Multiresolution Time-domain Scheme Research Articles

A study on reflection and transmission characteristics of magnetized plasma based on S-MRTD scheme

Employing symplectic algorithm in electromagnetic simulation enables the advantages of energy conservation, high stability, low dispersion and high accuracy to be maintained. A new numerical scheme for simulating magnetized plasma, which is symplectic multi-resolution time-domain (S-MRTD) scheme is presented. First, the discrete iterative process of S-MRTD scheme for magnetized plasma is constructed based on the symplectic operator technique. Then, the correctness and effectiveness of the S-MRTD scheme framework are verified by the numerical simulation of left-handed circular polarized wave (LCP) and right-handed circular polarized wave (RCP). Finally, the influence of electron cyclotron frequency(wb) on reflection and transmission coefficients is analyzed based on S-MRTD scheme.

Studies on photonic bandgap and its defect mode characteristics of plasma photonic crystals based on S-MRTD scheme

Photonic bandgap (PBG) and its defect mode are two representative characteristics of plasma photonic crystals (PPC), which make them have important industrial applications in photonic crystal waveguides, filters, antennas, and other devices. In this paper, we apply the symplectic multi-resolution time-domain (S-MRTD) scheme to analyze these two properties. Firstly, the characteristics of PBG are analyzed. Secondly, the characteristics of defect mode in the case of a single defect layer and multi-defect layers are adequately studied. Finally, two types of ternary PPC are further simulated. Numerical simulations demonstrate the feasibility and effectiveness of the proposed scheme, a desirable PBG and its defect mode can be obtained by altering the corresponding plasma parameters and dielectric parameters.

Study on electromagnetic characteristics of plasma model-based on the symplectic multiresolution time-domain scheme

A novel numerical computation scheme, which is symplectic multiresolution time-domain (S-MRTD) scheme, for modeling plasma model is proposed. The loss plasma dispersive model is taken into account in S-MRTD scheme, and the detailed formulations of the proposed S-MRTD scheme are also provided. A one-dimensional perfectly matched layers (PML) are used to terminate the computational domain. The analyses of stability and numerical dispersion demonstrate that S-MRTD scheme is more efficient than traditional finite-different time-domain (FDTD) and MRTD methods. The energy conservation characteristics of S-MRTD scheme in electromagnetic simulation are proved by the propagation of pulse in free space for long-term simulation. In the end, the S-MRTD formulations are confirmed by computing the electric field intensity, reflection and the transmission coefficients for the pulse wave through an unmagnetized plasma slab. A favorable agreement between the numerical solutions is demonstrated, and the efficiency of the proposed scheme is verified. Meanwhile, numerical results show that plasma frequency, collision frequency and thickness are important factors affecting reflection and transmission coefficients.

A novel symplectic MRTD scheme studies on numerical characteristics of plasma photonic crystals

A novel symplectic multi-resolution time-domain (S-MRTD) scheme is put forward for simulating the one-dimensional unmagnetized plasma photonic crystals (PPCs). The lossless plasma model is taken into account in S-MRTD scheme, and the detailed calculation formulas of the proposed scheme are provided. An one-dimensional perfectly matched layers (PML) technique is used to truncate the computational domain, and the corresponding formulas are also derived. From the perspective of numerical stability and dispersion characteristics, it is shown that the S-MRTD scheme is more effective than the traditional time-domain methods. The propagation process of electromagnetic (EM) waves in one-dimensional PPCs structure are simulated by S-MRTD scheme, and from the perspective of frequency domain, the reflection and transmission cofficients of EM pulse waves through the PPCs are analyzed. Meanwhile, The characteristics of photonic band gaps (PBGs) are studied based on different parameters. Numerical simulations show that plasma frequency, dielectric constant, periodic thickness, number of periods, the thickness ratio of plasma and medium are important factors affecting the characteristics of PBGs.

An Analysis of Entropy-Based Eye Movement Events Detection.

Analysis of eye movement has attracted a lot of attention recently in terms of exploring areas of people’s interest, cognitive ability, and skills. The basis for eye movement usage in these applications is the detection of its main components—namely, fixations and saccades, which facilitate understanding of the spatiotemporal processing of a visual scene. In the presented research, a novel approach for the detection of eye movement events is proposed, based on the concept of approximate entropy. By using the multiresolution time-domain scheme, a structure entitled the Multilevel Entropy Map was developed for this purpose. The dataset was collected during an experiment utilizing the “jumping point” paradigm. Eye positions were registered with a 1000 Hz sampling rate. For event detection, the knn classifier was applied. The best classification efficiency in recognizing the saccadic period ranged from 83% to 94%, depending on the sample size used. These promising outcomes suggest that the proposed solution may be used as a potential method for describing eye movement dynamics.

Light scattering computation model for nonspherical aerosol particles based on multi-resolution time-domain scheme: model development and validation

Due to the inadequate understanding of the scattering properties of nonspherical aerosols, considerable uncertainties still exist in the radiative transfer numerical simulation. To this end, a new scattering model for nonspherical aerosols is established based on Multi-Resolution Time-Domain (MRTD) scheme. The model is comprised of three modules: near field calculation module, near-to-far transformation module and scattering parameters computation module, in which, the near electromagnetic field is calculated by MRTD technique, the near-to-far transformation scheme is performed by volume integral method, and the calculation models for extinction and absorption cross section are directly derived from Maxwell's curl equations in the frequency domain. To achieve higher computational efficiency, the model is further parallelized by MPI non-blocking repeated communication technique. The accuracy of the scattering model is validated against Lorenz-Mie, Aden-Kerker and T-matrix theories for spherical particles, particles with inclusions and nonspherical particles. At last, the parallel computational efficiency of the MRTD scattering model is quantitatively discussed as well. The results obtained by parallel MRTD scattering model show an excellent agreement with those of the well-tested scattering theories, where the relative simulation errors of the phase function are less than 5% for most scattering angles. In backward directions, the simulation errors are much larger than that in forward scattering directions due to the stair approximation in particle construction. The computational accuracy of the integral scattering parameters like extinction and absorption efficiencies is higher than phase matrix, where the simulation errors of extinction and absorption efficiencies for the particle with a size parameter of 10 achieve -0.4891% and -1.6933%, respectively.

Multiresolution Time-Domain Analysis of Multiconductor Transmission Lines Terminated in Linear Loads

This paper derives a multiresolution time-domain (MRTD) scheme for the multiconductor transmission line (MTL) equations based on Daubechies’ scaling functions. The terminations are characterized by a state-variable formulation which allows a general description of the termination networks. For the linear load terminations, a method incorporating the terminal constraints is proposed to work out the scheme at and close to the terminations. The MRTD scheme is implemented with different basis functions for linear components including resistances, inductances, and capacitances. Numerical results show that the MRTD schemes obtain a more stable result than the conventional finite difference time-domain (FDTD) method with a coarse space step.

The Alternating Direction Implicit Body of Revolution Multiresolution Time Domain Method with Convolution Perfect Matched Layer

Overmuch memory and time of CPU have been taken by multiresolution time domain (MRTD) method in three-dimension issues. In order to solve this problem, the alternating direction implicit body of revolution multiresolution time domain (ADI-BOR-MRTD) scheme is presented. Firstly, based on body of revolution finite difference time domain (BOR-FDTD) method, equations of body of revolution multiresolution time domain (BOR-MRTD) method are implemented. Then alternating direction implicit (ADI) is introduced into BOR-MRTD method. Lastly, convolution perfect matched layer (CPML) is applied for ADI-BOR-MRTD method. Numerical results demonstrate that ADI-BOR-MRTD method saves more memory and time of CPU than FDTD and MRTD methods.

Multiresolution Time-Domain Scheme for Terminal Response of Two-Conductor Transmission Lines

This paper derives a multiresolution time-domain (MRTD) scheme for the two-conductor lossless transmission line equations based on Daubechies’ scaling functions. And a method is proposed to generate the scheme at the terminal and near the terminal of the lines. The stability and numerical dispersion of this scheme are studied, and the proposed scheme shows a better dispersion property than the conventional FDTD method. Then the MRTD scheme is extended to the two-conductor lossy transmission line equations. The MRTD scheme is implemented with different basis functions for both lossless and lossy transmission lines. Numerical results show that the MRTD schemes which use the scaling functions with high vanishing moment obtain more accurate results.

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.

Implementation and application of a convolution PML using the MRTD algorithm

In this paper, a novel implementation of convolution perfectly matched layer (CPML) is proposed for the multiresolution time-domain (MRTD) method. The implementation is completely independent of the host material and easier to obtain than that of the popularly used anisotropic perfectly matched layer, when treating more generalized media. The absorbing effectiveness of the CPML is discussed and validated in a two-dimensional case, and we apply the CPML in three-dimensional cases with different microwave circuit components. Numerical results show that the CPML performs well for absorbing electromagnetic waves in the MRTD scheme.

Efficient design of optical delay lines based on slotted‐ring resonators

In this study, a novel design of coupled-resonator optical waveguide delay line based on slotted ring resonators (SCROW) is proposed and analysed. The coupling efficiency between the resonators, which can be controlled either by changing the slot position inside the cavity or by varying the separation distance between the rings, plays an essential role in controlling both group velocity and delay time of the suggested SCROW. The simulation results are obtained using multi-resolution time domain scheme in conjunction with uniaxial perfectly matched layer boundary conditions. By introducing a slot inside the microring resonator of the suggested structure, a quality factor of about 5 × 103 and high delay time are obtained with small ring size.

A Novel Symplectic Multi-Resolution Time-Domain Scheme for Electromagnetic Simulations

A symplectic scheme is applied to the multi-resolution time-domain (MRTD) method, resulting in a highly stable novel symplectic MRTD scheme. First, the time-domain Maxwell's equations are rewritten as a matrix equation. Then, we discretize the Maxwell's equations in the time direction using symplectic propagation integrator (SPI) technique and evaluate the equations in the spatial direction with high order spatial multi-resolution approximation to construct novel symplectic MRTD scheme. The stability and numerical dispersion analysis are also included. Numerical results are given to show the high efficiency and accuracy of the method.

A Cylindrical MRTD Algorithm With PML and Quasi-PML

In this paper, we develop an explicit multiresolution time-domain (MRTD) scheme based on Daubechies' scaling functions with a cylindrical grid for time-domain Maxwell's equations. The stability and dispersion property of the scheme is investigated and it is shown that larger cells decrease the numerical phase error, which makes it significantly lower than finite difference time domain (FDTD) for low and medium discretizations, and the MRTD scheme has a slight advantage of high-order FDTD (2, 6). Moreover, two absorbing boundary conditions (ABCs) are derived for the cylindrical MRTD grids. The first one is the perfectly matched layer (PML) based on stretched coordinates, and the other is the straightforward extension of Berenger's PML, which is called the quasi perfectly matched layer (QPML), as it is no longer perfectly matched for cylindrical interfaces. The absorbing effectiveness of the two ABCs are compared and the numerical simulations validate that both PML schemes can provide a satisfactory ABC, while the QPML can save more computation time and computer memory.

MULTIRESOLUTION TIME DOMAIN SCHEME USING SYMPLECTIC INTEGRATORS

We incorporate high-order symplectic time integrators into multiresolution time domain (MRTD) schemes. The stability and numerical dispersion analysis are presented. The proposed scheme preserves the symplectic structure of Maxwell's equations and can be easily implemented in program codes. Compared to Runge-Kutta (RK)-MRTD, the suggested scheme is more accurate in long-term simulations and requires less computational resource.

Design considerations of microcavity ring resonators

This study presents an accurate numerical analysis of a microcavity ring resonator based on high-index-contrast waveguide. The analysis is carried out using a multiresolution time domain (MRTD) scheme that provides high numerical precision without the strict limitation on the space discretisation as compared to the commonly used finite-difference time domain (FDTD). By relying on higher-order approximation of discretisation in space, the proposed MRTD approach outperforms the FDTD method and is thus a more suitable candidate for large-scale simulations. The uniaxial perfectly matched layer is carefully applied to truncate the computational domain. The analysed parameters are the coupling coefficients between the input/output waveguides and the ring, the resonance frequencies and the free spectral range. The effect of the structure geometry parameters such as the gap between the ring and input/output waveguides, the ring radius and the width of the input/output waveguide and the ring resonator is thoroughly investigated. The numerical results reveal that the suggested MRTD allows using about twice the spatial step size required by FDTD yet providing same level of accuracy.

An Improved Split-Step Method in Scaling Function Based MRTD

A split-step method with four sub-steps is applied to the multiresolution time-domain scheme and combined with the dispersion-error control parameters. From the discussed numerical dispersion, it is obvious that the phase velocity an- isotropic error and absolute error of the introduced method are much lower than alternating direction implicit and the original split-step MRTD method. The results show that this method can use three times the time step of the original SS-MRTD method.

ANALYSIS OF CHARACTERISTICS OF TWO-DIMENSIONAL RUNGE-KUTTA MULTIRESOLUTION TIME-DOMAIN SCHEME

In this paper, the stability condition of the Runge- Kutta m-order multiresolution time-domain (RKm-MRTD) scheme has been studied. By analyzing the ampliflcation factors, we derive the numerical dispersion relation of the RK-MRTD scheme. The numerical dispersive and dissipative errors are investigated. Finally, the theoretical predictions of the numerical errors are calculated through the numerical simulations.

Efficient Second Harmonic Generation Through Selective Photonic Crystal-Microcavity Coupling

In this paper, a new 2-D frequency converter based on second harmonic generation (SHG) in GaAs photonic crystal waveguides is proposed. The input waveguide, where the second order nonlinear process takes place, is coupled to a secondary waveguide that is designed to allow only SH propagation. A row of photonic crystal microcavity resonators is then placed parallel to the waveguides in order to assist the field coupling. By tuning the resonance of the microcavities at second harmonic wave, the waveguides-microcavities arrangement showed good enhancement of conversion efficiency and selectivity. The performance of the proposed frequency converter has been analyzed by using multiresolution time domain (MRTD) scheme developed for nonlinear problems in conjunction with uniaxial perfectly matched layer (UPML) boundary conditions that rigorously truncate the computational window.

Reduction of Numerical Dispersion Error in 3-D ADI-MRTD Method With the Coarse Mesh

In order to reduce the numerical dispersion in three-dimensional alternating-direction implicit multiresolution time-domain scheme, a correction procedure is introduced. The numerical dispersion relation and the anisotropic correction parameters are considered. The reduction of the numerical dispersion is investigated for single frequency problem and wide-band simulation with the coarse mesh.