Dissipative Slab Research Articles

The calculation of the atomic spontaneous emission rate between two dielectric slabs

In this paper, the spontaneous emission rate of an excited atom between the two dispersive and dissipative dielectric slabs is determined. It is assumed that the atom has a definite transition electric dipole moment, and the dielectric function of the slabs is an arbitrarily complex function of frequency satisfying Kramers–Kronig relations. In this research, by noting to the connection between the spontaneous emission rate and the imaginary part of the vector potential Green function, only by evaluating the vector potential Green function tensor of the system of the two slabs, an expression for the spontaneous emission rate is introduced. In this formalism, it is needless to derive the vacuum electric field operator. The emission rate is obtained in terms of the dielectric function, the thickness and the distance between the slabs. By considering a Lorentz model for the dielectric function of the slabs, the typical spatial variations of the spontaneous emission rate between the two slabs are demonstrated.

Revisiting the Balazs thought experiment in the case of a left-handed material: electromagnetic-pulse-induced displacement of a dispersive, dissipative negative-index slab

We propose a set of postulates to describe the mechanical interaction between a plane-wave electromagnetic pulse and a dispersive, dissipative slab having a refractive index of arbitrary sign. The postulates include the Abraham electromagnetic momentum density, a generalized Lorentz force law, and a model for absorption-driven mass transfer from the pulse to the medium. These opto-mechanical mechanisms are incorporated into a one-dimensional finite-difference time-domain algorithm that solves Maxwell's equations and calculates the instantaneous force densities exerted by the pulse onto the slab, the momentum-per-unit-area of the pulse and slab, and the trajectories of the slab and system center-of-mass. We show that the postulates are consistent with conservation of global energy, momentum, and center-of-mass velocity at all times, even for cases in which the refractive index of the slab is negative or zero. Consistency between the set of postulates and well-established conservation laws reinforces the Abraham momentum density as the one true electromagnetic momentum density and enables, for the first time, identification of the correct form of the electromagnetic mass density distribution and development of an explicit model for mass transfer due to absorption, for the most general case of a ponderable medium that is both dispersive and dissipative.

Casimir energy and entropy between dissipative mirrors

We discuss the Casimir effect between two identical, parallel slabs, emphasizing the role of dissipation and temperature. Starting from quite general assumptions, we analyze the behavior of the Casimir entropy in the limit T → 0 and link it to the behavior of the slab's reflection coefficients at low frequencies. We also derive a formula in terms of a sum over modes, valid for dissipative slabs that can be interpreted in terms of a damped quantum oscillator.

Optimal dispersion relations for enhanced electromagnetic power deposition in dissipative slabs.

Broadband analysis of a prototype model associated with electromagnetic waves absorption in a lossy dielectric slab renders a closed-form theoretical prediction of an infinite number of optimal absorption paths in the complex refractive index domain. While for thin slabs (in terms of incident wavelength range) each path corresponds to a lossy Fabry-Perot-type resonance modes of order m=0,1,2,... and provides at least 50% absorption of the incident wave power even for ultrathin slabs, for optimal thick slabs, the fraction of absorbed power, asymptotically estimated via Lambert W function, increases up to 100% for consecutive continuation of the m=1 normal mode only.

Propagating behavior of rectangular waveguide loaded with dissipative magnetic slab by using new algorithm

Propagating constants of rectangular waveguide loaded with dissipative slab obey complex transcendental equation, of which the property of multiroot and the dependence of modes on those roots often make people puzzled, especially for dissipative magnetic materials in an asymmetrically filling situation. An effective new algorithm combining Genetic Algorithm (GA) with Parameter Tracking Scheme (PTS) and Dynamic Searching Area (DSA) technique is developed. By using the algorithm, the propagating constants of waveguide symmetrically or asymmetrically loaded with dissipative magnetic slab are solved successfully and tightly linked to certain designated modes. The results also reveal some interesting phenomena, such as for some high‐order modes and certain thickness of loaded slab, the negative phase velocity may occur.

Casimir force between two dielectric slabs

We examine the Casimir effect between two dispersive dissipative slabs in three dimensions. The dielectric function of the slabs is assumed to be an arbitrary complex function of frequency satisfying Kramers-Kronig relations. The Maxwell stress tensor is used to evaluate the vacuum radiation pressure of the electromagnetic field on each slab in terms of the field correlation functions. These correlations are simply related to the imaginary part of the vector potential Green function by using the fluctuation dissipation theorem and Kubo's formula. The response function is obtained by employing the standard method for the present configuration. The formalism enables us to calculate the attractive Casimir force between a pair of dielectric slabs without resorting to the electromagnetic field quantization. Special attention is paid to the various limits of the general expression and the results are compared with previous work whenever possible. The Lorentz model of the dielectric function is also used to show the typical behavior of this force in terms of the slab thickness. We also consider the effect of finite temperature on the Casimir force between two dielectric slabs.

An optimization approach to time-domain electromagnetic inverse problem for a stratified dispersive and dissipative slab

The one-dimensional electromagnetic inverse problem for a stratified dispersive and dissipative slab is considered in the time domain. An optimization approach is used to reconstruct the parameters using the measured reflected field and/or transmitted field. Wave-splitting is used, and an explicit expression for the gradient is derived by introducing dual functions. The reconstruction algorithm is tested with both synthetic and experimental data.

A ‘‘compact Green function’’ approach to the time-domain direct and inverse problems for a stratified dissipative slab

A new type of Green function approach is introduced for time-domain scattering for a stratified dissipative slab. The new Green functions are defined as mappings from the transmitted field to the split fields (i.e., the right-moving and left-moving fields) at any point within the stratified slab. Unlike the usual Green functions, the present Green functions have compact support in the time variable. The new technique is illustrated for the case of normally incident electromagnetic waves on a stratified slab where the permittivity, permeability, and conductivity vary with the depth. The linear and homogeneous partial differential equations (PDEs) for these ‘‘compact Green functions’’ are derived. The PDEs together with the initial and boundary conditions are well suited for a numerical treatment. Numerical results for the compact Green functions are presented in the direct problem, while in the inverse problem the permittivity and conductivity (or the permeability and conductivity) are reconstructed simultaneously using the reflection and transmission data for the first round trip. The present method is useful and attractive for both the direct and inverse problems due to its simplicity, high speed, and high accuracy in numerical computations.

Frequency and Time Domain Green Function Technique for Nonuniform LCRG Transmission Lines with Frequency-Dependent Parameters

The reflection and transmission of waves on a nonuniform LCRG transmission line of finite length with frequency-dependent parameters are considered. A Green function technique combined with wave splitting is used both in the frequency domain and the time domain. In the frequency domain ordinary differential equations (ODEs) for the time-harmonic Green functions are obtained. In the time domain the transmission line model is established through a set of dispersion kernels. Partial differential equations (PDEs) for the time-domain Green functions are derived. Numerical results for transient reflected, transmitted and internal currents are presented. Furthermore, it is noted that a special case of the present formalism can be used to determine the reflected, transmitted and internal fields for normal plane wave incidence on a stratified dispersive and dissipative slab.

The electromagnetic inverse problem in the time domain for a dissipative slab and a point source using invariant imbedding: reconstruction of the permittivity and conductivity

He, S. and S. Ström, The electromagnetic inverse problem in the time domain for a dissipative slab and a point source using invariant imbedding: Reconstruction of the permittivity and conductivity, Journal of Computational and Applied Mathematics 42 (1992) 137-155. We consider the electromagnetic inverse problem for a point source above an inhomogeneous dissipative slab of permittivity ∈( z) and conductivity σ( z), where z is the depth. Two inversion algorithms based on the invariant imbedding equations derived in previous work are used to reconstruct both the permittivity and the conductivity. Both algorithms use two-sided reflection data and one of them also uses transmission data. Results are presented for clean and noisy data.

The electromagnetic scattering problem in the time domain for a dissipative slab and a point source using invariant imbedding

A vertical magnetic dipole source above an inhomogeneous slab is considered where the permittivity ε=ε(z) and conductivity σ=σ(z) vary with the depth z. Using the axial symmetry of the problem, a Hankel transform is introduced. Besides physical scattering kernels, ‘‘nonphysical’’ scattering kernels are introduced and the direct and inverse transformed problem is solved by means of wave splitting in an invariant imbedding approach. The imbedding equations for the nonphysical scattering kernels are simpler than the corresponding equations for the physical kernels and they are solved using existing techniques for the imbedding equations for normally incident plane waves. The solution for the physical kernels is obtained by establishing relations between the two sets of kernels. These relations are given by Volterra equations of the second kind and thus are very easy to solve numerically. Some applications and extensions of the results derived in the paper are discussed.

Theory of Optical Second-Harmonic Generation in Slab Waveguides with Dissipative Nonlinear Dielectric Cores

A theory of optical second-harmonic generation (SHG) in a dissipative slab waveguide is presented, where Cerenkov-radiation-type SHG and guided-mode-type SHG are treated on an equal basis. Analytical solutions of the field distribution are obtained for TE-mode second-harmonic waves generated in a slab waveguide consisting of a dissipative nonlinear-dielectric core and nondissipative linear-dielectric claddings. We then study the effects of absorption on the conversion efficiency, providing typical examples of numerical calculation for Cerenkov-radiation-type SHG.

The optimization of electromagnetic energy within a dissipative slab

Consider an electromagnetic plane wave impinging normally on a one-dimensional dissipative medium characterized by spatially varying permitivity and conductivity profiles. In this paper a technique is presented for choosing from among all incident plane waves with fixed energy and duration, one which maximizes the electromagnetic energy within a specified region of the medium. This is done by using the Green's operator for dissipative media of Krueger and Ochs to formulate the problem as an optimization problem in which a weakly continous functional is maximized over a weakly compact set of square- integrable functions. The maximizing incident signal is seen to be an eigenfunction of a compact. Fredholm integral operator. The efficacy of this technique is demonstrated by numerically computing these eigenfunctions for one example medium and comparing the resulting energy distribution with that of an analogous minimizing signal.

Scaling Laws for the Scattering of Resonance Line Photons

Resonance lines of ions with a large Z are broadened essentially by natural damping, and therefore photons with frequencies larger than a few Doppler widths are scattered almost coherently. This "coherent" scattering of resonance-line photons can be described by a space and frequency diffusion process when the mean number of scatterings undergone by the photons is sufficiently large. Some asymptotic scaling laws for the radiation field of these resonance lines are given (in terms of the mean number of scatterings), and an approximation for the mean number of scatterings in a dissipative slab is suggested.

Radio Loss of Lateral Waves in Forest Environments

The radio loss between two small dipoles located in a forest is examined in the frequency range of 2–200 MHz by characterizing the forest in terms of a dissipative slab backed by an imperfectly conducting ground. A careful derivation of the total radio loss L shows that it consists of four distinct constituents: (1) a basic loss L0 associated with the forest‐air interface, (2) a separation loss L8 due to the vegetation above the antenna, (3) a wave‐interference loss Li due to field reflections at the ground plane, and (4) an antenna input resistance loss Lr produced by the ground proximity. The functional variation of these losses is consistent with previously obtained results that viewed the field in terms of a lateral wave, which now affords a simple physical interpretation for each of the separate factors enumerated above. By choosing parameters describing typical forests, we show that the variation of the four constituents leads to a total loss whose behavior agrees with available experimental data and with previous theoretical considerations pertinent to high antennas. In contrast to these, the present investigation predicts, for low antennas, that vertical polarization is preferable to the horizontal one and that communication conditions may be further improved if the operating frequency is increased rather than decreased. The antenna height gain effect is also examined in detail, and it is shown to be strongly affected by the ground proximity in a manner that had not been recognized hitherto.

On radio-wave propagation in forest environments

Propagation of electromagnetic waves in forest environments at medium and high (1-100 MHz) frequencies is examined for the case where both the transmitting and receiving points are situated within the vegetation. A dissipative slab in the presence of a reflecting ionosphere is employed to describe the forest configuration. If the effect of the ground-forest interface is disregarded, the radiated field of an arbitrarily oriented, small dipole is found to consist primarily of two separate waves: a lateral wave which skims along the tree tops, and a sky wave which is produced by a single-hop reflection at the ionospheric layer. These two field constituents are compared and their domains of preponderance are calculated for a large range of the pertinent parameters; it is then found that the lateral wave plays the major role since the sky wave is restricted to a narrow frequency band and its amplitude is appreciable only at large distances. The lateral-wave field is examined in detail and is shown to yield a simple physical picture for the propagation mechanism in forests. Its features are found to be qualitatively consistent with the field behavior reported in the literature and the quantitative aspects agree well with the available experimental data. The observed variation of the field with distance, the height-gain effect, the vegetation factor, the basic path loss, and depolarization effects are separately examined and are all shown to express merely one or another of the intrinsic properties of a lateral wave. The ground-proximity effect produced by the presence of a planar-conducting ground is also estimated and shown to be of minor importance in most cases.