Modeling light propagation in liquid crystal devices with a 3-D full-vector finite-element beam propagation method

A full-vector finite-element beam propagation method in 3-D is introduced for the simulation of light propagation in liquid crystal (LC) devices. The three electric field components are expressed in terms of mixed finite elements, providing the correct enforcement of boundary conditions. Moreover, the optical dielectric tensor of the medium can have all its nine elements nonzero, thus allowing the LC director to have an arbitrary orientation. A photonic crystal fiber with a LC infiltrated core and a homeotropic to multi-domain cell are analyzed. Comparison with other existing simulation techniques is provided, in order to validate the accuracy of the proposed method.     

Transient heating effects in electromagnetic launchers with complex geometries: A 3D hybrid FE/BE analysis

A time-stepping finite-element (FE) and boundary-element (BE) coupling method was implemented to include 3D transient eddy current under electromagnetic heating effects in electromagnetic launchers. Lagrangian formulations were used to model electromagnetic and thermal diffusive processes with moving conductors. The finite-element formulation was employed for the general diffusion equation in a bounded conductor region including rail and armature; while, in the exterior region, the boundary element method was developed for Laplace's equation. The coupled boundary was employed directly on the surface of conductors and no special treatment on boundary was required. The electromagnetic and temperature fields were coupled through iterative calculations. This method results in considerable time saving in modeling as it eliminates the surrounding air region.     

Theoretical investigation of hierarchical sub-wavelength photonic structures fabricated using high-order waveguide-mode interference lithograph

This paper presents the theoretical investigation of hierarchical sub-wavelength photonic structures with various periods and numbers of layers, which were fabricated using a high-order waveguide-mode interference field. A 442-nm laser was used to excite high-order waveguide modes in an asymmetric metal-cladding dielectric waveguide structure. The dispersion curve of the waveguide modes was theoretically analyzed, and the distribution of the interference field of high-order waveguide modes was numerically simulated using the finite-element method. The various dependences of the characteristics of hierarchical sub-wavelength photonic structures on the thickness and refractive index of the photoresist and the waveguide mode were investigated in detail. These hierarchical sub-wavelength photonic structures have various periods and numbers of layers and can be fabricated by a simple and low-cost method.     

Application of modified integration rule to time-domain finite-element acoustic simulation of rooms

The applicability of the modified integration rule for time-domain finite-element analysis is tested in sound field analysis of rooms involving rectangular elements, distorted elements, and finite impedance boundary conditions. Dispersion error analysis in three dimensions is conducted to evaluate the dispersion error in time-domain finite-element analysis using eight-node hexahedral elements. The results of analysis confirmed that fourth-order accuracy with respect to dispersion error is obtainable using the Fox-Goodwin method (FG) with a modified integration rule, even for rectangular elements. The stability condition in three-dimensional analysis using the modified integration rule is also presented. Numerical experiments demonstrate that FG with a modified integration rule performs much better than FG with the conventional integration rule for problems with rectangular elements, distorted elements, and with finite impedance boundary conditions. Further, as another advantage, numerical results revealed that the use of modified integration rule engenders faster convergence of the iterative solver than a conventional rule for problems with the same degrees of freedom.     

Validation of the effective-medium approximation for the dielectric permittivity of oriented nanoparticle-filled materials: effective permittivity for dielectric nanoparticles in multilayer photonic composites

A formula for the effective permittivity for two-dimensional particles embedded in a host matrix is derived and a method for its numerical evaluation is described. The method is applied to specific cases of circular, square, rectangular and triangular particles. Shapes are assumed for the inclusion particles. Data for obtaining the effective permittivity is provided for a wide range of filling fractions, geometries and dielectric contrasts between the particles and the matrix under the assumption of the quasi-static approximation, that is, the wavelength of the electric field is assumed to be much larger than the particle size. Metallic particles with complex and frequency-dependent dielectric constants are treated, as well as no-loss dielectric inclusions. Calculations are validated by comparing the results of the reflectivity obtained for a composite layer using the transfer-matrix method, assuming the layer to be an effective medium, to those using the finite-element method and accounting for the heterogeneous material. PACS 78.20.-e; 78.20.Bh; 78.20.Ci; 78.66.Sq; 78.66.Vs     

有限元法求解任意折射率分布光纤模场分布

 应用有限元方法求解了任意径向非均匀折射率分布园柱对称介质波导中纵向场耦合波动方程定解问题所对应的变分问题,该方法不受弱导或高斯模场分布等限制,可方便地求解光纤中介质波导的模场分布。用此方法研究了带阶跃环的三角型分段折射率分布光纤中归一化模场半径与芯层传输功率比值随光纤不同结构参数的变化规律。     

有限元法求解任意折射率分布光纤模场分布

应用有限元方法求解了任意径向非均匀折射率分布园柱对称介质波导中纵向场耦合波动方程定解问题所对应的变分问题,该方法不受弱导或高斯模场分布等限制,可方便地求解光纤中介质波导的模场分布。用此方法研究了带阶跃环的三角型分段折射率分布光纤中归一化模场半径与芯层传输功率比值随光纤不同结构参数的变化规律。     

Hybrid power flow analysis using coupling loss factor of SEA for low-damping system—Part II: Formulation of 3-D case and hybrid PFFEM

The hybrid power flow analysis (PFA) is an analytic method proposed for the effective prediction of vibrational and acoustic responses of low-damping system in the medium-to-high frequency ranges by using the PFA algorithm and statistical energy analysis (SEA) coupling concepts. This paper presents the hybrid boundary condition on 3-D case for hybrid PFA in addition to 1-D and 2-D cases which are derived in the other companion paper, and formulates the hybrid power flow finite-element method (PFFEM) including coupling loss factor (CLF) of SEA to extend the application area of hybrid PFA to built-up structures. To verify the derived boundary condition and hybrid PFFEM, numerical analyses were successfully performed for various analytic models and reverberance factors.     

Electrostatic resonance of clusters of dielectric cylinders: A finite element simulation

Based on the finite-element method, it is demonstrated that the electrostatic resonance features of a range of heterostructures made of clusters of dielectric cylinders depend sensitively on the shape and arrangement of the inclusions in the background matrix, and on the polarization of the applied electric field.     

二维椭圆形散射转移斗篷的设计研究

基于变换光学理论设计了椭圆形散射转移斗篷,并推导了相应的本构参数张量表达式,根据得到的本构参数,利用基于有限元算法的软件分别对椭圆形介质柱、导体柱进行了全波仿真验证.仿真结果证实了所得本构参数的正确性,验证了散射转移斗篷可以模拟任意物体,包括介质、导体的幻象,这些结果为设计隐身斗篷提供了一种新的理论途径.     

Design of sharp bends with transformation plasmonics

We report a design method of surface plasmon polaritons sharp bends based on transformation optics. Plasmonic waveguide bends with different angles, which possess little radiation loss, are proposed. Transformation media can be simply achieved with homogeneous and nonmagnetic materials, which can be constructed by altering two different dielectric films. Electromagnetic simulations by a finite-element method on detailed examples have been performed to validate the designs.     

Oxygen-vacancy-related dielectric relaxation and conduction mechanisms in Bi5TiNbWO15 ceramics

This paper reports that the intergrowth ceramics Bi5TiNbWO15 （BW-BTN） have been prepared with the conventional solid-state reaction method. The dielectric and conductivity properties of samples were studied by using the dielectric relaxation and AC impedance spectroscopy in detail. Two distinct relaxation mechanisms were detected both in the plots of dielectric loss （tanδ） and the imaginary part （Z″） versus frequency in the frequency range of 10 Hz-13 MHz. We attribute the higher frequency relaxation process to the hopping process of the oxygen vacancies inside the grains, while the other seems to be associated with the space charges bound at the grain boundary layers. The AC impedance spectroscopy indicates that the conductivities at 625 K for bulk and grain boundary are about 1.12 × 10^-2 S/m and 1.43 × 10^-3 S/m respectively. The accumulation of the space charges in the grain boundary layers induces a space charge potential of 0.52 eV.     

Review of numerical and approximate methods for the modal analysis of general optical dielectric waveguides

AbstactAbstact This paper reviews numerical and approximate methods for the modal analysis of general optical dielectric waveguides with emphasis on recent developments. Six groups of methods are reviewed, covering (1) the finite-element method, (2) the finite-difference method, (3) the integral-equation method, (4) methods based on series expansion, (5) approximate methods based on separation of variables, and (6) methods that do not fit into the above groups, ranging from the specialized ones for analysing restricted classes of waveguides to the most general ones for analysing inhomogeneous, arbitrarily-shaped, anisotropic waveguides. Some suggestions with regard to the selection of methods for particular applications are given.     

Reformulation for Latent-Image Formation Model in Photolithography Using Numerical Absorbing Boundary Condition

A method for simulating latent image formation in a photoresist illuminated by an arbitrary imaging system is presented. A variational formulation for light scattering, which does not depend on a specific configuration of the imaging system, is derived and solved using the finite-element method. The perfectly matched layer absorbing boundary condition is applied to take wave propagation in the infinite region surrounding the photoresist into account. The validity of the method is examined by comparing the results with those made by the vertical propagation model and the previous two-dimensional models.     

Determination of dynamic three-dimensional displacement fields on a shell surface

This paper presents a solution to the problem of dynamic three-dimensional displacement distributions on a curved surface under impact-loading by utilizing photomechanics and the finite-element method. An impulsive force is applied by using a new type of electromagnetic forcing mechanism, which gives good repeatability. The relation between instataneous loading and time that is set for the force-voundary condition in the finite-element calculation of the displacement components is recorded experimentally. It is found that the experimental results are in good agreement with those of the finite-element method.     

1维介质光栅近场及其衍射的FDTD分析

 应用FDTD方法计算了单色平面波斜入射时1维介质光栅的近场，进而求出介质光栅的衍射效率。借助于周期边界条件，整个计算区域为周期结构的一个单元。考虑入射波在两种介质界面上会产生反射和透射，故在总场边界上引入入射波、反射波和透射波。给出了光栅单元截面为矩形和梯形的算例。该方法可用于斜入射情形下具有复杂结构和任意单元截面的介质栅近场及其衍射特性分析。     

Three-dimensional finite-element simulation of Zener pinning dynamics

The Zener pinning dynamics of a moving boundary interacting with one or more particles is described by a three-dimensional (3D) finite-element model. The model, based upon a variational formulation for boundary motion by viscous drag, is solved by a finite-element method to obtain the velocity at each node of triangular linear elements on the grain boundary. It is first applied to relatively simple and validated cases, for which analytical and numerical results are available. These cases correspond to an axisymmetrical geometry, in which the grain boundary interacts with a centred particle. A simple analytical pinning criterion is derived from these simulations. The model is then applied to general 3D cases, in which the grain boundary interacts with arbitrarily localized and sized particles. The aim of these 3D simulations is to quantify the influence of the position and the number of particles on the average grain-boundary velocity. It is shown, for example, that the drag effect is enhanced when the particle, or the cluster of particles, is off-centre and that pinning is less efficient with several particles than with a single particle producing the same Zener force.     

Dielectric properties of ultrathin films of molecular crystals

Dielectric properties of thin films (TF) of molecular crystals, including the effect of size and the boundary surfaces were analysed using Green's function method. Polarisability of molecules in various film layers and dielectric susceptibility of TF were calculated. A comparison with crystal bulk has shown that dielectric properties of TF are strongly influenced both by the sample dimensions and by the boundary conditions.The frequency dependence of the dielectric susceptibility has also been derived. One obtains the monotonous variation for the frequencies above and below exciton band. However, for the frequencies within the exciton band there appears to be complicated, non-monotonous dependence. The relationship between the dielectric susceptibility and the film width for the same frequency shows a complex, oscillatory behaviour. Furthermore, the amplitude of these oscillations increases with increasing film width, demanding the introduction of a damping factor. Finally, the thickness dependence of dielectric susceptibility was analysed in the Cole-Cole plot.     

Direct tunneling current model for MOS devices with ultra-thin gate oxide including quantization effect and polysilicon depletion effect

An efficient direct tunneling current model is presented for the ultra thin gate dielectric MOS structure. The tunneling current is modeled by including the inversion layer quantization effect with a finite potential barrier height as the boundary condition and the modified WKB method for calculating the transmission probability. The model is in good agreement with the full quantum calculation and the experiments. The results indicate that the finite boundary condition has to be considered for the ultra thin gate dielectric and the gate dielectric materials with lower barrier height. This model is accuracy and computational efficient and suitable to be used in characterized the sub-100 nm MOSFET with gate oxide below 2.0 nm.