隨著超大型積體電路的發展，訊號傳遞的速度已經成為電子系統效能的主要瓶頸，然而近年來因為矽基積體光學(Silicon-Based Integrated Optics)的突破，目前已有相當成熟的光學元件製程以及整合電子與光學系統的技術，若在關鍵的通訊模組採用光學元件，訊號就能以更有效率的方式傳遞，因此，矽基光電系統整合(Optoelectronic System Integration in Silicon)漸漸受矚目。
積體光學的其中一個重要議題為波導(Waveguide)繞線，波導的交錯(Crossing)與彎曲(Bend)的位置，會造成繞射或干涉的現象，使得訊號品質下降，由於光學訊號沒有像電子訊號一般的修復能力，在做波導繞線時應盡量避免可能造成訊號損失的狀況，現今已有相關的文獻，以傳統的演算法為基礎，在保證交錯的數量為最小的前提減少轉彎的數量，然而，在轉彎數量上似乎仍有改進的空間。因此本論文提出了一個以圖形為基礎的演算法來表示轉彎的真實情況，並藉由分組的技術使轉彎數大幅度減少。實驗結果顯示我們提出的方法能有效率降低訊號的損失。

With the advance of Very-Large-Scale Integration (VLSI) circuits, signal propagation delay has become the major bottleneck that limits circuits. Recently, due to the breakthroughs in silicon-based integrated optics, mature optical device process is available now for the integration optics between electronic and optics. If optical devices are used in critical communication module, signals can be propagated in a more efficient way. Therefore, Optoelectronic System Integration in Silicon (OPSIS) has become a popular research direction.
One of the key issues in integrated optics is waveguide routing. Waveguide crossings and bends will incur diffraction and refraction and degrade the signal quality. Unlike electrical signals, optical signals lack the signal restoration capability. Those possible signal losses should be avoided in waveguide routing. There are some previous works that can guarantee the minimal number of crossings and reduce the number of bends based on traditional routing algorithms. However, the number of bends in previous works is still possible to be reduced. Therefore, this thesis proposes a graph-based algorithm to model the waveguide bends and reduce the number of bends by a grouping technique in the graph. The experimental results have demonstrated the efficiency of our methodology on decreasing the signal loss in waveguides.

[1] Christopher Condrat, Priyank Kalla and Steve Blair, “Crossing-Aware Channel Routing for Integrated Optics,” IEEE Transactions Computer-Aided Design of Integrated Circuits and Systems., vol. 33, no. 6,pp. 814–825, Jun. 2014.
[2] Takeshi Yoshimura and Ernest Kuh, “Efficient algorithms for channel routing,” IEEE Transactions Computer-Aided Design of Integrated Circuits and Systems., vol. 1, no. 1,pp. 25–35, Jan. 1982.
[3] Wim Bogaerts, Pieter Dumon, Dries Van Thourhout, and Roel Baets, “Low-loss, low-cross-talk crossings for silicon-on-insulator nanophotonic waveguides,” Optical Society of American., 32(19), pp. 2801-2803. Oct. 2007
[4] Fang Xu and Andrew Poon, “Silicon cross-connect filters using microring resonator coupled multimode-interference-based waveguide crossings,” Optical Society of American., vol. 16, no. 12, pp. 8649–8657, Jun. 2008.
[5] Jaime Cardenas, Carl B. Poitras, Jacob T. Robinson, Kyle Preston, Long Chen and Michal Lipson, “Low loss etchless silicon photonic waveguides,” Optical Society of American., vol. 17, no. 6, pp. 4752–4757, Mar. 2009.

[6] Yurii Vlasov and Sharee McNab, “Losses in single-mode silicon-oninsulator strip waveguides and bends,” Optical Society of American., vol. 12, no. 8,pp. 1622–1631, Apr. 2004.
[7] Yusheng Qian, Seunghyun Kim, Jiguo Song, Gregory P. Nordin, and Jianhua Jiang, “Compact and low loss silicon-on-insulator rib waveguide 90◦ bend,” Optical Society of American., vol. 14,no. 13, pp. 6020–6028, Jun. 2006.
[8] Guoliang Li, Jin Yao, Hiren Thacker, Attila Mekis, Xuezhe Zheng, Ivan Shubin, Ying Luo, Jin-hyoung Lee, Kannan Raj, John E. Cunningham, and Ashok V. Krishnamoorthy, “Ultralow-loss, high-density SOI optical waveguide routing for macrochip interconnects,” Optical Society of American., vol. 20, no. 11, pp. 12035–12039, May 2012.
[9] Kamal Chaudhary and Peter Robinson, “Channel routing by sorting,” IEEE Transactions Computer-Aided Design of Integrated Circuits and Systems., vol. 10, no. 6,pp. 754–760, Jun. 1991.
[10] Jin-Tai Yan, “An improved optimal algorithm for bubble-sorting-based non-Manhattan channel routing,” IEEE Transactions Computer-Aided Design of Integrated Circuits and Systems., vol. 18, no. 2, pp. 163–171, Feb. 1999.

[11] Akihiro Hashimoto, and James G. Stevens, “Wire routing by optimizing channel assignment within large apertures,” in Proc. 8th DAC, New York, NY, USA, 1971, pp. 155–169.
[12] David N. Deutsch, “A dogleg channel router,” in Proc. 13th DAC, New York, NY, USA, 1976, pp. 425–433.
[13] Enrique A. J. Marcatili and Stewart E. Miller,“Improved relationships describing directional control in electromagnetic wave guidance,” Bell Syst. Tech.J., vol. 48, pp. 2161–2188, Jan. 1969.