A massively parallel time-domain coupled electrodynamics–micromagnetics solver

We present a high-performance coupled electrodynamics–micromagnetics solver for full physical modeling of signals in microelectronic circuitry. The overall strategy couples a finite-difference time-domain approach for Maxwell’s equations to a magnetization model described by the Landau–Lifshitz–Gilbert equation. The algorithm is implemented in the Exascale Computing Project software framework, AMReX, which provides effective scalability on manycore and GPU-based supercomputing architectures. Furthermore, the code leverages ongoing developments of the Exascale Application Code, WarpX, which is primarily being developed for plasma wakefield accelerator modeling. Our temporal coupling scheme provides second-order accuracy in space and time by combining the integration steps for the magnetic field and magnetization into an iterative sub-step that includes a trapezoidal temporal discretization for the magnetization. The performance of the algorithm is demonstrated by the excellent scaling results on NERSC multicore and GPU systems, with a significant (59×) speedup on the GPU using a node-by-node comparison. We demonstrate the utility of our code by performing simulations of an electromagnetic waveguide and a magnetically tunable filter.

Trapezoid-Grid Finite-Difference Time-Domain Method for 3D Seismic Wavefield Modeling Using CPML Absorbing Boundary Condition

The large computational memory requirement is an important issue in 3D large-scale wave modeling, especially for GPU calculation. Based on the observation that wave propagation velocity tends to gradually increase with depth, we propose a 3D trapezoid-grid finite-difference time-domain (FDTD) method to achieve the reduction of memory usage without a significant increase of computational time or a decrease of modeling accuracy. It adopts the size-increasing trapezoid-grid mesh to fit the increasing trend of seismic wave velocity in depth, which can significantly reduce the oversampling in the high-velocity region. The trapezoid coordinate transformation is used to alleviate the difficulty of processing ununiform grids. We derive the 3D acoustic equation in the new trapezoid coordinate system and adopt the corresponding trapezoid-grid convolutional perfectly matched layer (CPML) absorbing boundary condition to eliminate the artificial boundary reflection. Stability analysis is given to generate stable modeling results. Numerical tests on the 3D homogenous model verify the effectiveness of our method and the trapezoid-grid CPML absorbing boundary condition, while numerical tests on the SEG/EAGE overthrust model indicate that for comparable computational time and accuracy, our method can achieve about 50% reduction on memory usage compared with those on the uniform-grid FDTD method.

From Time-Collocated to Leapfrog Fundamental Schemes for ADI and CDI FDTD Methods

The leapfrog schemes have been developed for unconditionally stable alternating-direction implicit (ADI) finite-difference time-domain (FDTD) method, and recently the complying-divergence implicit (CDI) FDTD method. In this paper, the formulations from time-collocated to leapfrog fundamental schemes are presented for ADI and CDI FDTD methods. For the ADI FDTD method, the time-collocated fundamental schemes are implemented using implicit E-E and E-H update procedures, which comprise simple and concise right-hand sides (RHS) in their update equations. From the fundamental implicit E-H scheme, the leapfrog ADI FDTD method is formulated in conventional form, whose RHS are simplified into the leapfrog fundamental scheme with reduced operations and improved efficiency. For the CDI FDTD method, the time-collocated fundamental scheme is presented based on locally one-dimensional (LOD) FDTD method with complying divergence. The formulations from time-collocated to leapfrog schemes are provided, which result in the leapfrog fundamental scheme for CDI FDTD method. Based on their fundamental forms, further insights are given into the relations of leapfrog fundamental schemes for ADI and CDI FDTD methods. The time-collocated fundamental schemes require considerably fewer operations than all conventional ADI, LOD and leapfrog ADI FDTD methods, while the leapfrog fundamental schemes for ADI and CDI FDTD methods constitute the most efficient implicit FDTD schemes to date.

Investigation on Light Extraction Behavior of Surface Plasmon-Coupled Deep-Ultraviolet LED in Different Emission Directions

The light extraction behavior of an AlGaN-based deep-ultraviolet LED covered with Al nanoparticles (NPs) is investigated by three-dimensional finite-difference time-domain simulation. For the transmission spectra of s- and p-polarizations in different emission directions, the position of maximum transmittance can be changed from (θ = 0°, λ = 273 nm) to (θ = 0°, λ = 286 nm) by increasing the diameter of Al NPs from 40 nm to 80 nm. In the direction that is greater than the critical angle, the transmittance of s-polarization is very small due to the strong absorption of Al NPs, while the transmittance spectrum of p-polarization can be observed obviously for the 80 nm Al NPs structure. For a ~284 nm AlGaN-based LED with surface plasmon (SP) coupling, although the luminous efficiency is significantly improved due to the improvement of the radiation recombination rate as compared with the conventional LED, the light extraction efficiency (LEE) is lower than 2.61% of the conventional LED without considering the lateral surface extraction and bottom reflection. The LEE is not greater than ~0.98% (~2.12%) for an SP coupling LED with 40 nm (80 nm) Al NPs. The lower LEE can be attributed to the strong absorption of Al NPs.

Q-BOR–FDTD method for solving Schrodinger equation for rotationally symmetric nanostructures with hydrogenic impurity

An efficient method inspired by the traditional body of revolution finite-difference time-domain (BOR-FDTD) method is developed to solve the Schrodinger equation for rotationally symmetric problems. As test cases, spherical, cylindrical, cone-like quantum dots, harmonic oscillator, and spherical quantum dot with hydrogenic impurity are investigated to check the efficiency of the proposed method which we coin as Quantum BOR-FDTD (Q-BOR-FDTD) method. The obtained results are analysed and compared to the 3-D FDTD method, and the analytical solutions. Q-BOR-FDTD method proves to be very accurate and time and memory efficient by reducing a three-dimensional problem to a two-dimensional one, therefore one can employ very fine meshes to get very precise results. Moreover, it can be exploited to solve problems including hydrogenic impurities which is not an easy task in the traditional FDTD calculation due to singularity problem. To demonstrate its accuracy, we consider spherical and cone-like core-shell QD with hydrogenic impurity. Comparison with analytical solutions confirms that Q-BOR–FDTD method is very efficient and accurate for solving Schrodinger equation for problems with hydrogenic impurity

Theoretical fabrication of subwavelength structures by surface plasmon interference based on complementary grating

This paper presents a surface plasmon interference lithography technique based on the complementary grating, which comprises silicon gratings and complementary aluminum grating masks, for fabricating subwavelength structures. In this theoretical study, the optimal parameters of the complementary grating structure were determined using the reflectance spectrum. The optical field distributions of one- and two-dimensional subwavelength structures were obtained using the finite-difference time-domain method and rotation-related formulas. The results of numerical evaluations show that a one-dimensional periodic structure with a half-pitch resolution of 60.5 nm (approximately [Formula: see text]/6.7) can be fabricated. In addition, subwavelength structures can be diversified using different rotation methods to expose the photolithography samples, such as square dot arrays and quasi-hexagonal closely packed structures. The proposed method combines surface plasmon interference with sample rotation, thereby enabling fabrication of abundant subwavelength structures.

Plasmonic Refractive Index Sensor and Plasmonic Bandpass Filter Including Waveguide and Four Teeth Based On Fano Resonances

A plasmonic refractive index sensor including a Metal-Insulator-Metal waveguide (MIM) with four teeth is proposed. Transmittance (T), Sensitivity (S) and Figure of Merit (FOM) investigated numerically and analysed via Finite Difference Time Domain method (FDTD). The simulation results show the generation of double Fano resonances in the system that the resonance wavelength and the resonance line-shapes can be adjusted by changing the geometry of the device. By optimizing the structure in the initial configuration, the maximum sensitivity of 1078nm/RIU and FOM of 3.62×105 is achieved. Then change the structure parameters. In this case, the maximum sensitivity and FOM are 1041nm/RIU and 2.94×104 respectively, thus two detection points can be used for the refractive index sensor. Due to proper performance and adjustable Fano resonance points, this structure is significant for fabricating sensitive refractive index sensor and plasmonic bandpass filter.

Оптические свойства кремниевых нанопилларов со встроенным вертикальным p-n-переходом

Resonance reflection of light from the ordered arrays of silicon nanopillars (Si NP) was investigated. The height of Si NP was 450 nm. The effect of Si NP oxidation in concentrated nitric acid on the position of resonances in reflection spectra was studied. A weak influence of the additional polymeric coating on the characteristics of reflection from the structures was proven. It is established on the basis of the results of experimental investigation and direct numerical modeling by means of three-dimensional finite difference time domain algorithm (3D FDTD) that the dependence of the resonant wavelength for Si NP on the diameter of Si NP is a linear function with nonzero displacement depending on the pitch.

Benchmarking 2D against 3D FDTD codes for the assessment of the measurement performance of a low field side plasma position reflectometer applicable to IDTT

O-mode reflectometry, a technique to diagnose fusion plasmas, is foreseen as a source of real-time (RT) plasma position and shape measurements for control purposes in the coming generation of machines such as DEMO. It is, thus, of paramount importance to predict the behavior and capabilities of these new reflectometry systems using synthetic diagnostics. Finite-difference time-domain (FDTD) time-dependent codes allow for a comprehensive description of reflectometry but are computationally demanding, especially when it comes to three-dimensional (3D) simulations, which requires access to High Performance Computing (HPC) facilities, making the use of two-dimensional (2D) codes much more common. It is important to understand the compromises made when using a 2D model in order to decide if it is applicable or if a 3D approach is required. This work attempts to answer this question by comparing simulations of a potential plasma position reflectometer (PPR) at the Low Field-Side (LFS) on the Italian Divertor Tokamak Test facility (IDTT) carried out using two full-wave FDTD codes, REFMULF (2D) and REFMUL3 (3D). In particular, the simulations consider one of IDTT’s foreseen plasma scenarios, namely, a Single Null (SN) configuration, at the Start Of Flat-top (SOF) of the plasma current.