the basis of a previously developed analytical approach, which gives accurate results for fairly shallow and shallow gratings (surface profiles). It is proved that the value of the found maximum of the energy flux monotonically increases with increasing lattice depth. **Kats A.V., Kuzmenko A.O., Spєvak I.S.**

# 2014

The principle of superposition is established for nonlinear Josephson plasma waves in layered superconductors, which is very unusual for nonlinear media. The reflection and transmission of terahertz waves through a superconducting plate of finite dimensions, which is placed in a rectangular waveguide, is considered theoretically. It is assumed that the superconducting layers are parallel to the waveguide axis. It is shown that there are waves with two mutually orthogonal polarizations, which, in spite of the nonlinearity, are reflected and pass through the superconductor independently of each other. The wave of the first polarization induces a strong screening current along the crystallographic plane ab, and therefore it is almost completely reflected. The wave of the second polarization does not contain the component of the electric field, which is parallel to the surface of the sample and the plane ab. This non-linear wave does not induce strong screening currents, it is partially reflected and partially passes through the sample. Based on the open principle of superposition, we have proposed a new general method for solving nonlinear problems of the propagation of Josephson plasma waves. **Rokhmanova T.N., Apostolov S.S., Maizelis Z.A., Yampolsky V.A. and Nori F.**

Transition radiation of bulk and surface Josephson plasma waves by an electron crossing the isotropic dielectric-layered superconductor interface is studied theoretically. A geometry is considered in which the direction of motion of the electron and the orientation of the superconducting layers are perpendicular to the interface between the media. It is shown that, in contrast to the case of isotropic media, due to the very strong anisotropy of the properties of a layered superconductor, Cherenkov radiation is clearly distinguished against the background of transition radiation. **Averkov Yu.O., Yakovenko V.M., Yampolsky V.A. and Nori F.**

The coexistence of TM- and TE-polarized localized electromagnetic waves, which can propagate along a graphene layer placed in a dielectric photonic crystal, is predicted. The excitation of these modes by an external wave is studied theoretically and it is shown that, regardless of the polarization of the external wave, due to the excitation of localized modes, resonance peaks of the transparency coefficient should be observed as a function of the angle of incidence and frequency. The simplicity of the obtained dispersion equations for localized modes and the possibility of exciting modes of both polarizations provide a new method for measuring the conductivity of graphene. **Averkov Yu.O., Yakovenko V.M., Yampolsky V.A. and Nori F.**

# 2013

Oblique surface waves (CSWs), which propagate along the interface between a dielectric and a layered superconductor, have been studied theoretically. A geometry is considered in which the superconductor layers are located perpendicular to the interface and waves can propagate at an arbitrary angle to them. A dispersion equation for the CPV is obtained and it is shown that the dispersion curves have end points, where the evanescent extraordinary modes turn into bulk modes. The problem of resonant excitation of CPV is analytically solved by the method of disturbed total internal reflection using an additional dielectric prism. It is shown that, owing to the very strong current anisotropy of the superconductor surface, the excitation of CPV is accompanied by an additional significant phenomenon: a component with orthogonal polarization appears in the wave reflected from the bottom of the prism. It is shown that for certain values of the parameters of the problem, a complete transformation of the polarization of terahertz electromagnetic waves occurs upon reflection from a highly anisotropic surface of a layered superconductor. **Yakovenko V.M., Yampolsky V.A. and Averkov Yu.O.**

The effect of a significant suppression of the transmission coefficient of teracertz radiation through a periodically modulated plate of a layered superconductor, which is caused by diffraction of the incident wave and resonant excitation of eigenmodes, has been predicted and theoretically investigated. It is assumed that the thickness of the plate is much less than the depth of the skin layer, and in the absence of modulation, the transparency of the plate is close to unity. **Yampolsky** **V****.****A****. ****and** **Kadygrob** **D****.****V****.**

The temperature dependence of the high-frequency dynamic susceptibility χ (T) = χ ′ (T) + iχ ″ (T) of YBCO ribbons of the second generation in a parallel magnetic field in both the Meissner and vortex states has been studied theoretically and experimentally. In the vortex state, two maxima were found in the χ ″ (T) dependence. The position and magnitude of one of these maxima are satisfactorily described by the nonlocal critical state model. The second maximum and the corresponding kink in the function χ ‘(T), which are observed at temperatures close to the transition temperature of the superconductor, turned out to be unexpected. The nature of this maximum cannot be explained within the framework of the conventional theory of superconductivity, including all versions of the theory of high-temperature superconductivity. There is reason to believe that the appearance of a new maximum is associated with the structural magnetic rearrangement in the superconducting layer. **Yampolsky V.A., Fisher L.M. and Voloshin I.F.**

The results of experimental and theoretical studies of the suppression of specular reflection during diffraction of terahertz radiation of an HCN laser by an InSb grating under conditions of plasmon-polariton resonance are presented. The dependence of the position of the resonance and its width on the depth of the grating grooves is investigated. It is shown that a dielectric film deposited on the grating surface increases the width of the resonance and shifts its maximum relative to the Rayleigh point. Theoretical estimates based on the resonance theory of diffraction are in good agreement with experimental data, which makes it possible to investigate the influence of the parameters of the problem on the characteristics of the resonance. **Kats A.V., Spevak I.S. and Timchenko M.A.**

It is shown that one-dimensional electrons with a linearized dispersion law are equivalent to a set of harmonic plasma modes, which are long-wavelength oscillations of the electron density. In the Luttinger model, the absence of inelastic scattering processes responsible for the relaxation of nonequilibrium states is a direct consequence of linearization. In a nonlinear Luttinger fluid, plasmons can decay and thus acquire a finite lifetime. It is shown in the work that the establishment of the equilibrium of plasmons has a significant effect on the dynamics of the liquid after thermal quenching. The theory of thermal transport is developed and the thermal conductance of a nonlinear Luttinger fluid is calculated using the integral of collisions of plasmons. **S****. ****S****. ****Apostolov** **and** **Z****. ****A****. ****Maizelis**

Linear antennas are studied in which the intensities of the dipole radiators and the distances between them are random values. The intensity of the interference radiation field is expressed through the correlation functions of random variables. A method for constructing two random sequences with given binary correlation and autocorrelation functions has been developed. This made it possible to solve the inverse problem of synthesizing random antennas with a given directional pattern. **Melnik S.S., Pritula G.M. and Usatenko O.V.**

A new nonlinear electromagnetic phenomenon in a sample of a layered superconductor of finite dimensions located in a waveguide with ideal walls has been predicted and studied theoretically. Two geometries are considered, when the superconductor layers are located either parallel or perpendicular to the waveguide axis. It is shown that the coefficient of transmission of a nonlinear wave through a superconductor plate can vary over a very wide range, from almost zero to almost unity, depending on the amplitude of the incident wave. Thus, it is possible to achieve complete transparency or complete opacity of the sample by changing the amplitude of the wave. In addition, the dependence of the wave transmission coefficient on the amplitude turned out to be hysteresis with jumps. **Rokhmanova T.N., Apostolov S.S., Maizelis Z.A., Yampolsky V.A. and Nori F.**

Resonant diffraction of electromagnetic waves on the surface of metals and semiconductors with periodic modulation of surface impedance under conditions of excitation of surface electromagnetic waves (SEW) is considered. It is shown that the nonresonant conversion coefficients, except for the specular one, are in any case much less than unity, while the resonant ones turn out to be of the order of or much more than unity. It is proved that the specular reflection coefficient can significantly decrease near resonance and even vanish. For typical periodic structures, the dependence of the conversion coefficients on the angle of incidence is investigated, and the parameters of the periodic structures are indicated at which a maximum of the SEW amplitude is observed and, accordingly, a significant suppression of specular reflection occurs. It is shown that the specular reflection coefficient has a nonmonotonic dependence both on the angle of incidence and on the modulus of the resonant Fourier amplitude of the surface impedance. The conditions for the complete suppression of specular reflection are found and it is shown that they can differ significantly from the conditions for the maximum of the resonant conversion coefficient. The results obtained are important for preparing an experimental study of resonant diffraction with SEW excitation. **Kats A.V., Spevak I.S. and Timchenko M.A.**

# 2012

A complete transformation of the polarization of terahertz electromagnetic waves is predicted upon reflection from a highly anisotropic surface of a layered superconductor. The case is considered when the superconducting layers are perpendicular to the sample surface, and the wave is incident on the superconductor from a dielectric prism, which is separated from the superconductor by a thin vacuum gap. The physical reason for the predicted phenomenon is associated with the resonant excitation of oblique surface waves, it is similar to the Woods reflection coefficient anomaly known in optics. We also analyzed the dispersion equation for oblique surface Josephson plasma waves propagating at a certain angle to the superconducting layers and their excitation by the method of disturbed total internal reflection. **Yakovenko V.M., Yampolsky V.A., Averkov Yu.O. and Nori F.**

Enhanced transparency of a modulated layer of a layered superconductor for terahertz radiation is predicted under conditions when the thickness of the plate is much greater than the depth of the skin layer. The plate becomes transparent due to the diffraction of the incident wave and the resonant excitation of its own electromagnetic waves. The electromagnetic field is transferred from the irradiated side of the sample to the opposite excited waveguide mode, which does not attenuate into the depth of the plate, in contrast to the case of a normal metal, where increased transparency is provided by resonant excitation of inhomogeneous surface waves. **Yampolsky V.A., Kadygrob D.V., Slipchenko T.M., Makarov N.M. and Perez-Rodriguez F.**

The interaction of densely focused polarized light with a slot on a metal surface, which supports plasmon-polariton electromagnetic modes, is studied theoretically. It is shown that this simple system can be very sensitive to the polarization of light and therefore be the perfect instrument for weak quantum measurements**. ****Blioh** **K****. ****Yu****.**

The reflection and transmission of electromagnetic waves in the terahertz range, which propagate in a waveguide through a sample of a layered superconductor of a finite length, are theoretically investigated. Excitation of two types of Josephson plasma waves, ordinary and extraordinary, in the sample leads to a partial or complete transformation of the polarization of the incident wave. The conditions under which a complete transformation of polarization is possible are determined. **Yakovenko V., Yampolsky V., Apostolov S. S., Rokhmanova T. N. and Khankina S. I.**

# 2011

A theoretical study is made of natural electromagnetic oscillations in layered superconductors of finite dimensions, which fill a rectangular resonator. The spectra of both ordinary and extraordinary modes were obtained. The nonlinear effect of lowering the natural frequencies of extraordinary modes is analyzed, and the generation of the third harmonic of the oscillations is also studied. The nonlinearity of the system is associated with the nonlinear relationship between the Josephson current density across the superconducting layers and the interlayer gauge invariant phase difference of the order parameter. A study was made of Josephson plasma waves traveling along a waveguide filled with a layered superconductor and nonlinear effects that arise during the propagation of these waves. In addition, we predicted the effect of stopping terahertz waves in waveguides associated with the joint action of nonlinearity and wave attenuation. **Khankina** **S****., ****Yakovenko** **V****. ****and** **Yampolsky** **V****.****A****.**

The nonlinear response of laminated superconductor plates to unilateral electromagnetic excitation in the terahertz frequency range is studied theoretically. It is shown that the surface reactance of the plate has a hysteresis dependence with jumps on the amplitude of the exciting wave. Interestingly, this unusual nonlinear phenomenon can be observed even at low wave amplitudes, if the frequency is close to the Josephson plasma frequency**. ****Apostolov** **S****.****S****. ****and** **Yampolsky** **V****.****A****.**

In cooperation with scientists from the RI NASU and Jilin University, Changchun, China, the features of the interaction of radiation with interfaces between media, which support the propagation of surface plasmon polaritons, were investigated. In particular, the problem of determining the parameters of periodic structures (gratings) that provide a predetermined energy distribution between reflected waves of different diffraction orders is considered. An approximate analytical solution is obtained for the case of strong plasmon-polariton resonances. Direct numerical calculations confirm the very high accuracy of the solution found, which makes it possible to significantly simplify the development of unique lattices. In addition, the possibility of observing resonance effects in the terahertz frequency range is theoretically analyzed and it is found that strong resonance effects can be observed on periodically modulated surfaces of semiconductor materials. The results of the performed theoretical analysis were confirmed by direct experiments on the surface of indium antimonide using a terahertz laser. **Kats A.V., Spevak I.S. and Timchenko M.A.**

The propagation of pulses (solitons) in nonlinear media with nonlinear Kerr type is studied. Mathematically, this problem is formulated as an analysis of integrable equations such as the nonlinear Schrödinger equation. One of these equations is the recently proposed Lenels-Fokas model. An infinite set of symmetries for this model is found, and solutions of the type of dark solitons are obtained. Another problem that has been solved is related to dispersion effects, which are of great importance for the formation and propagation of so-called nonlinear Alfvén waves. These waves are described by the so-called derivative nonlinear Schrödinger equation. This equation was compared with the standard nonlinear Schrödinger equation, Bäcklund transformations were obtained, which make it possible to obtain a solution to one equation, knowing the solution to another. It was found that both models are closely related and that they can be viewed as separate cases of a more general system. It was shown that this general system can be integrated by a method recently proposed by the authors. This method is based on splitting the original equations into several equations of lower order and reducing them to already known integrable models such as the discrete nonlinear Schrödinger equation. Various nonlocal effects can be found among the effects that play an important role in the formation and propagation of solitons. This predetermines the importance of studying nonlocal modifications of the nonlinear Schrödinger equation. A number of such models were analyzed and cases were found when they can be reduced to already known local models, probably of a higher order, such as, for example, the sinusoidal Gordon equation and the Landau-Lifshitz model. **Vekslerchik** **V****.****E****.**

The propagation of symmetric and antisymmetric Josephson plasma waves in a plate of a layered superconductor located between two identical dielectrics is studied. The existence of two branches of surface waves in the terahertz frequency range is predicted, one above and the other below the Josephson plasma frequency. In addition, there is a discrete series of waveguide modes, the electromagnetic fields of which oscillate across the plate and exponentially decay in external dielectrics. The excitation of the predicted waves using the method of disturbed total internal reflection is also studied theoretically. It is shown that with a special set of structure parameters, the excitation of waveguide modes is accompanied by a total suppression of specular reflection of waves. **Slipchenko T.M., Yampolsky V.A. and Krokhin A.**

# 2010

The existence of a new branch of surface Josephson plasma waves in layered superconductors, located at frequencies higher than the frequency of the Josephson plasma resonance, is predicted. In this frequency range, the components of the dielectric constant tensor along and across the superconducting layers have different signs, which usually leads to negative refraction of electromagnetic waves. It was found, however, that negative refraction can be observed only in a narrow frequency gap of the spectrum of surface waves. Thus, a peculiar principle of complementarity between negative refraction and the existence of surface waves in layered superconductors has been revealed. A theory is also proposed for the excitation of high-frequency surface Josephson plasma waves by the method of disturbed total internal reflection in a dielectric prism. **Yampolsky V.A., Kadygrob D.V., Ivanov B.A. and Nori F.**

The nonlinear response of a layered superconductor to electromagnetic radiation symmetric in the magnetic field is investigated theoretically. An ambiguous dependence of the phase of the reflected signal on the amplitude of the irradiating wave is predicted. This ambiguity is the reason for the appearance of hysteresis jumps in the amplitude dependence of the surface reactance of the superconductor. If the frequency of the wave is close to the Josephson plasma frequency, then this unusual nonlinear effect can be observed at not very strong amplitudes of the ac field. The conditions for the occurrence of hysteresis are obtained. The expression for the phase shift of the reflected wave is derived using the coupled sinusoidal Gordon equations. In addition, the class of coordinate-discontinuous solutions of these equations is studied, which correspond to the continuous spatial distribution of the magnetic field in the superconductor. Such solutions lead to the appearance of additional branches of the dependence of the phase shift of the reflected wave on the amplitude of the incident wave. **Yampolsky V.A., Maizelis Z.A. and Apostolov S.S.**

The excitation of nonlinear surface Josephson plasma waves in plates of layered superconductors is studied theoretically using the method of disturbed total internal reflection of light in a dielectric prism. The case of two-sided magnetic field symmetric irradiation is considered. Excitation of surface waves leads to resonant suppression of specular reflection of waves (so-called Woods anomalies). Due to the nonlinearity, the specular reflection coefficient resonantly depends not only on the frequency and angle of incidence of the irradiation, but also on the wave amplitude. **Yampolsky V.A., Maizelis Z.A. and Apostolov S.S.**

A new nonlinear electromagnetic phenomenon is predicted in a layered superconductor plate irradiated from one of its sides by an external wave in the terahertz frequency range. It is shown that the coefficients of reflection and transmission of a wave through a plate can vary over a very wide range, practically from zero to unity (if we neglect weak absorption), with a change in the amplitude of the wave that irradiates the plate. The reason for this phenomenon is related to the fact that nonlinearity effectively reduces the frequency of the Josephson plasma resonance in such a way that at high amplitudes the wave has the opportunity for propagation (instead of damping due to the skin effect, which is observed at low amplitudes). In addition, it was found that the dependence of the coefficients of reflection and transmission of the wave through the plate on the amplitude of the incident wave have an unusual hysteresis dependence with jumps. **Yampolsky V.A., Maizelis Z.A. and Apostolov S.S.**

Together with scientists from FTINT NASU, the absorption spectrum of electromagnetic radiation in the range of 40-200 GHz at temperatures of 1.4-2.75 K in superfluid helium has been studied. It was found that a narrow resonant absorption line near the roton frequency actually exists against the background of a wide pedestal. The results obtained are compared with the roton spectrum known from neutron scattering data. A theoretical model is proposed that explains the possible reason for the appearance of a narrow resonant absorption peak, by analogy with the Mössbauer effect. The importance of the results obtained is predetermined by the great interest of scientists around the world in the recently revealed unexpected electromagnetic properties of superfluid helium. **Usatenko O., Tarapov S. and Derkach V.**

Strongly anisotropic nonlinear two-dimensional and three-dimensional gratings are studied. The results obtained in the framework of the theory of integrable one-dimensional systems are extended to the multidimensional case. Mathematically, this problem is formulated as an analysis of connected integrable systems of the Toda type. The theory of such systems has not yet been developed. A method for solving some of these systems is proposed. This method is based on splitting the original equations into several equations of lower order and reducing them to already known integrable models such as the discrete nonlinear Schrödinger equation. This method was applied to two models. First, a two-dimensional anisotropic Fermi-Pasta-Ulam lattice was studied in the long-wave approximation, which is mathematically described by the coupled Korteweg-de Vries equations. Another model is a model of three-dimensional ferromagnets with graphite-like lattices: in each layer it can be described by the Landau-Lifshitz model, while the interaction between different layers is approximated by a nonlinear Heisenberg-type coupling. A wide range of solutions were obtained for both models, such as solitons and quasiperiodic waves. **Vekslerchik** **V****.****E****. ****and** **Pritula** **G****.****M****.**

# 2009

The resonant excitation of terahertz surface Josephson plasma waves in layered superconductors is studied theoretically. The excitation mechanism is associated with the diffraction of the incident wave due to periodic modulations of the Josephson current density. It is shown that the excitation of surface Josephson plasma waves is accompanied by a resonant decrease in the specular reflection coefficient of the wave. The conditions for the complete suppression of the reflection coefficient are revealed. **Yampolsky V.A., Kats A.V., Nesterov M.L., Nikitin A. Yu., Slipchenko T.M. and Nori F.**

A method for the synthesis of diffraction gratings with predetermined optical properties is proposed. This was done by obtaining an analytical solution to the diffraction problem by the method of resonance perturbation theory. The parameters of the gratings are determined, which provide a given distribution of energy fluxes over different diffraction orders. **Kats** **A****.****V****. ****and** **Spevak** **I****.****S****.**

# 2008

An unusual nonmonotonic temperature dependence of the Casimir attraction force of thin metal films is predicted within the framework of the Drude dispersion model. This force can decrease with increasing temperature due to a decrease in the conductivity of the metal, but at high temperatures this force increases due to an increase in the pressure of thermal radiation. Experimental observation of the predicted non-monotonic temperature dependence of the Casimir force may put an end to a long discussion about the role of electron relaxation in the Casimir effect. **Yampolsky V.A., Apostolov S.S., Maizelis Z.A., Saveliev S. and Nori F.**

The transmission and reflection of electromagnetic radiation in the optical and infrared ranges of the spectrum when it is incident on metal films with a thinner skin-layer depth is studied theoretically. It was found that almost one hundred percent transmission of radiation can change to almost complete non-transmission in the presence of spatial periodic modulation of the electromagnetic properties of the film. This nontrivial result is a consequence of the resonant excitation of the film’s eigenmodes, the so-called plasmon polaritons. **Kats** **A****. ****V****., ****Spevak** **I****. ****S****., ****Nikitin** **A****. ****Yu****.**

# 2007

Unusual (for nonrelativistic quantum mechanics) electronic states in graphenes localized inside high potential barriers of finite width are predicted. The density of localized electronic states has a number of singularities at certain energies. These singularities provide quantum oscillations of the transport and thermodynamic properties of graphene with a change in the height or width of the potential barrier. The predicted oscillations are similar to the quantum oscillations of Shubnikov-de-Haas, but in this case they occur when the electric field, rather than the magnetic field, changes. **Yampolsky** **V****.****A****., ****Saveliev** **S****. ****and** **Nori** **F****.**

A new method is proposed for constructing diffraction gratings with the desired properties, based on their comparison with multistep Markov chains. **Usatenko O.V., Melnik S.S., Apostolov S.S., Maizelis Z.A., Makarov N.M. and Yampolsky V.A.**

# 2006

A new approach is proposed for the theoretical description of random one-dimensional discrete systems with long-range correlations, based on their comparison with multistep Markov chains. On the basis of this model, for the first time, non-extensive thermodynamics of ising chains with long-range inter-spin interaction was constructed. In addition, a convenient method is proposed for constructing a random binary potential in one-dimensional systems with an arbitrary correlation function, which provides the desired metal-insulator transition. **Usatenko O.V., Melnik S.S., Apostolov S.S., Maizelis Z.A. and Yampolsky V.A.**

The properties of surface electromagnetic waves propagating along the interface between media with different ratios between the signs of the dielectric and magnetic permeability are studied. Conditions are found under which the properties of surface waves are similar to those of bulk waves in left-handed media; in other words, the waves at the “left-handed interfaces between the media” were studied. A number of phenomena are predicted that accompany the propagation of such unusual surface waves (negative refraction, anomalous Doppler effect, transition radiation). The investigated waves can be observed in the optical, near-infrared and terahertz ranges of the spectrum. **Kats A.V., Yampolsky V.A., Saveliev S. and Nori F.**

Anomalies in the diffraction spectra of refracted and reflected electromagnetic waves from the surface of a periodically modulated layered superconductor are studied theoretically. The dependences of the reflection and transmission coefficients on the parameters of the problem are analyzed, and the conditions for the complete suppression of specular reflection of terahertz waves are revealed**. Kats A.V., Nesterov M.L., Nikitin A. Yu., Slipchenko T.M. and Yampolsky V.A.**

# 2005

The existence of surface Josephson plasma waves in layered superconductors is predicted. The excitation of these waves leads to resonant Woods anomalies in the angular dependence of the reflection coefficient of terahertz radiation. **Yampolsky** **V****.****A****., ****Saveliev** **S****. ****and** **Nori** **F****.**

An approach has been developed for calculating the optical properties of artificial media – two-dimensional photonic crystals. With the help of the constructed theory, the dependence of the coefficients of reflection and transmission of electromagnetic waves through periodically modulated metal films on frequency, parameters of the periodic structure, angle of incidence and polarization of radiation in the optical and infrared ranges of the spectrum is found. The optimal parameters of the structure are found and simple explanations are given of experiments on the observation of anomalous transparency of thick metal films, based on an analytical study of the resonant excitation of eigenmodes in such structures **A. V. Kats, A. Yu. ****Nikitin****, ****and** **M****. ****L****. ****Nesterov****.**