Matched Layer Absorbing Boundary Condition Research Articles

2D Efficient Unconditionally Stable Meshless FDTD Algorithm

This paper presents an efficient weighted Laguerre polynomials based meshless finite-difference time domain (WLP-MFDTD). By decomposing the coefficients of the system matrix and adding a perturbation term, a factorization-splitting scheme is introduced. The huge sparse matrix is transformed into two N×N matrices with 9 unknown elements in each row regardless of the duplicated ones. Consequently, compared with the conventional implementation, the CPU time and memory requirement can be saved greatly. The perfectly matched layer absorbing boundary condition is also extended to this approach. A numerical example demonstrates the capability and efficiency of the proposed method.

Tuning the Fano resonances in a single defect nanocavity coupled with a plasmonic waveguide for sensing applications

A novel surface plasmon polaritons (SPPs) refractive index sensor based on a single defect nanocavity coupled with a metal–insulator–metal (MIM) waveguide is proposed and numerically simulated by using the finite difference time domain (FDTD) method with perfectly matched layer absorbing boundary condition. It is found that the defect structure can realize two Fano resonances and these two Fano resonances originate from two different mechanisms. The results demonstrate the liner correlation between the resonance wavelengths of the device and the refractive index of the material under sensing. Through the optimization of structural parameters, we achieve a theoretical value of the refractive index sensitivity as high as 1800.4 nmRIU[Formula: see text]. It could be utilized to develop ultra-compact nanodevice for high-resolution biological sensing.

UPML‐ABC and TF/SF boundary for unconditionally stable AH‐FDTD method in conductive medium

For analysing the scattering problem in conductive medium with the new unconditionally stable associated Hermite (AH) finite-difference time-domain (FDTD) method, the formulation of uniaxial anisotropic perfectly matched layer absorbing boundary condition (UPML-ABC) and the total-field/scattered-field (TF/SF) implementation scheme are deduced. By virtue of AH differential transformation matrix and the eigenvalue transformation, frequency-dependent parameters of the lossy medium can be well treated in AH-UPML, without using any additional auxiliary variables. Numerical verification for the scattering of buried conductor in lossy half-space is performed. Compared with Mur's ABC, UPML increases the absorbing performance by more than 80 dB in AH-FDTD analysis.

Perfectly matched layer absorbing boundary condition for nonlinear two-fluid plasma equations

Numerical instability occurs when coupled Maxwell equations and nonlinear two-fluid plasma equations are solved using finite difference method through parallel algorithm. Thus, a perfectly matched layer (PML) boundary condition is set to avoid the instability caused by velocity and density gradients between vacuum and plasma. A splitting method is used to first decompose governing equations to time-dependent nonlinear and linear equations. Then, a proper complex variable is used for the spatial derivative terms of the time-dependent nonlinear equation. Finally, with several auxiliary function equations, the governing equations of the absorbing boundary condition are derived by rewriting the frequency domain PML in the original physical space and time coordinates. Numerical examples in one- and two-dimensional domains show that the PML boundary condition is valid and effective. PML stability depends on the absorbing coefficient and thickness of absorbing layers.

Full-Vectorial Analysis of Optical Waveguide Discontinuities Using Denman–Beavers Iterative Scheme

An accurate and efficient full-vectorial numerical approach for analyzing three-dimensional optical waveguide discontinuities is proposed, where the resulting square root of the characteristic matrix from the field-based operators is approximated by the Denman-Beavers iterative scheme with a branch-cut rotation in the complex plane. Both the magnetic and electric field formulations are rigorously derived along with the robust perfectly matched layer absorbing boundary conditions. Numerical results from a typical buried waveguide, a channel waveguide, and a rib waveguide show that the present scheme is more accurate and stable than the widely used Padé approximation, while the computational load is comparative.

Convolution Approximating Perfect Matched Layer Absorbing Boundary Condition of 3D Scalar Acoustic Wave Equation

Because traditional displacement form of 3D acoustic perfectly matched layer (PML) absorbing condition needs to split the displacement into three parts, which requires solving a third-order differential equation in time and occupies a large amount of memory. In order to solve the above problems, this paper puts forward an Convolution approximating PML absorbing boundary condition based on the previous works, and discusses the basic construction of the traditional perfectly matched layer absorbing boundary condition and the new arithmetic in detail, then the new method is compared with absorbing condition of low order paraxial approximation and traditional PML, investigating the absorbing effects of 3D acoustic wave’s numerical records.

Acoustic eigenanalysis of 2D open cavity with Vekua approximations and the method of particular solutions

This paper discusses the efficient extraction of acoustic resonances in 2D open cavities using a meshless method, the method of particular solutions. A first order, local non-reflecting boundary condition is chosen to account for the opening and Fourier-Bessel functions are employed to approximate the pressure at the borders of the cavity and inside. A minimization problem is then solved for the complex frequency range of interest. For the investigated cavity, the minimum values obtained match those found in previously published studies or by other numerical methods. But, unlike the perfectly matched layer absorbing boundary conditions now usually employed, this approach is free from spurious eigenfrequencies. Moreover, the specific treatments of the geometric singularities allow this method to be particularly efficient in the presence of corner singularities.

Novel Integrated Demultiplexer with the Bragg Grating Structure Based on Surface Plasmon Polaritons

A novel demultiplexer based on surface plasmon polaritons with the Bragg structure has been proposed and numerically investigated. The finite difference time domain method with perfectly matched layer absorbing boundary condition is adopted to simulate and study their properties. By introducing Bragg grating structure in the couple area, high extinguish ratio can be achieved. The extinction ratio in 1550nm was 27.5db. Meanwhile, the photonic device can be made in the way of high level of integration, because SPPs has the ability of strongly localizing the signal mode in the area beyond the limit of diffraction. The longitudinal dimension of this demultiplexer was 650nm. The demultiplexer may become a good choice for the design of devices in highly integrated optical circuits.

A New Plasmonic Filter through Double Metal Films Perforated with Rectangular Grooves and Circular Holes

A novel plasmonic passband filter consisting of metal-insulator-metal perforated with an array of rectangular grooves and circular holes is proposed and demonstrated. The transmission property of the proposed structure is obtained by employing the finite difference time domain with perfectly matched layer absorbing boundary condition. The result reveals that a passband with high transmission can be achieved. And the transmission peak position can be efficiently tuned by changing the factors of the structure, such as the sizes of circular holes and grooves. The proposed filter has potential applications for integrated optoelectronic devices due to its miniaturized size.

Modified Unsplitted Perfectly Matched Layer Absorbing Boundary Conditions for Truncating Anisotropic Medium

To simulate Electromagnetic wave propagation in anisotropic media, absorbing boundary conditions are needed to truncate the computation domains. Based on the finite difference time domain method in anisotropic medium, the implementation of the modified nearly perfectly matched layer absorbing boundary conditions for truncating anisotropic medium is presented. By using the partial derivatives of space variables stretched-scheme in the coordinate system, the programming complexity is reduced greatly. According to one dimensional numerical simulation analysis, the modified nearly perfectly matched layer absorbing boundary condition is validated.

A new circular photonic crystal fiber for effective dispersion compensation over E to L wavelength bands

This paper presents a new circular photonic crystal fiber (C-PCF) for effective dispersion compensation covering E to L wavelength bands ranging from 1360-1625 nm. To investigate its guiding properties, finite element method (FEM) with a perfectly matched layer absorbing boundary condition is used. From our numerical simulation, it is found that the designed C-PCF simultaneously shows a large negative dispersion of about -248.65 to -1069 ps/(nm.km) over E to L wavelength bands and a relative dispersion slope (RDS) exactly equal to that of a single mode fiber (SMF) at 1.55 µm wavelength. It is also found that residual dispersion after compesating 40 km long SMF is within ±62 ps/nm which ensures application of C-PCF in high speed WDM system. Besides, dispersion slope, slope compensation ratio, effective area and confinement loss of the proposed C-PCF are also evaluated and discussed.

Nonorthogonal LOD-FDTD Method for EM Scattering from Two-Dimensional Structures

In this paper, a nonorthogonal locally 1-D finite difference time-domain (LOD-NFDTD) method is presented for electromagnetic (EM) scattering involving curvilinear coordinate system. Formulations of scattered field and convolutional perfectly matched layer absorbing boundary condition in generalized nonorthogonal grids for LOD-NFDTD are also presented. The nonorthogonal grids are used to fully mesh the computational domain which leads to efficient computation. Moreover, the proposed technique requires fewer arithmetic operations than the alternating direction implicit NFDTD method leading to a reduction of CPU time. The numerical dispersion of the proposed method as a function of Courant-friedrich-lewy number (CFLN) is also presented. Computational results for EM scattering from 2-D conducting, dielectric, and coated cylinders as well as overfilled dielectric and bent cavity structures are presented.

A compact frequency selective stop-band splitter by using Fabry—Perot nanocavity in a T-shaped waveguide

By utilizing a Fabry—Perot (FP) nanocavity adjacent to T-shaped gap waveguide ports, spectrally selective filtering is realized. When the wavelength of incident light corresponds to the resonance wavelength of the FP nanocavity, the surface plasmons are captured inside the nanocavity, and light is highly reflected from this port. The resonance wavelength is determined by using Fabry—Perot resonance condition for the nanocavity. For any desired filtering frequency the dimension of the nanocavity can be tailored. The numerical results are based on the two-dimensional finite difference time domain simulation under a perfectly matched layer absorbing boundary condition. The analytical and simulation results indicate that the proposed structure can be utilized for filtering and splitting applications.

Vector analysis of bending waveguides by using a modified finite-difference method in a local cylindrical coordinate system

A vector mode solver for bending waveguides by using a modified finite-difference (FD) method is developed in a local cylindrical coordinate system, where the perfectly matched layer absorbing boundary conditions are incorporated. Utilizing Taylor series expansion technique and continuity condition of the longitudinal field components, a standard matrix eigenvalue equation without the averaged index approximation approach for dealing with the discrete points neighboring the dielectric interfaces is obtained. Complex effective indexes and field distributions of leaky modes for a typical rib bending waveguide and a silicon wire bend are presented, and solutions accord well with those from the film mode matching method, which shows the validity and utility of the established method.

Nanometeric plasmonic refractive index senor

A novel surface plasmon-polaritons (SPPs) refractive index sensor based on tooth-shaped metal–insulator–metal structure is proposed and numerically simulated by using the finite difference time domain method with perfectly matched layer absorbing boundary condition. Both analytic and simulated results show that the transmission minima wavelengths in the transmitted spectrum of the sensor have a linear relationship with the refractive index of material under sensing. Based on the relationship, the refractive index of the material can be obtained from the detection of one of the transmission minima wavelengths in the transmitted spectrum. The resolution of refractive index of the nanometeric sensor can reach as high as 10−6, given the wavelength resolution of 0.01nm. It could be applied to high-resolution biological sensing.

Characteristic analysis of a directional coupler in horizontal multiple-slotted silicon wires with slanted sidewalls

The characteristics of the directional couplers based on the horizontal multiple-slotted waveguides with slanted sidewalls are analyzed in detail by using a mode solver based on the full-vectorial finite element method with perfectly matched layers absorbing boundary conditions. The coupling length of the directional coupler as functions of the structural parameters including waveguide spacing, sidewalls angle, the thickness and refractive index of the slot regions, both in quasi-TE and quasi-TM modes, is obtained. The effective indexes and the field distributions of the even and odd modes also are presented. The numerical results show that polarization-independent directional couplers can be realized by properly choosing structural and material parameters.

General ADI-FDTD Formulations for Multi-Term Dispersive Electromagnetic Applications

General formulations of the alternating direction implicit finite difference time domain method are presented for modeling multi-term dispersive electromagnetic applications. The proposed formulations, which are based on the exponential evolution operator scheme, allow modeling different types of frequency dependent materials in the same manner and can be easily incorporated with the nearly perfectly matched layer absorbing boundary conditions to model open region problems. 2-D numerical example is included to show the validity of the proposed formulations.

Compact Terahertz Wave Collimator Design with Photonic Crystal Slabs

A compact terahertz (THz) wave collimator is proposed, which works under the frequency from 2.4 THz to 2.7 THz with a photonic crystal (PC) slab based on the self-collimation effect. The plane wave expansion (PWE) method is used to calculate the dispersion surfaces and the equal-frequency contours (EFCs) and optimize the structure. The propagation of the THz waves in the structure is simulated and the normalized transmission is calculated by using the finite-difference time-domain (FDTD) method with perfectly matched layer (PML) absorbing boundary conditions. Numerical simulations show that the designed collimator has a good collimation property and a high transmittance.

Improved Models for Plasmonic Waveguide Splitters and Demultiplexers at the Telecommunication Wavelengths

Single output channel selective plasmonic filter structure based on a nanocavity is proposed and numerically simulated by using the finite difference time domain method with perfectly matched layer absorbing boundary condition. The required filtered wavelength can be obtained by selecting an appropriate length of the nanocavity. Nanocavity model and gain model are introduced and analyzed. Two output channels structure based on two nanocavities is proposed to design a subwavelength plasmonic splitter and demultiplexer operating around 1310 nm and 1550 nm. The finite-difference time-domain (FDTD) simulation results reveal that this new structure is suitable for wideband wavelengths demultiplexing. Finally, we propose a multiwavelength demultiplexing structure based on multinanocavity connected to the bus waveguide.

A Laser Structure Based on Metal-Dielectric-Metal Plasmonic Nanocavity

A subwavelength plasmonic laser structure based on a metal-dielectric-metal nanocavity is proposed and numerically simulated by using the finite difference time domain method with perfectly matched layer absorbing boundary condition. The nanocavity model and gain analysis are respectively given. The simulation results show that the losses within the nanocavity (including surface plasmon losses) can be compensated by the gain material and the threshold gain of the laser is about 1.5 × 103 cm−1 with the peak wavelength around 1,550 nm. The new device would be an important step toward a fully integrated surface plasmon circuits.