Two-dimensional Finite-difference Time-domain Research Articles

Enhancing azimuth estimation in low-resolution underwater acoustic lens systems for advanced communication and positioning

Here we aimed to enhance azimuth estimation to accurately locate a communication partner’s position by utilizing a low-resolution underwater acoustic lens system for communication. We proposed a method to accurately estimate the direction-of-arrival (DoA) by finding the center of gravity of the focal distribution using two adjacent elements of the transducer array. Ranging was to be based on time-of-flight (ToF). The method’s effectiveness was evaluated by two-dimensional finite difference time domain simulation. The lens’s focused sound field was calculated and the array was designed based on the result. DoA and ToF were estimated from the received signals and evaluated by comparing them with the true values under conditions involving 1-, 2-, and 3- users. The results confirmed DoA estimation with an error of almost 4°, even when using a lens system with an azimuth resolution of 10°. As the number of users increased, the maximum error value increased, though slightly.

Accurate Nonstandard Path Integral Models for Arbitrary Dielectric Boundaries in 2-D NS-FDTD Domains.

An efficient path integral (PI) model for the accurate analysis of curved dielectric structures on coarse grids via the two-dimensional nonstandard finite-difference time-domain (NS-FDTD) technique is introduced in this paper. In contrast to previous PI implementations of the perfectly electric conductor case, which accommodates orthogonal cells in the vicinity of curved surfaces, the novel PI model employs the occupation ratio of dielectrics in the necessary cells, providing thus a straightforward and instructive means to treat an assortment of practical applications. For its verification, the reflection from a flat plate and the scattering from a cylinder using the PI model are investigated. Results indicate that the featured methodology can enable the reliable and precise modeling of arbitrarily shaped dielectrics in the NS-FDTD algorithm on coarse grids.

A tunable flat terahertz lens using Dirac semimetals: a simulation study

We propose and design a flat and tunable terahertz lens achieved through a two-dimensional photonic crystal composed of an array of rods made of a Dirac semimetal placed in air as the background medium. The structure of interest is a graded index photonic crystal, made possible by the slight variations in the rods’ radii in a direction perpendicular to the direction of the light propagation. Dirac semimetals' ability to respond to variations in their Fermi energy level manifested as a change in the refractive index provides the tunability of our proposed lens. The interaction of electromagnetic waves with the designed structure is investigated for both transverse magnetic and transverse electric polarizations using two-dimensional finite-difference time-domain method.

Finite-frequency modeling of regional tropospheric infrasound using realistic atmospheres and terrain.

Infrasonic waves have been observed to propagate to regional (greater than 15 km) distances through the troposphere. Infrasound propagation in the geometric acoustics approximation has shown that realistic terrain can scatter acoustic energy from tropospheric ducts; however, ray methods cannot intrinsically capture finite-frequency behavior such as diffraction. A two-dimensional finite-difference time-domain (FDTD) method has been developed to solve linearized equations for infrasound propagation with realistic terrain. Acoustic wave propagation over 100 km with both flat terrain and a Gaussian hill was first simulated in order to compare finite-frequency propagation with ray predictions. The effects of realistic terrain and atmospheres on infrasound signals from a 2012 surface explosion at the Utah Testing and Training Range are then investigated. Propagation through the troposphere is suggested by array processing results, but eigenrays are not predicted due to weak to nonexistent ducting conditions. FDTD modeling suggests that the inclusion of terrain and finite frequency effects helps explain much of the observed signal in a realistic scenario. These results suggest that geometric acoustics may underestimate propagation through the troposphere, and that recorded waveforms at regional distances may be noticeably affected by terrain.

All-optical simultaneous OR and NAND gates using photonic crystal ring resonator and Kerr effect

All-optical simultaneous OR and NAND gates design is proposed using a simple nonlinear photonic crystal ring resonator based on the chalcogenide glass (Ag20As32Se48) material which is one of the promising materials for all-optical devices. The structure consists of an octagonal ring resonator between two waveguides, which uses the switching threshold mechanism based on the Kerr effect to perform two simultaneous logic gates functions. The plane wave expansion (PWE) method is used to obtain the band diagram in the proposed structure, and the two-dimensional finite difference time domain (2D-FDTD) method is used in the simulation to evaluate the performance of the proposed design. The resonance wavelength is 1551.3 nm, with a high transmission and coupling efficiency of about 100%. The proposed optical OR and NAND logic gates have high contrast ratios of 21.15 dB and 28.19 dB, respectively, with a quality factor of 596.65. The operating power intensity of the proposed structure is 1 kW μm−2, and the threshold power intensity is obtained at 2.8 kW μm−2. The proposed gates provide transmitted power of not less than 0.5. The size of the structure is 20.5 μm × 18.17 μm. The proposed structure is compact, works on low operational power intensity, and has the ability for dense integration. The simplicity and small size of the structure make it easy to fabricate for future integration in all-optical circuits.

A hybrid 2D-FDTD/3D-MoM method used for the analysis of MRI RF coils

The design of radiofrequency (RF) coils is crucial for ultra-high field (UHF) magnetic resonance imaging (MRI) systems. To analyze RF coils, various numerical methods, such as finite-difference time-domain (FDTD) and method of moments (MoM), are usually adopted. In this paper, we present a novel hybrid approach that combines a two-dimensional (2D) FDTD with a three-dimensional (3D) MoM to analyze MRI RF problems. In our algorithm, the MoM is utilized for calculating the coil current, and FDTD is assigned for solving the electromagnetic (EM) fields in the imaging region. The hybrid method achieves superior efficiency and acceptable accuracy than using either method individually. To validate the hybrid method, we analyze an ellipse coil loaded with a uniform phantom and a realistic human head model, with the objective of tailoring the magnetic field intensity by adding a multilayer dielectric pad (DP). The results show an improvement in the magnetic field after optimizing the DP configuration. These simulation studies indicate the potential of the new numerical method for the design and analysis of RF systems for ultra-high field applications.

Full-wave modeling of EMIC wave packets: ducted propagation and reflected waves

Electromagnetic ion cyclotron (EMIC) waves can scatter radiation belt electrons with energies of a few hundred keV and higher. To accurately predict this scattering and the resulting precipitation of these relativistic electrons on short time scales, we need detailed knowledge of the wave field’s spatio-temporal evolution, which cannot be obtained from single spacecraft measurements. Our study presents EMIC wave models obtained from two-dimensional (2D) finite-difference time-domain (FDTD) simulations in the Earth’s dipole magnetic field. We study cases of hydrogen band and helium band wave propagation, rising-tone emissions, packets with amplitude modulations, and ducted waves. We analyze the wave propagation properties in the time domain, enabling comparison with in situ observations. We show that cold plasma density gradients can keep the wave vector quasiparallel, guide the wave energy efficiently, and have a profound effect on mode conversion and reflections. The wave normal angle of unducted waves increases rapidly with latitude, resulting in reflection on the ion hybrid frequency, which prohibits propagation to low altitudes. The modeled wave fields can serve as an input for test-particle analysis of scattering and precipitation of relativistic electrons and energetic ions.

Numerical Stability and Dispersion Analysis of the 2-D FDTD Method Including Lumped Elements

The numerical stability and dispersion analysis of the extended two-dimensional finite-difference time-domain (2D-FDTD) method are systematically studied. Particularly, three different passive linear lumped elements including the resistor, inductor, and capacitor are analyzed, respectively. Moreover, three different formulations of the explicit, semi-implicit, and implicit schemes are discussed, respectively. Furthermore, by combining the von Neumann technique and Jury criterion, the numerical stability of the extended 2D-FDTD method is analyzed, which has not been reported thus far. Theoretical results show that: 1) For the resistor, the stability condition is same as the FDTD method unloaded case. 2) For the inductor, in the explicit and implicit schemes, the stability is connected with the value of the inductance; for the semi-implicit scheme, the stability is independent of the value of the inductance. 3) For the capacitor, the stability relationship is related to both the mesh size and the value of the capacitance. On the other hand, based on the Norton equivalent circuit, the analysis of the numerical dispersion of the extended 2D-FDTD is presented; and some interesting theoretical results are deduced. Finally, the microstrip circuits including the three lumped elements are simulated to demonstrate the validity of the theoretical results.

Kerr effect based optical switching for the assessment of all-optical sequence generator and decoder circuits

Abstract The sequence generator and decoders are used for noise analysis, signal propagation, data processing, and bit error rate analysis. The semiconductor and modern electronic components are facing challenges in terms of processing speed and data rates. However, by using photons rather than electrons as the information carriers, these difficulties can be reduced. Photonic devices attained the operating speed in the regime of terahertz, but sit back due to the diffraction limit, which can be overcome by employing plasmon-based devices or all-optical devices. This work presents a numerical investigation of metal-insulator-metal (MIM) plasmonic waveguides based two-bit sequence generator (SG) and decoder. The structure of SG and decoder circuits are designed within the footprints of 86 × 9 and 140 × 9 µm, by cascading one power splitter (PS) and four Mach-Zehnder interferometers (MZIs), and two PS and five MZI, respectively. To design the MZI, the optimization of the S-bend waveguide, the coupling length of the power splitter, and the length of the interferometric arm are done by recording the output power. The highest extinction ratio of 22.1 dB is attained at the coupling and interferometric arm lengths of 1.5 µm and 5 µm, respectively. The propagation of the optical signal through the structure of SG is observed by using a two-dimensional finite difference time domain method-based tool.

Theoretical investigation of F-P cavity mode manipulation by single gold nanoparticles

Abstract The ability to manipulate microlaser is highly desirable towards high-performance optoelectronic devices. Here we demonstrate feasible mode manipulation of Fabry-Pérot type microlasers of a perovskite nanowire via incorporation of single gold nanoparticles. The influences of resonant wavelength, quality factor and emission directions are successively investigated using a two-dimensional finite-difference time-domain method. It is found that blueshift of resonant wavelength could be achieved together with either promoted or degraded quality factor of microlaser via single Au NPs with varied sizes. Unidirectional emission could also be realized that is favorable for on-chip integration. Our results provide useful reference for feasible manipulation of light-matter interactions and mode selection.

A Two-Dimensional Unsteady FDTD Model for Radon Transport with Multiple Sources Emanation from Soil Layers

A two-dimensional numerical model for radon transport based on the finite difference time domain (FDTD) method have been developed. The model is governed by the radon transport equation taking into account the mechanisms of diffusion, advection, and decay. The purpose of this model is to simulate the evolution of radon concentration which can be influenced by various parameters including depth and diffusion coefficient of the soil layer plus the velocity and initial concentration of radon. The obtained results were compared to an analytical solution to demonstrate the ability of this model for predicting the spatio-temporal evolution of radon transport in the porous media of soil layers.

A rapid 2D-FDTD method for damage detection in stiffened plate using time-reversed Lamb wave

This study proposes an improved two-dimensional finite-difference time-domain method (2D-FDTD) to simulate the propagation of guided waves in three-dimensional (3D) stiffened plates, which can greatly reduce the calculation amount and accelerate the simulation process. This method can be used for damage-detection imaging based on time-reversal with wavefield reconstruction (TR-RW) as a quick numerical simulation of wavefield is available. First, the piezoelectric wafer active sensors excite and collect Lamb wave signals in the damaged stiffening plate, after which these signals are reversed in the time domain. Second, the TR signals are again triggered by each sensor in turn on the reconstructed numerical model of the tested structure with 2D-FDTD. Third, the wavefield animation is obtained through simulation. Finally, the energy of the wavefield can be focused in certain areas, indicating the location of the damage. As an example, TR-RW, combined with 2D-FDTD method, is adopted to detect damage in an integral grid-stiffened plate, showing that the proposed 2D method can decrease the calculation time from dozens of minutes in the 3D model to dozens of seconds, which is of great significance for damage-detection applications. Furthermore, compared with the virtual TR method, the combined TR-RW and 2D-FDTD method can overcome the multipath effect and improve the damage location accuracy of stiffened structures.

Two-dimensional finite-difference time-domain simulation of moving sound source and receiver with directivity

This paper reports on the implementation of a moving sound source and receiver with directivity in the two-dimensional finite-difference time-domain (FDTD) method. A two-dimensional fundamental solution of a moving monopole source is theoretically derived. Then, a fundamental solution of a moving dipole source is obtained by differentiating the fundamental solution of a monopole source in space. Finally, the directivity of moving monopole, dipole, and cardioid sources is theoretically derived. Numerical experiments performed on the two-dimensional sound field showed that the effect of moving velocity on amplitude differs for the monopole and dipole sources. Furthermore, it was found that directivity characteristics of dipole and cardioid sources vary depending on the beam steering angle and moving direction. The present method can be accurately applied to the moving sound source and receiver with directivity.

Parallel computing for modeling multilayer photonic crystals

A simulation framework is developed for the two-dimensional finite-difference time-domain to model multilayer photonic crystal structures. The framework includes the recording process in a photosensitive material through a coherent light source and then a subsequent interrogation with a broadband spectrum. Moreover, the tunable response of the photonic crystal is simulated for different film thicknesses (recorded from 5 to 20 μm), refractive indices contrast (ranging from 4% to 24%), film expansions (interrogated with expansions ranging 110% to 160%), and lattice spacings (recorded with wavelengths from 360 to 560 nm). A parallelization method was implemented in a computer cluster to alleviate the required high computational demand. Through this simulation framework, it is now possible to retrieve relevant information about realistic photosensitive multilayer structures. This method will support the design of multilayer structures utilized in sensors, lasers, and other functional nanostructured photonic devices.

A Novel Microstructure of 2-Bit Optical Analog to Digital Converter Based on Kerr Effect Nonlinear Nanocavities in 2D Photonic Crystal

In this paper, an all-optical analog-to-digital converter based on nonlinear with silicon materials is designed and simulated. The proposed structure consists of three nonlinear nanocavity that control the optical signal power intensity. The nonlinear material used is aluminum gallium arsenide (AlGaAs). Aluminum gallium arsenide (AlGaAs) with a linear refractive index of n 0 = 1.4 and a nonlinear refractive index of n 2 = 1.5 × 10 − 17 . Due to the small path length of the waveguides, the optical signals move a short distance and as a result, the power optical losses along the path are reduced and on the other hand, the speed of the structure is increased. The transmission percentage is between 90% and 100%. The overall dimensions of the structure are 324 μm2. The plane wave expansion (PWE) method is used to calculate the band structure. The two-dimensional finite difference time domain (2D-FDTD) method is used to calculate the transmission power spectrum and the simulation results.

Optical simulations and optimization of highly sensitive biosensor for cancer cell detection

In this work, using the two-dimensional finite difference time domain method, we are theoretically studying the optical properties of a two-dimensional photonic crystal biosensor based on silicon rods arranged as a square structure in an air bottom with two waveguides and a nanocavity. For this purpose, six different cells are infiltrated into the point defect. These six cells are Jurkat, HeLa, PC-12, MDA-MB-231, MCF-7, and basal cells. As a result, we have successfully detected cancer and benign cases of these cells through resonance peaks in the transmission spectrum. We evaluated the sensitivity, quality factor, detection limit, and figure of merit at different values for sensing region radius for optimization purposes. We report that we observed the maximum sensitivity of 1350 nm/RIU at 0.15 μm for the basal cell. Finally, the proposed biosensor can be a miniaturized structure with extreme sensitivity in cancer cell detection models.

All-optical nano logical gates AND, NOR, OR, and NOT based on plasmonic waveguides with Kerr nonlinear cavity

In this paper, all-optical logical gates were designed and simulated based on Kerr nonlinear circular resonators in order to increase the computational power of an optical central processing unit (CPU) using the two-dimensional finite-difference time-domain (FDTD) method. All the logical gates were designed with a simple and single plasmonic composition in which the switch between the gates is done only by changing the intensity and location of the pumps, signal, and monitor. And this is the novelty of this study, which has been optimized by changing the offset and pulse length of the springs to achieve the maximum transmittance between the OFF and ON states. In addition to the above, a manufacturing tolerance simulation was performed for each gate, which takes into account the probability of error in the experimental production process. Overall, the results showed that the difference in transmission rate for AND, NOR, OR, and NOT was 42%, 95%, 55%, and 92% respectively with an ultrafast time response of up to about 50 fs. The benefits of the present study’s design include the number of gates, high transmission rate, manufacturing tolerance, and a smaller device footprint dimension, all of which make it a good base for the future of photonic computational circuits.

Influences of Soil Water Content and Porosity on Lightning Electromagnetic Fields and Lightning-Induced Voltages on Overhead Lines

This study is performed to analyze the effects of both soil water content and porosity, two of the influencing factors of the finite conductivity, on the propagation of lightning electromagnetic fields (LEMFs) and lightning-induced voltages (LIVs) on overhead lines. A two-dimensional finite difference time domain (FDTD) model together with an improved Archie’s soil model is adopted for the field calculation at close distances from the lightning channel. The obtained results confirm that the soil water content and porosity have notable impacts on the peak values of LEMFs, especially the horizontal electric field. Moreover, the soil water content and porosity are correlated when acting together. The peak values of the horizontal electric field are found to be markedly influenced by the porosity changes at high water content or the water content changes at low porosity. The LIVs on overhead lines in these two cases are also studied. There appear to be greater differences in the induced voltages as the water content changes at low porosity.

Design of inclined omni-directional reflector for sidewall-emission-free micro-scale light-emitting diodes

Micro-scale light emitting diode (µLED) reduces the front self-luminous display area by orders of magnitude, which brings the increase of sidewall emission and the resulting crosstalk between adjacent sub-pixels of displays. Reflector coating on the µLED’s sidewall is effective for the collection and utilization of side emission light. However, the existing multilayer periodic dielectric mirrors are undesirable for all angular reflection. In this paper, an omni-directional reflector (ODR) is designed for the µLED display pixel to effectively utilize light leakage from the sidewall emission and improve the total light extraction efficiency (LEE). The designed ODR is insensitive to the angular distribution of the incident light, and has the capability to reflect the light reaching the µLED’s sidewall into the escape cone for front emission. By introducing the two-dimensional finite-difference time-domain method, the µLED laminated structure is established to analyze the sidewall emission with an optimal inclination angle. By introducing the ODR for the inclined µLED pixel, the overall LEE can be increased by 2.24 times and the sidewall emission is reduced by 99.6% compared with conventional vertical µLEDs. Simulation and experimental results are in good agreement. The proposed ODR is expected to achieve the increase of LEE and sidewall-emission-free µLED displays.

Two-dimensional finite difference-time domain analysis of focus boom noise with velocity disturbance in the atmosphere

In this paper, two-dimensional linear sound wave analysis in the stratified atmosphere with temperature gradient and velocity disturbance is numerically applied to the analysis and prediction of focus boom noise. Focus boom occurs when a supersonic transport accelerates or ascent or descent maneuvers at supersonic speed. Its overpressure is typically more than three times greater than that of a cruise sonic boom. As a result, supersonic transports in future commercial operation are likely to face restrictions on their flight conditions. The compact-explicit finite difference-time domain method is applied to the analysis of two-dimensional linear sound wave propagation. Some numerical experiments are carried out for the case of acceleration. As a result, it is shown that the complex wavefront is accurately analyzed by the FDTD method compared with the ray tracing method. It is also shown that a noise disturbed by velocity disturbance in the atmosphere reaches the ground over a wider area than the focus boom in the no disturbance case.