Homogeneous Dielectric Medium Research Articles

On the Axion Electrodynamics in a two-dimensional slab and the Casimir effect

We analyze the Axion Electrodynamics in a two-dimensional slab of finite width L containing a homogeneous and isotropic dielectric medium with constant permittivity and permeability. We start from the known decomposition of modes in the nonaxion case and then solve perturbatively the governing equations for the electromagnetic fields to which the axions are also coupled. This is a natural approach, since the finiteness of L destroys the spatial invariance of the theory in the z-direction normal to the plates. In this way, we derive the value of the axion-generated rotation angle of the electric and magnetic fields after their passage through the slab, and use the obtained results to calculate the Casimir force between the two conducting plates. Our calculations make use of the same method as previously outlined by [J. S. Høye and I. Brevik, Eur. Phys. J. Plus 135, 271 (2020)] for the case of Casimir calculations in chiral media and extend former results on the Casimir force in Axion Electrodynamics.

Drag Resistivity of Hole-Hole Static Interactions with the Effect of Non- Homogeneous Dielectric Medium

BACKGROUND: We have study the Coulomb drag phenomena for hole-hole static potentials theoretically and measured numerically using the random phase approximation (RPA) method OBJECTIVE: The drag resistivity is evaluated at low temperature, large interlayer separation limit and weakly screening regime, with the geometry of two atomically thin materials, such as, BLG/GaAs based multilayer system, is a promising systems in nanomaterials and technology METHOD: Static local field corrections (LFC) are considered to take into account the Exchange-correlations (XC) and mutual interaction effects with varying concentrations of active and passive layer RESULT: It is found that the drag resistivity is found enhanced on using the LFC effects and increases on increasing the effective mass. In Fermi-Liquid regime, drag resistivity is directly proportional to T^2, n^(-3), d^(-4) and ϵ^2 with respect to temperature (T), density (n), interlayer separation (d~nm) and dielectric constant (ϵ_2), respectively. CONCLUSION: Dependency of drag resistivity is measured and compared to 2D e-e and e-h coupled-layer systems with and without the effect of non-homogeneous dielectric medium.

Electromagnetoelastic transport through a piezoelectric slab: Selective parity interplay of electromagnetic and acoustic resonances

We present the complete solution concerning to transport properties of coupled transverse electromagnetic and shear acoustic waves propagating via a piezoelectric slab embedded into a homogeneous dielectric medium. Since the electroacoustics of our setup is governed by four electromagnetoelastic eigenmodes, we had to succeed in developing a 4 × 4 transfer matrix method to analytically resolve the problem. As a result, the exact frequency spectra of the transmission, reflection, and transformation transport coefficients were obtained and analyzed in detail for two basic cases where the piezoelectric slab subjected by electromagnetic/acoustic perturbation generates acoustic/electromagnetic response. We establish that wave transformation is effectively realized in vicinities of electromagnetic and acoustic Fabry–Pérot resonances. Surprisingly, as a consequence of the problem geometry and accepted 4 mm symmetry of the piezoelectric medium, the phenomenon of the resonant parity selection arises: in the vicinity of an electromagnetic Fabry–Pérot resonance of the given (odd/even) parity, only acoustic Fabry–Pérot resonances with opposite (even/odd) parity are excited in the coefficient of generation. The piezoelectric coupling vanishes when the parities of both resonances coincide. The changes in transmission and reflection spectra turn out to be more sophisticated. The phenomenon is observed due to quite great distinction between electromagnetic and acoustic wave numbers provided by the fundamental difference between light and sound velocities. In our analysis, particular attention is also paid to the ability of increasing the mutual transformation of electromagnetic and acoustic fluxes.

Axionic and nonaxionic electrodynamics in plane and circular geometry

Various aspects of axion electrodynamics in the presence of a homogeneous and isotropic dielectric medium are discussed. First, we consider the ``antenna-like'' property of a planar dielectric surface in axion electrodynamics, elaborating on the treatment given earlier on this topic by Millar et al. [J. Cosmol. Astropart. Phys. 01 (2017) 061.]. We calculate the electromagnetic energy transmission coefficient for a dielectric plate, and compare with the conventional expression in ordinary electrodynamics. Second, we consider the situation where the medium exterior to the plate, assumed elastic, is ``bent back'' and glued together, so that we obtain a circular dielectric string in which the waves can propagate clockwise or counterclockwise. As will be shown, a stationary wave pattern is permitted by the formalism, and we show how the amplitudes for the two counterpropagating waves can be found. Third, as a special case, by omitting axions for a moment, we analyze the Casimir effect for the string, showing its similarity as well as its difference from the Casimir effect of a scalar field for a piecewise uniform string [I. Brevik and H. B. Nielsen, Phys. Rev. D 41, 1185 (1990).]. Finally, including axions again we analyze the enhancement of the surface-generated electromagnetic radiation near the center of a cylindrical haloscope, where the interior region is a vacuum and the exterior region a high refractive index medium. This enhancement is caused by the curvature of the boundary, and is mathematically a consequence of the behavior of the Hankel function of the second kind for small arguments. A simple estimate shows that enhancement may be quite significant, and can therefore be of experimental interest. The presence of an absorber in the center and the possibility of adopting it to search for axions with mass in the THz region, and possibly the GHz region too, is also discussed. This proposal is suggested as an alternative to the reflector arrangement in a similar arrangement recently discussed by Liu et al. [, Phys. Rev. Lett. 128, 131801 (2022).].

A regularization approach for solving the super-Gaussian Poisson-Boltzmann model with heterogeneous dielectric functions

A regularization method is introduced for the first time in the literature for treating charge singularities in the heterogeneous dielectric Poisson-Boltzmann (PB) model. In the existing Gaussian and super-Gaussian electrostatic analysis, the singular sources in terms of Dirac delta functions are approximated by trilinear interpolation, which introduces a large error in potential solutions, and has to rely on an error cancellation for delivering acceptable estimates of the electrostatic free energy. To overcome this difficulty, a dual decomposition of potential and dielectric function is carried out in the proposed regularization, so that the charge singularities can be analytically captured by the Coulomb potential, while the reaction field potential satisfies a regularized PB equation with a new source term. A rigorous analysis has been conducted to show that a super-Gaussian density, instead of a Gaussian one, is required to guarantee a small neighborhood around each atom center with a nearly homogeneous dielectric medium, so that the source term can be well defined in the sense of distribution. Moreover, the well-posedness of the regularized formulation has been proved, and the regularity of the weak solution has been clarified. In the numerical implementation, special considerations are given in calculating the source term, by using analytical differentiations, instead of numerical approximations, whenever possible. The accuracy, convergence, efficiency, and robustness of the proposed regularization are numerically verified via benchmark studies. It is found that the regularization is more accurate than the trilinear method, as well as produces a faster convergence in energy estimation. Moreover, the grid artifact or artificial grid energy is completely eliminated in the present finite difference PB model.

Theory of perturbation of electric potential by a 3D object made of an anisotropic dielectric material

The extended boundary condition method (EBCM) was formulated for the perturbation of a source electric potential by a 3D object composed of a homogeneous anisotropic dielectric medium whose relative permittivity dyadic is positive definite. The formulation required the application of Green’s second identity to the exterior region to deduce the electrostatic counterpart of the Ewald–Oseen extinction theorem. The electric potential inside the object was represented using a basis obtained by implementing an affine bijective transformation of space to the Gauss equation for the electric field. The EBCM yields a transition matrix that depends on the geometry and the composition of the 3D object, but not on the source potential.

Determination of Permittivity of Homogeneous Dielectric Medium Using Rectangular Patch Antenna

In this article, a design guide line is proposed to determine the permittivity of homogeneous dielectric medium using rectangular patch antenna. The numerical values obtained with present model are compared with experimental results. The very close correlation is seen between the computed and measured values.

The problem of a hydrogen atom in a cavity: Oscillator representation solution versus analytic solution

Abstract A solution to the problem of a hydrogenic atom in a homogeneous dielectric medium with a concentric spherical cavity using the oscillator representation method (ORM) is presented. The results obtained by the ORM are compared with a known exact analytic solution. The energy levels of the hydrogenic atom in a spherical cavity exhibit a shallow-deep instability as a function of the cavity radius. The sharpness of the transition depends on the value of the dielectric constant of the medium. The results of the ORM agree well with the results obtained by the analytic solution when the shallow-deep transition is not too sharp (i.e., when the dielectric constant is not too large) for all values of the cavity radius. The ORM results in the zeroth order approximation diverge significantly in the region of the shallow-deep transition (i.e., for the values of the radius where the shallow-deep transition occurs) when the dielectric constant is high and as a result the transition is sharp. Even for the sharp transition, the ORM results again agree very well with the analytic results at least for the ground state when a commonly used approximation in the ORM is removed. The ORM methodology for the cavity model presented in this article can potentially be used for two-electron systems in a quantum dot.

Example of a simple thought experiment that goes in favor of the Minkowski form of the photon momentum in medium

A novel approach to the Abraham-Minkowski dilemma based on a simple thought experiment is presented. The mathematical analysis of the simple thought experiment, which is based on a plane, monochromatic, uniform electromagnetic wave that propagates through the infinite, homogeneous, linear and isotropic dielectric medium without losses and impinges the surface of a perfect mirror, shows that the presented thought experiment goes in favor of the Minkowski form of the photon momentum in medium.

Влияние однородной диэлектрической среды на люминесценцию синглетного кислорода

Presents the results of an analysis of our and literature data devoted to the study of the effect of a homogeneous dielectric medium on the rate constant of the radiative transition 1Dg in singlet oxygen. It is shown that the influence of the refractive index n on the radiative rate constant is due to a change in both the density of photon states and the local field factor. At the same time, in a dielectric medium, the transition dipole moment increases significantly as a result of the contact of singlet oxygen with solvent molecules. Only taking into account all of the above factors will provide a consistent explanation of the influence of the medium on the rate constant of the luminescence of singlet oxygen.

Generation of twisted photons by undulators filled with dispersive medium

The radiation of twisted photons by undulators filled with a homogeneous dielectric dispersive medium is considered. The general formulas for the average number of radiated twisted photons are obtained. The radiation of undulators in the dipole regime and the radiation of the helical and planar wigglers are studied in detail. It is shown that the selection rules for radiation of twisted photons established for undulators in a vacuum also holds for undulators filled with a dielectric medium. In the case of a medium with plasma permittivity the lower undulator harmonics do not form. This fact can be used for generation of twisted photons with nonzero orbital angular momentum on the lowest admissible harmonic. The use of the effect of inverse radiation polarization for generation of twisted photons with larger orbital angular momentum is described. The influence of the anomalous Doppler effect on the projection of the total angular momentum of radiated twisted photons is investigated. The parameters of the undulator and the charged particles are found such that the produced radiation, in particular, the Vavilov-Cherenkov radiation, is a pure source of twisted photons with definite nonzero orbital angular momentum. The developed theory is used to describe the radiation of twisted photons by beams of electrons and protons in the undulators filled with helium. We also consider the radiation of X-ray twisted photons by electrons in the undulator filled with xenon. The parameters are chosen so as to be achievable at the present experimental facilities.

Gating of Hydrophobic Nanopores with Large Anions.

Understanding ion transport in nanoporous materials is critical to a wide variety of energy and environmental technologies, ranging from ion-selective membranes, drug delivery, and biosensing, to ion batteries and supercapacitors. While nanoscale transport is often described by continuum models that rely on a point charge description for ions and a homogeneous dielectric medium for the solvent, here, we show that transport of aqueous solutions at a hydrophobic interface can be highly dependent on the size and hydration strength of the solvated ions. Specifically, measurements of ion current through single silicon nitride nanopores that contain a hydrophobic-hydrophilic junction show that transport properties are dependent not only on applied voltage but also on the type of anion. We find that in Cl--containing solutions the nanopores only conducted ionic current above a negative voltage threshold. On the other hand, introduction of large polarizable anions, such as Br- and I-, facilitated the pore wetting, making the pore conductive at all examined voltages. Molecular dynamics simulations revealed that the large anions, Br- and I-, have a weaker solvation shell compared to that of Cl- and consequently were prone to migrate from the aqueous solution to the hydrophobic surface, leading to the anion accumulation responsible for pore wetting. The results are essential for designing nanoporous systems that are selective to ions of the same charge, for realization of ion-induced wetting in hydrophobic pores, as well as for a fundamental understanding on the role of ion hydration shell on the properties of solid/liquid interfaces.

Wavelength-stabilized near-field laser.

Surface-trapped electromagnetic waves can be localized at a boundary between a semiconductor distributed Bragg reflector (DBR) and a homogeneous dielectric medium or air. These waves enable a novel class of in-plane-emitting optical devices including edge-emitting lasers, disk microlasers or near-field fiber-coupled lasers. We show that the surface-trapped modes can be controlled by tuning the thickness of a single DBR layer. Diagrams in variables "wavelength - thickness of the control layer" are constructed for both TM and TE optical modes revealing the parameter domains, in which surface-trapped modes exist. The domains contain cusps, in the vicinity of which a surface-trapped optical mode is allowed only in a narrow spectral region, enabling wavelength-stabilized operation of a laser. For a structure designed for lasing at ∼1 µm, the lasing wavelength shifts upon temperature increase at a rate ∼0.08 nm/K. The fraction of the optical power of the surface-trapped mode accumulated in the homogeneous dielectric can reach ∼50%. Thus, such structure is a near-field wavelength-stabilized semiconductor laser. Further, such structure can be applied as a wavelength-stabilized semiconductor optical amplifier adjacent to a dielectric waveguide or an optical fiber, both for integrated photonics and for ultrahigh-brightness laser diodes and diode arrays and stacks.

Characterization of the essential spectrum of the Neumann–Poincaré operator in 2D domains with corner via Weyl sequences

The Neumann–Poincaré (NP) operator naturally appears in the context of metamaterials as it may be used to represent the solutions of elliptic transmission problems via potentiel theory. In particular, its spectral properties are closely related to the well-posedness of these PDE’s, in the typical case where one considers a bounded inclusion of homogeneous plasmonic metamaterial embedded in a homogeneous background dielectric medium. In a recent work, M. Perfekt and M. Putinar have shown that the NP operator of a 2D curvilinear polygon has an essential spectrum, which depends only on the angles of the corners. Their proof is based on quasi-conformal mappings and techniques from complex-analysis. In this work, we characterise the spectrum of the NP operator for a 2D domain with corners in terms of elliptic corner singularity functions, which gives insight on the behaviour of generalized eigenmodes.

Reconciliation of the Rosen and Laue theories of special relativity in a linear dielectric medium

The theory of dielectric special relativity was derived by Laue from a fundamental physical basis in Einstein's special relativity and the relativistic velocity sum rule. The Laue theory is experimentally verified by the Fizeau water tube experiment. In contrast, the Rosen version of dielectric special relativity was derived heuristically and has no experimental validation. Consequently, the Rosen theory and its consequences are mostly ignored in the scientific literature and there is little to no discussion about the incompatibility of the two theories of relativity in a dielectric. In this article, the Laue theory is developed from boundary conditions using inertial reference frames moving at constant velocity along the interface between a simple linear dielectric medium and the vacuum. Then, the Rosen theory is derived in the context of inertial frames of reference moving at constant velocity in the interior of an arbitrarily large linear isotropic homogeneous dielectric medium. These derivations show that the Laue and Rosen theories of dielectric special relativity are both correct but have different regimes of applicability. The Rosen theory applies to physics in the interior of a simple linear dielectric and the Laue theory is used to relate these physics to a Laboratory Frame of Reference in the vacuum where measurements can be performed.

Theoretical analysis of screened many-body electrostatic interactions between charged polarizable particles

This paper builds on two previous studies [Lindgren et al., J. Comput. Phys. 371, 712 (2018) and Quan et al., "A domain decomposition method for the Poisson-Boltzmann solvation models," SIAM J. Sci. Comput. (to be published); e-print arXiv:1807.05384] to devise a new method to solve the problem of calculating electrostatic interactions in a system composed by many dielectric particles, embedded in a homogeneous dielectric medium, which in turn can also be permeated by charge carriers. The system is defined by the charge, size, position, and dielectric constant of each particle, as well as the dielectric constant and the Debye length of the medium. The effects of taking into account the dielectric nature of the particles are explored in selected scenarios where the presence of electrolytes in the medium can significantly influence the total undergoing interactions. The description of the mutual interactions between all particles in the system as being truly of many-body nature reveals how such effects can effectively influence the magnitudes and even directions of the resulting forces, especially those acting on particles that have a null net charge. Particular attention is given to a situation that can be related to colloidal particles in an electrolyte solution, where it is shown that polarization effects alone can substantially raise or lower-depending on the dielectric contrast between the particles and the medium-the energy barrier that divides particle coagulation and flocculation regions, when an interplay between electrostatic and additional van der Waals forces is considered. Overall, the results suggest that for an accurate description of the type of system in question, it is essential to consider particle polarization if the separation between the interacting particles are comparable to or smaller than the Debye length of the medium.

Анализ и синтез несимметричных связанных линий в однородной диэлектрической среде

Анализ и синтез несимметричных связанных линий в однородной диэлектрической среде

Ellipsoidal Inclusion with a Shell in an Anisotropic Medium Subjected to a Uniform Electric Field

An electrostatic problem has been solved for a dielectric inclusion consisting of an anisotropic core and a shell immersed in a homogeneous anisotropic dielectric medium (matrix) subjected to a uniform electric field. The outer boundaries of the core and shell are assumed to be ellipsoids, which are confocal after a linear nonorthogonal transformation that eliminates the anisotropy of the dielectric properties of the shell. Analytical expressions have been obtained for the potential and the electric field strength in the matrix, in the shell and core, and an expression for the inclusion polarizability tensor. A special case of inclusion with an isotropic shell is considered. The expressions obtained are applied to the case of an anisotropic sphere with an isotropic shell immersed in an anisotropic medium. It is also shown that in the limiting case of a homogeneous ellipsoidal inclusion in an anisotropic medium, the obtained result agrees with known solutions.

An integral equation approach to calculate electrostatic interactions in many-body dielectric systems

In this article, a numerical method to compute the electrostatic interaction energy and forces between many dielectric particles is presented. The computational method is based on a Galerkin approximation of an integral equation formulation, which is sufficiently general, as it is able to treat systems embedded in a homogeneous dielectric medium containing an arbitrary number of spherical particles of arbitrary size, charge, dielectric constant and position in the three-dimensional space. The algorithmic complexity is linear scaling with respect to the number of particles for the computation of the energy which has been achieved through the use of a modified fast multipole method. The method scales with the third power of the degree of spherical harmonics used in the underlying expansions, for general three-dimensional particle configurations. Several simple numerical examples illustrate the capabilities of the model, and the influence of mutual polarization between particles in an electrostatic interaction is discussed.

TESTING OF NUMERICAL SOLUTION OF THE PROBLEM OF DETERMINING SOURCES OF MAGNETOSTATIC FIELD IN MAGNETIZED MEDIUM

Purpose. Testing of numerical solution algorithm for integral equation for calculation of plane meridian magnetostatic field source distribution at interfaces of piecewise homogeneous magnetized medium by means of electrostatic analogy. Methodology. The piecewise homogeneous medium consists of three regions with different magnetic permeabilities: the shell of arbitrary meridian section, external unlimited medium outside the shell, and the medium inside the shell. For testing external homogeneous magnetic field effect on spherical shell is considered. The analytical solution of this problem on the basis of electrostatic analogy from the solution of the problem uniform electrostatic field effect on dielectric shell is obtained. We have compared results of numerical solution of integral equation with the data obtained by means of analytical solution at the variation of magnetic permeabilities of regions of medium. Results. Integral equation and the algorithm of its numerical solution for calculation of source field distribution at the boundaries of piecewise homogeneous medium is validated. Testing of integral equations correctness for calculation of fictitious magnetic charges distribution on axisymmetric boundaries of piecewise homogeneous magnetized medium and algorithms of their numerical solutions can be carried out by means of analytical solutions of problems of homogeneous electrostatic field effect analysis on piecewise homogeneous dielectric medium with central symmetry of boundaries – single-layer and multilayer spherical shells. In the case of spherical shell in wide range of values of the parameter λk, including close to ± 1, numerical solution of integral equation is stable, and relative error in calculating of fictitious magnetic charges surface density and magnetic field intensity inside the shell is from tenths of a percent up to several percent except for the cases of very small values of these quantities. Originality. The use analytical solutions for problems of calculation of external electrostatic field effect on piecewise homogeneous dielectric bodies for testing integral equations of magnetostatics and algorithms for their numerical solutions. Practical value. The described method of testing integral equations of magnetostatics and their numerical solutions can be used for calculation of magnetic fields of spacecraft control system electromagnets.