arXiv subjects

Yu. V. Tarasov

Publications and source records attributed to Yu. V. Tarasov.

At least 19 recordsLinked to original sources

arXiv2023

The effect of Anderson localization on surface plasmon polariton propagation and outward leakage when scattered by a randomly corrugated section of the interface

The practical applications of surface plasmon polaritons (SPPs) require the deep understanding of the impact of electrical characteristics variability and geometrical irregularity of the metal-dielectric interface. Traditional methods in the theory of wave scattering at rough interfaces fail to treat simultaneously the interference (Anderson) localization of the SPP, which may arise due to its multiple back-scattering by random distortions of surface relief, and the leakage into the uniform dielectric half-space. In our previous works [Low Temp. Phys. \textbf{42}, 685 (2016); Ann.~Phys.~\textbf{455}, 169378 (2023)], by representing the perturbation of surface impedance as an effective potential in the Schrödinger-like equation, we suggested the way to describe the interplay between Anderson localization and the leakage of the SPP. In the present study we show that the problem of SPP scattering from finite geometrically rough region of the interface can be reduced to the problem of its scattering from the same region but with effective random impedance. We calculate the radiation pattern and demonstrate its pronounced anisotropy that arises due to the interplay between different geometrical parameters of the interface roughness.

physics.optics↗

arXiv2023

he plasmon-polariton scattering by random-impedance surface defects: The interplay between localization and outflow

We study the scattering of surface TM-polarized plasmon-polariton waves (PPWs) by the finite red region of plane metal-vacuum boundary with randomly inhomogeneous impedance. We analyze the solution of the integral equation connecting the scattered field with the field of the oncoming PPWs, that is valid for any strength of the scattering and dissipative properties of the conducting half-space. As a measure of scattering strength, the Hilbert norm of the intermode scattering operator is used. It is shown that the intensity of the scattering is not only determined by the parameters of the random impedance (the variance, correlation radius, the length of the heterogenious region), but it also crucially depends on the metal substrate conductivity. For a small norm of the integral operator, the incident surface plasmon polariton (SPP) radiates effectively into vacuum, loosing the part of its energy for excitation of quasi-isotropic Norton-type waves above the conducting surface. The intensity of the leaking field is expressed in terms of the pair correlation function of the impedance, the dependence of which on wave numbers of incident and scattered waves demonstrates the possibility to observe a phenomenon similar to Wood's anomalies of wave scattering by periodic lattices. With strong scattering, when the norm of the scattering operator becomes large as compared to unity, the radiation into the volume is highly suppressed and the PPW is basically mirrored from the heterogeneous surface area in backward direction. In the model of dissipationless conducting halfspace, the surface plasmon-polariton becomes unstable for arbitrarily small fluctuations of the conductor polarizability. The mirroring also takes place at small norm of the scattering operator, yet in this case it is related to Anderson's localization of the SPP within the disordered region.

physics.optics↗

arXiv2020

A method of effective potentials for calculating the frequency spectrum of eccentrically layered spherical cavity resonators

A novel method for the calculation of eigenfrequencies of non-uniformly filled spherical cavity resonators is developed. The impact of the system symmetry on the electromagnetic field distribution as well as on its degrees of freedom (the set of resonant modes) is examined. It is shown that in the case of angularly symmetric cavity, regardless of its radial non-uniformity, the set of resonator modes is, as anticipated, a superposition of TE and TM oscillations which can be described in terms of a single scalar function independently of each other. The spectrum is basically determined through the introduction of effective ``dynamic'' potentials which encode the infill inhomogeneity. The violation of polar symmetry in the infill dielectric properties, the azimuthal symmetry being simultaneously preserved, suppresses all azimuthally non-uniform modes of electric-type (TM) oscillations. In the absence of angular symmetry of both electric and magnetic properties of the resonator infill, only azimuthally uniform distribution of both TM and TE fields is expected to occur in the resonator. The comparison is made of the results obtained through the proposed method and of the test problem solution obtained with use of commercial solvers. The method appears to be efficient for computational complex algorithms for solving spectral problems, including those for studying the chaotic properties of electrodynamic systems' spectra.

cond-mat.dis-nn↗

arXiv2018

The spectrum of non-centrosymmetrically layered spherical cavity resonator. I.The mode decomposition method

We develop a theoretical method for solving Maxwell's equations to obtain the frequency spectra of inhomogeneous and asymmetric cavity resonators using a couple of effective Debye-type potentials. The structure we study specifically is the layered spherical cavity resonator with symmetrically or asymmetrically inserted inner dielectric sphere. The comparison of the exact numerical results obtained for the frequency spectrum of layered cavity resonator with centrosymmetrically inserted sphere and the spectrum found from the suggested theory reveals good agreement at the initial part of the frequency axis. The coincidence accuracy depends on the number of trial resonant modes that we use while approving our method numerically.

physics.comp-ph↗

arXiv2018

The plasmon-polariton mirroring due to strong fluctuations of the surface impedance

Scattering of TM-polarized surface plasmon-polariton waves (PPW) by a finite segment of the metal-vacuum interface with randomly fluctuating surface impedance is examined. Solution of the integral equation relating the scattered field with the field of the incident PPW, valid for arbitrary scattering intensity and arbitrary dissipative characteristics of the conductive medium, is analyzed. As a measure of the PPW scattering, the Hilbert norm of the integral scattering operator is used. The strength of the scattering is shown to be determined not only by the parameters of the fluctuating impedance (dispersion, correlation radius and the length of the inhomogeneity region) but also by the conductivity of the metal. If the scattering operator norm is small, the PPW is mainly scattered into the vacuum, thus losing its energy through the excitation of quasi-isotropic bulk Norton-type waves above the conducting surface. The intensity of the scattered field is expressed in terms of the random impedance pair correlation function, whose dependence on the incident and scattered wavenumbers shows that in the case of random-impedance-induced scattering of PPW it is possible to observe the effect analogous to Wood's anomalies of wave scattering on periodic gratings. Under strong scattering, when the scattering operator norm becomes large compared to unity, the radiation into free space is strongly suppressed, and, in the limit, the incoming PPW is almost perfectly back-reflected from the inhomogeneous part of the interface. This suggests that within the model of a dissipation-free conducting medium, the surface polariton is unstable against arbitrary small fluctuations of the medium polarizability. Transition from quasi-isotropic weak scattering to nealy back-reflection under strong fluctuations of the impedance is interpreted in terms of Anderson localization.

cond-mat.dis-nn↗

arXiv2015

Dual nature of localization in guiding systems with randomly corrugated boundaries: Anderson-type versus entropic

A unified theory for the conductance of a long multimode quantum wire whose finite segment has randomly rough boundaries is developed. It enables one to take account of all mechanisms of wave scattering, both related to boundary roughness and to contacts between the wire rough section and the leads within the same technical frameworks. The rough part of the conducting wire is shown to act as a mode-specific randomly modulated effective potential barrier whose height is governed essentially by the asperity slope. The mean height of the barrier specifies the number of conducting channels. Under relatively small asperity amplitude this number can take on arbitrary small values if the asperities are sufficiently sharp. The channel cut-off that arises when the asperity sharpness increases can be regarded as a kind of localization, which is not related to the disorder but rather is of entropic origin. The fluctuating part of the barrier results in two fundamentally different types of guided wave scattering, viz., inter- and intramode scattering. The intermode scattering is shown to be for the most part very strong except in the cases of (a) extremely smooth asperities, (b) excessively small length of the corrugated segment, and (c) the asperities sharp enough for only one conducting channel to remain in the wire. Under strong intermode scattering, a new set of conducting channels develops, which have the form of decoupled extended modes subject to individual random potentials. In view of this fact, two transport regimes only are realizable in randomly corrugated multimode wires, specifically, the ballistic and the localized regime, the latter characteristic of one-dimensional random systems. Two kinds of localization are thus shown to coexist in waveguide-like systems with randomly corrugated boundaries, specifically, the entropic localization and the one-dimensional Anderson localization.

cond-mat.dis-nn↗

arXiv2013

The mechanism of quantum chaos manifestations in the spectra of singularly perturbed wave-billiard systems

The spectra of a microwave cylindrical resonator with the embedded thin metal rod playing the role of a singular perturbation are studied both theoretically and experimentally. The intra- and inter-mode scattering caused by the perturbation are clearly distinguished and recognized to play essentially different parts in the appearance of spectrum chaotic properties. The analysis based on the mode-mixing operator norm shows that the inter-mode scattering dominates over the intra-mode scattering and basically determines statistical properties of the resonator spectrum. The results we have obtained in the experiment are in good conformity with our theory. Clear manifestations of quantum chaos are revealed for the resonator with the asymmetrically inserted rod, namely, the Wigner-type distribution of the inter-frequency intervals, the apparent correlation between spectral lines, and the characteristic curve of the spectral rigidity. By comparing the theory and the experiment we succeeded in establishing for the first time that it is just the inter-mode scattering that is responsible for the quantum chaos manifestations in the singularly perturbed integrable wave-billiard system.

cond-mat.dis-nn↗

arXiv2012

The sharpness-induced mode stopping and spectrum rarefication in waveguides with periodically corrugated walls

Starting from the rigorous excitation equation, the propagation of waves through a 2D waveguide with the periodically corrugated finite-length insert is examined in detail. The corrugation profile is chosen to obey the property that its amplitude is small as compared to the waveguide width, whereas the sharpness of the asperities is arbitrarily large. With the aid of the method of mode separation, which was developed earlier for inhomogeneous-in-bulk waveguide systems [Waves Random Media \textbf{10}, 395 (2000)], the corrugated segment of the waveguide is shown to serve as the effective scattering barrier whose width is coincident with the length of the insert and the average height is controlled by the sharpness of boundary asperities. Due to this barrier, the mode spectrum of the waveguide can be substantially rarefied and adjusted so as to reduce the number of extended modes to the value arbitrarily less than that in the absence of corrugation (up to zero), without changing considerably the waveguide average width.

cond-mat.mes-hall↗

arXiv2011

Spectral properties of cylindrical quasi-optical cavity resonator with random-inhomogeneous side boundary: correlation between dephasing and dissipation

A rigorous solution for the spectrum of quasioptical cylindrical cavity resonator with a randomly rough side boundary has been obtained for the first time. To accomplish this task, we have developed a novel method for variables separation in wave equation, which enables one, in principle, to rigorously examine any limiting case --- from negligibly weak to arbitrarily strong disorder. It is shown that the effect of disorder-induced scattering can be properly described in terms of two geometric potentials, specifically, the "amplitude" and the "gradient" potentials, which appear in wave equation in the course of conformal smoothing of the resonator boundaries. The scattering resulting from the gradient potential appears to be dominant, and its impact on the whole spectrum is governed by the unique sharpness parameter $Ξ$, the mean tangent of the asperity slope. As opposed to the resonator with bulk disorder, the distribution of nearest-neighbor spacings (NNS) in the rough-resonator spectrum acquires Wigner-like features only when the wave operator loses its unitarity, i.e., with the availability in the system of either openness or dissipation channels. Our numeric experiments suggest that in the absence of dissipation loss the random-rough resonator spectrum is always regular, whatever the degree of roughness. Yet, the spectrum structure is quite different in the domains of small and large values of the parameter $Ξ$. For the dissipation-free resonator, the NNS distribution changes its form with growing the asperity sharpness from Poissonian-like distribution in the limit of $Ξ<<1$ to the bell-shaped distribution in the domain where $Ξ>>1$.

cond-mat.dis-nn↗

arXiv2008

The Effect of Random Surface Inhomogeneities on Microresonator Spectral Properties: Theory and Modeling at Millimeter Wave Range

The influence of random surface inhomogeneities on spectral properties of open microresonators is studied both theoretically and experimentally. To solve the equations governing the dynamics of electromagnetic fields the method of eigen-mode separation is applied previously developed with reference to inhomogeneous systems subject to arbitrary external static potential. We prove theoretically that it is the gradient mechanism of wave-surface scattering which is the highly responsible for non-dissipative loss in the resonator. The influence of side-boundary inhomogeneities on the resonator spectrum is shown to be described in terms of effective renormalization of mode wave numbers jointly with azimuth indices in the characteristic equation. To study experimentally the effect of inhomogeneities on the resonator spectrum, the method of modeling in the millimeter wave range is applied. As a model object we use dielectric disc resonator (DDR) fitted with external inhomogeneities randomly arranged at its side boundary. Experimental results show good agreement with theoretical predictions as regards the predominance of the gradient scattering mechanism. It is shown theoretically and confirmed in the experiment that TM oscillations in the DDR are less affected by surface inhomogeneities than TE oscillations with the same azimuth indices. The DDR model chosen for our study as well as characteristic equations obtained thereupon enable one to calculate both the eigen-frequencies and the Q-factors of resonance spectral lines to fairly good accuracy. The results of calculations agree well with obtained experimental data.

cond-mat.mes-hall↗

arXiv2006

Influence of Random Bulk Inhomogeneities on Quasi-Optical Cavity Resonator Spectrum

We suggest the statistical spectral theory of oscillations in quasi-optical cavity resonator filled with random inhomogeneities. It is shown that inhomogeneities in the resonator result in intermode scattering leading to the shift and broadening of spectral lines. The shift and broadening of each line essentially depends on frequency distance to adjacent spectral lines. With increasing the distance the influence of inhomogeneities sharply reduces. The solitary spectral lines which have the distance to the nearest lines quite large is slightly changed due to small inhomogeneities. Owing to such selective influence of inhomogeneities on the spectral lines the effective spectrum rarefaction appears. Both the shift and broadening of spectral lines as well as spectrum rarefaction in quasi-optical cavity millimeter wave resonator were detected experimentally. We found out that inhomogeneities result in stochastization of the resonator spectrum in that mixed state appears, i.e. the spectrum acquires both regular and random parts. The active self-oscillator system based on the inhomogeneous quasi-optical cavity millimeter wave resonator with Gunn diode was studied as well. The inhomogeneous quasi-optical cavity millimeter wave resonator (passive and active) can serve as a model of semiconductor quantum billiard. Based on our results we suggest using such billiards with spectrum rarefied by random inhomogeneities as an active system of semiconductor laser.

cond-mat.dis-nn↗

arXiv2004

Metal-insulator transition in a two-dimensional electron system: the orbital effect of in-plane magnetic field

The conductance of an open quench-disordered two-dimensional (2D) electron system subject to an in-plane magnetic field is calculated within the framework of conventional Fermi liquid theory applied to actually a three-dimensional system of spinless electrons confined to a highly anisotropic (planar) near-surface potential well. Using the calculation method suggested in this paper, the magnetic field piercing a finite range of infinitely long system of carriers is treated as introducing the additional highly non-local scatterer which separates the circuit thus modelled into three parts -- the system as such and two perfect leads. The transverse quantization spectrum of the inner part of the electron waveguide thus constructed can be effectively tuned by means of the magnetic field, even though the least transverse dimension of the waveguide is small compared to the magnetic length. The initially finite (metallic) value of the conductance, which is attributed to the existence of extended modes of the transverse quantization, decreases rapidly as the magnetic field grows. This decrease is due to the mode number reduction effect produced by the magnetic field. The closing of the last current-carrying mode, which is slightly sensitive to the disorder level, is suggested as the origin of the magnetic-field-driven metal-to-insulator transition widely observed in 2D systems.

cond-mat.mes-hall↗

arXiv2004

Spectrum of an open disordered quasi-two-dimensional electron system: strong orbital effect of the weak in-plane magnetic field

The effect of an in-plane magnetic field upon open quasi-two-dimensional electron and hole systems is investigated in terms of the carrier ground-state spectrum. The magnetic field, classified as weak from the viewpoint of correlation between size parameters of classical electron motion and the gate potential spatial profile is shown to efficiently cut off extended modes from the spectrum and to change singularly the mode density of states (MDOS). The reduction in the number of current-carrying modes, right up to zero in magnetic fields of moderate strength, can be viewed as the cause of magnetic-field-driven metal-to-insulator transition widely observed in two-dimensional systems. Both the mode number reduction and the MDOS singularity appear to be most pronounced in the mode states dephasing associated with their scattering by quenched-disorder potential. This sort of dephasing is proven to dominate the dephasing which involves solely the magnetic field whatever level of the disorder.

cond-mat.dis-nn↗

arXiv2002

The metal-insulator transition in 2D systems at T = 0: one-particle approach

The conductance of a disordered finite-size electron system is calculated by reducing the initial dynamic problem of arbitrary dimensionality to strictly one-dimensional problems for one-particle mode propagators. The metallic ground state of a two-dimensional conductor, which is considered as a limiting case of the actually three-dimensional quantum waveguide, is shown to result from its multi-modeness. On lowering the waveguide thickness, in practice, e.g., due to application of the ``pressing'' potential (depletion voltage), the electron system undergoes a set of continuous phase transitions connected with the discrete change in the number of extended modes. The closing of the last current-carrying mode is interpreted as the electron system transition from metallic to dielectric state. The results obtained agree qualitatively with the observed ``anomalies'' of the resistance of different electron and hole systems.

cond-mat.dis-nn↗

arXiv2002

"Unusual" metals in two dimensions: one-particle model of the metal-insulator transition at T=0

The conductance of disordered nano-wires at T=0 is calculated in one-particle approximation by reducing the original multi-dimensional problem for an open bounded system to a set of exactly one-dimensional non-Hermitian problems for mode propagators. Regarding two-dimensional conductor as a limiting case of three-dimensional disordered quantum waveguide, the metallic ground state is shown to result from its multi-modeness. On thinning the waveguide (in practice, e. g., by means of the ``pressing'' external electric field) the electron system undergoes a continuous phase transition from metallic to insulating state. The result predicted conform qualitatively to the observed anomalies of the resistance of different planar electron and hole systems.

cond-mat.dis-nn↗

arXiv2001

Propagation of wave packets in randomly stratified media

The propagation of a narrow-band signal radiated by a point source in a randomly layered absorbing medium is studied asymptotically in the weak-scattering limit. It is shown that in a disordered stratified medium that is homogeneous on average a pulse is channelled along the layers in a narrow strip in the vicinity of the source. The space-time distribution of the pulse energy is calculated. Far from the source, the shape of wave packets is universal and independent of the frequency spectrum of the radiated signal. Strong localization effects manifest themselves also as a low-decaying tail of the pulse and a strong time delay in the direction of stratification. The frequency-momentum correlation function in a one-dimensional random medium is calculated.

cond-mat.dis-nn↗

arXiv2001

Electron localization in two-dimensional surface-corrugated conductors: manifestation of competing scattering mechanisms

Transport properties of narrow two-dimensional conducting wires in which the electron scattering is caused by side edges' roughness have been studied. The method for calculating dynamic characteristics of such conductors is proposed which is based on the two-scale representation of the mode wave functions at weak scattering. With this method, fundamentally different {\it by-height} and {\it by-slope} scattering mechanisms associated with edge roughness are discriminated. The results for single-mode systems, previously obtained by conventional methods, are proven to correspond to the former mechanism only. Yet the commonly ignored by-slope scattering is more likely dominant. The electron extinction lengths relevant to this scattering differ substantially in functional structure from those pertinent to the by-height scattering. The transmittance of ultra-quantum wires is calculated over all range of scattering parameters, from ballistic to localized transport of quasi-particles. The obtained dependence of scattering lengths on the disorder parameters is valid qualitatively for arbitrary inter-correlation of the boundaries' defects.

cond-mat.mes-hall↗

arXiv2000

Elastic Scattering as a Cause of Quantum Dephasing: The Conductance of Two-Dimensional Imperfect Conductors

A method is proposed for studying wave and particle transport in disordered waveguide systems of dimension higher than unity by means of exact one-dimensionalization of the dynamic equations in the mode representation. As a particular case, the T=0 conductance of a two-dimensional quantum wire is calculated, which exhibits ohmic behaviour, with length-dependent conductivity, at any conductor length exceeding the electron quasi-classical mean free path. The unconventional diffusive regime of charge transport is found in the range of conductor lengths where the electrons are commonly considered as localized. In quantum wires with more than one conducting channel, each being identified with the extended waveguide mode, the inter-mode scattering is proven to serve as a phase-breaking mechanism that prevents interference localization without real inelasticity of interaction.

cond-mat.dis-nn↗