具有不連續接面之抗諧振反射光波導元件之分析與設計

Abstract

本論文中，我們發展一套特徵模展開理論系統用以分析並最佳化設計具有不連續接面之抗諧振反射光波導元件。這個理論藉著探討光波導的特徵模，將入射場以特徵模組成的展開群組來展開，並計算各個不連續接面間的模耦合關係，即可分析模擬具有不連續接面之光波導。本論文特別著重於分析抗諧振反射光波導的洩漏模，用以取代連續且計算費時的輻射模，做為特徵模展開理論中的展開群組。我們也提出一些利用抗諧振反射光波導來設計的積體光學元件，以做為光學通訊、光積體電路、光學連線及光感測的應用。 為配合目前發展已成熟之積體電路技術，我們選擇以矽材料做為波導基片，搭配氮化矽、二氧化鈦、二氧化矽等薄膜做為抗諧振反射光波導各層介質的材料來設計抗諧振反射光波導元件。所設計的元件包括能量分配元件、混成耦合器、漸細耦合器及偏極化分光元件等耦合元件，單轉折、雙轉折、曲線轉折等彎曲元件，及化學感測器、微位置感測器等感測元件。我們利用特徵模展開理論來設計和最佳化元件，並利用光束傳播理論來驗證所設計的元件。

In this dissertation, we developed a systematic method of eigenmode expansion analysis to analyze and design antiresonant reflecting optical waveguide (ARROW) devices with discontinuities. In the eigenmode expansion analysis, eigenmodes of optical waveguides are used to form an expansion set, which can be superposed with their individual expansion coefficients to construct any field distribution. By analyzing the coupling behavior between eigenmodes of discontinuous regions, characteristics of optical waveguides can be evaluated. Due to the leaky properties of ARROWs, the discrete leaky modes are employed instead of continuous radiation modes as an expansion set to simplify calculation. We also proposed various ARROW devices for applications to optical communications, optical integrated circuits, optical interconnects, and optical microsensing systems. The ARROW devices we designed on a Si substrate with SiO$_{2}$ as the guiding and the low-index cladding layers, and Si$_{3}$N$_{4}$, TiO$_{2}$ or other glass materials as the high-index cladding layers, which are compatible with mature silicon IC technology. The devices we proposed were classified into the coupler devices including power dividers, optical hybrid couplers, taper couplers, and polarization beam splitters, the bending devices including single-bend waveguides, double-bend waveguides, and curved-bend waveguides, and the sensing devices including chemical sensors, and micro-position sensors. With the analysis and optimum design of these devices by eigenmode expansion analysis, beam propagation method (BPM) was also performed to verify these devices.