scholarly journals Effective Electrodynamics Theory for the Hyperbolic Metamaterial Consisting of Metal–Dielectric Layers

Crystals ◽  
2020 ◽  
Vol 10 (10) ◽  
pp. 863
Author(s):  
Pi-Gang Luan
Keyword(s):  
Energy Density ◽  
Electromagnetic Fields ◽  
Lagrangian Density ◽  
Effective Medium ◽  
Polarization Field ◽  
Lagrangian Description ◽  
Dynamical Equations ◽  
Hamiltonian Density ◽  
Hyperbolic Metamaterial ◽  
Dielectric Layers

In this work, we study the dynamical behaviors of the electromagnetic fields and material responses in the hyperbolic metamaterial consisting of periodically arranged metallic and dielectric layers. The thickness of each unit cell is assumed to be much smaller than the wavelength of the electromagnetic waves, so the effective medium concept can be applied. When electromagnetic (EM) fields are present, the responses of the medium in the directions parallel to and perpendicular to the layers are similar to those of Drude and Lorentz media, respectively. We derive the time-dependent energy density of the EM fields and the power loss in the effective medium based on Poynting theorem and the dynamical equations of the polarization field. The time-averaged energy density for harmonic fields was obtained by averaging the energy density in one period, and it reduces to the standard result for the lossless dispersive medium when we turn off the loss. A numerical example is given to reveal the general characteristics of the direction-dependent energy storage capacity of the medium. We also show that the Lagrangian density of the system can be constructed. The Euler–Lagrange equations yield the correct dynamical equations of the electromagnetic fields and the polarization field in the medium. The canonical momentum conjugates to every dynamical field can be derived from the Lagrangian density via differentiation or variation with respect to that field. We apply Legendre transformation to this system and find that the resultant Hamiltonian density is identical to the energy density up to an irrelevant divergence term. This coincidence implies the correctness of the energy density formula we obtained before. We also give a brief discussion about the Hamiltonian dynamics description of the system. The Lagrangian description and Hamiltonian formulation presented in this paper can be further developed for studying the elementary excitations or quasiparticles in other hyperbolic metamaterials.

scholarly journals Dynamics of Electromagnetic Fields and Structure of Regular Rotating Electrically Charged Black Holes and Solitons in Nonlinear Electrodynamics Minimally Coupled to Gravity

Universe ◽  
2019 ◽  
Vol 5 (10) ◽  
pp. 205 ◽  
Author(s):  
Irina Dymnikova ◽  
Evgeny Galaktionov
Keyword(s):  
Black Holes ◽  
Electromagnetic Fields ◽  
Nonlinear Electrodynamics ◽  
Axially Symmetric ◽  
De Sitter ◽  
Dynamical Equations ◽  
Naked Singularities ◽  
Charged Black Holes ◽  
De Sitter Vacuum ◽  
Electrically Charged

We study the dynamics of electromagnetic fields of regular rotating electrically charged black holes and solitons replacing naked singularities in nonlinear electrodynamics minimally coupled to gravity (NED-GR). They are related by electromagnetic and gravitational interactions and described by the axially symmetric NED-GR solutions asymptotically Kerr-Newman for a distant observer. Geometry is described by the metrics of the Kerr-Schild class specified by T t t = T r r ( p r = − ρ ) in the co-rotating frame. All regular axially symmetric solutions obtained from spherical solutions with the Newman-Janis algorithm belong to this class. The basic generic feature of all regular objects of this class, both electrically charged and electrically neutral, is the existence of two kinds of de Sitter vacuum interiors. We analyze the regular solutions to dynamical equations for electromagnetic fields and show which kind of a regular interior is favored by electromagnetic dynamics for NED-GR objects.

Interaction Between the Magnetic Polariton and Surface Plasmon Polariton

2013 ◽  
Author(s):  
Yu-Bin Chen ◽  
Chien-Jing Chen
Keyword(s):  
Energy Density ◽  
Electromagnetic Fields ◽  
Surface Plasmon ◽  
Surface Plasmon Polariton ◽  
Reflectance Spectra ◽  
Resonance Excitation ◽  
Contour Plot ◽  
Magnetic Polariton ◽  
Plasmon Polariton ◽  
Poynting Vectors

This work numerically investigated the interaction between two resonances: the magnetic polariton (MP) and surface plasmon polariton (SPP). A reflectance contour plot of deep silver slit arrays quantitatively identified the MP mode and the SPP excitation’s dependence on the period. Five arrays were selected for their SPP excitation wavenumber that approached and then diverged from that of an MP mode. Reflectance spectra from arrays showed dips associated with the two resonances between 10000 cm−1 and 25000 cm−1. Both the magnitude and corresponding wavenumber of nearby dips were modified by the interaction. Moreover, a third dip might appear or two dips might merge into a wider valley when two resonance excitation wavenumbers are close enough. The interaction was further elucidated with electromagnetic fields, Poynting vectors, and the energy density corresponding to representative reflectance dips.

Dispersion relations and wave propagation in photonic hypercrystals

2018 ◽  
Vol 32 (02) ◽  
pp. 1750320 ◽  
Author(s):  
Munazza Zulfiqar Ali
Keyword(s):  
Wave Vector ◽  
Dielectric Material ◽  
Effective Medium ◽  
Evanescent Waves ◽  
Dispersion Relations ◽  
Matrix Approach ◽  
Periodic Medium ◽  
Hyperbolic Metamaterial ◽  
Propagating Waves ◽  
Transfer Matrix Approach

A photonic hypercrystal is a subwavelength periodic structure consisting of alternate layers of hyperbolic metamaterial and dielectric material. The structure can be treated as an effective medium as well as a periodic medium. Since two length scales are involved, the better treatment is to treat the hyperbolic metamaterial as an effective medium and the overall structure as a periodic medium. The dispersion relations are derived and plotted to show the appearance of propagating bands and gaps in the frequency and wave vector domains. Then using the transfer matrix approach, the transmissivity versus the frequency plot for propagating waves and grayscale plot of the transmission coefficient in the frequency versus wave vector plane for the evanescent waves are plotted and analyzed.

scholarly journals DYONS OF ONE-HALF MONOPOLE CHARGE

2006 ◽  
Vol 21 (26) ◽  
pp. 5285-5298
Author(s):  
ROSY TEH ◽  
KHAI-MING WONG
Keyword(s):  
Energy Density ◽  
Electromagnetic Fields ◽  
Axially Symmetric ◽  
Yang Mills ◽  
First Order ◽  
Line Singularity ◽  
Infinite Energy

We would like to present some exact SU(2) Yang–Mills–Higgs dyon solutions of one-half monopole charge. These static dyon solutions satisfy the first order Bogomol'nyi equations and are characterized by a parameter, m. They are axially symmetric. The gauge potentials and the electromagnetic fields possess a string singularity along the negative z-axis and hence they possess infinite energy density along the line singularity. However the net electric charges of these dyons which varies with the parameter m are finite.

scholarly journals First Order Framework for Gauge k-Vortices

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
D. Bazeia ◽  
L. Losano ◽  
M. A. Marques ◽  
R. Menezes
Keyword(s):  
Scalar Field ◽  
Energy Density ◽  
Boundary Conditions ◽  
Unit Circle ◽  
Analytical Solutions ◽  
Covariant Derivative ◽  
Lagrangian Density ◽  
Kinetic Term ◽  
First Order

We study vortices in generalized Maxwell-Higgs models, with the inclusion of a quadratic kinetic term with the covariant derivative of the scalar field in the Lagrangian density. We discuss the stressless condition and show that the presence of analytical solutions helps us to define the model compatible with the existence of first order equations. A method to decouple the first order equations and to construct the model is then introduced and, as a bonus, we get the energy depending exclusively on a function of the fields calculated from the boundary conditions. We investigate some specific possibilities and find, in particular, a compact vortex configuration in which the energy density is all concentrated in a unit circle.

scholarly journals Applications of Hyperbolic Metamaterial Substrates

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Yu Guo ◽  
Ward Newman ◽  
Cristian L. Cortes ◽  
Zubin Jacob
Keyword(s):  
Surface Plasmon ◽  
Surface Plasmon Polaritons ◽  
Radiative Decay ◽  
Thermal Emission ◽  
Effective Medium ◽  
Radiative Decay Engineering ◽  
Hyperbolic Metamaterials ◽  
Hyperbolic Metamaterial ◽  
Subsurface Sensing ◽  
Plasmon Polaritons

We review the properties of hyperbolic metamaterials and show that they are promising candidates as substrates for nanoimaging, nanosensing, fluorescence engineering, and controlling thermal emission. Hyperbolic metamaterials can support unique bulk modes, tunable surface plasmon polaritons, and surface hyperbolic states (Dyakonov plasmons) that can be used for a variety of applications. We compare the effective medium predictions with practical realizations of hyperbolic metamaterials to show their potential for radiative decay engineering, bioimaging, subsurface sensing, metaplasmonics, and super-Planckian thermal emission.

scholarly journals THE FOCUSING OF VACUUM FLUCTUATIONS

2002 ◽  
Vol 17 (29) ◽  
pp. 4393-4402
Author(s):  
L. H. FORD ◽  
N. F. SVAITER
Keyword(s):  
Energy Density ◽  
Electric Field ◽  
Electromagnetic Fields ◽  
Electric Fields ◽  
Negative Energy ◽  
Parabolic Mirror ◽  
Vacuum Fluctuations ◽  
Negative Energy Density ◽  
Cylindrical Mirror ◽  
The Mean

The quantization of the scalar and electromagnetic fields in the presence of a parabolic mirror is developed in the context of a geometric optics approximation. We calculate the mean squared scalar and electric fields near the focal line of a parabolic cylindrical mirror. These quantities are found to grow as inverse powers of the distance from the focus. We give a combination of analytic and numerical results for the mean squared fields. In particular, we find that the mean squared electric field can be either negative or positive, depending upon the choice of parameters. The case of a negative mean squared electric field corresponds to a repulsive Van der Waals force on an atom near the focus, and to a region of negative energy density. Similarly, a positive value corresponds to an attractive force and a possibility of atom trapping in the vicinity of the focus.

scholarly journals On the Synergic Relationships between Special Relativity and Quantum Theories

2020 ◽  
pp. 34-43
Author(s):  
E. Comay
Keyword(s):  
Lagrangian Density ◽  
Energy Momentum Tensor ◽  
Quantum Particle ◽  
Momentum Tensor ◽  
Lagrange Equations ◽  
Quantum Theories ◽  
Hamiltonian Density ◽  
Relativistic Form ◽  
Lorentz Scalar ◽  
Conservation Laws Of Energy

The successful results of the relativistic form of a quantum field theory that is derived from aLagrangian density justify its general usage. The significance of the Euler-Lagrange equations of a quantum particle is analysed. Many advantages of this approach, like abiding by the conservation laws of energy, momentum, angular momentum, and charge are well known. The merits of this approach also include other properties that are still not well known. For example, it is shown that a quantum function of the form ψ(t, r) describes a pointlike particle. Furthermore, the Lagrangian density and the Hamiltonian density take a different relativistic form – the Lagrangian density is a Lorentz scalar, whereas the Hamiltonian density is the T00 component of the energy-momentum tensor. It is proved that inconsistencies in the electroweak theory stem from negligence of the latter point.

The thermodynamics of bodies in static electromagnetic fields

1956 ◽  
Vol 52 (3) ◽  
pp. 546-552 ◽  
Author(s):  
V. Heine
Keyword(s):  
Electromagnetic Field ◽  
Energy Density ◽  
Magnetic Fields ◽  
Electromagnetic Fields ◽  
Permanent Magnets ◽  
Entropy Density ◽  
The Body ◽  
Thermodynamic Behaviour ◽  
Electric And Magnetic Fields

ABSTRACTThe thermodynamic behaviour of a body in a static electromagnetic field depends only on the field over the region of the body itself, whence its own thermodynamic behaviour is determined even in the presence of other polarizable media. Its behaviour depends only on the entropy density, for in fact no real energy density need exist. Also new formulae are developed for the energy and for the entropy of a body in electric and magnetic fields, including those due to permanent magnets.

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