Highly efficient noniterative full-vectorial beam propagation method based on the alternating-direction implicit scheme

A novel alternating-direction implicit method is developed for the full-vectorial wave equation. The cross-coupling terms are split off from the full-vectorial propagation operator, and their inversions are performed separately by a noniterative method at each step. The present method shows good performance in efficiency by comparison with the iterative method. It can be proved that the algorithm is of second-order accuracy along the propagating direction. To examine the accuracy of the present algorithm, it is compared with previously presented formulas, and the results show that it maintains high accuracy.     

A Modified full-vectorial finite-difference beam propagation method based on H-fields for optical waveguides with step-index profiles

A modified full-vectorial finite-difference beam propagation method based on H-fields in solving the guided-modes for optical waveguides with step-index profiles is described. The propagation is split into two substeps. In the first substep, the field propagates in the absence of the cross-coupling terms, and then they are evaluated and double used in the second substep. An improved six-point finite-difference scheme is constructed to approximate the cross-coupling terms along the transverse directions. By using the imaginary-distance procedure, the field patterns and the normalized propagation constants of the fundamental modes for a buried rectangular waveguide and rib waveguide are presented, and the hybrid nature of the full-vectorial guided-modes is demonstrated. Solutions are in good agreement with the benchmark results from film mode matching method, which tests the validity and utility of the present method.     

A novel color fringe projection based Fourier transform 3D shape measurement method

A novel Fourier transform 3D shape measurement method based on color fringe projection is proposed in order to solve the spectrum overlapping and phase unwrapping problems existed in Fourier transform profilometry (FTP). The R and G components of the color fringe are set to two sinusoidal patterns with different frequencies and the B component is set to the average value of R or G component. Then this pattern is projected to the object and the deformed fringe image is captured. Three gray patterns are separated from the color fringe, the background and high frequency noise can be eliminated using our method and the accurate unwrapped phase can be got. Only one shot color pattern is projected to get the 3D information of the object. Experiment results show that the 3D information of an object can be obtained rapidly and accurately.     

Simulation of longitudinally magnetized three-dimensional magneto-optical devices by a full-vectorial beam propagation method

A full three-dimensional vector finite-difference beam propagation method is developed and tested. In this scheme, a delicate way to discretize the coupled equations is incorporated. The resulting matrix for the difference equation then has a tri-diagonal structure, which makes the program robust and, computationally, efficient. The transparent boundary condition is also improved so that any exponential growth at a boundary is suppressed. The method is applied to the simulation of magneto-optical devices and the design of a waveguide-based optical switch, with −25 dB isolation, is presented.     

Complex modes and instability of full-vectorial beam propagation methods

Full-vectorial beam propagation methods (FVBPMs) are widely used to model light waves propagating in high-index-contrast optical waveguides. We show that the paraxial FVBPM and wide-angle FVBPMs based on diagonal Padé approximants are analytically unstable for waveguides with complex modes. The instability cannot be removed by enlarging the computational domain, increasing the numerical resolution, or using perfectly matched layers, because the complex modes are highly confined around the waveguide core.     

Beam propagation analysis using higher-order full-vectorial finite-difference method

We develop a beam propagation method based on full-vectorial higher-order finite-difference formulation to model optical waveguides. Simulation of a photonic crystal fiber coupler is used as assessment of different schemes and convergence behaviors. Results including error convergence and field calculation show that they are improved by using higher-order scheme.     

Wide-angle split-step spectral method for 2D or 3D beam propagation

We develop a method for non-paraxial beam propagation that obtains a speed improvement over the Finite-Difference Split-Step method (FDSSNP) recently reported by Sharma et al. The method works in the eigen-basis of the Laplace operator ${\left(\nabla_T^2\right)}$ , and in general requires half as many operations to propagate one step forward so that a 2X speedup can be realized. However, the new formulation allows the Fast Fourier Transform (FFT) algorithm to be used, which allows an even greater speedup. The method does not require a numerical matrix inversion, diagonalization, or series evaluation. The diffraction operator is not approximated, and in the absence of refractive index fluctuations the method reduces to an exact solution of the Helmholtz equation.     

一种新的基于最小平方逼近的广角光束传播方法

用最小平方逼近展开传播算子，实现了一种新的半矢量显式高阶有限差分光束传播方法-这种方法中不需要选择参考折射率，并在整个传播常数（包括辐射模的传播常数）分布区域进行逼近，解决了在泰勒展开和庞德逼近中存在的参考折射率选择和远离展开点误差增大等问题-用这种方法对几种典型波导结构进行了数值模拟，模拟结果验证了算法的正确性和可靠性- 关键词： 光束传播方法 有限差分 集成光学 数值方法     

Finite difference split step method for non-paraxial semivectorial beam propagation in 3D

A non-paraxial semivectorial method in the finite difference split step scheme is proposed. The method can model wide-angle beam propagation in waveguides with high index contrast and gives good accuracy even for moderate discretization. A new method for splitting of operators is used to maintain the continuity of terms. This splitting also makes the propagation more efficient. The method is relatively insensitive to the choice of the reference refractive index.     

一种新颖的用于光腔模式及光束传输模拟的特征向量法

根据有限元法单元划分的思想，提出了一种新颖的模拟光腔模式及光束传输的特征向量法. 该方法的关键之处在于基于衍射积分理论构造了一种新的光束传输矩阵，通过求解特征矩阵方程可一次性得到谐振腔的一系列特征向量，每一列特征向量即代表了腔镜上光场的一个确定模式的振幅及相位分布. 并可采用该方法模拟光场传输到腔内或腔外任意地方的场分布. 该方法将传统方法中大量的迭代过程转化成为本征积分方程特征向量的求解过程，并与初值取值无关，且可一次性求得多个模式分布，从而可方便地分析谐振腔的模式鉴别能力. 特征向量法对圆形镜共焦 关键词： 谐振腔 特征向量法 模式分布     

A novel fast 3D measurement method based on phase-coded fringe projection

Optical Review - Fringe projection profilometry is widely used for the 3D measurement of real-world objects; however, quickly obtaining high-precision 3D measurements is an issue that needs to be...     

The threaded BPM: A novel extension to the two-dimensional scalar beam propagation method

The two-dimensional scalar beam propagation method (BPM) is a widely used, computationally efficient tool for the analysis of planar optical waveguides and devices. The inherent paraxial limitations and rectilinear analysis grid limit its application to slightly curved structures and waveguides. In this novel extention to the BPM algorithm, the curvature restrictions are removed and in many cases the paraxial restrictions can be avoided, allowing for the first time, the efficient analysis of arbitrarily curved structures, such as S- or U-shaped bends, curved transitions of progressively varying curvature, and curved couplers. It can also handle concatenated devices and the curved interconnect sections between them. The process operates by the concatenation of micro-conformal maps, which progressively re-orientate the problem optimally towards a straight BPM analysis.     

On a novel mode-solver and beam propagation method based on Galerkin approach and Arnoldi iteration technique

In this work, a modified Galerkin method is used to study the modal and propagation behaviour of generic integrated optical structures. The paraxial propagation equation is solved through non-linear mapping of the transverse plane and subsequent Galerkin approach. The differential equation is thus transformed into a specific finite-dimension linear problem. The field evolution is then calculated step-wise by approximating the exponential propagator through an Arnoldi iterative procedure. A similar approach is applied to the corresponding eigenproblem.     

On a novel mode-solver and beam propagation method based on Galerkin approach and Arnoldi iteration technique

In this work, a modified Galerkin method is used to study the modal and propagation behaviour of generic integrated optical structures. The paraxial propagation equation is solved through non-linear mapping of the transverse plane and subsequent Galerkin approach. The differential equation is thus transformed into a specific finite-dimension linear problem. The field evolution is then calculated step-wise by approximating the exponential propagator through an Arnoldi iterative procedure. A similar approach is applied to the corresponding eigenproblem.     

基于空间二进制编码的3 D形貌测量方法

介绍了一种基于空间二进制编码的非接触３ Ｄ 形貌测量方法。它用一台ＬＣＤ 投影仪对被测物体表面进行空间编码,再用一台ＣＣＤ 摄像机获取物体编码信息,最后用三角法原理从摄像机图像中获取三维形貌数据。提出了基于三角法的空间二进制码的重要特性,描述了高效编码的构造方法。用这个构造方法构造出一个完全数字化的７ 位字长的二进制编码。基于这种编码的３ Ｄ 形貌测量方法在被测物体表面非常不连续和非构造的环境下取得了良好的测量结果。     

基于轴棱锥产生近似无衍射Mathieu光束的新方法

提出了一种基于轴棱锥产生零阶近似无衍射Mathieu光束的新方法,利用轴棱锥聚焦具有椭圆高斯振幅调制的平面波,得到近似零阶无衍射Mathieu光束.根据椭圆高斯平面波经轴棱锥衍射的衍射积分公式,对光强分布进行了数值模拟,依据几何光学模型计算了近似无衍射Mathieu光束的最大无衍射距离,并设计了实验对理论模拟的结果进行了验证.实验采用柱透镜和准直扩束系统变换圆高斯光束产生具有椭圆高斯振幅调制的平面波,用轴棱锥聚焦该平面波后得到近似无衍射Mathieu光束,实验结果与理论模拟和计算相符.     

用于微位移测量的笔束激光干涉仪

介绍了一种基于空间干涉原理的亚微米零差干涉位移测量方法。该方法是对笔束激光干涉仪在微位移测量领域的应用 ,干涉仪的测量精度不受光束波前畸变等光源噪声的影响。给出了干涉仪主要结构参数的选取原则 ;构建了用于微位移测量的笔束激光干涉仪实验系统。实验结果表明 ,该系统具有纳米测量分辨率。     

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.     

Studies of beam propagation characteristics on apertured fractional Fourier transforming systems

Based on the principle that a rectangular function can be expanded into a sum of complex Gaussian functions with finite numbers, propagation characteristics of a Gaussian beam or a plane wave passing through apertured fractional Fourier transforming systems are analyzed and corresponding analytical formulae are obtained. Analytical formulae in different fractional orders are numerically simulated and compared with the diffraction integral formulae, the applicable range and exactness of analytical formulae are confirmed.It is shown that the calculating speed of using the obtained approximate analytical formulae, is several hundred times faster than that of using diffraction integral directly. Meanwhile, by using analytical formulae the effect of different aperture sizes on Gaussian beam propagation characteristics is numerically simulated, it is shown that the diffraction effect can be neglected when the aperture size is 5 times larger than the beam waist size.     

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.