Finite-difference Time-domain Algorithm Research Articles

Optimization of Purcell-enhanced microcavities with the cylindrical finite-difference time-domain algorithm

Optimization of Purcell-enhanced microcavities with the cylindrical finite-difference time-domain algorithm

975 nm multimode semiconductor lasers with high-order Bragg diffraction gratings

The 975 nm multimode diode lasers with high-order surface Bragg diffraction gratings have been simulated and calculated using the 2D finite difference time domain (FDTD) algorithm and the scattering matrix method (SMM). The periods and etch depth of the grating parameters have been optimized. A board area laser diode (BA-LD) with high-order diffraction gratings has been designed and fabricated. At output powers up to 10.5 W, the measured spectral width of full width at half maximum (FWHM) is less than 0.5 nm. The results demonstrate that the designed high-order surface gratings can effectively narrow the spectral width of multimode semiconductor lasers at high output power.

Iteration-Based Temporal Subgridding Method for the Finite-Difference Time-Domain Algorithm

A novel temporal subgridding technique is proposed for the finite-difference time-domain (FDTD) method to solve two-dimensional Maxwell’s equations of electrodynamics in the TEz mode. Based on the subgridding FDTD algorithm with a separated spatial and temporal interface, our method focuses on the temporal subgridding region, as it is the main source of late-time instability. Different from other subgridding algorithms that work on the interpolation between coarse and fine meshes, our method stabilizes the solution by using iterative updating equations on the temporal coarse–fine mesh interface. This new method presents an alternative approach aimed at improving the stability of the subgridding technique without modifying the interpolation formulas. We numerically study the stability of the proposed algorithm via eigenvalue tests and by performing long-term simulations. We employ a refinement ratio of 2:1 in our study. Our findings indicate the stability of the conventional temporal subgridding FDTD algorithm with a magnetic field (Hz) interpolation. However, when electric fields (Ex and Ey) are utilized in interpolation, late-time instability occurs. In contrast, the proposed iteration-based method with an electric field interpolation appears to be stable. We further employ our method as the forward problem solver in the Through-the-Wall Radar (TWR) imaging application.

Explicit and unconditionally stable finite-difference time-domain subgridding algorithm based on hanging variables

Due to the limitation of the stability condition, the finite-difference time-domain (FDTD) method cannot efficiently deal with electromagnetic problems containing fine structures. The explicit and unconditionally stable (EUS) FDTD method can eliminate the constraint of the stability condition and improve the simulation efficiency of fine structures by filtering out the unstable modes for the system matrix. However, the EUS-FDTD method needs to solve the eigenvalues of the numerical system matrix, and the symmetry of the numerical system matrix needs to be ensured when the subgridding scheme is used to discretize targets containing fine structures. The existing EUS-FDTD subgridding method encounters some problems such as complex implementation and insufficient accuracy. In order to solve the above problems, in this work, the hanging variables subgridding (HVS) algorithm is applied to the EUS-FDTD algorithm. Starting from the symmetry of the system matrix, the stability of the hanging variables subgridding algorithm is proven, and a high-precision, stable, and easy-to-implement HVS-EUS-FDTD scheme is proposed. Numerical examples of the radiation of linear magnetic currents in free space, electromagnetic scattering of multiple dielectric objects, and a three-dimensional cavity containing a medium demonstrate the stability, high accuracy and efficiency of the proposed method. Numerical experiments show that the computational efficiency of the HVS-EUS-FDTD algorithm can be improved hundreds of times compared with that of the uniform fine grid FDTD algorithm, and the highest computational efficiency can be improved up to ratio (the size ratio of coarse grid to fine grid) times compared with that of the HVS-FDTD algorithm.

A Hybrid Chebyshev Pseudo-Spectral Finite-Difference Time-Domain Method for Numerical Simulation of 2D Acoustic Wave Propagation

In this study, a hybrid Chebyshev pseudo-spectral finite-difference time-domain (CPS-FDTD) algorithm is proposed for simulating 2D acoustic wave propagation in heterogeneous media, which is different from the other traditional numerical schemes such as finite element and finite difference. This proposed hybrid method integrates the efficiency of the FDTD approach in the time domain and the high accuracy of the CPS technique in the spatial domain. We present the calculation formulas of this novel approach and conduct simulation experiments to test it. The biconjugate gradient is solved by combining the large symmetric sparse systems stabilized algorithm with an incomplete LU factorization. Three numerical experiments are further presented to illustrate the accuracy, efficiency, and flexibility of the hybrid CPS-FDTD algorithm.

High-power narrow spectral width 975 nm semiconductor laser with high process compatibility achieved by high-order gratings.

We present broad-area semiconductor lasers with a 100th-order high-order distributed Bragg reflection (HO-DBR) grating structure, fabricated with the conventional UV lithography techniques. Based on the finite-difference time-domain (FDTD) algorithm, a maximum output power of 10.5 W, emitting around 975 nm with a spectral width of less than 0.5 nm FWHM has been achieved. This method provides insights for reducing the manufacturing costs of the high-power narrow spectral width DBR lasers.

FDTD Method for Electromagnetic Simulations in Media Described by Time-Fractional Constitutive Relations

In this paper, the finite-difference time-domain (FDTD) method is derived for electromagnetic simulations in media described by the time-fractional (TF) constitutive relations. TF Maxwell’s equations are derived based on these constitutive relations and the Grünwald–Letnikov definition of a fractional derivative. Then the FDTD algorithm, which includes memory effects and energy dissipation of the considered media, is introduced. Finally, one-dimensional signal propagation in such electromagnetic media is considered. The proposed FDTD method is derived based on a discrete approximation of the Grünwald–Letnikov definition of the fractional derivative and evaluated in a code. The stability condition is derived for the proposed FDTD method based on a numerical-dispersion relation. The obtained numerical results are compared with the outcomes of reference frequency-domain simulations, proving the accuracy of the proposed approach. However, high spatial resolution is required in order to obtain accurate results. The developed FDTD method is, unfortunately, computation and memory demanding when compared to the ordinary FDTD algorithm.

High-Field Nonresonant Response of Zundel Cations to Intense Terahertz Radiation

The fundamental unit for comprehending the physicochemical properties of water, the Zundel cation configuration H5O2+, has yet to be exhaustively evaluated in terms of its interaction with terahertz (THz) electromagnetic waves, characterized by sub-picosecond oscillation periods or pulse widths. In this study, we embark on an investigation of the broad resonance and high-field nonresonant effects of intense THz radiation (ITR) on Zundel cations, utilizing a multifaceted methodological approach that includes density functional theory (DFT) calculations, finite difference time domain (FDTD) algorithm of the Schrödinger equation, and ab initio molecular dynamics (AIMD) simulations. Our analysis reveals that the proton potential energy surface (PES) varies in response to the external electric (E) field, suggesting that the interaction frequency of the central proton with the electromagnetic wave encompasses the THz band. This resonance effect is associated with proton behavior that may oscillate or demonstrate periodic tunneling. Moreover, our work uncovers the high-field nonresonant effects of ITR on Zundel cations, manifesting in proton transfer and vibrational excitation of the system. Our findings contribute to the understanding of the interaction between Zundel species and electromagnetic waves by presenting a microscopic view of proton transfer as informed by wavefunction evolution.

A Compact Microwave-Driven UV Lamp for Dental Light Curing

The size of current microwave-driven UV lamps limits their direct application in dental light curing. This article proposes a coaxial structure to miniaturize the UV lamp. First, the Drude model and the finite difference time domain algorithm were used to analyze the multi-physical field coupling and the complex field distribution within the lamp. Second, the dimensional parameters of the lamp were optimized, which enabled the lamp to be miniaturized and operate with high performance. Third, to analyze the sensitivity of the lamp, the effects of input power, gas pressure, and gas composition on its performance were investigated. It was found that an input power of 6 watts was enough to light the bulb with over 90% energy utilization. Finally, to verify the feasibility, an experimental system was set up. The lamp was successfully lit in the experiment, and its spectral output was tested. The results show that the microwave-driven UV lamp based on a coaxial structure is miniaturized and broad-spectrum, making it suitable for clinical dental light curing.

Identification of Ballast Fouling Status and Mechanized Cleaning Efficiency Using FDTD Method

Systematic assessment of ballast fouling and mechanized cleaning efficiency through ground penetrating radar (GPR) is vital to ensure track stability and safe train transportation. Nevertheless, conventional methods of ballast fouling inspection and evaluation impede construction progress and escalate the cost of maintenance. This paper proposes a novel method using random irregular polygons and collision detection algorithms to model the ballast layer and simulated using the finite-difference time-domain (FDTD) algorithm. Hilbert transform energy, S-transform, and energy integration curve are employed to identify ballast fouling and cleaning efficiency. The highly fouled ballast exhibits concentrated Hilbert transform energy, increased energy attenuation rate in S-transform with depth in the 1.0-3.0 GHz, along with a stronger energy integration curve. Clean or post-cleaning ballast shows opposite results. Experiments on a passenger trunk line in southern China validated the method’s accuracy after mechanized ballast cleaning. This approach guides GPR-based detection and supports railway maintenance. Future studies will consider heterogeneous properties and the three-dimensional structure of the ballast layer.

Preparation and cooling performance analysis of double-layer radiative cooling hybrid coatings with TiO2/SiO2/Si3N4 micron particles

Passive daytime radiative cooling is achieved by radiating heat into outer space through electromagnetic waves without energy consumption. A scalable double-layer coating with a mixture of TiO2, SiO2, and Si3N4 micron particles for radiative cooling is proposed in this study. The finite-difference time-domain algorithm is used to analyze the influence of particle size and coating thickness on radiative cooling performance. The results of the simulation show that the particle size of 3 μm can give the best cooling performance, and the coating thickness should be above 25 μm for SiO2 coating. Meanwhile, the mixture of SiO2 and Si3N4 significantly improves the overall emissivity. Through sample preparation and characterization, the mixture coating with a 1:1 ratio addition on an Al substrate exhibits high reflectivity with a value of 87.6% in the solar spectrum, and an average emissivity of 92% in the infrared region (2.5 μm–15 μm), which can be attributed to the synergy among the optical properties of the material. Both coatings can theoretically be cooled by about 8 °C during the day and about 21 °C at nighttime with h c = 4 W⋅m−2⋅K−1. Furthermore, even considering the significant conduction and convection exchanges, the cooling effect persists. Outdoor experimental results show that the temperature of the double-layer radiative cooling coating is always lower than the ambient temperature under direct sunlight during the day, and can be cooled by about 5 °C on average, while lower than the temperature of the aluminum film by almost 12 °C.

Efficient Recursive Convolution Schemes for the Accurate FDTD Modeling of Graphene Interband Contribution via Complex Conjugate Pairs

The accurate time-domain numerical modeling of graphene surface conductivity due to the interband contribution is presented in this paper. Initially, the lower frequency limit for the interband conductivity inclusion is studied, highlighting that even in the far-infrared regime it should not be ignored. Then, a precise vector-fitting technique is utilized to decompose the analytical conductivity function into complex conjugate pairs. Every pair is connected to a complex surface current, while the frequency dispersion is evaluated via a proper recursive convolution scheme. Finally, a straightforward algebraic manipulation is conducted to eliminate the complex terms from the update equations of the electromagnetic components, concerning the finite-difference time-domain (FDTD) algorithm. The precision and efficiency of the proposed methodology are thoroughly validated by comparing the numerically extracted surface wave propagation characteristics to those obtained in terms of analytical expressions.

Enhancing light extraction efficiency of GaN LED by combining complex‐period photonic crystals with doping

AbstractThe light extraction efficiency (LEE) of GaN‐based light‐emitting diodes (LEDs) was limited by intense total internal reflection and the photothermal effect. In order to solve this problem, a method to synergistically control the LEE of GaN‐based LEDs by ​​combining the complex‐period photonic crystals (PhCs) with M (M = Al, In) material doping is proposed. The forbidden band width of two‐dimensional (2D) PhC array, three‐dimensional (3D) LED model, M doping, and electromagnetic field distribution are investigated respectively. By doping the M, the LED emission wavelength range is regulated to achieve the dual‐band emission. Furthermore, a triangular complex‐period photonic structure is introduced to establish stacked or etched PhCs models. By combining the plane wave expansion and finite difference time domain algorithm, the structural parameters of PhCs and M concentration dependent LEE are investigated, and the electromagnetic field distribution is explored also. The results show that the optimal LEEs can be achieved are 19.08% and 13.96% for blue light and ultraviolet, respectively, which are larger than that of traditional flat‐panel LED (4%). This work provides theoretical results and technical support for the design of LEDs with high luminous efficiency.

Cube-corner retroreflectors for acoustic support outdoors: A comparison of simple and optimised designs

Activities conducted outdoors have reduced risk of disease transmission and yield positive mental and physical effects, but outdoor environments commonly suffer from acoustic problems such as urban noise, rapid spatial sound decay and insufficient acoustic support. This paper addresses the last problem, i.e., people's poor self-hearing due to lack of reflecting surfaces, which can reduce speaking comfort. The performance of easily fabricable, portable and deployable cube-corner retroreflectors (CCRs) is investigated through finite-difference time-domain (FDTD) acoustic simulations, omnidirectional measurements and oral-binaural measurements of physical prototypes. The CCRs' geometry is optimised to reduce sound dispersion using a process integrating parametric modelling, FDTD and genetic algorithms. Results show that optimisation can significantly boost the performance of CCRs by concave deformation of several centimetres, leading to more than doubling of the speech-weighted retroreflected energy of CCRs of 1 m edge lengths, and that of 0.5 m CCRs also substantially increased. Greatest improvements are achieved at high frequencies. Four CCRs of 0.5 m or one of 1 m, either simple or optimised, achieve speech-weighted voice support (STV) ranging from −19.1 to −15 dB over a 3 × 3 m area, better than common outdoor elements such as the ground or a wall and similar to typical enclosed rooms. CCRs are more effective for spectra emphasizing high frequencies, e.g., loud speech over normal speech, and larger CCRs have more balanced retroreflective spectra. This study provides a practical solution to improving weakly supported environments and thus contributes to improving the feasibility and acoustic quality of outdoor activities.

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.

Research on Interferences of VFTO to Irregular Distributions of Secondary Side Cables

In the digital era, the secondary equipment of power system is becoming more and more sensitive to electromagnetic interference. Gas insulated switchgear (GIS) in substations will generate very fast transient overvoltage (VFTO) after switching action. The VFTO will generate transient electromagnetic fields and cause interferences to the secondary side cables. In recent years, the anti-interference measures for cable protection have been greatly improved. However, in the current cable trenches of some substations, there are still many irregular cable arrangements. It may have some influences on the electromagnetic interference to the cable generated by VFTO. This paper expresses a method for finding the exact interference areas of the cable and standardizing the wiring standard of the cable. Firstly, the relationship between the cable position variation and parameters is analyzed. Then, simulation experiments based on speculation are conducted to observe the effect of irregular cable arrangement on port voltage, and computer software simulation is performed for comparison. After that, an irregular cable is simulated and an interval type Ⅱ fuzzy neural network is used to predict the parameters of the shielding layer of the cable at each irregularly arranged point. Finally, the voltage and current at each point of the cable shield are calculated through the finite-difference time-domain (FDTD) algorithm. In this manner, the actual position of the higher interference voltage can be determined, which can provide a reference standard for cable arrangement.

Numerical study of transmissive liquid crystal Pancharatnam–Berry gratings with small periods

Advances in patterning molecular orientations in liquid crystals have made possible the fabrications of various high-quality flat optical elements, ranging from gratings to beam shaping devices. These devices are based on modulating the Pancharatnam–Berry (PB) phase. It is well known that the diffraction efficiency for liquid crystal PB optical elements decreases for large diffraction angles. Here we study this issue using numerical simulations based on finite-difference time-domain algorithms and show that the optical efficiency formula commonly used for liquid crystal gratings deviates significantly from numerical results and is inaccurate for small grating periods because of its assumption that light beams do not diffract inside the liquid crystal films. We show that, for large diffraction angles, the polarization of the diffracted beam is generally elliptically polarized, and we further show that, by using liquid crystal materials with larger birefringence Δ n ∼ 0.4 , the diffraction efficiency for a grating period of 0.8 µm can go above 90%, which can be used for various flat optical elements with numerical aperture ∼ 0.7 .

Fast Computation of Resonant Metasurfaces in FDTD Scheme Using Dispersive Surface Susceptibility Model

A new framework of scattering analysis of metasurfaces composed of an assemble of resonant scatterers, with a multistage analysis procedure, is presented. The metasurface analysis using this framework utilizes a dispersive surface susceptibility model (SSM) and a finite-difference time-domain (FDTD) method, replacing the traditional brute force simulation with the physics-based SSM. The SSM extraction for characterizing scatterers is provided, which then is used to replace detailed practical scatterers in numerical simulation. The SSM with the frequency-dependent features’ behavior is described by multiple-Lorentz pole pairs, and the coefficients of the Lorentz model are obtained by using a rational fitting method. An easy-to-implement FDTD algorithm combined with the Lorentz-described SSM is proposed and presented. The efficiency of the proposed framework is proven by comparing it with conventional FDTD. The validity of the proposed framework is verified using commercial EM simulation software. The use of this analysis procedure is demonstrated by two example scatterers. Through the examples, we discuss the requirement of the meshing lattice size, sensitivity of the algorithm to the incident angle, and influence of the edge effects on the bistatic radar cross section (RCS) computation.

Modeling of catenary electromagnetic emission with electrified train passing through neutral section

Rail transit entering the airport facilitates people’s travel, but it also brings potential electromagnetic interference. In this paper, based on the transmission line model of the arc harmonic conduction current generated by the pantograph and the catenary with the highly insulated ballastless railway, the electromagnetic emission model of the traction network is proposed in the working frequency band of the nondirectional beacon when the train passes through the neutral section of the electric phase separation. And the simplification of the transmission line model is realized by deforming the transmission line equation. Then, the finite difference time domain algorithm is used to solve the distributed current on the transmission line. However, the terminal of the conventional finite difference time domain algorithm can only be a pure resistive load. Therefore, the backward difference and the Implicit Wendroff difference format are used to extend the finite difference time domain algorithm to a more general case. Combined with a real ballastless railway in China, the effectiveness and accuracy of the proposed method are verified. From the perspective of magnetic field attenuation, ballastless railway is easier to pass the electromagnetic environment assessment of the airport than ballasted railway.

Simulation study of alleviating the communication blackout using high-power microwave irradiating plasma sheaths

During hypersonic vehicle flight at high speed, plasma sheath on the vehicle surface will attenuate or even interrupt the communication signal, leading to the “communication blackout” problem. The vehicle probably moves a long distance during the communication blackout due to its high speed, which is a serious threat to the safety of the vehicle. This paper proposes a method to solve the communication blackout problem using high-power microwave (HPM) irradiation. The multicomponent compressible model, finite difference time domain algorithm, and multi-fluid model are used to simulate the interaction between HPM and plasma sheath. The results show that after HPM irradiation, the electromagnetic (EM) wave transmissivity of the plasma sheath will change, and the electric field (E-field) amplitude and irradiation time of HPM significantly influence the change of transmissivity. Thereafter, analyses of the changes of the collision and plasma frequencies of the plasma sheath after HPM irradiation showed the transmissivity of the plasma sheath to low-frequency EM waves is improved by optimizing E-field amplitude and irradiation time of HPM. Therefore, HPM irradiation can be performed to enhance the transmissivity of the plasma sheath to the communication signal, thus alleviating the communication blackout problem.