A new rigorous model for calculating Casimir-Lifshitz forces for thin dielectric or conductive filaments based on the Lorentz force is proposed. We use the formulas of G.T. Markov and the fluctuation-dissipation theorem. The only approximation used is the small ratio of the radii to the distance between the threads, which allowed the transverse structure of the fields in the threads to be considered constant. The results are obtained for metallic and dielectric filaments, as well as for carbon nanotubes.
The problems of passing and tunneling a plane electromagnetic wave through a dielectric layer and two dielectric layers separated by a vacuum gap are considered. It is shown that there are no superluminal motions, and the transit time is always longer when passing at the speed of light.
A model is proposed for calculating the Casimir-Lifshitz force between two finite rectangular and infinite graphene sheets in a vacuum, based on the classical electrodynamic Green’s function method and two-dimensional conductivity model. The force is calculated using the Maxwell’s tension tensor by solving the integral equations in the spectral spacefrequency domain. It is shown that its origin is due to random vibrations associated with long-wave surface plasmons.
We consider the photon tunneling through the structure with bang gap formed from layers with negative dielectric permittivity or from transparent layers, supporting due to the periodicity of the barrier the band with a low coefficient of transparency. The rate of energy transfer in such structure and the time of its transfer are investigated. It is shown that in all cases the rate of energy transfer does not exceed the speed of light. Therefore, the known paradoxes using BohmWigner time of the Hartmann paradox type are precisely paradoxes, i.e. the false statements.
We consider the plasmon-polaritons along a layer of hyperbolic metamaterial propagating in the plane of the anisotropy axis with an arbitrary its orientation. As a layer material, we use periodic plane-layered artificial medium – hyperbolic metamaterial of thin metal and dielectric layers and produce its homogenization. The conditions for the existence of fast, slow, leakage, gliding flowing, forward and backward plasmon-polaritons are found. The Fresnel formulas for the diffraction of a plane wave of arbitrary polarization on such a structure are obtained. The dispersion of plasmonpolaritons and plane wave diffraction are calculated. It is proposed to use a strong magnetic field to control dispersion and scattering.
The linear theory of a traveling wave tube (TWT) or vacuum amplifier with a wide tape electron beam operating on plasmon modes is developed. The dispersion equation for electron waves and the gain per unit length with account for the dissipation in the structure are obtained. Strict solutions for dispersion and field distribution of surface plasmons in layered structures with conducting films and for electron waves amplified by a beam are obtained by the iteration method. To increase the gain, it is proposed to use active conductive semiconductor or graphene layers.
The maximum slowdown and the resonance frequency of plasmons in thin metallic layers and layered structures are obtained. We conside the anomalous negative dispersion and backward plasmons with dissipation. The conditions for the existence of inverse plasmons are obtained. It is shown that negative dispersion in structures with dissipation does not always mean the presence of reverse plasmon.
We consider the structures type of two-dimensional electron gas in the form of a thin conductive, in particular, graphene films described by tensor conductivity, which are isolated or located on the dielectric layers. The dispersion equation for hybrid modes, as well as scattering parameters. We show that free wave (eigenwaves) problem follow from the problem of diffraction when linking the amplitude of the current of the linear equations are unsolvable, i.e., the determinant of this system is zero. As a particular case the dispersion equation follow from the conditions of matching (with zero reflection coefficient).
The electric and magnetic surface plasmons in symmetric structures of metallic and dielectric layers are considered. The existence of backward and forward waves and the slow and fast plasmon-polaritons are obtained. It is shown that the anomalous negative dispersion in the structures with dissipation does not necessarily indicate the backward surface plasmons.
The dispersion equation and the analysis and homogenization in periodic and quasiperiodic plane layered structures with alternating dielectric layers of metal and dielectric layers, as well as a graphene sheet and SiO2 layers have been investigated. The cases are considered when these patterns become the properties of hyperbolic metamaterials, i.e., having different signs of the real parts of the tensor components of the effective dielectric constant. It is shown that usage only dielectric layers is perspective in reducing losses.
Metamaterials, made in form of periodically arranged metal and dielectric cylindrical inclusions, have been investigated
on the basis of the integral equation method, based on periodic Green's function. Metal rods are described in terms of
complex permittivity [see manuscript]. Along the rods terahertz and infrared waves propagate substantially with the speed of
light c and small losses weakly depending on the transverse wave number, whereas in the optical range, in particular in
the shortwave part of a spectrum, they turn into the slow -waves of a dielectric waveguide.
The simplest dispersion lows in the dissipative media, the density of energy, and the characteristic velocities of
monochromatic wave process: phase, group and energy velocities have been considered. It has been shown that for
polar dielectrics with anomalous positive dispersion and Debye low the velocity of energy coincides with the phase
velocity, and the group velocity may exceed the velocity of light.
The dispersion in one-dimensional periodic and one-dimensional pseudoperiodic flat-layered magnetodielectric
structures with dissipative and active layers has been calculated. It has been shown that the bandgap zones are
destroying (washing out) under the loss, and there are forbidden bands in the wavevector space for structures with
common dissipative and active layers. The group velocity may exceed the velocity of light up to infinity in the
points of junction of direct and backward waves.
In the present paper the excitation of cylindrical structures (waveguide and resonator) by helix and axial electric currents have been considered using exact electromagnetic approach. In the solution of the problem the coupling of resonator with input and output coaxial lines and possible excitation by elecon beam and by input signal are considered. Beam current is supposed to be given and problem is linear and time-independent. The results can be used for processes simulation in the systems with helical slow-wave structures, such as TWT. This approach can be applied also for investigation of wave propagation in photonic crystals with small helical inclusions. Using such artificial environment allows to well simulate environment with large permittivity.
The Green functions and corresponding integral and integro-differential equations for periodic structures are introduced. Some results based on this approach for 2D and 3D photonic crystals are presented. We consider the simplest photonic crystals, but the method is applicable to arbitrary shaped structure and may use the volumetric finite elements. The solutions of integral and integro-differential volumetric and combined surface-volumetric equations are considered and discussed. Also the method which reduces the kernel singularity is proposed and considered. The method is based on the transferring of differential operators from the kernel to the unknown functions under the integral. The dispersion equations is based on the variation formulation for integral and integro-differential equations and have been used to obtain the permittivity and permeability tensors for photonic ciystal's equivalent complex media.
The Green functions and corresponding integral and integral-differential equations for periodic structures are introduced. Some results based on this approach for 1D, 2D, and 3D photonic crystals are presented.
A full-wave transverse transfer matrix method have been used for analysis of cylindrical and rectangular hollow center waveguides with multilayered coating. The complex modes of leaky-wave character have been investigated in such waveguides with lossy materials filling the covering. The dispersion equations for investigated structures have been introduced and solved in the complex plane region and the propagation and attenuation constants have been obtained. Using this technique the numerical synthesis of the optimal coating profile have been performed. The wide-band, band-path, and narrow-band mode self-filtration, and the possibility of reduction of the dominant mode propagation constant are considered. In this paper the complex permittivities and permeability are neither restricted by any conditions, and nor associated with concrete materials, and the main goal is the synthesis of permittivity and permeability distribution, which are most fitted to our purposes. For example, such coatings may be implemented using composite and artificial materials by means of ion implantation or other technique.
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