折射率梯度表面机理的研究

本文构建了一种折射率梯度表面,并利用几何光学法对其物理机理作了研究,发现这种折射率梯度表面可以实现入射波到正常反射波,异常反射波,以及介质波的转换.当入射点介质折射率大于某一阈值时,异常反射波束方向角正弦值与入射波束方向角正弦值存在线性关系,意味着平行入射的波经介质后将平行出射到空气;而当折射率梯度常数大于某一阈值时,任何方向入射的波在透射到介质后,将发生全反射,被束缚在介质中.总而言之,通过调节结构参数,可以实现对波束方向与强度的人工调控,从而提供了一种人工可控的全介质梯度表面的工程实现思路.     

一维辐射系统吸收系数的反问题

辐射反问题是当前的研究热点之一。本文采用离散坐标法求解正问题,用共轭梯度法求解一维系统吸收系数的反问题。用正问题的计算结果加上误差作为反问题的求解条件。数值计算的结果表明,共轭梯度法可以比较好的反演辐射系统的吸收系数。在考虑散射时,反演效果比不考虑散射的反演效果好。     

基于频域辐射传输模型的光学成像研究

本文以超短脉冲激光照射参与性介质的光学成像为研究背景,分别构建了短脉冲激光在参与性介质内的频域辐射传输正问题模型和根据边界探测所得频域信号重建介质内部光学参数的逆问题模型。在瞬态辐射传输方程的基础上,利用傅里叶变换得到频域辐射传输方程,采用有限体积法求解频域传输方程,模拟超短脉冲激光在二维参与性介质内传输的过程,得到介质边界的出射频域辐射信号。选取共轭梯度法作为反演算法,采用伴随差分模型求解目标函数梯度,重建了二维非均匀参与性介质内不同位置内含物的光学参数分布。结果表明,基于频域辐射传输方程的伴随差分模型能够较为准确地反演多维参与性介质内的光学参数。     

飞秒激光脉冲在正色散固体材料中的自压缩

实验研究了正色散固体介质中的激光脉冲自压缩现象,证明了无需任何外加色散补偿情况下，固体透明介质中的自聚焦传输过程可使高功率飞秒激光脉冲实现时域脉冲压缩，并详细研究了输出脉冲的时域和频域特性随入射脉冲强度的演化规律.实验结果表明脉冲自压缩量随入射脉冲强度的增加呈递增趋势，然而当入射光强增大到足以引起超连续谱及锥形辐射产生时，脉冲时域形状会发生分裂.此外还发现发散光束入射情况下同样可以观察到脉冲自压缩现象. 关键词： 超短激光脉冲 脉冲压缩 非线性传输     

不同参数对一维光子晶体透射谱的影响

利用传输矩阵法计算并分析了垂直入射下一维光子晶体的透射谱特性,数值模拟得到两种介质的折射率不变,入射波长减小时中心波长减小,禁带宽度变窄。当入射波长不变时,两种折射率比值变大时禁带宽度变大,实验结果为一维光子晶体器件的设计提供了理论依据。     

基于瞬态辐射信号的各向同性散射均匀介质光学特性PSO反演

利用激光入射半透明介质时有限体积法（FVM）得到的时域反射和透射信号,结合标准微粒群（PSO）、随机微粒群（SPSO）和多相微粒群（MPPSO）三种不同的智能算法反演短脉冲激光辐照下各项同性散射均匀参与性介质的吸收系数和散射系数,结果表明三种微粒群算法都能够高效准确地反演均匀介质内的光学参数。     

共轭梯度法求解双曲传热多宗量反问题

提出双曲传热反问题热物性参数和边界条件多宗量联合反演的一般数值求解模式,考虑了非均质和分布参数的影响,时域上采用时域精细算法进行离散,建立了便于敏度分析的有限元正演模型.由最小二乘原理建立反演模型,应用共轭梯度法进行求解.探讨了时间步长和测量误差对反演结果的影响,并进行了数值验证.     

二维有耗色散介质的时域逆散射方法

为了重建二维有耗色散介质的电参数分布,基于Debye模型,应用泛函分析和变分法,提出一种时域逆散射新方法.该方法首先以最小二乘准则构造目标函数,将逆问题表示为约束最小化问题,接着应用罚函数法转化为无约束最小化问题,然后基于变分计算导出闭式的Lagrange函数关于特征参数的Fréchet导数,最后借助梯度算法和时域有限差分法迭代反演Debye模型参数.为了对抗噪声污染和逆问题的病态特性,采用了一阶Tikhonov正则化方法.数值应用中,利用Polak-Ribière-Polyak非线性共轭梯度法,对二维乳     

Kerr缺陷一维耦合腔光波导的双稳态方向性

本文提出一种只在一层高折射率介质层中掺杂Kerr介质的一维耦合腔光波导.利用一维传输矩阵理论和非线性传输矩阵方法研究了此结构的光学双稳态.根据一维传输矩阵理论分析了此结构的线性特性,包括低频带边模的偏移及场分布的特点,讨论了此结构实现双稳态的原理.研究发现:由于缺陷层中场分布与入射光方向密切相关,而缺陷层光场的局域,将激发Kerr介质的三阶非线性效应,从而改变了缺陷层的折射率,所以不同方向的入射光具有不同的双稳态阈值.利用非线性传输矩阵方法研究了光学双稳态特性.结果表明:由于缺陷层的位置导致缺陷模正方向（由左到右）入射的场分布大于反方向（由右到左）入射的场分布,正方向的阈值低于反方向的阈值,相差一倍.     

飞秒激光脉冲在三能级有机分子介质中传播时的频谱分析

通过采用预估校正的时域有限差分法求解麦克斯韦-布洛赫方程,我们研究了飞秒激光脉冲在三能级有机分子(4,4-二甲氨基二苯乙烯分子)介质中传播时脉冲的频谱演化情况.在单光子共振情况下,即入射脉冲频率等于1、2能级之间的共振频率,对大面积入射脉冲,由于强的二次激发的作用,电场频谱中出现了在ω32附近振荡的频率成分,ω32是2、3能级之间的共振频率,说明对大面积入射脉冲二能级模型已经失效,需要采用多能级模型来描述分子介质.在双光子共振情况下,即入射脉冲频率等于1、3能级之间的共振频率的一半,由于介质中放大的自发辐射和四波混频的作用,部分入射脉冲能量转化为高频和低频电场成分的能量,分子介质表现出了很强的光功率限幅特性.     

Inverse radiation problem of temperature distribution in one-dimensional isotropically scattering participating slab with variable refractive index

In this paper, an inverse analysis is performed for estimation of source term distribution from the measured exit radiation intensities at the boundary surfaces in a one-dimensional absorbing, emitting and isotropically scattering medium between two parallel plates with variable refractive index. The variation of refractive index is assumed to be linear. The radiative transfer equation is solved by the constant quadrature discrete ordinate method. The inverse problem is formulated as an optimization problem for minimizing an objective function which is expressed as the sum of square deviations between measured and estimated exit radiation intensities at boundary surfaces. The conjugate gradient method is used to solve the inverse problem through an iterative procedure. The effects of various variables on source estimation are investigated such as type of source function, errors in the measured data and system parameters, gradient of refractive index across the medium, optical thickness, single scattering albedo and boundary emissivities. The results show that in the case of noisy input data, variation of system parameters may affect the inverse solution, especially at high error values in the measured data. The error in measured data plays more important role than the error in radiative system parameters except the refractive index distribution; however the accuracy of source estimation is very sensitive toward error in refractive index distribution. Therefore, refractive index distribution and measured exit intensities should be measured accurately with a limited error bound, in order to have an accurate estimation of source term in a graded index medium.     

Curved ray tracing method for one-dimensional radiative transfer in the linear-anisotropic scattering medium with graded index

The curved ray tracing method (CRT) is extended to radiative transfer in the linear-anisotropic scattering medium with graded index from non-scattering medium. In this paper, the CRT is presented to solve one-dimensional radiative transfer in the linear-anisotropic scattering gray medium with a linear refractive index and two black boundaries. The predicted temperature distributions and radiative heat flux at radiative equilibrium are determined by the proposed method, and numerical results are compared with the data in references. The results show that the CRT has a good accuracy for radiative transfer in the linear-anisotropic scattering medium with graded index and the dimensionless emissive power and dimensionless radiative heat flux depend on the dimensionless refractive index gradient. It can also be seen that the dimensionless refractive index gradient has important effects on the temperature discontinuity at the boundaries.     

Solution of the inverse radiative load problem in a two-dimensional system

An inverse radiation analysis is presented for estimating the temperature and the heat load distributions of the heating surface from the temperature and the heat flux measurements of the heated object. The Monte Carlo method is employed to solve the direct radiation problem. The inverse radiation problem is solved using the conjugate gradient and singular value decomposition methods. The measured data are simulated by adding random errors to the exact solution of the direct problem. The effects of the measurement errors on the accuracy of the inverse analysis are investigated. The study shows that the heat load distribution of the heating surface can be estimated accurately for the exact and noisy data. And the conjugate gradient method is better than the singular value decomposition method since the former can obtain more accurate results if the measurement errors are the same.     

半透明梯度折射率介质内辐射熵传递方程及其数值模拟

在非相干辐射条件下,基于Planck光谱辐射熵强度定义,导出半透明梯度折射率介质内光谱辐射熵传递方程,以及局部辐射熵产率理论表达式.基于离散坐标法对辐射熵传递方程进行数值求解.以一维半透明梯度介质平板为例,对辐射熵方程及其算法进行验证.平板整体无因次辐射熵产的计算结果与宏观热力学定律的结果一致.     

A numerical procedure for estimation of the melt depth in laser material processing

In this study, an algorithm based on conjugate gradient method (CGM) is applied to estimate the unknown time dependent melt depth during laser material processing in liquid phase. The determination of the melt depth is treated as a one-dimensional, transient, inverse heat conduction problem (IHCP). It is assumed that no prior information is available for the functional form of the unknown melt depth, but it can be estimated by an inverse analysis with temperature measurements near the heated surface. The algorithm has been applied to aluminum, titanium and fused quartz and accurate melting depth and temperature distributions can also be returned. In addition, this methodology can also be applied to solve other problems such as calculating the cutting forces in nanomachining by atomic force microscopy (AFM), and estimating the heat sources in a X-ray lithographic process.     

Discontinuous finite element method for radiative heat transfer in semitransparent graded index medium

To avoid the complicated and time-consuming computation of curved ray trajectories, a discontinuous finite element method based on discrete ordinate equation is extended to solve the radiative transfer problem in a multi-dimensional semitransparent graded index medium. Two cases of radiative heat transfer in two-dimensional rectangular gray semitransparent graded index medium enclosed by opaque boundary are examined to verify this discontinuous finite element method. Special layered and radial graded index distributions are considered. The predicted dimensionless net radiative heat fluxes and dimensionless temperature distributions are determined by the discontinuous finite element method and compared with the results obtained by the curved Monte Carlo method in references. The results show that the discontinuous finite element method has a good accuracy in solving the multi-dimensional radiative transfer problem in a semitransparent graded index medium.     

An Effective Multigrid Preconditioned CG Algorithm for Millimeter Wave Scattering by an Infinite Plane Metallic Grating

An effective multigrid based preconditioned conjugate gradient method is developed to solve electromagnetic large matrix problem for millimeter wave scattering application. By using multigrid technique we restrict the large matrix equation to a relative smaller matrix and which can be solved rapidly. The solution is prolonged as the initial guess for the conjugate gradient (CG) method. Numerical results show that our developed method can reach five times improvement of computational complexity.     

Meshless approach for coupled radiative and conductive heat transfer in one-dimensional graded index medium

A meshless local Petrov-Galerkin (MLPG) approach is employed for solving the coupled radiative and conductive heat transfer in a one-dimensional slab with graded index media. The angular distribution term in discrete ordinate equation of radiative transfer within a one-dimensional graded index slab is discretized by a step scheme, and the meshless approach for radiative transfer is based on the discrete ordinate equation. A moving least-squares approximation is used to construct the shape function. Two particular test cases for coupled radiative and conductive heat transfer within a one-dimensional graded index slab are examined to verify this new approximate method. The temperatures and the radiative heat fluxes are obtained. The results are compared with the other benchmark approximate solutions. By comparison, the results show that the MLPG approach has a good accuracy in solving the coupled radiative and conductive heat transfer in one-dimensional graded index media.     

Least-squares finite element method for radiation heat transfer in graded index medium

To avoid the complicated and time-consuming computation of curved ray trajectories, a least-squares finite element method based on discrete ordinate equation is extended to solve the radiative transfer problem in a multi-dimensional semitransparent graded index medium. Four cases of radiative heat transfer are examined to verify this least-squares finite element method. Linear and nonlinear graded index are considered. The predicted dimensionless net radiative heat fluxes are determined by the least-squares finite element method and compared with the results obtained by other methods. The results show that the least-squares finite element method is stable and has a good accuracy in solving the multi-dimensional radiative transfer problem in a semitransparent graded index medium, while the Galerkin finite element method sometimes suffers from nonphysical oscillations.