An efficient locally one-dimensional finite-difference time-domain method based on the conformal scheme

An efficient conformal locally one-dimensional finite-difference time-domain（LOD-CFDTD） method is presented for solving two-dimensional（2D） electromagnetic（EM） scattering problems. The formulation for the 2D transverse-electric（TE） case is presented and its stability property and numerical dispersion relationship are theoretically investigated. It is shown that the introduction of irregular grids will not damage the numerical stability. Instead of the staircasing approximation, the conformal scheme is only employed to model the curve boundaries, whereas the standard Yee grids are used for the remaining regions. As the irregular grids account for a very small percentage of the total space grids, the conformal scheme has little effect on the numerical dispersion. Moreover, the proposed method, which requires fewer arithmetic operations than the alternating-direction-implicit（ADI） CFDTD method, leads to a further reduction of the CPU time. With the total-field/scattered-field（TF/SF） boundary and the perfectly matched layer（PML）, the radar cross section（RCS） of two2 D structures is calculated. The numerical examples verify the accuracy and efficiency of the proposed method.

Uniform stable conformal convolutional perfectly matched layer for enlarged cell technique conformal finite-difference time-domain method

Based on conformal construction of physical model in a three-dimensional Cartesian grid,an integral-based conformal convolutional perfectly matched layer（CPML） is given for solving the truncation problem of the open port when the enlarged cell technique conformal finite-difference time-domain（ECT-CFDTD） method is used to simulate the wave propagation inside a perfect electric conductor（PEC） waveguide.The algorithm has the same numerical stability as the ECT-CFDTD method.For the long-time propagation problems of an evanescent wave in a waveguide,several numerical simulations are performed to analyze the reflection error by sweeping the constitutive parameters of the integral-based conformal CPML.Our numerical results show that the integral-based conformal CPML can be used to efficiently truncate the open port of the waveguide.

Investigation of three-pulse photon echo in thick crystal using finite-difference time-domain method

This paper investigates the phenomenon of three-pulse photon echo in thick rare-earth ions doped crystal whose thickness is far larger than 0.002 cm which is adopted in previous works.The influence of thickness on the three-pulse photon echo＇s amplitude and efficiency is analyzed with the Maxwell-Bloch equations solved by finite-difference timedomain method.We demonstrate that the amplitude of three-pulse echo will increase with the increasing of thickness and the optimum thickness to generate three-pulse photon echo is 0.3 cm for Tm^（3＋）：YAG when the attenuation of the input pulse is taken into account.Meanwhile,we find the expression 0.09 exp（α＇L）,which is previously employed to describe the relationship between echo＇s efficiency and thickness,should be modified as 1.3 · 0.09 exp（2.4 ·α＇L） with the propagation of echo considered.

Optical simulation of in-plane-switching blue phase liquid crystal display using the finite-difference time-domain method

The finite-difference time-domain method is used to simulate the optical characteristics of an in-plane switching blue phase liquid crystal display.Compared with the matrix optic methods and the refractive method,the finite-difference timedomain method,which is used to directly solve Maxwell＇s equations,can consider the lateral variation of the refractive index and obtain an accurate convergence effect.The simulation results show that e-rays and o-rays bend in different directions when the in-plane switching blue phase liquid crystal display is driven by the operating voltage.The finitedifference time-domain method should be used when the distribution of the liquid crystal in the liquid crystal display has a large lateral change.

A spherical higher-order finite-difference time-domain algorithm with perfectly matched layer

A higher-order finite-difference time-domain（HO-FDTD） in the spherical coordinate is presented in this paper. The stability and dispersion properties of the proposed scheme are investigated and an air-filled spherical resonator is modeled in order to demonstrate the advantage of this scheme over the finite-difference time-domain（FDTD） and the multiresolution time-domain（MRTD） schemes with respect to memory requirements and CPU time. Moreover, the Berenger＇s perfectly matched layer（PML） is derived for the spherical HO-FDTD grids, and the numerical results validate the efficiency of the PML.

Perfect plane-wave source for a high-order symplectic finite-difference time-domain scheme

The method of splitting a plane-wave finite-difference time-domain （SP-FDTD） algorithm is presented for the initiation of plane-wave source in the total-field / scattered-field （TF/SF） formulation of high-order symplectic finite- difference time-domain （SFDTD） scheme for the first time. By splitting the fields on one-dimensional grid and using the nature of numerical plane-wave in finite-difference time-domain （FDTD）, the identical dispersion relation can be obtained and proved between the one-dimensional and three-dimensional grids. An efficient plane-wave source is simulated on one-dimensional grid and a perfect match can be achieved for a plane-wave propagating at any angle forming an integer grid cell ratio. Numerical simulations show that the method is valid for SFDTD and the residual field in SF region is shrinked down to -300 dB.

Finite-difference time-domain modeling of curved material interfaces by using boundary condition equations method

To deal with the staircase approximation problem in the standard finite-difference time-domain（FDTD） simulation,the two-dimensional boundary condition equations（BCE） method is proposed in this paper.In the BCE method,the standard FDTD algorithm can be used as usual,and the curved surface is treated by adding the boundary condition equations.Thus,while maintaining the simplicity and computational efficiency of the standard FDTD algorithm,the BCE method can solve the staircase approximation problem.The BCE method is validated by analyzing near field and far field scattering properties of the PEC and dielectric cylinders.The results show that the BCE method can maintain a second-order accuracy by eliminating the staircase approximation errors.Moreover,the results of the BCE method show good accuracy for cylinder scattering cases with different permittivities.

Unconditionally stable Crank-Nicolson algorithm with enhanced absorption for rotationally symmetric multi-scale problems in anisotropic magnetized plasma

Large calculation error can be formed by directly employing the conventional Yee’s grid to curve surfaces.In order to alleviate such condition,unconditionally stable CrankNicolson Douglas-Gunn(CNDG)algorithm with is proposed for rotationally symmetric multi-scale problems in anisotropic magnetized plasma.Within the CNDG algorithm,an alternative scheme for the simulation of anisotropic plasma is proposed in body-of-revolution domains.Convolutional perfectly matched layer(CPML)formulation is proposed to efficiently solve the open region problems.Numerical example is carried out for the illustration of effectiveness including the efficiency,resources,and absorption.Through the results,it can be concluded that the proposed scheme shows considerable performance during the simulation.

Investigation of composite electromagnetic scattering from ship-like target on the randomly rough sea surface using FDTD method

Composite electromagnetic scattering from a two-dimensional （2D） ship-like target on a one-dimensional sea surface is investigated by using the finite-difference time-domain （FDTD） method. A uniaxial perfectly matched layer is adopted for truncation of FDTD lattices.The FDTD updated equations can be used for the total computation domain by choosing the uniaxial parameters properly. To validate the proposed numerical technique,a 2D infinitely long cylinder over the sea surface is taken into account first.The variation of angular distribution of the scattering changing with incident angle is calculated. The results show good agreement with the conventional moment method. Finally,the influence of the incident angle,the polarization,and the size of the ship-like target on the composite scattering coefficient is discussed in detail.

FDTD Simulation on Terahertz Waves Propagation Through a Dusty Plasma

The frequency dependent permittivity for dusty plasmas is provided by introducing the charging response factor and charge relaxation rate of airborne particles. The field equations that describe the characteristics of Terahertz（THz） waves propagation in a dusty plasma sheath are derived and discretized on the basis of the auxiliary differential equation（ADE） in the finite difference time domain（FDTD） method. Compared with numerical solutions in reference, the accuracy for the ADE FDTD method is validated. The reflection property of the metal Aluminum interlayer of the sheath at THz frequencies is discussed. The effects of the thickness, effective collision frequency, airborne particle density, and charge relaxation rate of airborne particles on the electromagnetic properties of Terahertz waves through a dusty plasma slab are investigated.Finally, some potential applications for Terahertz waves in information and communication are analyzed.

A Revised Piecewise Linear Recursive Convolution FDTD Method for Magnetized Plasmas

The piecewise linear recursive convolution （PLRC） finite-different time-domain （FDTD） method improves accuracy over the original recursive convolution （RC） FDTD approach and current density convolution （JEC） but retains their advantages in speed and efficiency. This paper describes a revised piecewise linear recursive convolution PLRC-FDTD formulation for magnetized plasma which incorporates both anisotropy and frequency dispersion at the same time, enabling the transient analysis of magnetized plasma media. The technique is illustrated by numerical simulations of the reflection and transmission coefficients through a magnetized plasma layer. The results show that the revised PLRC-FDTD method has improved the accuracy over the original RC FDTD method and JEC FDTD method.

Hybrid sub-gridding ADE–FDTD method of modeling periodic metallic nanoparticle arrays

In this paper, a modified sub-gridding scheme that hybridizes the conventional finite-difference time-domain（FDTD）method and the unconditionally stable locally one-dimensional（LOD） FDTD is developed for analyzing the periodic metallic nanoparticle arrays. The dispersion of the metal, caused by the evanescent wave propagating along the metal-dielectric interface, is expressed by the Drude model and solved with a generalized auxiliary differential equation（ADE） technique.In the sub-gridding scheme, the ADE–FDTD is applied to the global coarse grids while the ADE–LOD–FDTD is applied to the local fine grids. The time step sizes in the fine-grid region and coarse-grid region can be synchronized, and thus obviating the temporal interpolation of the fields in the time-marching process. Numerical examples about extraordinary optical transmission through the periodic metallic nanoparticle array are provided to show the accuracy and efficiency of the proposed method.

Theoretical Proof of Unconditional Stability of the 3-D ADI-FDTD Method

In order to eliminate Courant-Friedrich-Levy(CFL) condition restraint and improvecomputational efficiency,a new finite-difference time-domain(FDTD)method based on the alternating-direction implicit(ADI) technique is introduced recently.In this paper,a theoretical proof of the stabilityof the three-dimensional(3-D)ADI-FDTD method is presented.It is shown that the 3-D ADI-FDTDmethod is unconditionally stable and free from the CFL condition restraint.

SO-FDTD Analysis of the Plasma Reflectance of Epstein Distribution

The analysis of electromagnetic propagation in a dispersive medium is complicated in the time-domain because its dielectric constant is frequency-dependent. In this paper, the dielectric constant of the dispersive medium is written as a rational polynomial function, and the relationship between D and E is derived in the time-domain. It is referred to as the shift operator finite-different time-domain （SO-FDTD） method. Compared to an analytical solution and a piecewise linear current density recursive convolution （PLJERC） solution, the high accuracy and efl%iency of this method is verified by calculating the reflectance of the electromagnetic wave through a cold plasma slab. As the electron density in plasma is distributed as the Epstein formula, the effect of distribution grads and electron collision frequency on the reflectance is calculated by using the SO-FDTD method. The result shows that the increase in the distribution grads coefficient affects the reflectance sharply. When it comes to a smaller distribution grads coelBcient, the increase of the collision frequency showed a significant effect on the reflectance, but on the contrary, there is actually less and less effect till it disappears.

FDTD Simulations on Plasmonic Properties of End-to-End and Side-by-Side Assembled Au Nanorods

The surface plasmon resonance( SPR) of gold( Au) nanorod can be tuned in a large visible-near infrared( Vis-NIR) region by changing the aspect ratio of nanorod. Compared with the SPR of isolated Au nanorod,assembly of Au nanorods exhibits strong coupling effect in the nanogap and wealthy changes in the optical spectra. The SPR coupling effects and localized electronic fields for end-to-end( E-E) and side-by-side( S-S) assembled Au nanorods dimers are studied through finite-difference time-domain( FDTD) simulation. With decreasing the gap spacing,the longitudinal SPR( SPRL) red-shifts for the E-E orients Au nanorods dimer and blue-shifts for S-S orientes Au nanorods dimer. The transverse SPR( SPRT) has slight red-shifting for S-S assembly and no shifting for the E-E assembly. Moreover,a new coupling SPR appears for the E-E assembly in a long wavelength in the NIR region,blue-shifting and enhancing with decreasing the gap spacing. Based on the spring oscillator model and the polarization of nanoparticles with incident electric field,the SPR shifting and the appearance of new coupling SPR of assembled Au nanorods are proposed.

Optimization of band-notched UWB antenna using micro-genetic algorithm combined with FDTD

The micro-genetic algorithm (MGA) optimization combined with the finite-difference time-domain (FDTD) method is applied to design a band-notched ultra wide-band (UWB) antenna. A U-type slot on a stepped U-type UWB monopole is used to obtain the band-notched characteristic for 5 GHz wireless local area network (WLAN) band. The measured results show that voltage standing wave ration (VSWR) less than 2 covers 3.1-10.6 GHz operating band and VSWR more than 2 is within 5.150-5.825 GHz notched one with the highest value of 5.6. Agreement among the calculated, HFSS simulated and measured results validates the effiectiveness of this MGA-FDTD method, which is efficient for UWB antennas design.

Analysis of Complex Electromagnetic Structures by Hybrid FDTD/WCIP Method

This paper proposes a hybrid full-wave analysis using Finite-Difference Time-Domain (FDTD) and Wave Concept Iterative Process (WCIP) methods, developed to analyze locally arbitrarily shaped microwave structures and Multilayer Planar structure. Using the equivalence principle, the original problem can be decomposed into two sub regions and solve each sub region separately. An interpolation scheme is proposed for communicating between the FDTD fields and WCIP wave, which will not require the effort of fitting the WCIP mesh to the FDTD cells in the interface region. This method is applied to calculate the scattering parameters of arbitrary (3-D) microwave structures. Applying FDTD to 3D discontinuity and WCIP to the remaining region preserves the advantages of both WCIP flexibility and FDTD efficiency. A comparison of the results with the FDTD staircasing data verifies the accuracy of the proposed method.

Full-wave analysis and design of microstrip antenna in-pipe for rectenna using FDTD method

The circular polarized microstrip antenna in the stainless pipe is analyzed by the finite-difference time-domain （FDTD） method with PML absorbing boundary condition. The microstrip antenna is used as a microwave energy supply element for the in-pipe micromachine inspecting. The numerical results agree well with the measured ones.

Study on the Gain Material with Four Energy Level Model Using FDTD Method

A faster numerical method based on FDTD for the four energy level atomic system is present here. The initial conditions for the electrons of each level are achieving while the fields are in steady state. Polarization equation, rate equations of electronic population and Maxwell’s equations were used to describe the coupling between the atoms and electromagnetic wave. Numerical simulations, based on a finite-difference time-domain (FDTD) method, were utilized to obtain the population inversion and lasing threshold. The validity of the model and its theory is confirmed. The time, which we can observe the lasing phenomenon, is much shorter in our new model. Our model can be put into using in large scale simulations in mutiphysics to reduce the total simulated time.

An efficient absorbing boundary for finite-difference time-domain field modelling in acoustics

A highly efficient absorbing boundary condition suitable for use in the finitedtherence time-domain (FDTD) modelling of acoustic fields is presented in this paper. The new method seeks a least square esthoate of a transfer matrix for field components near truncating boundaries by matrir pseud-inversion. The proposed absorbing boundary is considerably more effective than most ekisting ones. The method is also computationally econondcal and robust.The performance of the new method is shown by numerical experiments on a point-source radiation problem, a wedge dimaction problem, and a scattering problem in which a plane wave is scattered by a circular cylinder.