臺灣博碩士論文加值系統

在矽奈米線波導設計原理中，高折射率差的結構能使整個元件縮小到次微米等級，對於積體化是一個非常重要的關鍵。然而幾何結構上非對稱的矽奈米線波導具有極化相依色散以及極化相依損耗等問題，而限制其與既有光纖通訊系統的整合，因此需要極化分集系統來減少極化相依性造成的影響，而極化分離器是極化分集系統中不可或缺的元件。一般而言，定向耦合器是一個可以達成極化分離效果的元件，而此類極化分離器可透過調整耦合區長度、波導寬度來達到最好的元件效能，但是傳統設計上可控制的變數不多。
在本論文中，提出一種基於基因演算法設計的寬頻極化分離器，設計上將結構切成若干小段，將每一小段的波導間距及波導寬度都當作變數，透過耦合模態理論計算出元件的頻率響應，再搭配基因演算法作最佳化，達到寬頻帶之頻率響應，最後再將元件以三維時域有限差分法作進一步驗證。針對 100 nm、200 nm 操作頻寬所設計兩種元件，變動區長度為 48 μm，其數值模擬結果呈現，比起其他文獻有更高的消光比，分別為 20.4 dB、17.6 dB，此外，透過製程容忍度分析，當製程誤差範圍為 ±10 nm 下，整體的消光比分別變為 17.1 dB、14.6 dB。另外，我們也針對更寬頻的操作頻寬 400 nm 進行初步元件設計，變動區長度為 192 μm，其消光比可達 15.3 dB。

In the design concept of silicon nanowires, because of large refractive index contrast, devices can be shrink devices to micrometer scale and this plays a major role in integration. However, the large birefrigence due to the asymmetric geometric structure of silicon nanowires leads to polarization dependent dispersion and polarization dependent loss, which restrict their integrations with optical fiber communication systems, so we need the polarization diversity technology to reduce the polarization dependence. The polarization beam splitter (PBS) is an indispensable device for the polarization diversity technology. Generally, directional couplers can be used to achieve polarization separation, in this way optimal performance can be obtained by adjusting the coupling length, waveguides width. However, the number of controllable variables is fewer in the conventional design.
In this thesis, the design of a broadband polarization beam splitter based on genetic algorithm is proposed. The structure is segmented into lots of short sections, gaps and waveguide widths in every section are the controllable variables in this optimization problem. The spectral response of the device can be obtained by using the Coupled Mode Theory (CMT), and it can be further optimized by the genetic algorithm and verified by 3D finite-difference time-domain calculations. Two separate 48-μm-long devices with operating bandwidths 100 nm and 200 nm are designed, respectively. Their simulation results show that the extinction ratios are 20.4 dB and 17.6 dB, respectively, which are better than those shown in previous literatures. Besides, the fabrication tolerance of the devices are also discussed. With the fabrication error of ±10 nm, the results show that the extinction ratios become 17.1 dB and 14.6 dB, respectively. In addition, the preliminary design of a 192-μm-long PBS with a larger bandwidth 400 nm is carried out, and an extinction ratio of 15.3 dB can be achieved.

口試委員會審定書 i
致謝 ii
中文摘要 iii
ABSTRACT iv
目錄 vi
圖目錄 viii
表目錄 xii
第一章 緒論 1
1.1 背景介紹 1
1.2 研究動機 5
第二章 文獻回顧 6
第三章 研究方法介紹 13
3.1 平板波導 13
3.2 矩形波導 15
3.3 耦合模態理論 18
3.4 模擬方法 22
3.4.1 基因演算法 22
3.4.2 時域有限差分法 24
第四章 基於基因演算法設計極化分離器 27
4.1 元件結構 27
4.2 轉移矩陣形式的耦合模態理論 30
4.3 利用基因演算法最佳化結構參數 31
4.3.1 元件一 (針對波長 1500 nm ‒ 1600 nm 操作之極化分離器，長度 48 μm) 之最佳化設計 39
4.3.2 元件二 (針對波長 1450 nm ‒ 1650 nm 操作之極化分離器，長度 48 μm) 之最佳化設計 43
4.4 模擬結果討論 47
4.4.1 元件一之數值模擬結果 48
4.4.2 元件二之數值模擬結果 51
4.4.3 製程容忍度分析 54
4.5 針對更寬操作頻寬之極化分離器之初步設計探討 57
第五章 結論 67
參考資料 69

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