小孔衍射和近场散射数值计算的格林函数方法  

Green Function Method for the Numerical Calculations of Pinhole Diffraction and Near-Field Light Scattering

作　　者：刘春香[1] 程传福[2] 任小荣[3] 刘曼[2] 贾天卿[2] 张道中[1] 徐至展[2] 

机构地区：[1]中国科学院物理研究所和凝聚态物理中心光物理实验室,北京100080 [2]中国科学院上海光学精密机械研究所,上海201800 [3]山东师范大学物理系,济南250014

出　　处：《光学学报》2004年第2期145-151,共7页Acta Optica Sinica

基　　金：国家自然科学基金 (6 99780 12 )资助课题

摘　　要：从简谐光波满足的亥姆霍兹方程出发 ,将由格林定理得到的介质分界面上的积分方程转化为以表面上的光波及其导数为未知量的线性方程组 ,并对其进行数值求解 ,实现了光场的数值计算。然后将这一方法应用于亚波长尺度的小孔衍射的光波以及自仿射分形表面产生的随机光场及其在近场区域范围内的传播的计算。在随机表面产生的光场计算中 ,提出了类比推导夫琅禾费面上散斑场自相关函数的方法产生随机表面 ,以及计算其导数的傅里叶变换方法。对光场的计算结果表明 ,在近场范围内 ,光场随离开表面的距离的增加而迅速变化 ,其传播特性完全不同于光场在远场范围内的传播特性。Starting from the Helmholtz Equation, the integral equation of light wave on medium interfaces is obtained by use of Green theorem. Then the integral equation is discretized into a set of linear equations with unknown values of light wave and its derivative on the interface. Numerical solutions of these linear equations give the values of light waves. This method is applied to the calculations of both the pinhole diffraction in subwavelength scale and random light field produced by random self-affine fractal surfaces in near field. A method for generation of random self-affine fractal surfaces is proposed by analogy to the derivation process of the autocorrelation functions of speckles in Frauhofer plane, and the Fourier transformation method for numerical derivative of the random surfaces is presented. The calculated results show that in near field, the random light fields vary dramatically with the distance increasing from the random surfaces, and the properties of light wave propagation are quite different from those of the light waves in far field.

关 键 词：近场光学 格林函数 物理光学 小孔衍射 近场散射 亥姆霍兹方程 夫琅禾费散斑 傅里叶变换 

分 类 号：O436.1[机械工程—光学工程] O436.2[理学—光学]