A New Technique Combining Boundary Integral Equation and Hybrid Ray-Mode Method for Wave Scatters in Layered Background with Applications in Optical Microscopy

这项工作获得了工程启动奖（EIA）的资助。本文采用边界积分方程和混合射线模方法来描述背景的格林函数，研究了嵌入在多层背景中的散射体的光波散射现象。该方法在广泛的参数范围内具有数值效率，并为计算结果提供了令人信服的物理解释。结构感兴趣的光学显微镜集成电路和集成光学将作为测试案例。研究了散射体的形状、大小和介电常数对散射特性的影响以及扫描显微镜对散射场的响应。从这项研究中获得的结果可以使扫描显微镜定量地评估尺寸在波长量级或小于波长的物体。潜在的应用是使用扫描光学显微镜对集成电路和集成光学器件中的亚微米结构进行自动无损评价和检查。该研究也将有助于其他工程学科，如无损检测、勘探、地球物理和水声等，在这些学科中使用弹性和声波来研究类似的结构。在集成电路和集成光学的扫描光学显微镜中，将采用一种新的理论技术来研究那些感兴趣的结构的波散射现象。这种结构由层状形成的材料组成，这些层状材料通常具有嵌入的不均匀性，与背景层状结构不同。识别和评估它们的最通用的方法之一是基于使用入射在多层结构上的透射和散射有界光束，对包含散射的区域进行扫描。为了利用散射场识别散射特性，必须解决多层结构中物体对波的直接散射问题。提出了一种结合边界积分方程和新发展的混合射线模法求解波散射问题的方法。

This work is funded as an Engineering Initiation Award (EIA). Optical wave scattering phenomena for scatters embedded in a multilayer background will be studied using a new technique which employs boundary integral equation to formulate the interaction processes and hybrid ray- mode method to provide the Green's function of the background. This method is numerically efficient in a broad range of parameter regimes and also provides cogent physical interpretations for the computed result. Structures of interest in the optical microscopy of integrated circuits and integrated optics will serve as test cases. The dependance of the scattering properties on the shapes, sizes and dielectric constants of the scatters and the response of the scanning microscope to the scattering fields are to be investigated. The results gained from this research may enable the scanning microscopy to assess quantitatively objects whose dimensions are on the order of, or less than, the wavelength. Potential application is to the use of a scanning optical microscope for automated nondestructive evaluation and inspection of sub-micron structures in integrated circuits and integrated optics devices. This study will be also beneficial to other engineering disciplines such as nondestructive testing, exploration, geophysics and underwater acoustics, etc., where similar structures are investigated using elastic and acoustic waves. A new theoretical technique will be employed to study wave scattering phenomena of those structures that are of interest in scanned optical microscopy of integrated circuits and integrated optics. Such structures are composed of material formed in layers which often have embedded inhomogeneities, different from the background layered structure. One of the most versatile methods to identify and evaluate them is based on the use of the transmission and scattering bounded beams incident on the multilayered structure that are scanned over the region containing the scatter. In order to use the scattered fields to identify the properties of the scatter, it is essential to solve the direct problem of wave scattering by an object in a multilayer structure. This proposal addresses a use of the combination of boundary integral equation and the newly developed hybrid ray-mode method to solve the wave scattering problem.