Finite Time Domain Dynamics of Dirac Fields

In the present paper we consider the case of a Dirac field in a finite time domain and coupled to an external field. We decompose the field and its Hamiltonian in terms of creation and annihilation operators and path integrate it via Grassmannian variables techniques. In that way we obtain its finite time domain Green function. We use it in the perturbative study of the interaction of Dirac particles with classical electromagnetic waves.

Finite-difference time-domain studies of low-frequency stop band in superconductor-dielectric superlattice

The transmission coefficients of electromagnetic （EM） waves due to a superconductor-dielectric superlattice are numerically calculated. Shift operator finite difference time domain （SO-FDTD） method is used in the analysis. By using the SO-FDTD method, the transmission spectrum is obtained and its characteristics are investigated for different thicknesses of superconductor layers and dielectric layers, from which a stop band starting from zero frequency can be apparently observed. The relation between this low-frequency stop band and relative temperature, and also the London penetration depth at a superconductor temperature of zero degree are discussed, separately. The low-frequency stop band properties of superconductor-dielectric superlattice thus are well disclosed.

H_∞ fault estimation for a class of linear time-delay systems in finite frequency domain

This paper deals with the problem of H∞ fault estimation for linear time-delay systems in finite frequency domain.First a generalized coordinate change is applied to the original system such that in the new coordinates all the time-delay terms are injected by the system＇s input and output.Then an observer-based H∞ fault estimator with input and output injections is proposed for fault estimation with known frequency range.With the aid of Generalized Kalman-Yakubovich-Popov lemma,sufficient conditions on the existence of the H∞ fault estimator are derived and a solution to the observer gain matrices is obtained by solving a set of linear matrix inequalities.Finally,a numerical example is given to illustrate the effectiveness of the proposed method.

A Novel Absorbing Boundary Condition for the Frequency-Dependent Finite-Difference Time-Domain Method

A new absorbing boundary condition (ABC) for frequency dependent finite difference time domain algorithm for the arbitrary dispersive media is presented. The concepts of the digital systems are introduced to the (FD) 2TD method. On the basis of digital filter designing and vector algebra, the absorbing boundary condition under arbitrary angle of incidence are derived. The transient electromagnetic problems in two dimensions and three dimensions are calculated and the validity of the ABC is verified.

Numerical Solutions of Finite Well in Two Dimensions Using the Finite Difference Time Domain Method

The higher excited states for two dimensional finite rectangular well potential are calculated numerically,by solving the Schrödinger equation using the finite difference time domain method.Although,this method is suitable to calculate the ground state of the quantum systems,it has been improved to calculate the higher excited states directly.The improvement is based on modifying the iterative process involved in this method to include two procedures.The first is known as cooling steps and the second is known as a heating step.By determining the required length of the cooling iteration steps using suitable excitation energy estimate,and repeating these two procedures using suitable initial guess function for sufficient times.This modified iteration will lead automatically to the desired excited state.In the two dimensional finite rectangular well potential problem both of the suitable excitation energy and the suitable initial guess wave function are calculated analytically using the separation of variables technique.

High Precision Time Domain Forward Modeling for Crosshole Electromagnetic Tomography

To improve the resolution of crosshole electromagnetic tomography, high precision of forward modeling is necessary. A pseudo-spectral time domain （PSTD） forward modeling was used to simulate electromagnetic wave propagation between two boreholes. The PSTD algorithm is based on the finite difference time domain （FDTD） method and uses the fast Fourier transform （FFT） algorithm for spatial derivatives in Maxwell＇s equations. Besides having the strongpoint of the FDTD method, the calculation precision of the PSTD algorithm is higher than that of the FDTD method under the same calculation condition. The forward modeling using the PSTD method will play an important role in enhancing the resolution of crosshole electromagnetic tomography.

NONEXISTENCE IN RECIPROCAL AND LOGARITHMIC REGRESSION

Fitting logarithmic b ln(c+x), a+bln(c+x) or reciprocal b/(c+x), a+b/(c+x) regression models to data by the least squares method asks for the determination of the closure of the set of each type of these functions defined on a finite domain. It follows that a minimal solution may not exist. But it does exist when the closure is considered.

Absorption enhancement and sensing properties of Ag diamond nanoantenna arrays

Noble metal nanoantenna could effectively enhance light absorption and increase detection sensitivity. In this paper,we propose a periodic Ag diamond nanoantenna array to increase the absorption of thin-film solar cells and to improve the detection sensitivity via localized surface plasmon resonance. The effect of nanoantenna arrays on the absorption enhancement is theoretically investigated using the finite difference time domain（FDTD） method with manipulating the spectral response by geometrical parameters of nanoantennas. A maximum absorption enhancement factor of 1.51 has been achieved in this study. In addition, the relation between resonant wavelength（intensity reflectivity） and refractive index is discussed in detail. When detecting the environmental index using resonant wavelengths, a maximum detection sensitivity of about 837 nm/RIU（refractive index unit） and a resolution of about 10-3RIU can be achieved. Moreover, when using the reflectivity, the sensitivity can be as high as 0.93 AU/RIU. Furthermore, we also have theoretically studied the effectiveness of nanoantennas in distinguishing chemical reagents, solution concentrations, and solution allocation ratios by detecting refractive index. From the results presented in this paper, we conclude that this work might be useful for biosensor detection and other types of detections.

Perfectly matched layer implementation for ADI-FDTD in dispersive media

Alternating direction implicit finite difference time domain （ADI-FDTD） method is unconditionally stable and the maximum time step is not limited by the Courant stability condition, but rather by numerical error. Compared with the conventional FDTD method, the time step of ADI-FDTD can be enlarged arbitrarily and the CPU cost can be reduced. 2D perfectly matched layer （PML） absorbing boundary condition is proposed to truncate computation space for ADI-FDTD in dispersive media using recursive convolution（RC） method and the 2D PML formulations for dispersive media are derived. ADI-FDTD formulations for dispersive media can be obtained from the simplified PML formulations. The scattering of target in dispersive soil is simulated under sine wave and Gaussian pulse excitations and numerical results of ADI-FDTD with PML are compared with FDTD. Good agreement is observed. At the same time the CPU cost for ADI-FDTD is obviously reduced.

ANALYSIS OF FDTD TO UPML FOR MAXWELL EQUATIONS IN POLAR COORDINATES

An FDTD system associated with uniaxial perfectly matched layer（UPML） for an electromagnetic scattering problem in two-dimensional space in polar coordinates is considered.Particularly the FDTD system of an initial-boundary value problems of the transverse magnetic（TM） mode to Maxwell＇s equations is obtained by Yee＇s algorithm,and the open domain of the scattering problem is truncated by a circle with a UPML.Besides,an artificial boundary condition is imposed on the outer boundary of the UPML.Afterwards,stability of the FDTD system on the truncated domain is established through energy estimates by the Gronwall inequality.Numerical experiments are designed to approve the theoretical analysis.

Photocurrent improvement of an ultra-thin silicon solar cell using the localized surface plasmonic effect of clustering nanoparticles

The cluster-shaped plasmonic nanostructures are used to manage the incident light inside an ultra-thin silicon solar cell.Here we simulate spherical,conical,pyramidal,and cylindrical nanoparticles in a form of a cluster at the rear side of a thin silicon cell,using the finite difference time domain(FDTD)method.By calculating the optical absorption and hence the photocurrent,it is shown that the clustering of nanoparticles significantly improves them.The photocurrent enhancement is the result of the plasmonic effects of clustering the nanoparticles.For comparison,first a cell with a single nanoparticle at the rear side is evaluated.Then four smaller nanoparticles are put around it to make a cluster.The photocurrents of 20.478 mA/cm2,23.186 mA/cm2,21.427 mA/cm2,and 21.243 mA/cm2 are obtained for the cells using clustering conical,spherical,pyramidal,cylindrical NPs at the backside,respectively.These values are 13.987 mA/cm2,16.901 mA/cm2,16.507 mA/cm2,17.926 mA/cm2 for the cell with one conical,spherical,pyramidal,cylindrical NPs at the backside,respectively.Therefore,clustering can significantly improve the photocurrents.Finally,the distribution of the electric field and the generation rate for the proposed structures are calculated.

Design of the sample cell in near-field surface-enhanced Raman scattering by finite difference time domain method

The rational design of the sample cell may improve the sensitivity of surface-enhanced Raman scattering （SERS） detection in a high degree. Finite difference time domain （FDTD） simulations of the configuration of Ag film-Ag particles illuminated by plane wave and evanescent wave are performed to provide physical insight for design of the sample cell. Numerical solutions indicate that the sample cell can provide more ＂hot spots＂ and the massive field intensity enhancement occurs in these ＂hot spots＂. More information on the nanometer character of the sample can be got because of gradient-field Raman （GFR） of evanescent wave. OCIS codes： 290.5860, 240.0310, 240.6680, 999.9999 （surface-enhanced Raman scattering）.

FDTD Analysis of Nonuniform Lossy Cascade Multiconductor Transmission Lines

A hybrid algorithm is presented for nonuniform lossy multiconductor transmission lines (MTL) connected by arbitrary linear load networks. The networks are characterized by a state-variable equation which allows a general characterization of dynamic elements in the cascade networks. The method is achieved by the finite difference-time domain (FDTD) algorithm for the MTL, and the skin effect is taken into account, the more accurate method is used to compute the skin effect. And this method is combined with the computation of the nonuniform transmission lines. Finally, several numerical examples are given, these results indicate that: the current of the lossy MTL is smaller than the lossless of the MTL; and when the load networks contain the dynamic element, the transition time of the current is longer than the MTL connected by resistance only.

Design and analysis of multi-channel drop filter using dual L defected hexagonal photonic crystal ring resonator

In this paper,dual L defected hexagonal Photonic Crystal Ring Resonator(PCRR)using Channel Drop Filter(CDF)is designed for Coarse Wavelength Division Multiplexing(CWDM)systems.In this structure,the external rods of the ring resonator are arranged in a hexagon and the internal rods are removed in L arrangement for introducing defects.Scatter rods are used to prevent leakage.By using the L defected hexagonal resonator,a multi-channel CDF is designed,which exhibits multiple wavelengths of CWDM(1500 nm–1600 nm)region.In addition,the selection of rod size and the position of rods in the proposed multi-channel CDF are validated by varying the radius of coupling and scattering rods,as well as the position of resonators,respectively.By using plane wave expansion and opti Finite Difference Time Domain(FDTD)method,the electromagnetic wave propagation and the photonic band gap are obtained.

Selection of DBO measurement wavelength for bottom mark asymmetry based on FDTD method

A physical model for simulating overlay metrology employing diffraction based overlay(DBO)principles is built.It can help to optimize the metrology wavelength selection in DBO.Simulation result of DBO metrology with a model based on the finite-difference time-domain(FDTD)method is presented.A common case(bottom mark asymmetry)in which error signals are always induced in DBO measurement due to the process imperfection were discussed.The overlay sensitivity of the DBO measurement across the visible illumination spectrum has been performed and compared.After adjusting the model parameters compatible with the actual measurement conditions,the metrology wavelengths which provide the accuracy and robustness of DBO measurement can be optimized.

Temperature field simulation of polyolefin-absorber mixture by FDTD-FDM model during microwave heating

This work has performed a numerical simulation of the temperature field during microwave heating of polyolefin-absorber mixture by means of a combined electric and thermal model.A finite difference time domain was used to model the electric field distribution within the cavity,while the finite difference method was used to calculate the temperature field distribution in different reactors.This study has focused only on the process from room temperature to 500 K for reducing heating time and energy consumption.This temperature range is a process with high energy consumption,difficult to control and great influence on the follow-up reaction.Temperature dependence of dielectric properties and thermal properties of heated materials are fully considered and simulated through an iterative process.The simulation results show that input power,the size and location of the heated materials,the position of the waveguide,and the kinds of microwave absorbers are important factors affecting the heating process.As a result,the uniform temperature distribution(the temperature difference Tdb10 K)can be achieved by choosing the appropriate input power(500–2000 W),the appropriate proportion of microwave absorber(the volume ratio of Si C to HDPE is 30:70),and combining with the moving and rotating of the heated materials.The uniform temperature field obtained without mechanical stirring is very important for reducing energy consumption and subsequent reactions.

A New Dual Polarized Aperture-Coupled Printed Array for SAR Applications

This paper presents a new design of dual polarized aperture coupled printed antenna array. The finite difference time domain (FDTD) analysis of an aperture coupled microstrip element is performed, and the effects of antenna parameters on its characteristics are obtained to guide the design of the printed array. Then an 8×2 dual polarized array design in X band is introduced with configuration plots. In order to improve its isolation and cross polarization, an outphase displacement feeding technique is adopted in the feed network. Also, the round bends are used instead of conventional right angle bends so as to achieve better VSWR performance. Experimental results are presented, indicating the validity of the design. This dual polarized array can be applied as a sub array of spaceborne SAR systems.

Main Factors for Affecting Photonic Bandgap of Photonic Crystals

The factors affecting one dimensional （1D） and two dimensional （2D） photonic crystals （PhCs） are systemically analyzed in this paper by numerical simulation. Transfer matrix method （TMM） is employed for 1D PCs, both finite difference time domain method （FDTD） and plane wave expansion method （PWE） are employed for 2D PCs. The result shows that the photonic bandgaps （PBG） are directly affected by crystal type, crystal lattice constant, modulation of refractive index and periodicity, and it is should be useful for design of different type photonic crystals with the required PBG and functional devices. Finally, as an example, a near-IR 1D PCs narrow filter was designed.

Finite difference time domain analysis of two-dimensional surface acoustic wave piezoelectric phononic crystals at radio frequency

The finite-difference time-domain （FDTD） method is proposed for analyzing the surface acoustic wave （SAW） propagation in two-dimensional （2D） piezoelectric phononic crystals （PCs） at radio frequency （RF）, and also experiments are established to demonstrate its analysis result of the PCs＇ band gaps. The FDTD method takes the piezoelectric effect of PCs into account, in which periodic boundary conditions are used to decrease memory/time consumption and the perfectly matched layer boundary conditions are adopted as the SAW absorbers to attenuate artificial reflections. Two SAW delay lines are established with/without piezoelectric PCs located between interdigital transducers. By removing several echoes with window gating function in time domain, delay lines transmission function is achieved. The PCs＇ transmission functions and band gaps are obtained by comparing them in these two delay lines. When Aluminum/128°YX-LiNbO3 is adopted as scatter and substrate material, the PCs＇ band gap is calculated by this FDTD method and COMSOL respectively. Results show that computational results of FDTD agree well with experimental results and are better than that of COMSOL.

Optimizing bowtie structure parameters for specific incident light

We investigate optical properties of a bowtie-shaped aperture using the finite difference time domain method to optimize its geometric parameters for specific incident lights. The influence of the parameters on local field enhancement and resonant wavelength in the visible frequency range is numerically analysed. It is found that the major resonance of the spectrum is exponentially depended on the bowtie angle but independent of the whole aperture size. The simulation also demonstrates that increasing the aperture size raises the local field intensity on the exit plane due to an enlarged interaction area between the light and the metal medium. And the near-field spot size is closely related to the gap. Based on these results, the design rules of the bowtie structure can be optimized for specific wavelengths excited.