长方体内多量散射介质光子密度波扩散方程研究

进一步改进了已有物理模型,从理论上解决了三维有限体积内光子密度波扩散方程的求解问题,得到了长方体边界条件下的格林函数的解析解,给出了实验可测量光通量与待测物吸收系数改变量之间可进行数值计算的表达式。本物理模型更加接近实际情况,解决了已有模型与实际情况偏差较大的矛盾,为进行反演计算提高成像质量提供了理论保证。     

扩散过程中混沌场的演化

利用热纠缠态表象求解密度矩阵主方程的方法和有序算符内的积分技术,对扩散过程的密度矩阵主方程进行了求解,给出了主方程密度算符无限和表示的解的形式,导出了扩散过程混沌场密度算符的演化规律,并研究了平均光子数和光子数涨落的演化。研究结果表明:随着扩散过程的进行,混沌场密度算符的形式不变,仍然保持混沌场的性质,但其平均光子数随着扩散过程的进行线性增加,光子数涨落随扩散时间以二次函数形式扩大。     

边界条件微扰法计算非理想波导的传播常数

考虑到非理想导体波导壁金属损耗对传播常数的影响,对理想金属边界条件进行一阶近似微扰,得到了非理想波导的传播常数。和传统微扰法相比,能够在截止频率附近较为精确地计算衰减常数,也适用于导体损耗较大的情况;同时能给出非理想导体波导壁对相位常数的影响。将结果与Ansoft HFSS软件的仿真结果进行比较,两者具有较好的一致性。同时给出了边界条件微扰法解与解析解及传统微扰法解在一定条件下的联系,表明边界微扰法比解析法实现简单,比传统微扰法具有更广泛的适用性。     

人体组织中光子密度波漫射理论的模拟研究

运用矩阵变换方法对已有的无限长矩形条件下的扩散方程的解析解进行了化简,大大提高了计算机模拟的速度.利用给定的人体前臂组织的典型光学参数,给出了扩散方程解析解的模拟计算结果.分析了介质的基本光学特性参数对漫射光子密度的影响,在验证已有的理论基础上,发现该模型下的解析解不适用于漫射系数D较大的情况.     

微扰法在衍射光栅分析中的应用

在微电子结构中常见的二维衍射光栅的分析中,严格耦合波分析法（Rigorous Coupled Wave Analysis,RCWA）方法计算耗时,占用内存比较大.本文将微扰法与RCWA相结合的算法应用于二维衍射光栅分析中,以提高其计算效率.求解非矩形光栅问题时,需将光栅做阶梯近似.通过RCWA求解参考层的本征值,其余层的本征值可通过微扰法得到.实验表明,微扰法满足计算精度要求,且计算效率也能得到提高.对于本文中的例子,当光栅的截断阶数选为12时,计算时间可以节省45%.     

复折射率光纤传输特性的精确微扰分析

本文给出精确计算复折射率光纤复传播常数的简单微扰分析方法。光纤的复模折射率N=N′+iN″的实部N′由求解相应的实本征值方程得到,而虚部N″则由微扰计算得到。导出了计算阶跃型圆光纤基模衰减系数或增益系数的简单解析公式。本法计算结果与由解复本征值方程得到的精确数值结果符合很好。     

广义变系数五阶KdV和BBM方程的孤立子解

利用假设孤立波方法,研究了广义变系数五阶KdV方程和BBM方程,得到了广义变系数五阶KdV方程和BBM方程的孤立子解。对于得到的孤立子解,为了保证解的存在性,给出了孤立子解存在的条件。     

金属包层阶跃平板介质波导导模的二级微扰分析

直接求得的复本征值方程的解作为精确解,由微扰理论得到的一级和二级近似结果与之进行了分析比较,结果表明微扰法是相当好的近似方法,它们给出了与精确值符合相当好的数值结果。分析结果还表明微扰法的二级近似结果对一级近似结果的修正很小,一级近似已可以给出足够精确的结果。     

金属包层平板光波导在截止点附近的光学特性

本文利用二级微优近似方法分析了金属包层平板光波导在截止点附近的传输特性,将微扰近似所得的结果与本文直接求复本征方程所得的结果进行比较。结果表明,微扰法可以给出与精确值符合相当好的数值结果,并且可以给出直至截止点的解;微扰法的二级近似结果对一级近似结果的修正很小,一级近似已可以给出足够精确的结果。     

双异质结半导体激光器在阶跃和正弦电流调制下的行为

用数值计算方法求出了光子密度、载流子浓度的速率方程和场方程的自治解.给出了:1.当谐振腔中的光子密度,光和载流子的相互作用足够强时,在阶跃电流下可以产生自脉动.2.在正弦调制下,调制频率高时光输出发生畸变,而且在调制过程中光强度分布发生变化,并由此引起不同空间位置的光输出出现相位差.     

半无限空间中光子密度波扩散方程的求解

改进了原无限大模型，求解了无限大空间中光子密度波的扩散方程，找出了相应条件下的Green函数，演算出了与入射面相对应的光子通量和介质中的吸收系数改变量之间的关系，所用模型更接近于实验研究情况，所得结论能直接用于多散射介质中成像问题的实验研究。即通过对光子通量的检测，反演出吸收系数改变量的分布，从而实现用光子密度波理论在多散射介质中的成像问题的解决。     

多散射介质中光子密度波扩散方程的求解

将光源作为一个复数点光源,根据实验研究模型的要求,求解了多散射介质中光子密度波扩散方程,找出了与入射面相对应面的光子通量和介质中吸收系数改变量之间的关系。所得结论能直接用于多散射介质中成像问题的实验研究之中,即通过对光子通量的检测,反演出吸收系数改变量的分布,从而达到多散射介质中的成像问题的解决。     

四层匹配介质漫射方程的稳态研究

文中根据光在生物体内传播的漫射方程理论,以人体组织为多层介质,在平稳状态条件下,使用外推边界条件,精确给出了匹配介质中平稳状态下四层体系光的漫射方程格林函数的解,通过此解,可以算出空间分辨漫反射。使用蒙特卡罗方法来验证四层体系的漫射方程,发现,我们给出的理论解不仅可以包括两层体系模型的空间分辨漫反射的解,与A. Kienle的两层体系的结论一致,而且在四层体系中,四层体系漫射方程的空间分辨漫反射的解和蒙特卡罗方法的基本一致。通过估计吸收系数和等效各项同性散射系数,这个模型在医疗和诊断上具有潜在的应用价值。     

Self-Consistent Model and Numerical Analysis of VCSEL's Laser Diodes

A self-consistent model of vertical-cavity surface-emitting lasers (VCSEL's) is presented in this paper, in which the carrier diffusion rate equation, the photon density rate equation, and the thermal conduction equation are considered simultaneously. The nonuniform heat flux density distribution in the active region due to the current-spreading effect is taken into account. The effects of temperature on gain and transparency carrier density are also included in this model. It is nonlinearly and self-consistently solved in the Matlab environment. The transient and lateral distribution characteristics of the carrier and photon densities and the junction temperature are investigated. Some interesting results are gotten and analyzed.     

Steady-state photocarrier collection in silicon imaging devices

Solid-state imagers lose resolution when photocarriers generated in one imaging site diffuse to a nearby site where they are collected. These processes are modeled by solving the steady-state diffusion equation for minority carriers. A source term represents the absorption of photons and the generation of photocarriers, and a linear term represents the loss of photocarriers by recombination. This is equivalent to studying the Helmholtz equation with an inhomogeneous term. The problem is simplified when the light source has symmetry. A line source or a cylindrically symmetric source leads to a two-dimensional problem. The approach of Seib, Crowell, and Labuda allows a solution by quadrature if the further assumption of a smooth top boundary is made. We calculate the integrated normal flux over each imaging site to see how many carriers diffuse from under the illuminated site to another site. We compare our predicted line- and point-spread functions to those measured on imagers and find reasonable agreement. This allows us to extract minority-carrier diffusion lengths. Further calculations show how the diffusion of carriers depends on the photon wavelength and the pixel size. We generalize Seib's approach and apply it to a solid-state imager covered with color filters. This allows us to see the extent of color mixing due to carrier diffusion. We also discuss a finite-difference solution of the diffusion equation that employs the method of conjugate gradients. This approach is useful for problems where the top boundary is not smooth.     

Optical properties of wounds: diabetic versus healthy tissue

Diffuse photon density wave (DPDW) methodology at Near Infrared frequencies has been used to calculate absorption and scattering from wounds of healthy and diabetic rats. The diffusion equation for semi-infinite media is being used for calculating the absorption and scattering coefficients based on measurements of phase and amplitude with a frequency domain device. Differences observed during the course of healing in the two populations can be correlated to the delayed healing observed in diabetics. These results are encouraging and further work will focus on the implementation of this device to the clinical setting as a monitoring tool in chronic diabetic wounds.     

On the Diffusion of Electromagnetic Waves and Applicability of Diffusion Equation to Multipath Random Media

The diffusion behavior of electromagnetic (EM) waves in two dimensional (2-D) multipath media is studied through integral equation based full wave Monte Carlo simulations. The influences of some physical factors are explored, among which the area density of the embedded obstacles manifests itself to be the most important one in determining wave diffusion. A lossy system starts to behave diffusively when the area density approximately exceeds 5%, and the diffusion equations are generally applicable for predicting power decay. At low densities, the power-distance relation of the waves appears to follow power laws. The sizes and shapes of the obstacles have a secondary effect on the diffusion of waves. Whenever a system contains small objects or objects with reflecting sides, the waves therein are more diffusive and the diffusion equation approximates the reality more accurately. Absorption loss decreases wave diffusion in general, but our results show that the diffusion equation for a system with very lossy but small obstacles can work very well for predicting power decay.     

Modeling Active Microwave Remote Sensing of Snow Using Dense Media Radiative Transfer (DMRT) Theory With Multiple-Scattering Effects

Dense media radiative transfer (DMRT) theory is used to study the multiple-scattering effects in active microwave remote sensing. Simplified DMRT phase matrices are obtained in the 1-2 frame. The simplified expressions facilitate solutions of the DMRT equations and comparisons with other phase matrices. First-order, second-order, and full multiple-scattering solutions of the DMRT equations are obtained. To solve the DMRT equation, we decompose the diffuse intensities into Fourier series in the azimuthal direction. Each harmonic is solved by the eigen-quadrature approach. The model is applied to the active microwave remote sensing of terrestrial snow. Full multiple-scattering effects are important as the optical thickness for snow at frequencies above 10 GHz often exceed unity. The results are illustrated as a function of frequency, incidence angle, and snow depth. The results show that cross polarization for the case of densely packed spheres can be significant and can be merely 6 to 8 dB below copolarization. The magnitudes of the cross polarization are consistent with the experimental observations. The results show that the active 13.5-GHz backscattering coefficients still have significant sensitivity to snow thickness even for snow thickness exceeding 1 m     

Determination of the Photon Lifetime for DFB Lasers

The photon lifetime of the distributed feedback (DFB) laser is obtained through the relations between cavity photon flux and power associated with the electric fields. The solution of the coupled wave equations provides the propagation parameters and the amplitude gain coefficients for which numerical and approximate solutions are obtained. Using the photon lifetime the threshold condition of the DFB laser within a fixed mirror cavity is determined. The evaluation of both Fabry-Peacuterot and DFB modes is shown by the calculation, using two different photon lifetimes, of all modal concentrations, with the Fermi energy as the independent variable. The current density is also evaluated using the Fermi energy and threshold current is identified as the value when the Fermi energy clamps