在本研究中，我們根據基本幾何光學原理建構光纖光錐理論模型，並使用 TracePro 軟體繪製光纖光錐、透鏡、偵測器的3D模型。透過在TracePro中建立3D模型、設定材質、設定光源，我們對一光偵測器收光夠進行模擬光學追跡。綜合考慮光錐的大端、小端、長度、與偵測器之間的相對位置，對光纖光錐與偵測器之間的能量耦合特性，分析光纖光錐對收光架構能量耦合的能力。其中我們定義最大接收角度來作為比較及優化的基準，並與一般光學透鏡的性能進行比較，最後證實光錐在提升接收角度相較於透鏡是有優勢的。
接著我們在一個模擬之收光架構中量化分析使用光錐在耦合效率上的提升效果，得知在有使用光錐的收光架構中，最大接收角度相較於沒有使用光錐提升了3.78倍。最後我們在不考慮目前工藝極限的情況下，由模擬結果得知純粹使用光錐的收光架構相較於使用透鏡的收光架構其最大接收角度可擴大15倍。
總結來說，我們成功證實光纖光錐有助於提升偵測器的耦合能力，可有效增加收光架構的耦合能力以及最大接收角度，也提供了比較耦合元件收光性能的方法。

In the thesis, a theoretical model of the taper fiber is constructed based on the geometric optics principle. We use the TracePro software to draw 3D models of taper fiber, lens, and detector. By setting the materials, light sources, we simulate optical traces in TracePro. Considering the large end, small end, taper length and relative position of the taper fiber, the energy coupling between the taper fiber and the detector is analyzed to determine the capability of the energy coupling of the receiving structure. By using the maximum receiving angle as a reference, we compare the performance of the taper fiber and optical lens. It is confirmed that the taper fiber is advantageous in improving the receiving angle. By testing the coupling efficiency in a simulated light-receiving architecture, we show that the maximum receiving angle can increase 3.78 times when using the taper fiber. Theoretically, without considering current manufacturing limit, we show that the receiving angle using a pure taper fiber is 6$^\circ$, 15 times larger than using the lens from the simulation.
In sum, we successfully confirmed that the taper fiber can help to improve the coupling capability of the detecter, which efficiently increasing the maximum receiving angle and the coupling efficiency, we also established the method for comparing the receiving performance of the coupling components.

摘要 i
abstract ii
1、緒論 P1
1.1 簡介 P1
1.2 動機 P2
2、理論與模擬方法 P3
2.1 幾何光學 P4
2.2 光纖光錐的理論方法 P7
2.3 臨界角與光纖光錐尺寸之關係 P11
2.4 光線追跡 P13
2.5 TracePro軟體介紹 P13
2.6 建立光學模擬架構 P14
2.6.1 建立模擬光源 P14
2.6.2 建立光學物件模型 P14
2.6.3 模擬實驗參數定義 P15
3、模擬成果分析 P17
3.1 光纖光錐尺寸與偵測器接收能量的關係 P18
3.1.1 不同光錐比例下不同長度光纖光錐對於偵測器接收能量之變化 P18
3.1.2 比較光纖光錐與透鏡能量利用率之差異 P22
3.2 光纖光錐尺寸與偵測器收光角度的關係 P24
3.2.1 不同光纖光錐長度與不同焦距透鏡之接收角度 P24
3.2.2 固定小端下不同光錐比例光纖光錐之接收角度 P26
3.3 收光模組搭配光纖光錐的收光角度與傳遞效率 P27
3.3.1 優化搭配光纖光錐之收光模組 P29
3.3.2 比較有無使用光纖光錐收光模組之性能 P35
3.4 純粹使用光纖光錐收光架構之光角度與傳遞效率 P36
4、結論與未來展望 P39
4.1 結論 P39
4.2 未來展望 P40
Reference P41

[1] C.R. Xue, “Research of the tapered fiber properties,” Laser & Infrared, vol. 36, no.9, pp.886-888, September (2006).
[2] Y. Zhang, F. Zhang, H. Zhang, G. R. Xu, J. Deng, C. X. Liu, and M. Hu, “Preparation of tapered optical fiber and research of optical experiments,” Optical Communication Technology, vol. 37, no. 6, pp.14-15, November (2013).
[3] Y. J. Gao, S. L. Yao, G. Feng, W. Gue, Y. C. Li, and X. H. Miao, “Coupling study on optical fiber tapers with ccd camera,“ Guangzi Xuebao, vol. 28, no. 10, pp.947-950, October (1999).
[4] L. L. Wang, “Fiber-optical light corn and it’s application,” SCI/TECH information development & economy, vol. 12, no. 6, pp. 87-88, (2002).
[5] F. X. Xin, “Optical fiber coupling technique of iccd,” Infrared and Laser Engineering, vol. 30, no.3, pp. 210-213, June (2001).
[6] T. Alder, A. Stohr, R. Heinzelmann, and D. Jager, “ High-efficiency fiber-to-chip coupling using low-loss tapered single-mode fiber,” IEEE photonics technology letters, vol. 15, no. 8, pp.1016-1018, August (2000).
[7] H. H. Gao, Z. Chen, J. Kumar, S. K. Tripathy, and D. L. Kaplan, “Tapered fiber tips for fiber optic biosensors,“ Optical Engineering, vol. 34, no. 12, pp. 3465-3470, November (1995).
[8] H. Liu, A. Karellas, L. J. Harris, and C. J. D’Orsi, “Optical properties of fiber tapers and their impact on the performance of a fiber optically coupled ccd x-ray imaging system,” Proc. SPIE, vol. 1894, pp. 136-147, September (1993).
[9] Y. Wang, T. Weijian, H. Kun, Z. Wei, and W. Li, “Theoretical analysis of the coupling efficient between fiber taper and ccd,” Acta Photonica Sinica, vol. 33, no. 33, pp. 318-321, March (2004).
[10] B. J. Patrie, J. M. Seitzman, and R. K. Hanson, “Instantaneous three-dimensional flow visualization by rapid acquisition of multiple planar flow images,” Optical Engineering, vol. 33, no. 3, pp. 975-980, March (1994).
[11] 張從國, “ 錐形光纖的理論研究.” 北京交通大學電子資訊工程學院碩士論文, (2010).
[12] C. M. Sun, F. Zhao, and Z. Zhang, “Modeling and simulation of space object optical scattering characteristics using tracepro,” Acta Photonica Sinica, vol. 43, no. 11, p. 1122003, November (2014).
[13] Y. Wang, W. Tian, and X. Bin, “Theoretical model of the modulation transfer function for fiber optic taper,” Proc. SPIE, vol. 5638, pp. 865-872, February (2005).
[14] 方長壽, “以Tracepro輔助科學研究的視覺化.” 國立交通大學理學院科技與數位學習學程碩士論文, (2012).
[15] 葉玉堂、饒建珍、肖峻, 幾何光學. 台灣: 五南圖書出版股份有限公司, 初版, 12月 (2008).
[16] 訊技科技, TracePro快速學習手冊. 台灣: 五南圖書出版股份有限公司, 初版, 2月 (2007).
[17] 廖延彪、黎敏, 光纖光學. 中國: 清華大學出版社, 二版, 8月 (2013).
[18] J. Kerttula, V. Filippov, V. Ustimchik, Y. Chamorovskiy, and O. G. Okhotnikov, “Mode evolution in long tapered fibers with high tapering ratio,” OPTICS EXPRESS, vol. 20, no. 23, November (2012).
[19] C. R. Xue and H. H. Hou, “Structure and characteristics of tapered fiber,” Laser & Infrared, vol. 37, no. 9, pp. 882-884, September (2007).
[20] 林子堯, “以自由曲面之優化方式設計二次光學元件.” 國立中央大學光電科學與工程學系碩士論文, (2015).
[21] 林正斌, “應用於水下環境的光譜可調式LED光學特性研究.” 國立交通大學機械工程學系碩士論文, (2013).
[22] 劉祐丞, “發光二極體背光光源之光學與光機系統設計.” 中華大學機械工程學系碩士論文, (2010).
[23] H. Xin, W. P. Zhang, R. G. Yin, H. Li, L. F. Zhao, and Y. F. Liu, “Coupling efficiency and transmission mode of laser beam in tapered multimode fiber,” Infrared and Laser Engineering, vol. 42, no. 2, pp. 373-375, February (2013).
[24] R. G. Yin, H. Guo, W. W. Liang, W. P. Zhang, and H. Li, “The application of tapered multi-mode fiber in laser signal simulation,” Proc. SPIE, vol. 9684, p. 96843E, September (2016).