Debye Media Research Articles

FDTD Voxels-in-Cell method with Debye media

FDTD Voxels-in-Cell method with Debye media

Transient analysis of power loss density with time-harmonic electromagnetic waves in Debye media.

Due to the complex permittivity, it is difficult to directly clarify the transient mechanism between electromagnetic waves and Debye media. To overcome the above problem, the temporal relationship between the electromagnetic waves and permittivity is explicitly derived by applying the Fourier inversion and introducing the remnant displacement. With the help of the Poynting theorem and energy conservation equation, the transient power loss density is derived to describe the transient dissipation of electromagnetic field and the mechanism on phase displacement has been explicitly revealed. Besides, the unique solution can be obtained by applying the time-domain analysis method rather than involving the frequency-domain characteristics. The effectiveness of transient analysis is demonstrated by giving a comparison simulation on one-dimensional example.

FDTD Algorithm for Numerical Anatomical Models With Cells Containing Several Debye Media

In this article, we show that the previously published finite-difference time-domain (FDTD) thin-layer technique in Debye media can also be used to account for FDTD cells filled with several media. This permits either the accuracy to be improved or the computational time to be reduced by increasing the cell size. The numerical experiments were performed with a 2-D slice of an anatomical model.

Maloney and Smith Method for Modeling Debye-Media Thin Sheets in the FDTD Grid

The Maloney and Smith method used to account for sheets thinner than the cell size of the finite-difference time-domain (FDTD) method is extended to the case where both the sheet and the surrounding media are such dispersive Debye media as the Human Body tissues. The new method is then compared to the simpler Luebbers and Kuntz method that was previously extended to Debye media. The comparison relies on the reflection and transmission of plane waves and on 3-D experiments. It is concluded that the Maloney and Smith method permits a better accuracy to be achieved. It provides accurate reflection and transmission whatever may be the incidence angle of the wave that strikes the sheet.

Implementation of the Crank‐Nicolson Douglas‐Gunn finite‐difference time domain with complex frequency‐shifted perfectly matched layer for modeling unbounded isotropic dispersive media in two dimensions

AbstractTo model open‐domain problems with Drude, Lorentz, and Debye media, the complex frequency‐shifted perfectly matched layer (CFS‐PML) is adopted to truncate the Crank‐Nicolson Douglas‐Gunn finite‐difference time‐domain (CNDG‐FDTD) region. The auxiliary differential equation (ADE) and the bilinear Z‐transform methods are incorporated separately into the implementations of CNDG‐CFS‐PML formulations, while the ADE, piecewise linear recursive convolution (RC), and trapezoidal RC methods are utilized to model dispersive media. The proposed formulations can not only circumvent the stability condition, but also have the advantages of the CFS‐PML in attenuating the evanescent waves and reducing the late‐time reflection. Three numerical examples have been carried out to validate these formulations. The simulation results show that the proposed CNDG‐CFS‐PML algorithm is efficient in absorbing performance and saving more computational time compared with the conventional FDTD method, which leads to extensive applicability and acts as a very good prospect.

Huygens Excitation in Debye Media in the FDTD Method

The total-field/scattered-field method, also called the Huygens surface method, is a common method to enforce an incident wave in a finite-difference time domain grid filled with a vacuum. In this communication, it is shown that it can also be used in such dispersive media as the Debye media. The incident wave to be enforced on the Huygens surface is computed either by an analytical calculation in the general case or by means of the auxiliary grid technique in special cases. As in a vacuum, the leakage of energy outside the Huygens surface is lower than −40 dB with the analytical incident wave and it can be far lower with the auxiliary grid incident wave.

Brillouin precursors in Debye media

We theoretically study the formation of Brillouin precursors in Debye media. We point out that the precursors are visible only at propagation distances such that the impulse response of the medium is essentially determined by the frequency dependence of its absorption and is practically Gaussian. By simple convolution, we then obtain explicit analytical expressions of the transmitted waves generated by reference incident waves, distinguishing precursor and main signal by a simple examination of the long-time behavior of the overall signal. These expressions are in good agreement with the signals obtained in numerical or real experiments performed on water in the radio-frequency domain and explain in particular some observed shapes of the precursor. Results are obtained for other remarkable incident waves. In addition, we show quite generally that the shape of the Brillouin precursor appearing alone at sufficiently large propagation distance and the law giving its amplitude as a function of this distance do not depend on the precise form of the incident wave but only on its integral properties. The incidence of a static conductivity of the medium is also examined and explicit analytical results are again given in the limit of weak and strong conductivities.

Transient Power Loss Density of Electromagnetic Pulse in Debye Media

This paper is to point out the mistakes of previous expression of power loss density of the electromagnetic pulse (EMP) in Debye media. We derive the precise expression of transient power loss density both from the electrodynamic (ED) approach and equivalent circuit (EC) approach. In the ED approach, the expression is derived from the energy conservative law and Debye equation. For the harmonic field, the expression reduces to the well-known formula. The physical meaning can be clearly explained in the EC approach. The expression derived from the EC approach is consistent with that from the ED approach. A 1-D example is used to show the negative power loss of the EMP in Debye media and the error of temperature rise calculated from the previous expression.

Divergence-Preserving Alternating Direction Implicit Scheme for Multi-Pole Debye Dispersive Media

This letter presents the formulation of divergence-preserving alternating direction implicit (DP-ADI) scheme for multi-pole Debye dispersive media. The analytical proof of divergence-preserving property of the scheme in Debye media is provided. Numerical results of modeling human skin as Debye media further validate our proposed scheme.

An Error-Reduced ADI-FDTD Algorithm in Debye Media

The alternating direction implicit finite-difference time-domain (ADI-FDTD) method is an unconditionally stable numerical scheme, being proposed to remove stability limitations in conventional FDTD methods. Though the computation efficiency has been improved by ADI-FDTD, significant errors have been observed at large time steps. By compensating truncation errors, a low error ADI-FDTD method in Debye media is proposed based the ER(error reduced)-ADI-FDTD, complete three dimensional equations are derived. Simulation results are anlalyzed and compared with existing methods.

Modeling plasmonics: A Huygens subgridding scheme for Lorentz media

Huygens subgridding for the grid-based solution of the Maxwell equations is a new and promising technique that enables accurate computation of mixed systems, by efficiently reducing the computational cost for simulating structures where increased spatial resolution is required in part of space. The Huygens subgridding approach has previously been derived and tested for perfect electric conductors and Debye media. This work introduces a Huygens subgridding method that is applicable to Lorentz media, thus opening a range of new applications in the field of plasmonics.

Huygens Subgridding for 3-D Frequency-Dependent Finite-Difference Time-Domain Method

Subgridding methods are often used to increase the efficiency of the wave propagation simulation with the Finite-Difference Time-Domain method. However, the majority of contemporary subgridding techniques have two important drawbacks: the difficulty in accommodating dispersive media and the inability for physical interfaces to cross the subgridding interface. This paper presents an extension of the frequency-dependent Huygens subgridding method from one dimension to three dimensions. Frequency dependency is implemented via the Auxiliary Differential Equation approach using the one-pole Debye relaxation model. Numerical experiments indicate that subgridding interfaces can be placed in various Debye media as well as across the physical interface .

Bilinear Transform Implementation of the SC-PML for General Media and General FDTD Schemes

With the complex-frequency-shifted perfectly matched layer (CFS-PML) implemented based on both the stretched coordinates and the bilinear transform method as the absorbing boundary condition (ABC), a novel unified finite-difference time-domain (FDTD) algorithm is developed for general FDTD spatial schemes and general media. The proposed FDTD-PML algorithm employs a general expression for the permittivity of arbitrary linear dispersive media and also takes the nonlinear effects into account. The bilinear transform used in this paper has better accuracy than the frequently used forward, backward, and central difference schemes. Compared with the recursive convolution implementation of the CFS-PML, the bilinear transform implementation involves much simpler FDTD expressions and has better absorbing performance with the same computational cost. Several two-dimensional (2-D) and 3-D simulations involving the anisotropic media, the Debye media, the Drude media, and the Kerr nonlinear media have been done to validate the presented algorithm, and indicate the advantages of the bilinear transform implementation of the CFS-PML. A simulation involving the Lorentz media calculated with the proposed algorithm adopting the wavelet-based high-order FDTD scheme is also included to validate the accuracy and effectiveness of the developed method.

Numerical Evaluation of the Scattering of Brillouin Precursors From Targets Inside Water

In a dispersive medium excited by a wideband pulse, the appearance of the steady-state part of the propagated signal is preceded by oscillations known as precursors. Precursor fields in lossy Debye media have been shown to present a sub-exponential attenuation rate, thus becoming good candidates for applications requiring field penetration into such media. This communication aims to study the performance of a pulse consisting of two mutually delayed precursors for the detection of dielectric objects inside triply distilled water. Finite-difference time-domain (FDTD) simulations are employed to evaluate the strength of the scattered field obtained by illuminating the targets with the precursor-based pulse excitation and to compare it with other conventional alternatives, namely, Gaussian, rectangular and sinusoidal pulses.

On the Transmission and Propagation of Low Attenuation Rate Electromagnetic Pulses in Debye Media

In a dispersive medium, the appearance of the steady-state part of the signal is preceded by oscillations known as precursors. These early oscillations are the product of the interrelated effects of phase dispersion and frequency dependent attenuation. Inside water, the attenuation rate of the Brillouin precursor is sub-exponential, following the inverse square-root of the distance traveled. Based on that, a near-optimal pulse that could achieve this attenuation rate, and, hence, would lend itself to underwater detection and communication applications, was recently proposed. The ldquooptimalityrdquo of this pulse is shown to be related to the temporal support of the pulse and its spectral characteristics, rather than its shape. A family of alternative pulses is found to have the low attenuation feature of the ldquooptimalrdquo pulse, as they eventually evolve into the Brillouin precursor itself shortly after they enter water. In addition, this work considers the practical case when such a pulse would be generated in air, would impinge onto an air-water interface and then propagate inside water. It is shown how the presence of the interface affects the attenuation rate of the pulse inside water and a simple way to recover its low attenuation rate is suggested. The finite-difference time-domain technique is employed in all the simulations.

On the Solution of 3-D Frequency Dependent Crank-Nicolson FDTD Scheme

Unconditional stability of the Crank-Nicolson Finite Difference Time Domain (CN-FDTD) method permits us to use time steps over the Courant-Friedrich-Lewy (CFL) limit of conventional FDTD method. However, in this work it was realized that, when the time step is set above CFL limit the coefficient matrix arising from Crank-Nicolson method is no longer diagonally dominant and iterative solvers require longer solution time in each FDTD iteration. Frequency dependent CN-FDTD (FD-CN-FDTD) scheme for Debye media is formulated and numerical tests are performed with two widely used sparse iterative solvers, Bi-Conjugate Gradient Stabilised (BiCGStab) and Generalised Minimal Residual (GMRES), for comparison. BiCGStab outperforms GMRES in every aspect of the study.

The optimization of dissipation in dispersive dielectric slabs

Consider an electromagnetic plane wave incident on a dispersive dielectric slab with susceptibility kernel varying as a function of depth in the slab. After dissipation in Lorentz and Debye dielectric media, it is shown in this paper that it is possible to choose from among all plane waves of fixed energy and maximum duration a signal which maximizes joule heating in any preselected portion of the dielectric slab. This optimal signal is shown to be a normalized eigenfunction corresponding to the eigenvalue of a compact, self-adjoint, integral operator. Numerical approximations of these optimal signals are presented for examples of Lorentz and Debye media.