Composite coherence vortices in coherent and incoherent superpositions of two off-axis partially coherent vortex beams

The composite coherence vortices by coherently and incoherently superimposing two parallel, off-axis partially coherent vortex beams and their evolution in free space are studied. It is shown that the superposition scheme, off-axis distance, coherence parameter and propagation distance affect the position and number of composite coherence vortices. The motion, creation and annihilation of composite coherence vortices appear by varying the off-axis distance, coherence parameter and propagation distance. The coherent and incoherent superpositions result in the different position and number of composite coherence vortices and their different evolution behavior in the coherent limit.     

Correlated imaging with partially coherent light for remote sensing

Based on the extended Huygens–Fresnel integral and the theory of coherence of light field, we have investigated the correlated imaging by using the transverse normalized second-order intensity fluctuation correlation function with partially coherent light radiation. The imaging for a reflected object with relative long distance is determined by the feature of speckle-to-speckle correlation. By using the correlation function, we study the effects of imaging distance, the sizes of object lens and reference lens, the source’s transverse coherent width and its transverse size on the quality of correlated imaging. Numerical results show that the parameters of imaging system and the properties of partially coherent light source have significant influences on the imaging resolution and visibility. For an object lens with large enough diameter, the resolution is determined by the transverse coherent width of light source. On the contrary, it depends on the aperture of object lens. The magnification of the system depends only on the propagation distance. This speckle-to-speckle correlated imaging with unbalanced arms have potential applications in remote sensing due to its unique features.     

Topology optimization with geometric uncertainties by perturbation techniques

The aim of this paper was to present a topology optimization methodology for obtaining robust designs insensitive to small uncertainties in the geometry. The variations are modeled using a stochastic field. The model can represent spatially varying geometry imperfections in devices produced by etching techniques. Because of under‐etching or over‐etching parts of the structure may become thinner or thicker than a reference design supplied to the manufacturer. The uncertainties are assumed to be small and their influence on the system response is evaluated using perturbation techniques. Under the above assumptions, the proposed algorithm provides a computationally cheap alternative to previously introduced stochastic optimization methods based on Monte Carlo sampling. The method is demonstrated on the design of a minimum compliance cantilever beam and a compliant mechanism. Copyright © 2012 John Wiley & Sons, Ltd.     

Topology optimization of continuum structures with stress constraints and uncertainties in loading

Topology optimization using stress constraints and considering uncertainties is a serious challenge, since a reliability problem has to be solved for each stress constraint, for each element in the mesh. In this paper, an alternative way of solving this problem is used, where uncertainty quantification is performed through the first‐order perturbation approach, with proper validation by Monte Carlo simulation. Uncertainties are considered in the loading magnitude and direction. The minimum volume problem subjected to local stress constraints is formulated as a robust problem, where the stress constraints are written as a weighted average between their expected value and standard deviation. The augmented Lagrangian method is used for handling the large set of local stress constraints, whereas a gradient‐based algorithm is used for handling the bounding constraints. It is shown that even in the presence of small uncertainties in loading direction, different topologies are obtained when compared to a deterministic approach. The effect of correlation between uncertainties in loading magnitude and direction on optimal topologies is also studied, where the main observed result is loss of symmetry in optimal topologies.     

Channel correlation of transmit diversity FSO systems with partially coherent optical beams

Spatial diversity, including transmit diversity, has been proven to be a promising technique to mitigate turbulence-induced signal fading. However, due to the limitation of size in compact FSO (free-space optical) terminals, the transmit antennas cannot always be separated far enough from each other, resulting in increased channel correlation and deteriorated diversity performance. In this paper, we focus on the channel correlation statistics of transmit diversity FSO systems with two transmit beams. Specifically, we consider partially coherent optical beams, which reduce scintillation over fully coherent optical beams. We perform theoretical analysis and obtain some interesting numerical results, such as the degree of channel correlation which changed mainly with source correlation radius from 0.001 to 0.1 m. These results can be helpful for designing transmit diversity FSO systems with partially coherent beams.     

Focal shift and focal switch of partially coherent flat-topped beams passing through an alignment and misalignment lens system with aperture

The focal shift and focal switch of partially coherent flat-topped (PCFT) beams passing through a lens system with an aperture are studied in detail. We have shown that a focal shift is also present for beams propagating through an aligned optical system and the amount of the focal shift depends not only on the radius aperture of the focusing system, but also on the spatial coherence and order of the flat-topped beam of the incident partially coherent light. A new phenomenon called ‘focal switch’ occurs for misaligned optical systems, i.e. the focal shift experiences a sudden transition as the aligned optical system becomes misaligned, and the influence of the spatial coherence, order of flat-topped beam and aperture size reduction, on the focal switch is investigated in detail. Finally, the necessary conditions for the focal switch to take place are investigated.     

Theoretical study on the spectral shifts of partially coherent array beams passing through ABCD optical systems

According to the extended Huygens–Fresnel integral, the expressions for the on-axis spectrum of partially coherent Gaussian Schell-model (GSM) rectangular array beams passing through ABCD optical systems have been derived. The generalized Fresnel number of the system, the spatial coherent parameter of array beamlets and the array beam parameters including the number of beamlets and the separation distance between beamlets have been taken as the characteristic parameters to compare the spectral shifts of GSM array beams for the two types of the superposition, i.e. the correlated superposition and the uncorrelated superposition. In particular, the effect of characteristic parameters on the on-axis relative spectral shifts has been discussed in detail. The results show that the spectral intensity of GSM array beams for the two types of the superposition passing through ABCD systems depends on the source spectral density S ⁰(ω), the spatial coherent parameter of array beamlets β, the generalized Fresnel number of the system F and the array beam parameters. Furthermore, for the uncorrelated superposition, the spectrum of GSM array beams only exhibit the blue-shift, whereas for the correlated superposition, GSM array beams exhibit the spectral switch and the number of spectral switches increases with the increase of array beam parameters in the near field due to the interference between beamlets. In particular, the effect of the array beam parameters on the on-axis relative spectral shift is more obvious.     

Topology optimization of continuum structures subjected to uncertainties in material properties

This work addresses the use of the topology optimization approach to the design of robust continuum structures under the hypothesis of uncertainties with known second‐order statistics. To this end, the second‐order perturbation approach is used to model the response of the structure, and the midpoint discretization technique is used to discretize the random field. The objective function is a weighted sum of the expected compliance and its standard deviation. The optimization problem is solved using a traditional optimality criteria method. It is shown that the correlation length plays an important role in the obtained topology and statistical moments when only the minimization of the standard deviation is considered, resulting in more and thinner reinforcements as the correlation length decreases. It is also shown that the minimization of the expected value is close to the minimization of the deterministic compliance for small variations of Young's modulus. Copyright © 2016 John Wiley & Sons, Ltd.     

Propagation of a partially coherent higher-order cosh-Gaussian beam through a paraxial ABCD optical system

Based on the generalized Huygens–Fresnel integral, analytical expressions for the mutual coherence function, the spatial complex degree of coherence, and the effective size of a partially coherent higher-order cosh-Gaussian beam through a paraxial ABCD optical system have been derived. As a numerical example, the propagation of a partially coherent higher-order cosh-Gaussian beam through an optical Fourier-transforming system with a limiting aperture is illustrated. The normalized intensity distribution, the spatial complex degree of coherence, and the effective beam size for the partially coherent higher-order cosh-Gaussian beam are numerically demonstrated in the observation plane. The influences of the spatial coherence length and the limiting aperture on the normalized intensity distribution, the spatial complex degree of coherence, and the effective beam size are also examined in detail.     

Robust topology optimization of optical cloaks under uncertainties in wave number and angle of incident wave

This article presents a robust topology optimization method for optical cloaks under uncertainties in the wave number and angle in the incident wave. We first discuss the governing equation derived from Maxwell's equation, and extend it to the entire domain including the dielectric material and air, based on the level set-based topology optimization method. Next, a robust optimization problem is formulated as a minimization problem of the weighted sum of the scattered wave norm and its standard deviation with respect to the wave number and angle of the incident wave. The standard deviation is mathematically expressed by the Taylor series approximation and the use of the adjoint variable method. The design sensitivity of the objective functional is also derived by the adjoint variable method. An optimization algorithm is then constructed, based on the proposed formulation for robust designs of optical cloaks. Several numerical examples are finally provided to demonstrate the validity and utility of the proposed method.     

新型相干结构光场调控及应用研究进展

结构光场的空域调控包括振幅、相位、偏振、相干度等丰富自由度,对其自由度的单一或联合调控引发了一系列新奇物理效应,在新型结构光场构建及多种领域中具有重要应用。相比于完全相干光场,部分相干光场在抵抗散斑噪声和大气湍流扰动等方面具有独特优势。近年来,具有新型相干结构的部分相干光束在大气传输、光学加密与成像、信息鲁棒传输、高质量光束整形等领域有着重要研究价值。本文详细综述了具有新型相干结构部分相干光场的理论构建与实验合成的研究进展,并重点介绍了新型相干结构光场在复杂环境中的鲁棒传输特性及其在光学加密、成像、鲁棒信息传输及光束整形中的应用研究进展。研究表明,新型相干结构光场调控不仅提供了一种有效抵抗复杂环境扰动的有效手段,而且丰富了光场调控技术在多种领域中的应用。最后,对新型相干结构调控技术发展趋势及潜在应用前景进行了展望。

     

Partially coherent dark hollow beams propagating through real ABCD optical systems in a turbulent atmosphere

A closed-form analytical expression is derived for a partially coherent dark hollow beam (DHB) propagating through an arbitrary real ABCD optical system in a turbulent atmosphere. The average intensity of the beam in the output plane is investigated in the presence of, respectively, a thin lens image system and a two-lens system along the optical path. For a special thin lens image system, the partially coherent DHB and the fully coherent DHB have the same evolution properties, and the comparative analysis is made between the propagation of the focused DHB and the collimated DHB for direct propagation in turbulence to show the effect of the thin lens on the average intensity. As for the two-lens system, the effects of the lens systems, the structure constant in the turbulent medium and the parameters of the incident beam on the average intensity are evaluated and illustrated. The result shows that different lens systems and propagation parameters can evidently affect the evolution properties of the beam.     

Optical trapping Rayleigh dielectric particles with focused partially coherent dark hollow beams

The focusing properties of coherent and partially coherent dark hollow beams (DHBs) through a paraxial ABCD optical system are theoretically investigated. It is found that the evolution behavior of the intensity distribution of focused partially coherent DHBs is closely related to their spatial coherence. The radiation forces (RFs) of focused coherent and partially coherent DHBs acting on a Rayleigh dielectric particle are also theoretically investigated. Numerical results show that the coherent and partially coherent DHBs can be focused into a tight focal spot, which can be used to stably trap a Rayleigh dielectric particle with high refractive index at the focus point. The influences of different beam parameters, including the spatial coherence, beam waist width, beam order, and hollow parameter of partially coherent DHBs, on the RFs and the trap stiffness are analyzed in detail. Finally, the stability conditions for effective trapping particles are also discussed.     

Topology optimization of continuum structures with local stress constraints

We introduce an extension of current technologies for topology optimization of continuum structures which allows for treating local stress criteria. We first consider relevant stress criteria for porous composite materials, initially by studying the stress states of the so-called rank 2 layered materials. Then, on the basis of the theoretical study of the rank 2 microstructures, we propose an empirical model that extends the power penalized stiffness model (also called SIMP for Solid Isotropic Microstructure with Penalization for inter-mediate densities). In a second part, solution aspects of topology problems are considered. To deal with the so-called ‘singularity’ phenomenon of stress constraints in topology design, an ϵ-constraint relaxation of the stress constraints is used. We describe the mathematical programming approach that is used to solve the numerical optimization problems, and show results for a number of example applications. © 1998 John Wiley & Sons, Ltd.     

Topology optimization of continuum structures with bi-modulus materials

Since the elasticity of bi-modulus materials is stress dependent, it is difficult to apply most conventional topology optimization methods to such bi-modulus structures owing to great computational expense. Therefore, this study employs the material-replacement method to improve the computational efficiency for topology optimization of bi-modulus structures. In this method, first, the bi-modulus material is replaced by two isotropic materials which have the same tensile or compressive modulus. Secondly, the isotropic materials for finite elements are determined by the local stress/strain states. The local elemental stiffness can be modified according to the current modulus and stress state of the element. Thirdly, the relative densities of elements, acting as the design variables, are updated using the optimality criterion method. Finally, the distributions of elemental densities and moduli are obtained for further applications. Several typical numerical examples are used to demonstrate the effectiveness of the proposed method.     

多载荷多工位转盘拓扑优化设计

基于拓扑优化理论,以结构总质量最小为目标,利用SIMP材料插值方法,结合HyperWorks/Optistruct拓扑优化功能对自动化组装设备中常用的多工位转盘进行了拓扑优化．根据优化后的重构模型与原始结构模型的静力学对比分析知,优化后降低了多工位转盘的总质量,提高了多工位转盘的刚度,同时减小了多工位转盘的局部最大应力．数据结果表明本方法对多工位转盘优化设计是有效的．     

Topology optimization for nonlinear dynamic problems: Considerations for automotive crashworthiness

Crashworthiness of automotive structures is most often engineered after an optimal topology has been arrived at using other design considerations. This study is an attempt to incorporate crashworthiness requirements upfront in the topology synthesis process using a mathematically consistent framework. It proposes the use of equivalent linear systems from the nonlinear dynamic simulation in conjunction with a discrete-material topology optimizer. Velocity and acceleration constraints are consistently incorporated in the optimization set-up. Issues specific to crash problems due to the explicit solution methodology employed, nature of the boundary conditions imposed on the structure, etc. are discussed and possible resolutions are proposed. A demonstration of the methodology on two-dimensional problems that address some of the structural requirements and the types of loading typical of frontal and side impact is provided in order to show that this methodology has the potential for topology synthesis incorporating crashworthiness requirements.     

Topology optimization for free vibrations using combined approximations

This study shows how the Combined Approximations (CA) can be used for reducing the computational effort in Topology Optimization for free vibrations. The previously developed approach is based on the integration of several concepts and methods, including matrix factorization, series expansion, and reduced basis. In this paper the CA method is used for repeated eigenvalue analysis. Adjoint sensitivity analysis is developed such that the inaccuracies of the approximation are taken into consideration. Several 2‐D and 3‐D numerical examples show how optimal topology designs can be achieved by the reduced computational effort compared with the exact eigenvalue analysis. Copyright © 2009 John Wiley & Sons, Ltd.     

负泊松比微结构拓扑优化设计

在构建负泊松比结构拓扑优化模型时,直接用负泊松比的数学表达式构造目标函数,将使得目标函数高度非线性,迭代过程敏度分析困难。采用线性拟合法,构建了具有线性特征的负泊松比微结构拓扑优化目标函数,基于能量法和均匀化方法,结合拓扑优化理论,构建了一种可以快速准确求解负泊松比的拓扑优化设计模型,求解该模型得到了一种优化的拓扑构型及相应的负泊松比值。根据优化求解得到的结构模型,参考国家标准GB/T 22315-2008《金属材料弹性模量和泊松比试验方法》,利用有限元软件对其泊松比进行仿真计算,然后采用激光加工方式制造试样,并测试其泊松比,经过与优化模型求解得到的泊松比值对比分析,验证了所构建优化模型的正确性。本文方法既避免了以负泊松比表达式为优化函数时会出现的高度非线性问题,也降低了求解的复杂程度,为负泊松比微结构的设计提供了一种参考方法。