本論文設計矽光子晶片的光子晶體絕熱錐形週期波導之研究，設定錐形光子晶體波導的發光波長(λ)為1550 nm，對光子晶體陣列掃描模擬後，從掃描的數據中，得到a/λ= 0.3與r/a= 0.45，這兩個比值符合具有TM極化不存在的光子能隙，且計算出圓柱半徑(r)為210 nm，晶格常數(a)為465 nm。
先設計出線性曲線（Linear）的錐形光波導，線性錐形波導的寬度(Wt)為1.4 µm / 2.8 µm / 4.2 µm相對應的寬度(Wmmi)為4 µm / 8 µm / 12 µm以及相對應的錐形波導長度(Lt)為13 µm / 26 µm / 40 µm。會找出與錐形波導寬度相對應的最大發散角(θ)以及相對應的元件損耗。利用高斯光束(Gaussian beam)及束腰(Beam Waist)的公式，透過線性曲線計算出凹曲線（Concave）和凸曲線（Convex），再設計出凹凸的對稱曲線。設計錐形光子晶體波導的排列方式，是錐形的曲線需通過每個光子晶體圓柱圓心的位置，利用古斯-漢臣位移(Goos-Hanchen shift)的效應，將這線性、凹曲線與凸曲線設計出來的錐形光子體波導，模擬過後做比較，觀察哪種排列方式的錐形光子晶體波導輸出功率是更好。由上述設計出來的錐形光子晶體陣列是透過TM極化不存在的光波導來傳輸。之後會再探討對錐形的角度和光子晶體不同的週期做改變再去看模擬結果的變化。

In this thesis, research on the design of photonic crystal adiabatic tapered periodic waveguide for silicon photonic wafers is carried out. The emission wavelength (λ) of the tapered photonic crystal waveguide is set to 1550 nm. After scanning and simulating the photonic crystal array, a/ λ = 0.3 and r/a = 0.45, these two ratios correspond to the photon gap with TM polarization absent, and the calculated cylinder radius (r) is 210 nm and the lattice constant (a) is 465 nm.
First design a tapered optical waveguide with a linear curve (Linear), the width (Wt) of the linear tapered waveguide is 1.4 µm / 2.8 µm / 4.2 µm, and the corresponding width (Wmmi) is 4 µm / 8 µm / 12 µm and the corresponding The corresponding tapered waveguide lengths (Lt) are 13 µm / 26 µm / 40 µm. The maximum divergence angle (θ) corresponding to the width of the tapered waveguide is found, along with the corresponding component loss. Using the formula of Gaussian beam and beam waist (Beam Waist), calculate the concave curve (Concave) and convex curve (Convex) through the linear curve, and then design the concave-convex symmetrical curve. To design the arrangement of tapered photonic crystal waveguides, the conical curve needs to pass through the center of each photonic crystal cylinder, and use the effect of Goos-Hanchen shift to combine the linear and concave curves with the convex The tapered photonic crystal waveguide designed by the curve is compared after simulation to observe which arrangement of the tapered photonic crystal waveguide has the better output power. The tapered photonic crystal array designed above is transmitted through the optical waveguide where TM polarization does not exist. Later, we will discuss how to change the angle of the taper and the different periods of the photonic crystal, and then look at the changes in the simulation results.

目錄
摘要 V
ABSTRACT VII
致謝 IX
目錄 X
圖目錄 XII
表目錄 XVI
第一章 緒論 1
1.1 研究動機 1
1.2 論文架構 3
第二章 基本理論與高斯光束(Gaussian Beam) 5
2.1光子晶體介紹 5
2.2高斯光束(Gaussian Beam) 7
2.2.1束腰(Beam Waist) 9
第三章 研究方法 10
3.1 SOI結構 10
3.1.1 SOI光子晶體結構 11
3.2 利用模擬軟體中的BandSOLVE掃描 13
3.3 利用高斯光束(Gaussian Beam)中，光束腰(Beam Waist)公式計算出線性、凹曲線與凸曲線 16
3.4 線性、凹曲線與凸曲線的光子晶體錐形波導設計 26
3.5古斯-漢欣位移(Goos-Hänchen shift)效應 30
第四章 模擬結果 35
4.1 線性、凹曲線與凸曲線的光子晶體波導模擬 35
4.2模擬結果比較 44
第五章 結論與未來展望 46
5.1結論 46
5.2未來展望 48
參考文獻 49
附錄 52

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