Vector Finite Element Research Articles

The Use of Sparse Direct Solver in Vector Finite Element Modeling for Calculating Two Dimensional (2-D) Magnetotelluric Responses in Transverse Electric (TE) Mode

The late research, linear matrices of vector finite element in two dimensional(2-D) magnetotelluric (MT) responses modeling was solved by non-sparse direct solver in TE mode. Nevertheless, there is some weakness which have to be improved especially accuracy in the low frequency (10-3 Hz-10-5 Hz) which is not achieved yet and high cost computation in dense mesh. In this work, the solver which is used is sparse direct solver instead of non-sparse direct solverto overcome the weaknesses of solving linear matrices of vector finite element metod using non-sparse direct solver. Sparse direct solver will be advantageous in solving linear matrices of vector finite element method because of the matrix properties which is symmetrical and sparse. The validation of sparse direct solver in solving linear matrices of vector finite element has been done for a homogen half-space model and vertical contact model by analytical solution. Thevalidation result of sparse direct solver in solving linear matrices of vector finite element shows that sparse direct solver is more stable than non-sparse direct solver in computing linear problem of vector finite element method especially in low frequency. In the end, the accuracy of 2D MT responses modelling in low frequency (10-3 Hz-10-5 Hz) has been reached out under the efficient allocation memory of array and less computational time consuming.

Two Dimensional Finite Element Based Magnetotelluric Inversion using Singular Value Decomposition Method on Transverse Electric Mode

In this work, an inversion scheme was performed using a vector finite element (VFE) based 2-D magnetotelluric (MT) forward modelling. We use an inversion scheme with Singular value decomposition (SVD) method toimprove the accuracy of MT inversion.The inversion scheme was applied to transverse electric (TE) mode of MT. SVD method was used in this inversion to decompose the Jacobian matrices. Singular values which obtained from the decomposition process were analyzed. This enabled us to determine the importance of data and therefore to define a threshold for truncation process. The truncation of singular value in inversion processcould improve the resulted model.

Vectorial finite elements for solving the radiative transfer equation

The discrete ordinate method coupled with the finite element method is often used for the spatio-angular discretization of the radiative transfer equation. In this paper we attempt to improve upon such a discretization technique. Instead of using standard finite elements, we reformulate the radiative transfer equation using vectorial finite elements. In comparison to standard finite elements, this reformulation yields faster timings for the linear system assemblies, as well as for the solution phase when using scattering media. The proposed vectorial finite element discretization for solving the radiative transfer equation is cross-validated against a benchmark problem available in literature. In addition, we have used the method of manufactured solutions to verify the order of accuracy for our discretization technique within different absorbing, scattering, and emitting media. For solving large problems of radiation on parallel computers, the vectorial finite element method is parallelized using domain decomposition. The proposed domain decomposition method scales on large number of processes, and its performance is unaffected by the changes in optical thickness of the medium. Our parallel solver is used to solve a large scale radiative transfer problem of the Kelvin-cell radiation.

Polarization splitter based on dual-core photonic crystal fiber with tellurite glass

A polarization splitter based on dual-core photonic crystal fiber (PCF) with tellurite glass was proposed. The birefringence of the splitter was improved by introducing elliptical air holes. The full vector finite element method is used to analyze the impacts of structural parameters on the coupling length. The results show that the elliptical size is reasonably changed, the extinction ratio can reach 107.21 dB at the wavelength of 1.55 μm, the length of the splitter is 89.05 μm, and the bandwidth is 150 nm when the extinction ratio is more than 20 dB. Besides, we also compare the characteristics of tellurite glass and silica glass photonic crystal fiber polarization beam splitters with the same structural parameters.

Geometrical comparison of photonic crystal fiber-based surface plasmon resonance sensors

Numerical analysis and comparison of surface plasmon resonance (SPR)-based photonic crystal fiber (PCF) structures are presented. Full vectorial finite-element method (FEM) is employed to model and compare circular, elliptical, and square air hole-based PCF structures. The key propagation features, such as phase matching, sensitivity, resolution, and confinement loss behaviors of proposed structures, are reported. The effects of geometrical and design parameters are discussed and compared thoroughly. It is found that the sensitivity of circular air hole-based structure can reach up to 4200 nm/RIU, and the sensor resolution is 2.4 × 10 − 5 RIU.

Highly sensitive photonic crystal fiber biosensor based on titanium nitride

A highly sensitive surface plasmon resonance photonic crystal fiber (PCF) biosensor based on Titanium Nitride (TiN) as a new alternative plasmonic material is proposed and analyzed. The TiN has high stability, high conductivity, and corrosion resistance which make it an ideal material for nanofabrication. The suggested biosensor is analyzed by full vectorial finite element method with perfectly matched layer as boundary conditions. In this paper, the biosensor geometrical parameters are studied to achieve high sensitivity for both polarized modes. A refractive index sensitivity of 7700 and 3600 nm/RIU for quasi-transverse electric and quasi transverse magnetic modes, respectively, are obtained. Additionally, the reported biosensor could be used for detecting an unknown analyte refractive index ranging from 1.32 to 1.34 with a high linearity. Further, the proposed biosensor structure is easy for fabrication using standard PCF fabrication current technologies.

The Application of Ground-airborne TEM Systems for Underground Cavity Detection in China

Ground-based, electrical-source, and UAV-borne receiver TEM configurations have previously been used to map mines in Jiangsu Province, China. In this study, the EM responses of air-filled mine tunnels were simulated by using a three-dimensional (3D) vector finite element method. A new apparent resistivity formula has been proposed for the ground-airborne TEM configuration. In the study area, field measurements were carried out along 36 profiles for the ground-airborne TEM and 16 profiles for ground TEM. The ground-airborne TEM results were determined to be in good agreement with the ground TEM survey results using a surface central loop, and were also consistent with the known geologic conditions. The experiment was successful and showed that a ground-ground-airborne TEM method could potentially become a novel alternative for both future civilian and military applications. [Figure: see text]

Study on High Precision and Stable Finite Element Beam Propagation Method Based on Incomplete Third Order Hybrid Edge/Nodal Element

It has been reported that the full vectorial finite element beam propagation method (FV-FE-BPM) is not always stable. In this paper, we propose a stabilized FV-FE-BPM using a linear filter to suppress unstable modes. Moreover, aiming for improving the computational accuracy of FV-FE-BPM for longitudinally varying optical waveguides, we employ incomplete third order hybrid edge/nodal elements to reduce interpolation error which occurs in finite element mesh update process at each propagation step. The validity and effectiveness of this approach are verified through several numerical examples of uniform waveguides and longitudinally varying waveguides.

An enhanced effective mode area fluorine doped octagonal photonic crystal fiber with extremely low loss

In our paper an enhanced effective mode area octagonal photonic crystal fiber (PCF) is presented. This PCF ensures large effective mode area along with ultra-low confinement loss and bending loss. Both the elimination of air-holes from the rings near the core region and inclusion of low index fluorine doped silica rods in an octagonal pattern are the vital design features. We have used full vectorial finite element method (FEM) based software with circularly perfectly matched layer (PML) to simulate the guiding properties of PCF. Our proposed fiber achieves effective mode area of 1110 μm2. Moreover, it offers ultra-low confinement loss of 1.14 × 10−15 dB/m and can be bent as small as 30 cm without any significant bending loss of 6.49 × 10−9 dB/m. The PCF also ensures low non-linearity with small amount of splice loss. However, our proposed PCF can be used in applications like fiber amplifiers and lasers.

Label free detection for DNA hybridization using surface plasmon photonic crystal fiber biosensor

In this paper, a novel design of a highly sensitive surface plasmon (SP) photonic crystal fiber (PCF) biosensor for DNA hybridization detection is presented and analyzed. Through this study, the coupling between the core guided modes in a silica core D-shaped PCF and the SP modes around the gold nano-wires is studied and verified. Further, the structural geometrical parameters of the proposed biosensors are adjusted to achieve the highest sensitivity for DNA hybridization detection. The analysis is carried out using full vectorial finite element method. The proposed biosensor achieves a high sensitivity of 94.59 nm/RIU. To the best of the author’s knowledge, it is the first time to introduce a label free SP PCF DNA biosensor with high sensitivity. Moreover, the structure of the suggested sensor is easy for fabrication with standard PCF fabrication technologies. Furthermore, the suggested biosensor has a great potential for DNA classification based applications.

A Novel Approach for Spectroscopic Chemical Identification Using Photonic Crystal Fiber in the Terahertz Regime

A novel highly sensitive porous core-photonic crystal fiber (PC-PCF) has been designed and analyzed for detection of chemical analytes in the terahertz frequency range. The PC-PCF is designed using rectangular structured air holes in the core with a kagome structured cladding. The full vectorial finite-element method is used to tune the geometrical parameters and to characterize the fiber. Our results demonstrate a high relative chemical sensitivity with significantly lower confinement loss for different analytes. Moreover, the PCF shows near zero dispersion variation, high modal effective area, high birefringence, and high numerical aperture. The practical realization of the fiber is feasible with present fabrication techniques. Our optimized PCF has commercial applications in chemical sensing as well as applications in terahertz systems that require guided polarization preserving transmission.

A novel Zeonex based oligoporous-core photonic crystal fiber for polarization preserving terahertz applications

A novel waveguide consisting of oligo-porous core photonic crystal fiber (PCF) with a kagome lattice cladding has been designed for highly birefringent and near zero dispersion flattened applications of terahertz waves. The wave guiding properties of the designed PCF including birefringence, dispersion, effective material loss (EML), core power fraction, confinement loss, and modal effective area are investigated using a full vector Finite Element Method (FEM) with Perfectly Matched Layer (PML) absorbing boundary condition. Simulation results demonstrate that an ultra-high birefringence of 0.079, low EML of 0.05 cm−1, higher core power fraction of 44% and negligible confinement loss of 7.24×10−7 cm−1 can be achieved at 1 THz. Furthermore, for the y-polarization mode a near zero flattened dispersion of 0.49±0.05 ps/THz/cm is achieved within a broad frequency range of 0.8–1.7 THz. The fabrication of the proposed fiber is feasible using the existing fabrication technology. Due to favorable wave-guiding properties, the proposed fiber has potential for terahertz imaging, sensing and polarization maintaining applications in the terahertz frequency range.

Analysis of Spatially Doped Fused Silica Fiber Optic by Means of a Hamiltonian Formulation of the Helmholtz Equation

This paper discusses an alternative method for calculating modal parameters in optical fibers such as propagation constants, transverse distributions, and anisotropy, due to linear and nonlinear phenomena acting as perturbations caused by doped silica regions. This method is based on a Hamiltonian formulation of the Helmholtz equation and the stationary perturbation theory, which allows a full‐vectorial description of the electric field components when linear anisotropic inhomogeneities and Kerr nonlinearity are included. Linear and nonlinear parameters can be found for each propagating mode, and its accuracy has been successfully tested when compared to numerical calculations from the vector finite element method, and the results are published in the literature. This method facilitates the calculation of the spatial‐distributed perturbation effects on individual electric field components for each propagating mode.

Numerical modeling of a influence of a nanoparticle pair on the electromagnetic field in the near zone by the vector finite elements method

Here we propose a mathematical model based on a vector finite-element method for modeling the distribution of the electromagnetic field in the near zone of spherical particles. This model has allowed us to develop algorithms for the appropriate software. The verification of the model shows that the discrepancy between the research results of the proposed model and the available calculation results based on analytical formulas derived from the Mie theory for homogeneous spherical nanoparticles does not exceed 10 percent. Calculations were carried out to determine the relative positions of a pair of metal nanoparticles at which the intensity of the electromagnetic field reaches the maximum value in the near zone. The advantage of the proposed mathematical model and approach consists in the use of tetrahedrons as finite-elements. The tetrahedron finite-elements allow one to approximate the heterogeneous structure of the nanomaterial with the accuracy sufficient for the practical use. Furthermore, in this way the continuity of the tangential component of the electromagnetic field in the entire calculation region can be achieved.

A high extinction and wide bandwidth polarization filter based on surface plasmon resonance

A broad bandwidth polarization filter based on photonic crystal fiber (PCF) coated with gold layer is proposed and simulated by the full vector finite element method. The surface plasmon resonance coupling theory is studied, and the factors that affect the polarization filtering effect are analyzed. By changing the structural parameters of the PCF, we realize polarization filter at 1.55 and 1.48 μm. In the designed polarization filter, the maximum loss of the unwanted y-polarization at 1.55 μm is 803.56 dB/cm and at 1.48 μm is 732.69 dB/cm. Besides, a broad bandwidth of 1000 nm with the crosstalk better than 20 dB is obtained. The suggested PCF is competitive for polarization device.

Broadband supercontinuum generation spanning 1.5–13 μm in Ge11.5As24Se64.5 based chalcogenide glass step index optical fiber

We have reported a design of a step index optical fiber in Ge11.5As24Se64.5 chalcogenide glass. The proposed design of optical fiber is analyzed using full vectorial finite element method. The structure offers a high nonlinear coefficient of 1431 W−1 km−1. Due to this high nonlinearity of the optical fiber a supercontinuum spectrum ranging from 1.5–13 μm is generated in only 10 mm long fiber by applying 50 fs laser secant pulses of 4000 W peak power at the pump wavelength of 3.1 μm. The use of femtosecond pulse laser results in the supercontinuum with high shot-to-shot coherence. Broadband mid-infrared supercontinuum generation has many applications such as in medical diagnosis, food quality control, gas sensing, telecommunication, and optical metrology etc.

Design of a single‐mode photonic crystal fibre with ultra‐low material loss and large effective mode area in THz regime

A novel low-loss photonic crystal fibre (PCF) has been suggested for THz spectral applications. The proposed PCF contains five layers cladding with three layers core. The cladding and core region of the fibre are arranged in the octagonal and porous manner, respectively, where both the core and cladding vicinity are constituted by circular air cavities. The optical properties of the PCF are investigated by utilising the full vectorial finite-element method along with the perfect match layers boundary condition. All numerical outcomes show the ultra-low effective material loss of 0.049 cm−1 and large effective area of 3 × 10−7 m2 at 1 THz operating frequency. The power fraction is also considered as another significant parameter to design a low loss fibre. The almost more than half of the useful power (about 53.78% at f = 1 THz) goes through the core over the wider operating frequency. In addition this, the proposed single-mode PCF can be fabricated using the sol–gel method and is useful not only for high data traffic transmission applications but also for THz waveguide applications.

Design of photonic crystal fiber with elliptical air-holes to achieve simultaneous high birefringence and nonlinearity**Project supported by the National Natural Science Foundation of China (Grant No. 61475029).

A new type of V-shaped photonic crystal fiber with elliptical air-holes is proposed to realize simultaneous high birefringence and nonlinearity at a wavelength of 1.55 μm. The full vector finite element method was adopted to investigate its characteristics, including birefringence, nonlinearity, and dispersion. The PCF exhibited a very high birefringence of 2.89×10−2 and very high nonlinear coefficient of 102.69 W−1⋅km−1. In particular, there were two zero-dispersion wavelengths (ZDWs) in the visible (X: 640–720 nm and Y: 730–760 nm) and near-infrared regions (X: 1050–1606 nm and Y: 850–1500 nm). The combination of high birefringence and nonlinearity allowed the PCF to maintain the polarization state and generate a broadband super continuum, with potential applications in nonlinear optics.

Characteristics analysis of 3D marine CSEM response using the vector finite element method with secondary formulation

Characteristics analysis of 3D marine CSEM response using the vector finite element method with secondary formulation

A dual-core PCF polarization splitter with five elliptical air holes based on tellurite glass

A new kind of dual-core photonic crystal fiber polarization splitter based on tellurite glass is designed by introducing five elliptical air holes and octagonal lattice into the polarization splitter. The full vector finite element method and coupled-mode theory are used to study its characteristics. The structure parameters are optimized through the study of all parameters in the split structure. The results show that a polarization splitter with a short length of 105.156 μm can completely separate the two beams of polarization lights. And at the wavelength of 1.550 μm the extinction ratio can reach 124.920 dB. Meanwhile, the bandwidth is 165 nm when the extinction ratio is more than 20 dB and the wavelength range is from 1.467 to 1.632 μm, which covers the S + C + L wavelength bands. The bandwidth is 448 nm when the extinction ratio is more than 10 dB and the wavelength range is from 1.322 to 1.770 μm. The polarization splitter has a short length and a high extinction ratio and a wide bandwidth, which can be widely applied in large-capacity and integrated optical communication systems.