Numerical Simulation on Periodic Metal/Dielectric Structures Using Plane-Wave-Assisted Boundary Integral-Equation Method

本論文針對具一維週期之二維電磁繞射問題提出一新穎的數值方法：平面波輔助邊界積分方程法。本方法乃基於傳統邊界積分方程法之架構，並結合平面波展開的概念，充分利用兩種數值技巧的優點。吾人藉積分方程以規範週期性結構中具複雜幾何的區域之電磁場，並以平面波的線性組合描述垂直於週期方向之延伸背景中的波動行為。由於以自由空間格林函數及週期性邊界條件取代一般常用的週期性格林函數，本法可免於週期性格林函數級數展開之收斂困難。此外，基於局域線性基底展開之離散技巧，本方法之準確性與收斂性在不等分割之應用上亦得到驗證。此不等分割之應用使本法適於模擬具細微結構的電磁問題。針對表面電漿波異常穿透之相關議題，吾人藉數值模擬探討兩類含金屬材質之光柵的繞射問題。在第一類光柵（波浪狀多層結構）問題中，吾人探討了由耦合表面電漿波引起的光穿透增強效應，並將其與第二類光柵（具狹縫之金屬薄層）問題中主導增強穿透的狹縫共振效應作比較。在第二類光柵問題中，吾人解釋了由狹縫共振效應引發的增強性穿透之發生頻率與光柵結構參數間的關係，並以此光柵之其他變形的模擬結果進一步加強吾人的解釋。A novel hybrid numerical technique is proposed for analyzing general 2D electromagnetic problems with 1D gratings. The proposed method combines the conventional boundary integral-equation method (BIEM) with the plane-wave-expansion technique, taking the benefit from either method. In the framework of the proposed method, the BIEM is in charge of formulating the major part of the problem containing the grating structure, while the plane-wave expansion is for describing the nature of the outgoing wave and truncating the computation domain in the direction perpendicular to the grating extension. The free space Green’s function with the periodic boundary condition is used to replace the commonly used periodic Green’s function for dealing with the periodicity of the problem. This circumvents the convergence difficulty of the periodic Green’s function. The performance of the PW-BIEM with the non-uniform mesh is also verified, showing the capability of the PW-BIEM in modeling the grating structure with fine geometry. With the proposed method, the transmission behavior of the wavy layered structure with a substrate-metal-cover-air architecture is investigated. The enhanced transmission due to the mechanism of the coupled surface plasmon polariton (SPP) is discussed and compared with another enhancement mechanism, cavity resonance effect, of the slit grating. For slit gratings, in addition to that of the rectangular type, the modified slit gratings are also simulated. The transmission behavior is discussed and interpreted.1 Introduction 1 1.1 Surface Plasmon and Related Topics 1 1.1.1 Extraordinary Optical Transmission and Light Beaming 2 1.1.2 Sensor, Detector, and Optical Near-Field Microscopy 4 1.1.3 Other Related Topics 5 1.2 Methodology of SPP Investigation 5 1.3 Diffraction Issues on SPP Devices 6 1.4 Overview and Organization of the Dissertation 7 1.5 Contributions of the Present Work 9 2 Overview of Numerical Techniques for SPP Modeling 12 2.1 Fundamentals of Surface Plasmon Polaritons 12 2.2 Difference Method 15 2.3 Review of the Coupled-Wave Method 17 2.4 Unstructured-Mesh Method 21 3 Plane-Wave-Assisted Boundary Integral-Equation Method 26 3.1 Concept of the Boundary Integral-Equation Method 26 3.2 Basis Expansion and Discretization 28 3.3 Plane-Wave-Assisted Boundary Integral-Equation Method 30 3.3.1 Problem Description 31 3.3.2 Combining the Plane-Wave Expansion with the Boundary Integral Equation 32 3.4 Synthesis of the Matrix Equation 36 3.4.1 Matrix Representation of the Boundary Fields 36 3.4.2 Synthesis Details 42 3.4.3 Treatments for Boundary Junctions 49 4 Numerical Verification 63 4.1 Convergence Issue for Highly Conducting Materials 63 4.2 Performance for Real Metallic Gratings 64 4.3 Non-Uniform Mesh in PW-BIEM 65 5 Simulation Results: Diffraction Efficiency of Periodic Metal/Dielectric Structures 79 5.1 Diffraction Efficiency of Metallic Wavy Structures 79 5.2 Diffraction Efficiency of Slit Gratings 84 5.3 Diffraction Efficiency of Modified Slit Gratings 88 6 Conclusion 11