透明边界条件算法的比较研究及改进

研究了束传播算法(BPM)中简单透明边界条件(STBC)和完全透明边界条件(CTBC)两种边界处理算法对计算结果精度的影响.通过改进和综合两种边界条件算法,提出改进型透明边界算法(ITBC).该边界算法相对于STBC与CTBC降低了计算精度对于传播步长的依赖性,提高了计算精度,改善了透明边界条件算法在BPM中的稳定性.     

Temperature-dependent photoacoustic spectroscopy with a Helmholtz resonator

We describe and example the Beam Propagation Method (BPM) used to model and simulate nonlinear refractive and absorptive effects in materials with applications to optical limiting and switching. Various scenarios including laser-beam trapping and laser-beam division are investigated, in order to demonstrate the power of the BPM. A novel technique is also described for efficiently modelling the external far-field propagation from nonlinear media, including the propagation of non-Gaussian-shaped spatial profiles. The methods are finally combined with the phenomenon of nonlinear absorption to demonstrate enhanced power limiting in the presence of self-refraction. Optimal parameters for high-fluence power-limiting are subsequently discussed.     

Calculation of the spectral response of an arrayed-waveguide gating demultiplexer with a wide-angle beam propagation method in a cylindrical coordinate system

The spectral response of an arrayed-waveguide grating (AWG) demultiplexer is calculated by simulating the field propagation in the output section of an AWG with a wide-angle beam propagation method (BPM) in a cylindrical coordinate system. As in a practical design of an AWG demultiplexer, each output waveguide consists of two straight sections connected by a bending section. The spectral response obtained by the present algorithm is more accurate than those obtained with two popular approximate methods, namely, the conventional overlapped integral method and the standard BPM for radially straight and infinitely long output waveguides. With the present algorithm, the dependence of the spectral response on the parameters of the output section is analyzed. The channel crosstalk and the 3 dB passband width of the spectral response depend mainly on the length of the first straight section, the end separation and the angular separation of the output waveguides. The bending section results in an asymmetrical spectral response with remarkable sidelobes which can be reduced by increasing the bending radius.     

Three-dimensional hybrid modeling based on a beam propagation method and a diffraction formula for an AWG demultiplexer

An efficient and accurate three-dimensional (3D) hybrid modeling, which combines a 3D beam propagation method (BPM) and the two-dimensional (2D) Kirchhoff–Huygens diffraction formula, is developed to simulate the field propagation in an arrayed waveguide grating (AWG) demultiplexer. The 2D Kirchhoff–Huygens diffraction formula is used for the simulation of the light propagation in the free propagation regions (FPRs). A 3D BPM in a polar coordinate system is used to simulate the light propagation in the transition region between the input FPR and the arrayed waveguides so that the coupling coefficients for the arrayed waveguides are calculated conveniently and accurately. For the simulation in the transition region between the arrayed waveguides and the output FPR, only the central arrayed waveguide and several adjacent ones are needed in the computational window of a standard BPM and thus the computation efficiency is improved. Finally, a flat-top AWG is designed and fabricated to verify the reliability of the present simulation method. The calculated and measured spectral responses are in a good agreement.     

Analysis of curved bends in arbitrary optical devices using cylindrical coordinates

An extension of the beam propagation algorithm based on the method of lines (MoL–BPM) is proposed and substantiated for analysis of curved bends–constituent parts of complicated optical devices, connecting waveguides with different orientation. Cylindrical coordinates are introduced. The formulas are compatible with those in Cartesian coordinates for analysis of straight waveguides. So, in combination concatenations of curved bends and straight waveguides can be examined in a uniform way. For the purpose of analysis in cylindrical coordinates a suitable set of wave equations without any approximation and valid for a general hybrid case is derived. To prove the accuracy of the MoL–BPM in cylindrical coordinates applying the derived formulas, the curvature loss of a rib waveguide was computed and compared with other methods showing very good agreement. As an application of the method two straight waveguides are connected by a curved bend and the power flow is determined.     

Beam propagation method using a [(p- 1)/ p] Padé approximant of the propagator

A new beam propagation method (BPM) is developed based on a direct approximation to the propagator by its [(p-1)/p] Padé approximant. The approximant is simple to construct and has the desired damping effect for the evanescent modes. The method is applied to a tapered waveguide for TM-polarized waves, based on the energy-conserving improvement of the one-way Helmholtz equation. Numerical results are compared with those obtained with other variants of the BPM.     

A stable complex Jacobi iterative solution of 3D semivectorial wide-angle beam propagation using the iterated Crank–Nicholson method

An extension of the recently proposed three-dimensional (3D) wide-angle (WA) beam propagation method (BPM) using complex Jacobi iteration (CJI) taken into account polarization effects is presented. The resulting iterative BPM is faster than BPMs based on the traditional direct matrix inversion for waveguides with unchanging refractive index profiles during propagation direction. However, for varying refractive index waveguides the iterative method suffered from the fact that the iteration count between two successive cross-sections increases dramatically during the propagation direction. To overcome this problem, we propose the utility of the iterated Crank–Nicholson method. At each propagation step, the propagation equation is divided in multiple stages by the iterated Crank–Nicholson method and then each stage is recast in terms of a Helmholtz equation with source term, which is solved effectively by the complex Jacobi iterative method. The resulting approach is stable and well-suited for large structures with long propagation paths.     

采用三维波束传输法的多模干涉耦合器成像位置的数值计算

多模干涉(MMI)耦合器需要精确定位成像位置,以便器件的设计制作。针对强限制和弱限制的三维多模波导干涉耦合器,采用三维交替方向隐式有限差分光束传输法(BPM),数值计算得出多模波导长度、输入波导和输出波导位置。首先通过对对称干涉多模干涉耦合器的数值分析求得多模干涉耦合器的等效宽度Weq及最低二阶模之间的拍长Lc,然后将这些参量结合光束传输法直接用于器件设计。计算显示该方法得到的成像位置和导模传输分析法(MPA)的理论预测比较接近,但Weq和Lc却是由光束传输法计算得到的,导模传输分析法理论只能在得到Weq和Lc的前提下才能得到成像位置。该方法直接针对三维波导进行,没有采用基于等效折射率方法的从三维波导到二维波导的简化处理,并且也没有采用导模传输分析法所采用的近似,保证了计算精度,对于实际多模干涉器件的设计制作可起参考作用。     

自聚焦材料弧形全光开关的研究

应用光束传播法,比较基于自聚焦和自散焦材料的全光波导开关的开关特性,指出基于自聚焦材料的全光开关具有较低开关功率、数值化多次开关特性等优越性,并对波导参数进行了全面的优化设计。     

Numerical analysis of a swift, high resolution Generic Lightwave Integrated Chip wavelength monitor

A novel device capable of rapid and accurate wavelength determination in the C-Band of the telecommunications grid is presented. The device was developed with Planar Lightwave Circuit (PLC) technology, making it an ideal candidate for incorporation into next generation reconfigurable networks at add/drop sites that require stringent routing control. The described wavelength-meter can resolve any wavelength to a 2–5 pm precision within a sub-microsecond timeframe. The basic theory is outlined before the numerical aspects of the design and modelling are addressed. By establishing quadrature between two phase-shifted signals provided by two similar Fabry–Perot cavities, the interferometric throughput is referenced to a linear dielectric filter to resolve the wavelength in question. The elaborate mechanisms associated with multiple reflections in concatenated Fabry–Perot etalons warrant a meticulous verification by means of bidirectional beam propagation methods (BPM), discussed infra. Experimental characterisation verifies the theory. This signifies that concept of quadrature can also be applied in disciplines such as optical sensing and biophotonics. Thus, the device can be considered as a Generic Lightwave Integrated Chip (GLIC).     

Mach-Zehnder波导中TM波的FD-BPM分析

M-Z结构波导是许多集成光学器件中的重要组成单元。本文结合辐射透明边界条件(TBC)，由Maxwell方程导出了TM模有限差分光束传播法(FD-BPM)基本方程．用FD—BPM法系统地模拟了M-Z波导结构中TM模的传播情况，并着重对其结构进行了优化设计．取得了二维情况下的最佳尺寸。研究结果表明，该法在模拟分析集成光学中具有的有效性、方便性和优越性，为实际的设计制作提供了很好的模拟依据。     

Improving the beam propagation method for TM polarization

The beam propagation method (BPM) has been widely used in numerical simulations of optical waveguides that vary slowly in the propagation direction. However, when BPM is used over a large propagation distance, a significant amplitude error in the coefficient of the leading propagating mode can be observed. Energy-conserving corrections and the single scatter approximation have been used to improve the accuracy of the BPM.     

BPM Simulation and Comparison of 1 × 2 Directional Waveguide Coupling and Y-Junction Coupling Silicon-on-Insulator Optical Couplers

For developing large area opto-electronic silicon-on-insulator (SOI) devices, the optical coupler is a basic key device. In this article, the authors design and simulate 1 2 2 directional waveguide coupling and Y-branch coupling optical couplers based on Unibond SOI rib waveguides. The beam propagation method (BPM) is used for light propagation analysis. The simulation results and comparisons of the two kinds of optical couplers are reported. The S-bend waveguide for attaching to the two kinds of SOI optical coupler is also analyzed by BPM. We find that the directional coupler has lower power loss, but the Y-junction coupler is more wavelength insensitive with the same device size and splitting angle. The fabrication tolerance analysis shows Y-junction coupler has better fabrication characteristics.     

The beam propagation method: an analysis of its applicability

Simple quantitative conditions for the applicability of the beam propagation method (BPM) in isotropic and anisotropic media are given. These conditions are derived using the operator formalism employed in the BPM in its conventional formulation. The basic limitations of the BPM are highlighted at the same time.     

Efficient beam-propagation method based on Padé approximants in the propagation direction

We propose a novel beam-propagation method (BPM) based on the higher-order Padé approximants in both the transverse and the longitudinal directions. Extending the Padé approximation to the propagation direction and adopting the multistep method increase the programming effort by only a small amount. Compared with the conventional BPM's, this method is more accurate and efficient. The accuracy and the propagation step size are well predicted by a phase analysis.     

Mach-Zehnder结构波导调制器的模拟分析

 将三维级数展开法与光束传播法相结合，把标量光束传播法方程转化为一阶常微分方程组;在模拟中引入正切函数变换将无限平面映射为有限平面，避免了边界截断问题,与传统的BPM法相比，该方法具有计算方法简单和计算效率高的优点。运用该法分析了Mach-Zehnder结构的铌酸锂电光波导调制器，模拟了光场在器件中的分布情况，获得了这种调制器模场损耗曲线和最佳结构参数。     

平面光波导型单纤三向器的研究

利用光束传输法,分析设计了一种只由两个定向耦合器构成、能直接与单模光纤相耦合、易于集成的平面光波导（Planar Lightwave Circuit,PLC）型1.31/1.49/1.55 μm单纤三向器.该器件的输入输出弯曲波导和耦合区平行波导均采用光束传输法进行优化设计,并对器件的折射率进行了容差分析,获得了当两个定向耦合器的耦合长度分别为6 578 μm、3953 μm时,器件对各波长的隔离度均在47 dB以上,且插入损耗小于0.05 dB.     

An efficient algorithm for strongly focused optical beams propagating in Kerr media

Due to the lens-induced quadratic phase factor from converging lens, the beam-propagation method (BPM) is computationally expensive in simulations by the sampling theorem for lens-induced strongly focused beams propagating in nonlinear media. In the paper, we present a modified approach (MA) based on the separate envelope and lens-induced phase to only compute the envelope in the whole focal region. Then we demonstrate the correctness of MA analytically by the propagation of focused Gaussian beam and numerically by that of focused Super-Gaussian beam in linear media. Numerical simulations of strongly focused beams based on MA are in good agreement with those of BPM when propagating in Kerr media. The sampling requirement of MA which is similar with no lens-induced phase beam is lower than that of BPM which increases with the lens-induced chirp parameter and the propagation distance. Thus the computational efficiency can be greatly improved.     

Design and fabrication of the star coupler based on SOI material

A 1×25 star coupler is designed through calculation and beam propagation method (BPM) simulation. Improvement methods are focused on the design of the tapered waveguides in the device, improving the uniformity of the output light power of the star coupler. Utilizing the conventional Si process technology, the device is fabricated based on silicon-on-insulator (SOI) material. The test result shows that the star coupler has a perfect function of power splitting.