Full-vectorial finite-difference beam propagation method based on the modified alternating direction implicit method

A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.

Wavelet Beam Propagation Method for Study the Integrated Optical Waveguide

A new numerical technique based on the wavelet derivative operator is presented as an alternative to BPM to study the integrated optical waveguide. The wavelet derivative operator is used instead of FFT/IFFT or finite difference to calculate the derivatives of the transverse variable in the Helmholtz equation. Results of numerically simulating the injected field at z =0 are exhibited with Gaussian distribution in transverse direction propagating through the two dimensional waveguides (with linear and/or nonlinear refractive index) , which are similar to those in the related publications. Consequently it is efficient and needs not absorbing boundary by introducing the interpolation operator during calculating the wavelet derivative operator. The iterative process needs fewer steps to be stable. Also, when the light wave meets the changes of mediums, the wavelet derivative operator has the adaptive property to adjust those changes at the boundaries.

Modified Wide-angle Beam Propagation Method Using Douglas Operators

A modified wide-angle beam propagation based on the Douglas operators is presented.The truncation error in the modified wide-angle beam propagation is reduced to o (Δ x ) 4 in the transverse direction nearly without any increase of the computation time,whereas the error in the ordinary wide-angle beam propagation method is typically o (Δ x ) 2.With trivial programming changes,the accuracy is higher,especially in wide-angle propagation.

A Modified Beam Propagation Method Based on the Galerkin Method with Hermite-Gauss Basis Functions

A beam propagation method based on the Galerkin method with Hermite-Gauss basis functions for studying optical field propagation in weakly guiding dielectric structures is described. The selected basis functions naturally satisfy the required boundary conditions at infinity so that the boundary truncation is avoided. The paraxial propagation equation is converted into a set of first-order ordinary differential equations, which are solved by means of standard numerical library routines. Besides, the calculation is efficient due to its small resulted matrix. The evolution of the injected field and its normalized power along the propagation distance in an asymmetric slab waveguide and directional coupler are presented, and the solutions are good agreement with those obtained by finite difference BPM, which tests the validity of the present approach.

DYNAMIC ANALYSIS OF ARREST OF BUCKLE PROPAGATION ON A BEAM ON A NONLINEAR ELASTIC FOUNDATION BY FEM

Based on the dynamic governing equation of propagating buckle on a beam on a nonlinear elastic foundation, this paper deals with an important problem of buckle arrest by combining the FEM with a time integration technique. A new conclusion completely different from that by the quasi-static analysis about the buckle arrestor design is drawn. This shows that the inertia of the beam cannot be ignored in the analysis under consideration, especially when the buckle propagation is suddenly stopped by the arrestors.

Dynamic Analysis and Numerical Simulation of a Kind of Arrestor Arresting Buckle Propagation by FEM

For exact estimation of efficiency of a buckle arrestor, it is necessary to take the effect of structural inertia into account in the analysis of buckle propagation on elastic structures after meeting arrestors. Under this consideration, this paper deals with the dynamics of buckle arrest and its numerical simulation on the basis of the beam system model used by Chater and Hutchinson (1983). The FEM combined with an improving are-length control method is adopted to solve the dynamic equations describing the arresting of buckle propagation. A new group of parameters for arrestor design which differs greatly from that by the quasi-static analysis is obtained. The present results support the conclusion that the inertia of the beam cannot be neglected in such analysis.

An improved three-dimensional full-vectorial finite-difference imaginary-distance beam propagation method

A modified alternating direction implicit approach is proposed to discretize the three-dimensional full-vectorial beam propagation method （3D-FV-BPM） formulation along the longitudinal direction. The cross-coupling terms （CCTs） are neglected at the first substep, and then double used at the second substep. The order of two substeps is reversed for each transverse electric field component so that the CCTs are always expressed in an implicit form, thus the calculation is efficient and stable. Based on the multinomial interpolation, a universal finite difference scheme with a high accuracy is developed to approximate the 3D-FV-BPM formulation along the transverse directions, in which the discontinuities of the normal components of the electric field across the abrupt dielectric interfaces are taken into account and can be applied to both uniform and non-uniform grids. The corresponding imaginary-distance procedure is first applied to a buried rectangular and a GaAs-based deeply-etched rib waveguide. The field patterns and the normalized propagation constants of the fundamental and the first order modes are presented and the hybrid nature of the full-vectorial guided-modes is demonstrated, which shows the validity and utility of the present approach. Then the modal characteristics of the deeply- and shallow-etched rib waveguides based on the InGaAsp/InGaAsP strained multiple quantum wells in InP substrate are investigated in detail. The results are necessary for modeling and the design of the planar lightwave circuits or photonic integrated circuits based on these waveguides.

Vortex Field Propagation in a Hexagonal Multicore Fiber Array

The propagation of an optical vortex in a hexagonally arranged single mode multicore fiber structure is investigated for possible generation of additional vortices and their spread dynamics. Fields are separated into a slowly varying paraxial envelope and a rapidly changing exponential component. Solutions are derived from the paraxial inhomogeneous Schrodinger equation in two dimensions along with the index of refraction of the proposed structure. Numerical analyses are based on the beam propagation method and transparent boundary conditions in matrix form with different parameters to represent the intensity and phase of all derived fields. Vortices are numerically identified by their points of zero intensity and their phase change or polarity. The optical interferogram with a plane wave reference is also employed to distinguish the dislocation points in the transverse directions of the propagating fields.

ELASTIC IMPACT ON FINITE TIMOSHENKO BEAM

In this paper the analytical solutions of the impact of a particle on Timoshenko beams with four kinds of different boundary conditions are obtained according to Navier's idea, which is further developed. The initial values of the impact forces are exactly determined by the momentum conservation law. The propagation of the longitudinal and transverse waves along the beam, especially, the effects of boundary conditions on the characteristics of the reflected waves, are investigated in detail. Some results are compared with those by MSC/NASTRAN.

Three-dimensional beam propagation method based on the variable transformed Galerkin's method

A novel three-dimensional beam propagation method (BPM) based on the variable transformed Galerkin's method is introduced for simulating optical field propagation in three-dimensional dielectric structures. The infinite Cartesian x-y plane is mapped into a unit square by a tangent-type function transformation. Consequently, the infinite region problem is converted into the finite region problem. Thus, the boundary truncation is eliminated and the calculation accuracy is promoted. The three-dimensional BPM basic equation is reduced to a set of first-order ordinary differential equations through sinusoidal basis function, which fits arbitrary cladding optical waveguide, then direct solution of the resulting equations by means of the Runge-Kutta method. In addition, the calculation is efficient due to the small matrix derived from the present technique. Both z-invariant and z-variant examples are considered to test both the accuracy and utility of this approach.

Analytical structure of Hermite Gaussian beam in far field

Based on the vectorial structure of electromagnetic beam and the method of stationary phase, the analytical structure of Hermite Gaussian beam in far field is presented. The structural energy flux distributions are also investigated in the far field. The structural pictures of some Hermite Gaussian beams are depicted in the far field. As the structure of Hermite Gaussian beam is dominated by the transverse mode numbers and the initial transverse Gaussian half width, it is more complex than that of Gaussian beam. The ratios of the structural energy fluxes to the whole energy flux are independent of the transverse mode numbers and the initial transverse Gaussian half width. The present research reveals the internal vectorial structure of Hermite Gaussian beam from other viewpoint.

A Construction of Beam Propagation Methods for Optical Waveguides

This paper presents a systematic method to derive Beam Propagation Models for optical waveguides.The technique is based on the use of the symbolic calculus rules for pseudodifferential operators.The cases of straight and bent optical waveguides are successively considered.

Operator Splitting Method for Coupled Problems:Transport and Maxwell Equations

In this article a new approach is considered for implementing operator splitting methods for transport problems, influenced by electric fields. Our motivation came to model PE-CVD (plasma-enhanced chemical vapor deposition) processes, means the flow of species to a gas-phase, which are influenced by an electric field. Such a field we can model by wave equations. The main contributions are to improve the standard discretization schemes of each part of the coupling equation. So we discuss an improvement with implicit Runge- Kutta methods instead of the Yee’s algorithm. Further we balance the solver method between the Maxwell and Transport equation.

Gaussian Beam Propagation in a Kerr Type Metamaterial Medium Using ABCD Matrix Method

In this paper, a split step ABCD matrix method is suggested to investigate Gaussian beam propagation in a Kerr type metamaterial medium. This method is based on dividing the medium interval into subsequent steps.Meanwhile, Gaussian beam profile in every step is obtained by finding the ABCD matrix of that particular step, and is used to find the ABCD matrix of the next step. Results of the suggested matrix method have been compared with the results of numerical split-step Fourier method for a Kerr medium, which indicates a good agreement. Then, we use the ABCD matrix to investigate Gaussian beams propagation in a Kerr type metamaterial, which is also in agreement with pervious results by other methods.

侧边抛磨光纤的光传输特性研究

基于有限差分光束传播法,对侧边抛磨光纤的光传输特性进行了模拟计算。给出了应用自行研制的侧边光纤抛磨机的侧边抛磨光纤的制作方法,并研究了几个影响侧边抛磨光纤光传输特性的参量。实验表明,侧边抛磨光纤的抛磨面与纤芯的剩余厚度d越小,光功率衰减越大,对涂敷材料的折射率变化的灵敏度越大。在抛磨区域浸在折射率约为1.495的折射率液体的情况下,当d<5μm时衰减明显增大。抛磨区长度越长,光功率衰减越大;抛磨表面越粗糙,光功率衰减也越大。

(1+1)维光折变亮屏蔽孤子相互作用的数值分析

利用束传播法对(1+1)维光折变亮屏蔽孤子间的相互作用进行了详细地数值模拟研究.结果表明两同相孤子相互吸引,并伴有孤子融合现象,且孤子融合发生时的作用距离随着孤子初始间距的增大而增大;两反相孤子相互排斥,且排斥作用随着孤子初始间距的减小而增强;当两孤子的相位差位于区间(0,π)和(-π,0)中时,其相互作用过程将伴有能量转移,但两区间内能量转移的方向相反,并表现出反转对称性;由于孤子间的距离和相对相位对孤子间的相互作用均有很大的影响,因此多个孤子间的相互作用过程非常复杂,但可以通过分析相邻孤子间的相互作用对其进行定性的预测.

光子晶体光纤的纤芯等效半径分析

应用有限差分光束传播法和平面波展开法分别计算得到光子晶体光纤的基模有效折射率和包层有效折射率 ,结合阶跃折射率光纤的模色散方程解出该结构的等效芯半径 通过对不同结构下光子晶体光纤的研究 ,找到其等效芯半径随结构参数的变化规律 ,并根据计算结果将此规律以近似公式的形式给出

侧边抛磨光纤波导传输特性的理论分析

在建立侧边抛磨光纤D型光纤边界条件的基础上,用三维有限差分光束传输法计算和分析了侧边抛磨光纤器件的光功率衰减随光纤的侧边抛磨长度、光纤侧边抛磨后剩余包层的厚度、以及填充聚合物材料折射率三个参量变化的特性·结果表明,侧边抛磨光纤器件的光功率衰减随着抛磨长度的增加而增大;当抛磨长度等于9mm时,光功率衰减随着剩余包层厚度的增大而单调递减.而当抛磨长度大于9mm时,剩余包层厚度小于3μm的范围内,光衰减随着剩余包层厚度的增加出现振荡;当聚合物折射率与纤芯折射率相同时,光功率衰减最大·

侧边抛磨区材料折射率对光纤光栅波长的影响

针对轮式光纤侧边抛磨法,研究了在侧边抛磨光纤光栅抛磨区覆盖不同折射率的材料时,侧边抛磨光纤光栅Bragg波长随外界折射率的改变而变化的特性.理论计算与实验结果都表明,侧边抛磨光纤光栅Bragg波长会随抛磨区覆盖材料折射率的增大向长波长方向偏移;侧边抛磨面离光栅区纤芯表面越近,覆盖材料折射率对波长偏移的影响越大.实验指出,当侧边抛磨区覆盖材料的折射率从1.3897变到1.4479时,Bragg波长将会发生1.402nm的偏移.用轮式光纤侧边抛磨法制备的侧边抛磨光纤光栅可应用于光纤光栅的波长调谐或传感器.

光纤多模干涉应变传感器的数值模拟及实验研究

介绍了一种基于多模干涉理论的光纤应变传感器,它由两段单模光纤中间夹一段多模光纤组成。我们利用光束传播法(BPM)对这种结构进行了数值模拟,获得了多模光纤中被激励的所有高阶模式的耦合效率的解析解,通过计算得到其应变灵敏度是FBG型应变传感器的2.14倍。随后,对这种新型传感器进行了应变传感实验,实验结果为1.92倍,计算值与实验值基本一致,证明了此种数值模拟方法适于研究此类光纤多模干涉问题,并体现出这种单模-多模-单模结构的传感器在灵敏度方面的优势。