Analysis and Calculations of Forbidden Regions for Transverse-Electric-Guided Waves in the Three-Layer Planar Waveguide with Photonic Metamaterial

Abstract

In this article, the modal theory was used to analyze transverse electric waves in the three-layer planar waveguide with photonic metamaterial. The formulas for the electric fields of transverse electric modes in this structure have been proposed. There always exist two forbidden regions for transverse electric waves in the three-layer planar waveguide with photonic metamaterial. The complete set of modes of all possible solutions for the transverse electric waves in the three-layer planar waveguide with photonic metamaterial had been analyzed and discussed. Similar processes can be extensively used to predict the propagation characteristics of TM waves in the three-layer planar waveguide with photonic metamaterial. The analytical and numerical results show excellent agreement.     

Gauge Transformations for a Family of Nonlinear Schrödinger Equations

Abstract

An enlarged gauge group acts nonlinearly on the class of nonlinear Schrödinger equations introduced by the author in joint work with Doebner. Here the equations and the group action are displayed in the presence of an external electromagnetic field. All the gauge-invariants are listed for the coupled nonlinear “Schrödinger-Maxwell” theory. Time-dependent gauge parameters result in additional terms of the type introduced by Kostin and Bialynicki-Birula and Mycielski, but Maxwell’s equations for the (non-quantized) gauge-invariant electric and magnetic fields remain linear.     

Drift in a random walk along self-similar clusters

This paper is a study of the relationship between diffusion and conductivity when the random walks of particles occur via Lévy hops. It shows that because of the unusual nature of Lévy hops the particle mobility is a nonlinear function of the electric field in arbitrarily weak fields. The crossover to ordinary diffusion by introduction of a finite displacement in each step is also discussed. Zh. éksp. Teor. Fiz. 115, 1016–1023 (March 1999)     

Fluctuations in random RL-C networks: Nonlinear σ-model description

Disordered RL-C networks are known to be an adequate model for describing fluctuations of electric fields in a random metal-dielectric composite. We show that under appropriate conditions the statistical properties of such a system can be studied in the framework of Efetov’s nonlinear σ model. This fact provides a direct link to the theory of Anderson localization. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 11, 733–739 (10 December 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

On the relation between conduction and diffusion in a random walk along self-similar clusters

The relation between diffusion and conduction in the random walk of a particle by means of Lévy hops is investigated. It is shown that on account of the unusual character of Lévy hops, the mobility of a particle is a nonlinear function of the electric field for arbitrarily weak fields. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 7, 518–520 (10 April 1998)     

Analytical formulas for complex permittivity of periodic composites. Estimation of gain and loss enhancement in active and passive composites

ABSTRACT

The asymptotic homogenization method is applied to complex dielectric periodic composites. An equivalence to coupled dielectric problems with real coefficients is shown. This is similar to a piezoelectric problem: an out-plane mechanical displacement and an in-plane electric potential establishing a correspondence principle. Closed-form formulas for the complex dielectric effective tensor in the case of a square array of circular inclusions embedded in a matrix are given. These formulas are written in terms of a real and symmetric matrix which facilitates the implementation of the computational scheme. We also get similar formulas for multilayered complex dielectric composites. The real closed-form formulas are advantageous for estimating gain and loss enhancement properties of active and passive composites in certain volume fraction intervals. Numerical computations are performed and the results are compared with other approaches showing the usefulness of the obtained formulas. This may be of interest in the context of metamaterials.     

无电极电光M-Z型电场传感器LinbO3波导折射率变化研究

利用微扰近似法，导出了折射率的变化公式，通过数值计算，分析并讨论了电场与折射率变化的关系。得出了其函数关系式，通过对实验室制作的器件进行直流测试，进一步验证了函数关系式的正确性和无电极电光M－Z型电场传感器的可行性。     

Spectrum of the parametric down converted radiation calculated in the Wigner function formalism

We continue the study of parametric down conversion within the framework of the Wigner representation, by using a Maxwellian approach developed in a recent paper [A. Casado et al., Eur. Phys. J. D 11, 465 (2000)]. This gives a mechanism, inside the crystal, for the production of the down-converted radiation. We obtain the electric field to second order in the coupling constant by using the Green's function method, and compare our treatment with the standard Hamiltonian approach. The spectrum of the down-converted radiation is calculated as a function of the parameters of the nonlinear crystal (in particular the length) and the radius of the pumping beam. Received 15 May 2000     

Scattering of electrons by a potential step in a magnetic field

The scattering of two-dimensional electrons drifting in crossed electric and magnetic fields by an abrupt step in the external potential is discussed. The problem is reduced to solving a system of ordinary differential equations. It is shown that for moderate electric fields scattering with a change of Landau level numbers becomes appreciable. Zh. éksp. Teor. Fiz. 112, 1756–1762 (November 1997)     

Nonlinear moment method for the isotropic Boltzmann equation and invariance of the collision integral

A new approach is proposed for the development of a nonlinear moment method of solving the Boltzmann equation. This approach is based on the principle of invariance of the collision integral with respect to the choice of basis functions. Sonine polynomials with a Maxwellian weighting function are taken as these basis functions for the velocity-isotropic Boltzmann equation. It is shown that for arbitrary interaction cross sections the matrix elements corresponding to the moments of the nonlinear collision integral are not independent but are coupled by simple recurrence formulas by means of which all the nonlinear matrix elements are expressed in terms of linear ones. As a result, a highly efficient numerical scheme is constructed for calculating the nonlinear matrix elements. The proposed approach opens up prospects for calculating relaxation processes at high velocities and also for solving more complex kinetic problems. Zh. Tekh. Fiz. 69, 22–29 (June 1999)     

Relaxation of electric fields induced by mechanical loading in natural dielectrics

An investigation is made of electric fields induced in natural dielectrics by mechanical loading and electrical polarization. It is shown that the relaxation of the polarization is identical in nature for both cases and is basically a thermally activated process. The temperature dependence is obtained for the relaxation time of the electric fields. Also estimated is the activation energy for motion of charge carriers leading to the relaxation of these fields. Fiz. Tverd. Tela (St. Petersburg) 39, 1202–1204 (July 1997)     

On the unified nature of the longitudinal and transverse acoustoelectric effects in type-II superconductors

A longitudinal ultrasonic wave should drag the vortex structure of superconductors at an acute angle with respect to the direction of wave propagation. This motion engenders longitudinal and transverse electric fields in the superconductor and, moreover, effects of the “optical rectification” type contribute to the observed longitudinal and transverse electric fields. The effect should be observed in all type-II superconductors above the irreversibility line. Both fields have extrema with respect to temperature and magnetic field. In contrast to the acoustoelectric effect in the normal state, the sign of the induced electric field depends on the external magnetic field. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 3, 222–227 (10 February 1998)     

Breakdown of the homogeneity of weakly conducting liquids in high electric fields

A study of the structure of electrohydrodynamic flows shows that the electric charge carriers are ions that are practically frozen into the surrounding liquid. In other words, ions in weakly conducting liquids are capable of forming more or less stable structures whose viscoelastic properties are different from those of an uncharged liquid. One method of studying this effect is to investigate the velocity dispersion of ultrasound on charged supermolecular formations. The results of theoretical and experimental investigations of acoustic dispersion in liquid dielectrics subjected to prebreakdown electric fields are presented. A model problem of sound propagation in a liquid in which supermolecular structures have formed around elementary charge carriers is studied theoretically. Approximate formulas describing the dispersion of the acoustic phase velocity as a function of the electric field parameters and the electrophysical parameters of the liquid are obtained. The frequency dependence of the sound velocity is of a resonance character, the resonance frequency being determined by the electric charge density and the mass of the charged supermolecular structures. The experiments showed that the space charge affects the velocity of acoustic waves in liquid dielectrics. Zh. Tekh. Fiz. 67, 105–111 (October 1997)     

Calculation of the electrostriction effect in thin-film metal-ferroelectric-metal structures

An analysis is made of the influence of electron injection from the cathode on the electrical conductivity and nonuniform thickness distribution of the piezoelectric properties of metal-insulator-metal structures using an electrostrictive, optically transparent FE ceramic such as lanthanum-containing lead zirconate titanate (PLZT). Because thin-film insulators, in contact with metal electrodes, exhibit semiconducting properties, the theory put forward by Mott and Gurney for insulating diodes can be used to calculate the electric fields and currents. The distribution of the polarization over the thickness of the piezoelectric layer was determined by means of an asymptotic solution, and relations were formulated for the electroelasticity of FE ceramic plates and shells. A detailed analysis was made of the electromechanical bending effect in homogeneous piezoelectric plates used as optical radiation modulators. It is shown that these formulas can be used for a computational and experimental determination of the distribution of the polarization over the thickness of thin-film piezoelectric structures. Zh. Tekh. Fiz. 69, 120–124 (July 1999)     

Local Thermodynamical Stability of Fermion Lattice Systems

We study the magnetic moment of neutral atoms in large magnetic fields. Asymptotic formulas for the energy exist with high precision in different regions depending on how large the nuclear charge Z is compared to the magnetic field strength B. All these formulas take the splitting of the kinetic energy into Landau levels as the principal feature and then treat the electric potential as a perturbation. We prove that these approximate formulas predict correctly'(to highest order) the total magnetic moment of the atom. The proof of this fact relies on a 'virial theorem' for Coulomb systems in a constant magnetic field.     

The Difference Between the Standard and The Lorentz Transformations of the Electric and the Magnetic Fields

In this paper it is shown by using the Clifford algebra formalism that the usual Lorentz transformations of the three-dimensional (3D) vectors of the electric and magnetic fields E and B (which will be named as standard transformations (ST)) are different than the Lorentz transformations (LT) of well-defined quantities from the 4D spacetime. This difference between the ST and the LT is obtained regardless of the used algebraic objects (1-vectors or bivectors) for the representation of the electric and magnetic fields in the usual observer dependent decompositions of F. The LT correctly transform the whole 4D quantity, e.g., E_f : F · γ₀, whereas the ST are the result of the application of the LT only to the part of E_f, i.e., to F, but leaving γ₀ unchanged. The new decompositions of F in terms of 4D quantities that are defined without reference frames, i.e., the absolute quantities, are introduced and discussed. It is shown that the LT of the 4D quantities representing electric and magnetic fields correctly describe the motional electromotive force (emf) for all relatively moving inertial observers, whereas it is not the case with the ST of the 3D E and B.     

Nonlinear effects in a two-dimensional electron gas with a periodic lattice of scatterers

The magnetoresistance of two-dimensional (2D) electrons in a periodic lattice of antidots is found to be substantially influenced by an applied electric field. The non-Ohmic behavior of the resistance in the region of commensurability oscillations originates from the electric-field-induced breakdown of the trajectories skipping along the lattice arrays. In the region of magnetic fields where the cyclotron diameter is less than the distance between antidots the breakdown of the orbits skipping around antidots is responsible for the nonlinear behavior of the magnetoresistance. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 3, 237–241 (10 February 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Electric fields in dielectric structures with nonuniformly distributed surface charges

The distribution of the potential and intensity of the electric field in dielectric structures with a nonuniform surface charge is analyzed. Computational formulas are proposed and computational results are presented. Zh. Tekh. Fiz. 69, 138–140 (August 1999)     

Simulations of single charged particle motion in external magnetic and electric fields

In this paper we present a software package for computational modeling of single particle motion in static and dynamic external magnetic and electric fields and show applications of our package to general cases and particular cases of space, laboratory and fusion plasmas. In addition we further elaborate on the properties of a new concept named Larmor Center Trajectory that we introduced in our previous work [D. Erzen, J.P. Verboncoeur, J. Duhovnik, N. Jeli, Int. J. Multiphys. 1, 419 (2007)] as a generalization of the well known guiding center approximation, and show the ranges of applicability of this concept, especially in strongly inhomogeneous fields when adiabatic approximations break.     

Nonuniformity of the transverse distribution of the resonant field excited by a beam of electromagnetic waves at the critical surface of a radially nonuniform plasma sphere

Simple approximate formulas are obtained for the characteristic length of the transverse amplitude-phase nonuniformity of the resonant field excited by a beam of electromagnetic fields at the critical surface of a spherical plasma body. Zh. Tekh. Fiz. 67, 121–122 (June 1997)