Hybrid holographic-numerical method for modal analysis of complex structures

This paper presents a hybrid holographic-numerical method for modal analysis of complex structures. A continuous structure is first lumped into a number of discrete elements to form an elastically connected lumped linear system. The matrix of influence coefficients of the lumped linear system are then determined by exerting a static load to the element centers and measuring the corresponding whole-field displacement using digital holographic interferometry. The eigenvalues and eigenvectors of the influence coefficients, which in a physical sense represent the natural frequencies and mode shapes of the structure, are then calculated using the numerical method. A major advantage of the proposed hybrid method is that it is not necessary to know the Young's modulus, the Poisson's ratio of the material and the boundary conditions, as the displacement field measured by the optical method has automatically reflected the real boundary conditions and the material properties, which makes this method particularly useful for studying objects made from anisotropic materials such as composites. Another advantage of the proposed method is that structures of any complex and irregular shape will not increase the complexity of the characterization process. The proposed is also suitable for experimentally validating the modal analysis results from finite element method models.     

全矢量有限元模型及其在光波导中的应用

为了研究光波导和光子晶体光纤的模式特性和传输特性,从矢量波动方程出发,推导出了各向异性介质中场微分方程复数泛函表达式,利用棱边/节点混合元离散了该泛函,加入了各向异性介质匹配层边界条件,得到关于传播常量的广义特征值方程.以矩形波导为例,对各向异性介质匹配层边界条件的吸收特性进行了研究,得到了基模以及几个高阶模的场分布、色散曲线和损耗曲线.结果表明该方法可靠有效.对正六边形晶格光子晶体光纤进行了分析.数据表明：光纤有效折射率随空气孔直径或波长的增大而减小,但与空气孔圈数无关;光纤限制损耗(confinement loss)随波长增大近似成指数增大,而增加空气孔直径或者空气孔圈数则可使之显著降低.     

An Efficient Dispersion Calculation Method for Axially Symmetric Optical Fibers

An efficient numerical modal calculation method for an axially symmetric optical fiber is presented using a numerical Galerkin's method. By decomposing the transverse electric field of a guided wave with Bessel functions of the first kind in cylindrical polar coordinates, we have shown that dispersion characteristics of an optical fiber can be obtained very easily. In order to illustrate the effectiveness of this suggested method, numerical examples are given for a step index fiber, a W-shape depressed inner cladding fiber, and a dispersion-flattened fiber.     

车载红外探测设备的光机结构设计

为了实现空气质量的实时监测,设计了一种车载红外探测设备的光机结构。该结构采用大孔径、无焦反射式光学系统,即高精度扫描反射镜实现了方位和俯仰0～360°扫描。通过有限元方法对系统进行静力学分析,结果满足光机结构设计要求。用锤击法对样机进行了模态测试,并对车载环境下的设备进行了振动实验。结果表明,光机结构一阶频率为52Hz,相对于车载环境的12．5Hz具有足够的动态刚度及结构稳定性,可保证该设备正常工作。     

Manipulating optical tamm state in one dimensional magnetophotonic crystal by anisotropic materials

Based on transfer matrix method a tunable optical tamm state is revealed in a one dimensional heterogeneous photonic crystal by using anisotropic materials with arbitrary optical axis. Such a tunable effect originates from the optical axis-dependent permittivity of the anisotropic materials, which leads to obvious changes in the dispersion relation and transmission spectrum. Our results provide a new pathway for engineering the tamm state and are attractive for tunable electro-optical devices.     

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.     

高功率光纤中传输光模式与其波长相关性研究

针对高功率光纤激光模式诊断和光谱诊断的需求,研究了光纤中传输模式的波长相关性,数值计算了光纤中各个模式的模场分布随波长的变化曲线及相应的光束质量,采用双傅里叶变换F~2法实际测量了光纤模式成分与波长的关系曲线.结果表明,光纤中各个模式的模场分布随波长变化,波长越长,模场面积越大;模式的光束质量随波长变化不大,但在截止频率附近明显变差;光纤中各个模式的功率占比与波长有关.     

渐变折射率波导传播特性微扰计算的代数递推公式

应用量子力学的超位力定理（HVT）和赫尔曼－费恩曼（Hellmann-Feynman）定理（HFT），导出了用微扰法计算渐变折射率平面波导传播常数各级近似值的代数递推公式，并给出了由传播常数近似值计算模场近似表达式的代数式。计算了几个典型实例，此法的特点是便于直接计算任意级近似的传播常数及模场分布，且可推广到二维波导的计算。     

Eigenmodes of index-modulated layers with lateral PMLs

Maxwell equations are solved in a layer comprising a finite number of homogeneous isotropic dielectric regions ended by anisotropic perfectly matched layers (PMLs). The boundary-value problem is solved and the dispersion relation inside the PML is derived. The general expression of the eigenvalues equation for an arbitrary number of regions in each layer is obtained, and both polarization modes are considered. The modal functions of a single layer ended by PMLs are found, and their orthogonality relation is derived. The present method is useful to simulate scattering problems from dielectric objects as well as propagation in planar slab waveguides. Its potential to deal with more complex problems such as the scattering from an object with arbitrary cross section in open space using the multilayer modal method is briefly discussed.     

A computational approach to the optical Freedericksz transition

The optical Freedericksz transition in a homeotropic nematic liquid crystal cell is modeled using a solver which combines direct solution of Maxwell’s equations with a relaxation algorithm for the liquid crystal director. We find that even in the equal elastic constant case the continuous optical Freedericksz transition can be driven first order. For films in which the optical retardation of the extraordinary wave is sufficiently large, a whole set of discontinuous jumps in transmission coefficient can occur. These jumps correspond to the existence of optical resonances in the liquid crystal film. Our results agree in the short wavelength limit with paraxial approximation calculations, and provide a strong test of the FDTD method for anisotropic materials such as liquid crystals.