Vector Finite Element Research Articles

Analysis of Transmission Characteristic in Single Polarization Dual Elliptical Assistant Holes Hollow Fiber

To improve the propagation quality in photonic crystal fibers,a novel dual elliptical assistant holes hollow fiber is proposed. Numerical model of confinement loss has been modeled by vector finite element method, then the core loss characteristics and the power ratio of the hollow fiber has been simulated and analyzed. The results show that the x-polarization confinement loss and the core power ratio are 0.06dB/m and 98.2% at 1550nm, respectively. By contrast, the y-polarization confinement loss is up to 243.34dB/m while the core power ratio is 47.86%. The novel optical fiber exhibits good single polarization characteristics and transmission characteristics, and the bandwidth range of single mode single polarization is 55nm. The novel optical fiber is very good to satisfy the requirement of single mode single polarization at the 1550nm.

Analysis of the discontinuous Petrov–Galerkin method with optimal test functions for the Reissner–Mindlin plate bending model

We analyze the discontinuous Petrov–Galerkin (DPG) method with optimal test functions when applied to solve the Reissner–Mindlin model of plate bending. We prove that the hybrid variational formulation underlying the DPG method is well-posed (stable) with a thickness-dependent constant in a norm encompassing the L2-norms of the bending moment, the shear force, the transverse deflection and the rotation vector. We then construct a numerical solution scheme based on quadrilateral scalar and vector finite elements of degree p. We show that for affine meshes the discretization inherits the stability of the continuous formulation provided that the optimal test functions are approximated by polynomials of degree p+3. We prove a theoretical error estimate in terms of the mesh size h and polynomial degree p and demonstrate numerical convergence on affine as well as non-affine mesh sequences.

Research on terahertz photonic crystal fiber characteristics with high birefringence

A new high birefringence photonic crystal fiber is proposed within the terahertz frequency region. It has two types of claddings, the inner is composed of six ellipse air holes arranged in a honeycomb array and the outer surrounded by circle holes. By using the full vector finite element method with anisotropic perfectly matched layers absorption boundary condition, the birefringence, chromatic dispersion and confinement loss of the fundamental mode are evaluated. The results show that the birefringence can achieve 10−3 when the wavelength increases from 600μm to 900μm. This structure will provide some reference value for the designing of high birefringence terahertz photonic crystal fiber.

Electromagnetically induced transparency with hybrid silicon-plasmonic traveling-wave resonators

Spectral filtering and electromagnetically induced transparency (EIT) with hybrid silicon-plasmonic traveling-wave resonators are theoretically investigated. The rigorous three-dimensional vector finite element method simulations are complemented with temporal coupled mode theory. We show that ring and disk resonators with sub-micron radii can efficiently filter the lightwave with minimal insertion loss and high quality factors (Q). It is shown that disk resonators feature reduced radiation losses and are thus advantageous. They exhibit unloaded quality factors as high as 1000 in the telecom spectral range, resulting in all-pass filtering components with sharp resonances. By cascading two slightly detuned resonators and providing an additional route for resonator interaction (i.e., a second bus waveguide), a response reminiscent of EIT is observed. The EIT transmission peak can be shaped by means of resonator detuning and interelement separation. Importantly, the respective Q can become higher than that of the single-resonator structure. Thus, the possibility of exploiting this peak in switching applications relying on the thermo-optic effect is, finally, assessed.

Design optimization of microwave properties for polymer electro-optic modulator using full vectorial finite element method

In this paper, a polymer electro-optic modulator has been designed and optimized using the full vectorial finite element method. For this purpose, the effects of magnesium oxide (MgO) and down cladding thicknesses, distance between two ground electrodes, hot electrode and modulator widths modulator on the key modulator parameters, such as microwave effective index nm, the characteristic impedance ZC and the microwave losses α are presented. After selecting optimal dimensions of polymer electro-optic modulator, frequency dependent aforementioned parameters and the half-wave voltagelength product (VπL) parameter of polymer electro-optic modulator are extracted and as a consequence, an optimized design is reported. Finally, the optical and electrical modulation responses of polymer electro-optic modulator are calculated. The optimized polymer electrooptic modulator exhibits 3-dB electrical bandwidth of 260 GHz and VπL about 2.8 V·cm in this frequency.

Using Finite Element Method and Support Vector Machine to Evaluate Scour Bridge Condition

Scouring around bridge piers is one of the major reasons for bridge failures and makes disaster since it tends to occur suddenly and without prior warning. However, the mechanism of water flow around the pier structure is complicated, which makes it is very difficult to develop a generic model to evaluate the scour bridge condition and provide a safety level. In this study, an integrated model that combines support vector machine (SVM) and finite element simulation technology is introduced to estimate the scour depth and determinate the safety level of scour bridge by using the natural frequency of the bridge structure. The proposed model in this study provides effective way to have a prior understanding of scour bridge condition and avoid the disaster of bridge failure.

Numerical study of high-index-contrast Er:LiNbO3 photonic wire lasers optically pumped at 980 nm

For the first time [to our best knowledge] a high-index-contrast z-cut Er:LiNbO(3) photonic wire waveguide laser, optically pumped at 980 nm wavelength, is designed for continuous-wave operation. Waveguide modes and laser characteristics are numerically computed using a developed full vectorial finite-element method based tool. In order to maximize the output power of the laser, the active cavity length and output mirror's reflectivity have been optimized, considering different pump power and waveguide background losses. Efficient laser emission is theoretically predicted at 1531 nm wavelength for the fundamental TE mode and a value of threshold pump power as low as 0.2 mW has been computed.

TE/TM-Pass Polarizer Based on Lithium Niobate on Insulator Ridge Waveguide

We propose a TE/TM-pass polarizer based on a shallow X-cut lithium niobate-on-insulator (LNOI) ridge waveguide. In shallow X-cut LNOI ridge waveguides, the leaky mode is interchanged between TE and TM polarization waves depending on the ridge waveguide height. The phenomenon does not occur in silicon-on-insulator ridge waveguides. We use this special loss mechanism for TE/TM-pass polarizers. We evaluate structural and wavelength dependencies of polarizers by a vectorial finite-element method. The extinction ratios of 108 dB/mm and 27 dB/mm are obtained for TE-pass and TM-pass polarizers.

Plasmonics in the ultraviolet with the poor metals Al, Ga, In, Sn, Tl, Pb, and Bi

We discuss how the poor metals Al, Ga, In, Sn, Tl, Pb, and Bi can be used for plasmonics in the near to far ultraviolet (UV) range, similar to the noble metals Ag and Au in the visible (Vis) range. We first discuss the empirical dielectric functions of the poor metals, contrasting them with Ag and Au, and also fitting them to a Drude and multiple Lorentz oscillator form. Using Mie theory, we then compare the optical responses of spherical poor metal nanoparticles to noble metal ones. Finally, nanoparticle dimers are studied using a vectorial finite element method. We show how the poor metals exhibit large electric field enhancements in the UV, comparable to Au in the Vis, which makes them particularly attractive for sensing applications, such as surface enhanced Raman spectroscopy.

COMPLEX RECTANGULAR FILTER DESIGN USING HYBRID FINITE ELEMENT METHOD AND MODIFIED MULTIMODAL VARIATIONAL FORMULATION

We hybridize vector Finite Element Method (FEM) and a Modifled Multimodal Variational Formulation (MMVF) to the accurate and fast design of complex isotropic rectangular fllters. The MMVF is applied to the full-wave description in the rectangular waveguides while the FEM characterizes waves in the arbitrarily shaped discontinuities. The proposed hybrid method is applied to the full-wave analysis of circuits with great practical interest (i.e., cross-shaped iris and multimode fllters), thus improving CPU time and memory storage against several full-wave FEM based Computer Aided Design (CAD) tools (i.e., HFSS High Frequency Structural Simulator). The performances of the proposed hybrid method are validated with experimental results and HFSS simulations.

Ge-doped microstrutured fiber design by genetic algorithm for directional coupling

A new design of a microstructured optical fiber using cylindrical perfectly matched layers is proposed and analyzed through the vectorial beam propagation method (VBPM) in conjunction with genetic algorithm (GA). The fiber is made up from silica doped with germanium and it contains two and three identical horizontals cores surrounded by air holes. First, the signal power launched in the left core is completely transferred to the neighbor core with 100% of the coupling ratio. Next, the signal power launched in the central core is equally divided between the two neighboring cores with 50% of the coupling ratio. Through numerical simulations, it is demonstrated that the optical power can be completely transferred for a propagation distance around 6000 μm to the first application and 4000 μm to the second application. The behavior of the resulting geometry has been optimized by a genetic algorithm in conjunction with an efficient vectorial finite element formulation (GE-VBPM). © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:281–285, 2012; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.27308

Novel large mode area photonic crystal fibers with selectively material-filled structure

A novel large mode area (LMA) photonic crystal fibers (PCFs) are proposed in this paper. LMA is obtained by selectively material-filled structural PCFs in which six air-holes near the center are filled with high refractive index material. It provides a new method to design and realize LMA PCFs. The transmission characteristics such as effective mode areas, chromatic dispersion, and confinement losses are investigated and also the influences of structure parameters are numerically analyzed by employing the full vectorial finite element method (FEM). Numerical results demonstrate that effective mode area can improve, small and flat dispersion is achieved, and confinement losses are still acceptable by applying our novel selectively material-filled technology. Compared with the traditional method achieving LMA, it has perfect performances and it is simple and easy to fabricate.

Multicorelike guidance in a triangular-core hollow optical fiber and spectral evolution of its eigenmode degeneracy

A unique multicorelike guidance was achieved in a microstructured optical fiber composed of a circular air hole at the center surrounded by a high-index triangular core. Unique spectral evolution of the degeneracy was theoretically investigated using a vectorial finite element method to find a threefold degeneracy in both the fundamental and the first excited modes in the visible range, which evolved to twofold degeneracy as the wavelength increased to IR. Experimental measurements also confirmed evolution of the modal intensity from three spatially isolated patterns confined to individual corners into a supermode combining the three corners.

Three-Dimensional Finite-Element Solutions for Crossing Slot-Waveguides With Finite Core-Height

A three-dimensional vectorial finite element method (3-D-VFEM) for waveguide discontinuity problems is newly formulated and implemented. Through the use of the 3-D-VFEM, transmission characteristics of two types of crossing slot-waveguides with finite core-height are investigated for the first time. One is a direct crossing and the other is a crossing filling up the slots locally. Results show that three-dimensional analysis considering the finite core-height is indispensable.

Finite-element modeling of coupled optical microdisk resonators for displacement sensing

We analyze normal mode splitting in a pair of vertically coupled microdisk resonators. A full vectorial finite element model is used to find the eigen frequencies of the symmetric and antisymmetric composite modes as a function of coupling distance. We find that the coupled microdisks can compete with the best Fabry-Perot resonators in displacement sensing. We also show how we configured FreeFem++ for the sphere eigenvalue problem.

Method Study on System Reliability Calculation and Control

An intelligent method of reliability analysis based on compound algorithm is presented in this paper, support vector machine and analysis of finite element combined with Monte Carlo numerical simulation is integrated to improve simulation computing precision. Mathematic model of reliability calculation on catenary system and compound algorithm model are built, reliability of location supporting seat and location pipe are calculated by the method, location supporting seat and location pipe are critical force-bearing parts of catenary system in the high-speed electrified railway, and fault rate is very high, their reliability analysis is important research subject in railway system, it is difficult to built reliability model of location supporting seat and location pipe because they work in a complex and uncertain environment. In this paper, analysis method of location installation based on support vector machine and finite element combined with monte carlo is used, and the outside parameter influence on location installation is analyzed by the model.

High birefringence low-dispersion of nonlinear photonic crystal fiber

The paper presents a theoretical design of high nonlinear photonic crystal fiber (PCF) with high birefringence and low dispersion. Its birefringence, dispersion and nonlinear coefficient are investigated simultaneously by using the full vectorial finite element method with anisotropic perfectly matched layers. Numerical results show that the proposed highly nonlinear low-dispersion fiber has a total dispersion as low as ±12.6pskm−1nm−1 over ultrabroad wavelength range from 1.21 to 1.61μm, and the corresponding birefringence and nonlinear coefficient are about 2.1×10−3 and 28W−1km−1 at 1.55μm, respectively. The proposed PCF with high birefringence, low dispersion and high nonlinearity can have important application in supercontinuum (SC) generation, dispersion compensation, wavelength (frequency) converter, polarization maintaining transmission and Raman amplifier.

High Birefringence and Negative Dispersion Effect of Hybrid-Core Photonic Crystal Fiber

A novel type of hybrid-core photonic crystal fiber is proposed, whose core is composed of center-directionally decrescent air holes arrayed as pentagonal and an octagonal structure. Characteristics of the proposed PCF are analyzed theoretically by using all vector finite element method (V-FEM). Results show that high-birefringence and negative dispersion are obtained over the wavelength range from 0.8µm to 1.8µm, and the maximum of birefringence reaches 1.36×10-2 and negative dispersion achieves -600 ps•nm-1•km-1~-60 ps•nm-1•km-1, which will fulfill the requirement of high-birefringence polarization maintaining fiber fabricating and wideband dispersion compensating.

High performance micro-fiber coupler-based polarizer and band-rejection filter

Using full vector finite element method and super-mode theory, we analyzed the feasibility to fabricate micro-fiber-coupler-based optical polarizer. Our theoretical analysis showed that there exist a set of optimal pairs of two coupler geometric parameters, i.e. the coupling length and the micro-fiber diameter of the coupler, that can result in high performance polarizers. Experimentally, we fabricated three such coupler-based polarizers using the dual fiber drawing technique and characterized their performance. Our experimental measurement results confirmed our theoretical prediction in several aspects. When the diameter of the coupler-forming micro-fiber is relatively small (~3.5μm), the degree of polarization (DOP) of the fabricated polarizer was found relatively low (~50%) even over some coupling length range. However, when the diameter of the coupler-forming micro-fiber is larger (about 5μm to 9μm), a much higher DOP (>91.4%) and better linear polarization extinction ratio (LPER) of ~60dB could be achieved. The measured geometric parameters of two polarizer samples that showed high polarizing performance agreed very well with our theoretical values. Furthermore, we also demonstrated that such a coupler-based polarizer can be used as an optical filter as well. The filter exhibited an extinction ratio as high as 20dB at the center wavelength and the full width at half maximum (FWHM) was 10nm.

A New Design of Photonic Crystal Fiber with Fattened Dispersion and Low Effective Mode Area

We propose a novel type of photonic crystal fiber with low fattened dispersion and high nonlinearity for four wave mixing. The dispersion and nonlinearity coefficient are investigated simultaneously by using the full vectorial finite element method with anisotropic perfectly matched layers. The optimized result has been obtained by adjusting the design parameter of the proposed fiber, which has dispersion is -1.53 ps•nm−1 km−1 at wavelength of 1.55μm, and in addition the relatively small effective mode area of 2.23μm2 is obtained at the same wavelength, which will induce higher nonlinearity coefficient is close 54.8 W-1• km-1 at the wavelength of 1.55μm. The proposed PCF is suitable for applications as a chromatic dispersion controller, dispersion compensator, or as candidate for the nonlinear optical systems because of its small effective mode area.