Dispersive Finite-difference Time-domain Research Articles

A Numerical Study of Lossy Multipole Debye Dispersive Media Using a Recursive Integral-FDTD Method

A dispersive finite-difference time-domain (FDTD) method based on the recursive integration (RI) technique for the modeling of the lossy multipole Debye dispersive media is described in this article. The interaction between the electromagnetic (EM) field and the human tissues is simulated by means of the RI method, and the frequency-dependent formulations which possess good compatibility with the main FDTD algorithm are achieved. Next, the expression of the multipole Debye dispersion model is similar to the multipole complex frequency shift (CFS) stretching function which is utilized to build the multipole perfectly matched layer (MPML). Therefore, a significant feature of using the RI method is its overall modeling of both multipole Debye dispersive media and MPML boundary conditions. Furthermore, the stability analysis of the RI method in solving the lossy multipole Debye dispersive model indicates that the Courant–Friedrich–Levy (CFL) stability limit of the regular FDTD can be maintained. At last, the numerical cases performed in this work demonstrate the correctness of the RI method in modeling dispersive media.

Dispersive FDTD Scheme and Surface Impedance Boundary Condition for Modeling Pulse Propagation in Very Lossy Medium

A dispersive surface impedance boundary condition (SIBC) is implemented in a dispersive finite-difference time-domain (FDTD) scheme to model pulse propagation and scattering from an aquifer, which has high permittivity and high conductivity. A quadratic complex rational function (QCRF) is adopted to model the dispersive media over a wide frequency band for implementing the dispersive FDTD scheme. The proposed method is demonstrated by simulating the operation of ground-penetrating radar (GPR) in detecting water table. Group delay and pulse-broadening parameter (PBP) are defined to analyze the deformation of pulses propagating in a dispersive lossy medium.

FDTD Modeling for the Accurate Electromagnetic Wave Analysis of Graphene

We develop a finite-difference time-domain (FDTD) method suitable for the electromagnetic (EM) analysis of graphene. In this work, we employ the modified Lorentz model for dispersion modeling, the two-dimensional (2-D) sheet model for geometrical modeling, and the complex-frequency-shifted (CFS)-perfectly matched layer (PML) for the absorbing boundary condition. In specific, the accurate complex-conjugate pole-residue (CCPR) dispersion model is first adapted for the electrical modeling of graphene by using the robust vector fitting. Next, the CCPR parameters are converted to the modified Lorentz parameters and then the modified Lorentz-based dispersive FDTD formulation is used to enhance the computational efficiency. In FDTD cell modeling, the 2-D sheet cells are allocated for graphene rather than the conventional FDTD cell-based modeling. Finally, CFS-PML are employed for terminating the computational domain to avoid the late-time instability. The presented FDTD approach is validated in numerical examples for graphene-based parallel plate waveguides.

Comprehensive Study on Numerical Aspects of Modified Lorentz Model-Based Dispersive FDTD Formulations

Finite-difference time domain (FDTD) has been widely used to analyze electromagnetic wave interaction with dispersive media. It is of great necessity to incorporate a dispersion model into FDTD formulation for electromagnetic wave analysis of dispersive media. Recently, it was reported that the modified Lorentz model can cover Debye, Drude, Lorentz, critical point, and quadratic complex rational function models. In this work, it is illustrated that the modified Lorentz model can also cover the complex-conjugate pole-residue model which is one of the most popular dispersion models. Modified Lorentz-based dispersive FDTD has not been thoroughly studied, especially for numerical aspects. In this work, we investigate auxiliary differential equation (ADE)-FDTD formulations for the modified Lorentz model based on electric flux density (D), current (J), or polarization (P). We perform a comprehensive study on memory requirement, the number of arithmetic operations, numerical stability, and numerical permittivity for the above three ADE-FDTD formulations. In addition, the bilinear transformation (BT) is incorporated into modified Lorentz-based FDTD formulations and it will be shown that the utilization of the BT can lead to better performance in terms of numerical stability and numerical accuracy. Numerical examples are used to demonstrate our work.

Dispersive Contour-Path MNL-FDTD Scheme for Fast Analysis of Waveguide Metamaterials

A semi-implicit dispersive thin-wire finite-difference time-domain (FDTD) scheme is proposed for fast analysis of waveguide metamaterials. The proposed scheme is based on combining the Newmark-beta method with Makinen’s improved thin-wire FDTD model based on the contour-path integral of Maxwell’s equations around a wire corrected with scaling factors and Wait’s surface-impedance boundary condition for thin wires of finite conductivity. Its stability condition is determined by only the two meshes in the transverse plane to the wire axis. This feature allows using larger mesh steps than a wire radius without time step reducing. In order to verify the scheme, we demonstrate four device applications: plasmonic parallel-plate waveguide filled with only positive dielectrics, edge Fabry–Perot resonator, waveguide metatronic high-pass filter, and coaxial-to-waveguide matching with an epsilon-near-zero narrow channel. Its stability, accuracy, and computational efficiency are assessed in comparison with the standard FDTD explicit scheme, analytical solutions, and existing experimental data.

Numerical study of optical trapping properties of nanoparticle on metallic film with periodic structure**Project supported by the National Natural Science Foundation of China (Grant Nos. 61701382, 61601355, and 61571355), the China Postdoctoral Science Foundation (Grant No. 2016M602770), and the Xi’an Technological University Principal Foundation Key Project, China (Grant No. XAGDXJJ18001).

Based on the three-dimensional dispersive finite difference time domain method and Maxwell stress tensor equation, the optical trapping properties of nanoparticle placed on the gold film with periodic circular holes are investigated numerically. Surface plasmon polaritons are excited on the metal-dielectric interface, with particular emphasis on the crucial role in tailoring the optical force acting on a nearby nanoparticle. Utilizing a first order corrected electromagnetic field components for a fundamental Gaussian beam, the incident beam is added into the calculation model of the proposed method. To obtain the detailed trapping properties of nanoparticle, the selected calculations on the effects of beam waist radius, sizes of nanoparticle and circular holes, distance between incident Gaussian beam and gold film, material of nanoparticle and polarization angles of incident wave are analyzed in detail to demonstrate that the optical-trapping force can be explained as a virtual spring which has a restoring force to perform positive and negative forces as a nanoparticle moves closer to or away from the centers of circular holes. The results of optical trapping properties of nanoparticle in the vicinity of the gold film could provide guidelines for further research on the optical system design and manipulation of arbitrary composite nanoparticles.

Accurate and Efficient Finite-Difference Time-Domain Simulation Compared With CCPR Model for Complex Dispersive Media

Recently, it has received a great deal of attention to analyze the electromagnetic wave problems in dispersive media by using the finite-difference time-domain (FDTD) method. Accordingly, it is of great importance to employ a proper dispersion model which can fit the frequency-dependent permittivity of a medium considered. The reported dispersion models include Debye, Drude, Lorentz, modified Lorentz, quadratic complex rational function, complex-conjugate pole-residue (CCPR) models. The CCPR dispersion model has advantage over other dispersion models in the fact that accurate CCPR dispersion parameters can be simply extracted by using the powerful and robust vector fitting tool which has been widely used in the circuit theory. However, the arithmetic operation of CCPR-based FDTD implementation is involved with complex-valued numbers and thus its numerical computation is not efficient. In this work, we propose an accurate and efficient FDTD simulation for complex dispersive media. In specific, an accurate CCPR dispersion model is simply obtained using the vector fitting tool and then the CCPR dispersion model is converted to the modified Lorentz dispersion model which leads to the arithmetic operation of only real-valued numbers in its FDTD implementation. Numerical examples are used to illustrate the accuracy and efficiency of our dispersive FDTD simulation.

Effect of nanoscale roughness on optical trapping properties of surface plasmon polaritons exerted on nanoparticle

Based on the three-dimensional dispersive finite difference time domain method and Maxwell stress tensor equation, the effect of nanoscale surface roughness on the optical trapping properties of nanoparticle in a vicinity of the composite gold film with periodic structure is investigated numerically. The periodic structure is observed as circular holes which can excite the surface plasmon polaritons on the metal-dielectric interface with particular emphasis on its crucial role in tailoring the optical force acting on a nearby nanoparticle. Utilizing the Monte-Carlo method, the surface roughness is added into the calculation model of the proposed method to accurately investigate the optical performance of the film-tuned nanoparticle system. Selected calculations on the effects of root mean square height and correlation length of rough surface are analyzed in detail to demonstrate that the negative effect of the surface roughness on the optical trapping force can be eliminated when the ratio of correlation length to root mean square height is equal to 10. Accurate investigation of optical trapping properties of nanoparticle in a vicinity of the composite gold film could provide guidelines for further research on the optical system design and manipulation of arbitrary composite nanoparticles.

Beam steering of eye shape metamaterial design on dispersive media by FDTD method

AbstractThe finite difference time domain method is applied for numerical modelling of composite dispersive material‐based proposed metamaterial, where the electromagnetic waves are propagating along the y‐axis with some exceptional properties in this paper. The existing frequency dispersive finite difference time domain method can be categorised into auxiliary differential equation method and the Z‐transform method, both of them are analysed in this paper. The auxiliary differential equation method has been introduced additional differential equations for describing frequency‐dependent material characteristics, and Z‐transform converts the frequency domain constitutive relations to Z‐domain relation. The proposed left‐handed metamaterial, single unit cell shows resonance at 5.48 GHz and the beam refraction characteristics by the incident beams on the structure. The incident beams are refracted 90°, 45° (positive refraction), and −25° (negative refraction) with respect to the metamaterial structure.

Unified integro-differential equation for efficient dispersive FDTD simulations

PurposeThe purpose of this paper is to derive a unified formulation for incorporating different dispersive models into the explicit and implicit finite difference time domain (FDTD) simulations.Design/methodology/approachIn this paper, dispersive integro-differential equation (IDE) FDTD formulation is presented. The resultant IDE is written in the discrete time domain by applying the trapezoidal recursive convolution and central finite differences schemes. In addition, unconditionally stable implicit split-step (SS) FDTD implementation is also discussed.FindingsIt is found that the time step stability limit of the explicit IDE-FDTD formulation maintains the conventional Courant–Friedrichs–Lewy (CFL) constraint but with additional stability limits related to the dispersive model parameters. In addition, the CFL stability limit can be removed by incorporating the implicit SS scheme into the IDE-FDTD formulation, but this is traded for degradation in the accuracy of the formulation.Research limitations/implicationsThe stability of the explicit FDTD scheme is bounded not only by the CFL limit but also by additional condition related to the dispersive material parameters. In addition, it is observed that implicit JE-IDE FDTD implementation decreases as the time step exceeds the CFL limit.Practical implicationsBased on the presented formulation, a single dispersive FDTD code can be written for implementing different dispersive models such as Debye, Drude, Lorentz, critical point and the quadratic complex rational function.Originality/valueThe proposed formulation not only unifies the FDTD implementation of the frequently used dispersive models with the minimal storage requirements but also can be incorporated with the implicit SS scheme to remove the CFL time step stability constraint.

Observing the transient buildup of a superscatterer in the time domain.

Superscatterer is an intriguing electromagnetic device, which can enhance the wave scattering of a given object with an arbitrary magnification factor in principle. However, observing the transient buildup of a superscatterer in numerical time domain still has not been investigated yet. In this paper, by using the dispersive finite difference time domain method, the transient response of a dispersive superscatterer created with monotonic optical transformation function is studied. We find that the time delay grows dramatically when the magnification factor increases. In addition, we notice an interesting phenomenon that, placing a scattering body with more complicated structure leads to longer time delays. These findings are very useful to reveal the physics behind the superscatterer.

A Numerical Study of Debye and Conductive Dispersion in High-Dielectric Materials Using a General ADE-FDTD Algorithm

A new formulation of the auxiliary difference equation (ADE) finite-difference time-domain (FDTD) algorithm for the simulation of dispersive materials has been presented in the literature. Although flexible and efficient, this algorithm suffers from instability when modeling lossy high contrast dielectrics. In this paper, we adapt this ADE-FDTD formulation and present alternative algorithms for modeling static conductivity and Debye dispersion. The stability of these algorithms is assessed by numerical simulation in a wide variety of dielectric media, and their performance is compared to the existing algorithm by means of a simulation of the reflection of a plane wave from a dielectric boundary. Results and comparison with theory demonstrate the stability and accuracy of the new methods. The flexibility, computational efficiency, and ability to model a wide range of materials make these new methods highly attractive compared to other dispersive FDTD algorithms, particularly for modeling materials with multiple dispersion models.

A second order dispersive FDTD algorithm for transverse electric Maxwell’s equations with complex interfaces

This work overcomes the difficulty of the finite-difference time-domain (FDTD) algorithm in solving the transverse electric (TE) Maxwell’s equations with inhomogeneous dispersive media. For such TE problems, the electric fields are discontinuous across the dispersive interfaces. Moreover, such discontinuities are time variant. A novel matched interface and boundary time-domain (MIBTD) method is proposed to solve such problems through new developments in both mathematical formulations and numerical algorithms. Mathematically, instead of handling all zeroth and first order jump conditions in a local coordinate, we directly construct the TE jump conditions which are needed in the FDTD computations in the Cartesian coordinate. Such Cartesian direction conditions depend on the time, as well as tangential and normal components of the electric flux. Driven by the jump condition modeling, we adopt the standard Maxwell’s equations in coupling with the Debye auxiliary differential equations for the electric flux as the governing equations. Computationally, the leapfrog scheme is employed for integrating the Maxwell system and time dependent jump conditions. Sophisticated interface treatments are developed in both producing the TE jump conditions and enforcing them in the FDTD algorithm, based on a staggered Yee lattice. The numerical accuracy, stability, and efficiency of the proposed scheme are investigated by considering dispersive interfaces of various shapes. The MIBTD method achieves a spatially second order of convergence in all tests. To the best of our knowledge, the present MIBTD scheme is the first FDTD method in the literature that can restore second order accuracy in treating curved dispersive interfaces for the TE Maxwell system.

Parallel Dispersive FDTD Method Based on the Quadratic Complex Rational Function

Recently, the quadratic complex rational function (QCRF) function was proposed for accurate finite-difference time-domain (FDTD) dispersive modeling. First, this letter discusses two implementations of QCRF-FDTD to a zeroth-order temporal derivative term and it is observed that the numerical accuracy of the double averaging implementation is better than that of the direct implementation. Second, this work presents a fast QCRF-FDTD algorithm by employing a parallel processing algorithm. The proposed parallel QCRF-FDTD is validated in terms of the speedup fact and the computational accuracy. Finally, we analyze the shielding effectiveness of large-scale concrete structures by using our parallel QCRF-FDTD.

Optical Transmission Enhancement of Stacked Plasmonic Apertures

In this study, we demonstrate enhanced transmission for out-of-plane stacked plasmonic apertures through the interaction of localized surface plasmons of apertures using both numerical and theoretical approaches. A dispersive finite-difference time-domain (D-FDTD) model is used to investigate the systems through the numerical simulations. To explain the results of the FDTD numerical simulations and to bring further insight to this interaction, we use a magnetic coupled dipole approximation as the theoretical basis. Our results demonstrate that near-field in-phase and out-of-phase interactions of the stacked nanoholes increase or decrease the optical transmission. Plasmon hybridization is discussed for stacked nanohole dimers on out-of-plane metallic films.

FDTD Dispersive Modeling With High-Order Rational Constitutive Parameters

In this work, we present a dispersive finite-difference time-domain (FDTD) algorithm using a four-pole complex rational function (CRF). For the sake of a better curve fitting of the four-pole CRF dispersion model, we use a particle swarm optimization technique. We also discuss an efficient memory storage strategy using a state-space approach. The numerical aspects of four-pole CRF-FDTD, the numerical accuracy and the numerical stability, are investigated in detail. Numerical examples are used to validate four-pole CRF-FDTD and numerical stability issues are discussed in detail. We also discuss the computational accuracy and the computational efficiency of an arbitrary $N$ -pole CRF-FDTD.

A new high order dispersive FDTD method for Drude material with complex interfaces

In this paper, motivated by the needs of tracking the transient change in the regularity of the electromagnetic fields across a Drude interface, we propose a new Maxwell–Drude formulation for transverse magnetic problems with inhomogeneous Drude dispersive materials. Based on the auxiliary differential equation approach, the proposed formulation couples the wave equation for the electric component with Maxwell’s equations for the magnetic components. A new finite-difference time-domain (FDTD) algorithm is introduced for solving the proposed Maxwell–Drude system, in which the time dependent jump conditions across the Drude interface are enforced through the matched interface and boundary (MIB) method. The proposed FDTD method achieves a second order of accuracy in solving Drude interfaces with fluctuating curvatures and non-smooth corners based on a simple Yee lattice, while it can be generalized to up to sixth order in dealing with a straight Drude interface. Therefore, the proposed FDTD method is more accurate and cost-efficient than the classical FDTD methods for Drude material with complex interfaces.

Effective CNAD- and ADE-Based CFS-PML Formulations for Truncating the Dispersive FDTD Domains

An effective and unsplit-field implementation of the complex frequency-shifted perfectly matched layer (CFS-PML) based on the Crank-Nicolson-approximate-decoupling (CNAD) and the auxiliary differential equation (ADE) method is proposed to truncate the dispersive finite-difference time-domain (FDTD) domains. The proposed formulations take full advantage of the capacity of the CFS-PML for attenuating evanescent waves and reducing late-time reflections. Furthermore, the proposed formulations have an advantage of the unconditional stability of the original CN-FDTD method. Two numerical tests have been carried out to validate the proposed formulations in the two-dimensional FDTD domains composed of the linear Debye and the Lorentz dispersive media, respectively. It is shown in the numerical tests that the proposed formulations can not only increase the time step size over the Courant–Friedrichs–Lewy (CFL) limit as compared with the conventional FDTD, but also hold good absorbing performance.

Elliptic cylindrical pseudo-optical black hole for omnidirectional light absorber

An elliptic cylindrical omnidirectional light absorber forming a pseudo-optical black hole is studied both analytically and numerically. The conditions for permittivity tensors to trap optical rays are obtained from semiclassical analysis of the ray optic Hamiltonian. The dispersive finite-difference time-domain method is used to study the performance of these light-absorbing structures numerically. It is found that the permittivity of the structure in the form (1/sinhu u)≥(a/r)n traps the light ray efficiently into the elliptic absorber for n≥2, where u is the radial elliptic coordinate and a is the focal distance.

Accurate FDTD Dispersive Modeling for Concrete Materials

This work presents an accurate finite-difference time-domain (FDTD) dispersive modeling of concrete materials with different water/cement ratios in 50 MHz to 1 GHz. A quadratic complex rational function (QCRF) is employed for dispersive modeling of the relative permittivity of concrete materials. To improve the curve fitting of the QCRF model, the Newton iterative method is applied to determine a weighting factor. Numerical examples validate the accuracy of the proposed dispersive FDTD modeling.