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In this article, we review the basic concepts of quantum radars as such types of the devices while highlighting differences with their classical analogs. We discuss how several concepts from traditional radars technology, e.g., target detection sensitivity, noise resilience and ranging accuracy can be translated to quantum radars. We examine such new far-field sensing protocols as quantum illumination (QI), and engineering opportunities enabled by its different realizations. We consider possibilities of achieving super-sensitivity and super-resolution using quantum correlations, and discuss possibilities to create quantum correlated states in practice., It is a brief popular review (11 pages, 7 figures, 77 references)

We consider transformation of quantum states of electromagnetic field by scattering from a perfectly conducting cylinder with a circular cross-section. We introduce a quantization technique for the scattered field, and demonstrate how quantumness (in particular, entanglement) of field states is transferred to the scattered field. The obtained results may be useful for designing quantum antennas and for quantum-enhanced far-field sensing, i.e., quantum lidars/radars.

We propose a numerical technique for modeling the quantum multimode light scattering by a perfectly conducting body. Using the novel quantization technique, we give the quantum adaptation of the characteristic mode approach widely used in the classical electrodynamics. The method is universal with respect to the body's configuration, as well as its dimensions relative to the wavelength. Using this method and calculating the first- and the second-order field correlation functions, we demonstrate how scattering affects quantum-statistical features of the field. As an example, we consider scattering of the two single-photon incident Gaussian beams on the cylinder with circular cross-section. We show that the scattering is accompanied by the two-photon interference and demonstrates the Hong-Ou-Mandel effect. It is shown, that the scattered two-photon field and its correlations are able to manifest a varying directive propagation, which is controllable by various means (angles of incidence, configuration of the body, relations between its sizes with the frequency). We expect that this method will be useful for designing quantum-optical devices.

The scattering theory for two crossing metallic single-walled carbon nanotubes of finite length exposed to an electromagnetic field has been developed based on a synthesis of the quantum transport formalism and classical electrodynamics. The model of the point contact has been developed to be incorporated into the Hall\'en and Pocklington equations for crossing carbon nanotubes. The influence of the contact conductance and position as well as the angle between the tube axes on the tube polarizability has been analyzed in the range of 1 GHz to 10 THz. The physical mechanisms responsible for the electromagnetic interaction between crossing tubes with zero and nonzero intertube contact conductance are shown and discussed. The influence of the coupling between the tubes on the localized plasmon resonance in them has been demonstrated.

A novel terahertz detector is here proposed, based on the use of planar arrays of graphene nanoribbons of different widths and lengths. Two distinct mechanisms are exploited to detect an external incident field: the excitation of interband transitions and of the surface plasmon polaritons resonances. The tuning of such mechanisms allows strengthening the signal, so providing an alternative solution to the problem of the low efficiency of the resonant graphene antennas. This paper proposes a possible design solution and analyzes and the feasibility of tuning the two mechanisms in the THz range.

The dynamics of a charge bounded by a chain of coupled artificial atoms, interacting simultaneously with a single mode quantized electromagnetic field inside a cavity, and a constant electrostatic DC field is presented in this work. We develop an extended Jaynes-Cummings model describing this system and solve it both analytically and numerically, with good agreement between the two methods. It is shown that the charge-photon dressed state is modulated with the Bloch frequency due to the interaction with the DC field. This enables to control the quantum state of light by adiabatically changing the DC field. This novel effect might be important for the application of optical modulators, quantum computing and electrically controlled quantum antennas.

A theoretical concept on electrodynamics of carbon nanotubes (CNTs) based on the effective two-side impedance boundary conditions for electromagnetic field is presented. The effective tensor of sheet impedance is introduced as a phenomenological parameter for single- and double-walled CNTs basing on the quantum models of charge carrier transport. Two types of boundary value problems are formulated for CNT electrodynamics: (i) eigenmodes of CNTs and (ii) CNT excitation by the external field. The second type of the problems takes into account the finite-length effects basing on the integral equation technique. These problems have been applied to the surface plasmon propagation and antenna resonances. In particular, it gives an interpretation of the terahertz conductivity peak, which physical origin has been debated by different research groups for a long time. The generalization to the quantum optical problems based on the concept of the surface noise current is given. It is applied to analysis of Purcell effect and thermal radiation in CNT.

we present a model of a one-dimensional chain of two-level artificial atoms driven simultaneously with a dc field and a quantum light in the strong coupling regime. It is shown that the entanglement of the electron and photon (dressing of the atoms with light) dramatically changes the scenario of the Bloch oscillations (BO) compared with standard solution of the Bloch-Zener model. We considered the mutual influence of dressing and BO and show that the quantum properties of light become controllable via an adiabatic dc field tuning. The obtained results open new ways in quantum state engineering, nano-photonic spectroscopy and nano-antennas.

We present a model of one-dimensional chain of two-level artificial atoms driven with DC field and quantum light simultaneously in a strong coupling regime. The interaction of atoms with light leads to electron-photon entanglement (dressing of the atoms with light). The driving via dc field leads to the Bloch oscillations (BO) in the chain of dressed atoms. We consider the mutual influence of dressing and BO and show that scenario of oscillations dramatically differs from predicted by the Jaynes-Cummings and Bloch-Zener models. We study the evolution of the population inversion, tunneling current, photon probability distribution, mean number of photons, and photon number variance, and show the influence of BO on the quantum-statistical characteristics of light. For example, the collapse-revivals picture and vacuum Rabi-oscillations are strongly modulated with Bloch frequency. As a result, quantum properties of light and degree of electron-photon entanglement become controllable via adiabatic dc field turning. On the other hand, the low-frequency tunneling current depends on the quantum light statistics (in particular, for coherent initial state it is modulated accordingly the collapse-revivals picture). The developed model is universal with respect to the physical origin of artificial atom and frequency range of atom-light interaction. The model is adapted to the 2D-heterostructures (THz frequencies), semiconductor quantum dots (optical range), and Josephson junctions (microwaves). The data for numerical simulations are taken from recently published experiments. The obtained results open a new way in quantum state engineering and nano-photonic spectroscopy.

We proposed the general concept of quantum antenna in the strong coupling regime. It is based on the theory of open quantum systems. The antenna emission to the space is considered as an interaction with the thermal photonic reservoir. For modeling of the antenna dynamics is formulated a master equation with the correspondent Lindblad super-operators as the radiation terms. It is shown that strong coupling dramatically changes the radiation pattern of antenna. The total power pattern splits to three partial components; each corresponds to the spectral line of Mollow triplet. We analyzed the dependence of splitting from the length of antenna, shift of the phase, and Rabi-frequency. The predicted effect opens a way for implementation of multi-beam electrically tunable antennas, potentially useful in different nano-devices.

We consider the physical model of synthesis of Bloch and Rabi-oscillations. Consequently, the new effect of combined Rabi-Bloch oscillations (RBO) is created. The tunneling current in the lattice of two-level fermionic systems, driven by dc-ac electric field, have been calculated. RBO manifests itself in the superposition motion of intra-band and inter-band transitions. In spite of this components belong to the different frequency ranges, the total motion does not add up to their simple linear superposition. It is characterized by their strong mutual influence, which produces non-trivial dynamics and qualitative features of spectrums. An experimental implementation and potential applications of RBO in nano-antennas of terahertz and optical frequency ranges have been discussed.

A great progress has been achieved during last two decade in the synthesis and fabrication of different nanostructured artificial materials with fascinating mechanical, electronic and optical properties irreducible to properties of bulk media. Accompanied by the impressive parallel development of the characterization techniques and measurement instrumentation, this process necessitates the revision of traditional concepts of physics and chemistry of condensed matter, adapting them to peculiarities of the nanoworld and significantly extending our knowledge of the nature of solids and our capabilities to control their properties.

We consider the numerical modeling of synthesis of Bloch and Rabi-oscillations. Consequently, the effect of combined Rabi-Bloch oscillations (RBO) is created. The inversion in the lattice of two-level fermionic atoms, driven by dc-ac electric field, have been calculated. RBO manifests itself in the non-additive superposition movement of intra-band and inter-band transitions. An experimental implementation and potential applications of RBO in nanoelectronics have been discussed.

Integral equation technique of classical electrodynamics and the Landauer-Buttiker formalism of quantum transport were applied to develop electromagnetic scattering theory for a finite-length nanowire with embedded mesoscopic object. The theory is valid for a rather wide range of nanostructures, such as nanowires, nano-loops, nano-ribbons, Vivaldi antennas, etc.

We considered one-dimensional quantum chains of two-level Fermi particles coupled via the tunneling driven both by ac and dc fields in the regimes of strong and ultrastrong coupling. The frequency of ac field is matched with the frequency of the quantum transition. Based on the fundamental principles of electrodynamics and quantum theory, we developed a general model of quantum dynamics for such interactions. We showed that the joint action of ac and dc fields leads to the strong mutual influence of Rabi- and Bloch oscillations one to another. We focused on the regime of ultrastrong coupling, for which Bloch- and Rabi-frequencies are a significant values of the frequency of interband transition. The Hamiltonian was solved numerically with account of anti-resonant terms. It manifests by the appearance of great number of narrow high-amplitude resonant lines in the spectra of tunneling current and dipole moment. We proposed the new concept of THz spectroscopy promising for different applications in future nanoelectronics and nano-photonics., 26 pages, 20 figures

This paper introduces the paradigm of quantum light rectification by nano-rectennas. The theory is based on the synthesis of the quantum-optical light description and the scattering-matrix approach to phase-coherent electron transport in rectifying diodes (Landauer-Buttiker concept). The dc-current operator is expressed in terms of the special functions of the normally ordered electronic and photonic creation-annihilation operators. The observable dc-current is calculated as an expectation value of the current operator with respect to both electronic and light components of the rectenna state. Potential applications of the developed theory to the solar power conversion into the dc-current are discussed.

This research was supported in part by the EU Horizon 2020 project H2020-MSCA-RISE-2014-644076 CoExAN and EU FP7 projects, FP7-PEOPLE-2012-IRSES-316432 QOCaN and FP7-PEOPLE-2013-IRSES-612285 CANTOR. Discussions of the basic ideas underlying this work with Dr S Starobinets and Dr D Mogilevtsev are acknowledged.

In this paper, we recast the problem of interaction between a classical electromagnetic field and a pair of quantum dots coupled through dipoledipole interaction in terms of an equivalent circuit model. Then, we use the introduced circuit to investigate the electromagnetic scattering from a pair of interacting quantum dots. Equivalent circuits for complex systems of quantum dots greatly simplify the analysis and the design of light-matter interaction processes at the nanoscale.

We show that the electromagnetic coupling at the nanoscale may be accompanied by another coupling mechanism, related to quantum entanglement. Consequently, a combined "electromagnetic-quantum" coupling is created, which stipulates long-distance and long-living interactions in electric circuits. Manifestation of this effect in electromagnetic compatibility (EMC) is discussed. An efficient theoretical framework for EMC analysis in nanoelectronics is developed based on the generalized theory of electric circuits. It is shown that the action of quantum entanglement is equivalent to an addition of the supplementary elements in electric circuit with the effective admittances defined as general susceptibilities that can be calculated using the Kubo-technique.

A technique of two-phase EMC diagnostics of complex ground-based radio systems with the use of worst-case models of electromagnetic spurious couplings between antennas is introduced. At the first phase, the ultra wideband analytical model of antenna coupling developed in the framework of IEMCAP program is used, and the ensemble of potentially dangerous spurious couplings is found. For these couplings, the improved numerical worst-case models for the reduced frequency bands, as well as for given types, orientations, and relative positions of the antennas are developed at the second phase of EMC diagnostics. Each of these improved models is obtained by finding the envelope of results of multiple (based on variations of model parameter values) FDTD modeling of the corresponding coupling. The example of application of the introduced technique for diagnostics of intrasystem EMC of an operating radio-TV complex is provided: the computer model of its radio mast is developed, and the two-phase EMC diagnostics of this complex (which contains radio equipment of more than 20 systems of radio-TV broadcasting, fixed and mobile radio communication, radio navigation, and other services) is performed. The obtained results have confirmed the efficiency of the presented technique for the analysis of intrasystem EMC due to significant improvement in estimation of potentially dangerous spurious couplings between antennas at the second phase of EMC diagnostics (by 5…20 dB in comparison with analytical model of IEMCAP) with acceptable computational burden.

A short introduction to the electronics properties of carbon nanotubes (CNTs) is given and applied to the analysis of electric conductivity of isolated and bundled CNTs, either single-wall or multi-wall. The model of the electrical conductivity is presented in a wide frequency range, from DC to visible light. In the low-frequency range (up to the THz range), only intraband transitions are considered, whereas for higher frequencies also interband transitions are taken into account. The conductivity model is consistent with the classical Drude model and is able to describe novel phenomena associated with the signal propagation along CNTs, such as plasmon resonances of slow surface waves or intershell tunneling effect.

We consider the general concept of quantum field quantization in the nano-antenna modeled as an atomic chain. We show that the transformation of quantum near-field to the far-field is accompanied by the transformation of the quantum state of light. As a result, transmitting and receiving antennas cannot be considered separately, which has no analogs in classical antennas. Such behavior stems from the transmitting antenna quantum state destruction via the signal detection by the receiving antenna.

RF and Microwave Electrical Response of Carbon Nanotube Saline Solutions for Potential Biomedical Applications Mikhail V. Shuba1 ∗, Gregory Ya. Slepyan1, Sergey A. Maksimenko1, and George W. Hanson2 ∗ 1Institute for Nuclear Problems, Belarus State University, Bobruiskaya 11, 220030 Minsk, Belarus 2Department of Electrical Engineering, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53211, USA

In carbon nanotubes (CNTs) with large radii, either metallic or semiconducting, several subbands contribute to the electrical conduction, while in metallic nonarmchair nanotubes with small radii the wall curvature induces a large energy gap. In this paper, we propose a model for the signal propagation along single wall CNTs (SWCNTs) of arbitrary chirality, at microwave through terahertz frequencies, which takes into account both these characteristics in a self-consistent way. We first study an SWCNT, disregarding the wall curvature, in the frame of a semiclassical treatment based on the Boltzmann equation in the momentum-independent relaxation time approximation. It allows expressing the longitudinal dynamic conductivity in terms of the number of effective conducting channels. Next, we study the behavior of this number as the nanotube radius varies and its relation with the kinetic inductance and quantum capacitance. Furthermore, we show that the effects of the spatial dispersion are negligible in the collision dominated regimes, whereas they may be important in the collisionless regimes, giving rise to sound waves propagating with the Fermi velocity. Then, we study the effects on the electron transport of the terahertz quantum transition induced by the wall curvature by using a quantum kinetic approach. The nanotube curvature modifies the kinetic inductance and gives arise to an additional RLC branch in the equivalent circuit, related to the terahertz quantum transition. The proposed model can be used effectively for analyzing the signal propagation in complex structures composed of SWCNTs with different chirality, such as bundles of SWCNTs and multiwall CNTs, providing that the tunneling between adjacent shells may be disregarded.

A novel lightweight onion-like carbon (OLC) based Poly(methyl metacrylate) (PMMA) composite with high electromagnetic (EM) absorption capability determined earlier in microwave range is studied in low frequencies from 20 Hz to 1 MHz by dielectric spectroscopy. The investigation of dielectric properties of PMMA films with incorporated OLC in small concentration (0.5–2 wt.%) have been carried out by varying the temperature between 240 and 520 K. The temperature behavior of the complex permittivity at a given frequency is found to be strongly dependent on the OLC concentration. The experimental data are in quantitative agreement with the results of modified effective medium calculations of OLC-based polymer film's permittivity. Both the experimental observations and theoretical simulation demonstrate that small additions of onion-like carbon particles to a polymer matrix can noticeably modify the composite response to low-frequency EM radiation as well as improve its thermal stability (increased glass transition and melting temperatures, correspondingly).

Concept of edge polarizability produced by support of the edge quantum states is demonstrated by the example of graphene nanoribbon with zigzag edge configuration. This concept allows to formulate physically correct edge conditions for electromagnetic field in nanostructures instead of ordinary Meixner conditions in classical electrodynamics.

Current trends in Nan electro magnetics - a new field of research synthesizing classical radio physics and electrodynamics with quantum theory of solids, physical kinetics, quantum chemistry, computational mathematics - are analyzed with the focus on applications in the terahertz frequency range. The analysis is exemplified by the discussion of the THz response peculiarities of carbon nanostructures and composite materials with nanocarbon fillers. Some electromagnetic applications of nancaerbons are discussed, such as nanoantennas, amplifiers and generators of terahertz radiation, THz range functional materials for radar absorbing and reflective coatings.

This paper introduces the concept of equivalent electrical multiport for a quantum device made of a pair of two-level objects, coupled via entanglement. The coupled pair is described in terms of an equivalent 2×2 admittance matrix, derived from the theory of the generalized susceptibility. This result provides a valuable tool to analyze quantum circuits in the frame of the classical circuit theory. The study of the properties of the admittance matrix highlights the effect of a new coupling mechanism, due to entanglement, which adds to the classical electromagnetic coupling.

The solution of the Poisson equation is an essential stage in the calculation of quantum properties of materials as it appears both in the electrostatic Hartree term and in the Fock exchange operator. We discuss here an integral method for the calculation of Poisson potential and demonstrate its integration with a Density Functional Theory (DFT) code. We show some results on elongated carbon chains.

The concept of electromagnetic crosstalk in nano-circuits via quantum entanglement between the elements is considered. Manifestation of this effect in electromagnetic compatibility (EMC) and a solution for for its suppression are discussed.

The general-purpose set of resonator for the band 32–405 GHz has been studied both theoretically and experimentally. The described resonators are cylindrical cavities with corrugated side surfaces and flat end covers. The simple theoretical approach for TM0mn eigenmode analysis is given. Physical principles of $Q$-factor enhancement, mode selection, frequency stabilization, and matching with standard waveguides are discussed. Experimental techniques and measurement data are given. The loaded $Q$-factor of (0.6–1.0) × 105 at VSWR (voltage standing-wave ratio) < 2.0 has been achieved together with high mode selection and high-frequency stability. A wide range of applications is proposed.

The calculation of Fock-Exchange integral is becoming an important computational challenge in solving the quantum properties of systems with many electrons. In this work we show how techniques that are used in electromagnetic simulations for the similar Poisson equation can help in accelerating the calculation of such exchange integrals. The approach we present can be especially efficient for quasi-planar systems such as Graphene nano-ribbons (GNRs) or elongated systems such as carbon nano-tubes (CNTS) and the 1D Carbyne.

Summary Scattering of electromagnetic cylindrical waves by an isolated, semi-infinite, open-ended, single-shell, zigzag carbon nanotube (CN) is considered in the optical regime. The CN is modeled as a smooth homogeneous cylindrical surface with impedance boundary conditions known from quantum-mechanical transport theory. An exact solution of the diffraction problem is obtained by the Wiener-Hopf technique. The differences between the scattering responses of metallic and semiconducting CNs are discussed.

A phenomenological theory of electromagnetic response properties of regular ensembles of quantum dots has been elaborated on the basis of the effective medium approach. We show that the QD composite comprising QDs with a given axis of symmetry is effectively a uniaxial dielectric continuum and the phenomenon of birefringence is inherent in it. It has been shown that arrays of resonantly amplifying QDs exhibit, threefold splitting of the gain band. This fine structure of the gain band originates from both the diffraction of the electromagnetic field by single anisotropically shaped QD and the electromagnetic interaction of QDs in array. The analytical results are compared with that obtained via direct numerical simulation by a minimal autonomic block (MAB) method for a tetragonal array of disk-like and pyramidal QDs. The numerics quantitatively confirm our prediction.

Shortened equations for open diffraction structures with a weak nonlinearity have been obtained in the vicinity of a resonance. The parameters of the equivalent pendulum are generally expressed in terms of eigenfrequences and eigenfunctions of an open resonant structure. As an example, a grating with nonlinear bodies has been considered. Bistability in the vicinity of Woods' anomalies has been studied, and the stability of various branches of the solutions has been analyzed. © 1998 John Wiley & Sons, Inc. Microwave Opt Technol Lett 19: 203–208, 1998.

A nanotube is phenomenologically modeled as a chain of atoms wrapped helically on a right circular cylinder. The semiclassical Hamiltonian of an electron is derived, using the Wannier approach for the Schr\"odinger equation, when the nanotube is exposed to both constant (dc) and high-frequency (ac) electromagnetic fields. The Boltzmann kinetic equation is then solved in the framework of momentum-independent relaxation time approximation. An analytical expression for electric current in a nanotube is derived. The interaction of nonlinearity and chirality is analyzed, chiefly as the dependence of a current chiral angle on the amplitude of the ac electric field. The derived expressions for the electronic transport also help in stating anisotropic impedance boundary conditions on the nanotube surface. Surface wave propagation in a carbon nanotube (CN) is examined. The idea of using CN's as nanowaveguides in the infrared frequency range is established. Convective instability is shown to occur under special conditions in a CN exposed to an axial dc electric field.

Carbon nanotubes (CNs) are electrically small particles at infrared and microwave frequencies. The Mossotti–Clausius formalism for estimating the effective permittivity dyadic of a dilute composite containing CN inclusions is described, and simplifications for certain orientational statistics are discussed. The polarizability dyadic of an electrically small CN is estimated from that of an infinitely long CN of the same cross-sectional diameter. A collection of randomly dispersed, aligned, nonchiral, electrically small CNs is shown to be transparent in the axial direction, but it can be either opaque or transparent in the transverse plane. Its effective electromagnetic response properties can be manipulated by a biasing magnetic field.

We present a novel, general, semiclassical theory of electron transport in a carbon nanotube exposed to an external electric field. The charge carriers are treated in the framework of the simplified tight-binding model. Simultaneous exposure to rapidly oscillating (ac) and constant (dc) electric fields is considered to exemplify our theory. Nonlinear and chiral effects are found, and their interaction is delineated. We predict the effect of an ac electric field on the magnitude and the direction of the total time-averaged current. {copyright} {ital 1997} {ital The American Physical Society}

The propagation of a microwave phase-modulated pulse through a section of a circular corrugated waveguide with sinusoidal corrugation is considered in the single-mode approximation. The temporal transfer functions of the waveguide measured in transmission and reflection are presented and used for computation of output pulses’ intensities. It is shown that the effect of time compression of hoth output pulses can be observed under certain conditions.

We considered the excitation of nanoantenna based on the one-dimensional quantum dot (QD) chain by the Rabi wavepackets moving through the potential barrier or potential well. The theoretical investigation based on the general concept of Rabi-waves and scattering model of quantum transport. Results presented here show a unique ability of antenna characteristics control and, partially, electrical scanning by the radiation pattern in terahertz frequency range.

We predict a linear nonreciprocal effect that is based on the timed Dicke states in an ensemble of dipole-dipole coupled oscillators. This effect is examined on a nanoscale antenna array comprising two-level identical emitters. The studied nonreciprocity, which has no analogs in classical antennas, manifests itself in strong characteristic asymmetry of the radiation pattern, even for a single-photon laser pumping. Promising applications of our results for remotely tunable nanoantennas and nanocircuit elements are discussed.

We develop a theory for the interaction of classical light fields with an a chain of coupled quantum dots (QDs), in the strong-coupling regime, taking into account the local-field effects. The QD chain is modeled by a one-dimensional (1D) periodic array of two-level quantum particles with tunnel coupling between adjacent ones. The local-field effect is taken into regard as QD depolarization in the Hartree-Fock-Bogoliubov approximation. The dynamics of the chain is described by a system of two discrete nonlinear Schr\"{o}dinger (DNLS) equations for local amplitudes of the probabilities of the ground and first excited states. The two equations are coupled by a cross-phase-modulation cubic terms, produced by the local-field action, and by linear terms too. In comparison with previously studied DNLS systems, an essentially new feature is a phase shift between the intersite-hopping constants in the two equations. By means of numerical solutions, we demonstrate that, in this QD chain, Rabi oscillations (RO) self-trap into stable bright\textit{\ Rabi solitons} or \textit{Rabi breathers}. Mobility of the solitons is considered too. The related behavior of observable quantities, such as energy, inversion, and electric-current density, is given a physical interpretation. The results apply to a realistic region of physical parameters., Comment: 12 pages, 10 figures, Phys. Rev. B, in press

The Heisenberg uncertainty principle is one of the cornerstones of quantum mechanics. We show that the observable values of the electromagnetic field in the far- and near-field zones emitted by the quantum nanoantenna are coupled via uncertainty relations of the Heisenberg type. The similar uncertainty inequalities are obtained for the electric currents in the different branches of the quantum networks. Based on these, we predict the mechanism of high-level squeezing of light in the quantum antennas. We show that this mechanism is highly directive. The strong values of squeezing are reaching in the narrow directions of high emission (tops of the main lobes of the radiation pattern). We also discuss the quantum noise manifestation in nanoelectronics and nanophotonics from the point of the electromagnetic compatibility of nanoelectronic devices, densely placed in the limited areas of space.