在光子積體電路中傳輸波導的損耗影響著整個光路的效率，而其中彎曲波導更是重要，本論文致力於研究光學彎曲波導的設計與優化，利用不同窗函數來加寬波導寬度和改變曲率半徑，且對於不同窗函數的彎曲波導進行最佳化，我們的波導為絕緣層覆矽結構(silicon-on-insulator, SOI)，中心波長為1550nm。
根據不同窗函數的彎曲波導設計與模擬結果，在曲率半徑為1μm的情況下，彎曲波導的穿透係數從0.9432提升到0.9504 / 90°，此時的最大波導寬度為819nm，曲率半徑從1μm到0.839μm不等，對於曲率半徑為2μm、3μm而言雖然沒有優化出比前人設計更好的結構，但也根據模擬結果分析出可能的原因。

The transmission of the waveguide in the photonic integrated circuit plays a very important role in the efficiency of the entire circuit, and the bend waveguide is particularly important. This thesis is devoted to design and optimization of the optical curved waveguide, using different window functions to widen waveguide width and changing radius of curvature, and optimized for curved waveguides with different window functions. Our waveguide is a silicon-on-insulator (SOI) structure with a center wavelength of 1550nm, waveguide height of 220nm, and waveguide width (ω_0) is 450 nm.
According to the design and simulation results of the curved waveguide with different window functions, when the radius of curvature is 1 μm, the transmission coefficient of the curved waveguide is increased from 0.9432 to 0.9504 / 90°, the maximum waveguide width is 819 nm, and the radius of curvature is from 1 μm to 0.839μm, and for the radius of curvature of 2μm and 3μm, although a better structure was not optimized, the possible reasons were also analyzed according to the simulation results.

1. Wim Bogaerts, Roel Baets, Pieter Dumon, Vincent Wiaux, Stephan Beckx, Dirk Taillaert, Bert Luyssaert, Joris Van Campenhout, Peter Bienstman, and Dries Van Thourhout, "Nanophotonic Waveguides in Silicon-on-Insulator Fabricated With CMOS Technology", Journal of Lightwave Technology 23(1), pp. 401-412(2005).
2. Andy Eu-Jin Lim, Junfeng Song, Qing Fang, Chao Li, Xiaoguang Tu, Ning Duan, Kok Kiong Chen, Roger Poh-Cher Tern, and Tsung-Yang Liow, "Review of Silicon Photonics Foundry Efforts", IEEE Journal of Selected Topics in Quantum Electronics 20(4), pp. 405-416 (2014).
3. Yurii A. Vlasov ,Sharee J. McNab, "Losses in single-mode silicon-on-insulator strip waveguides and bends ", Optics Express 12(8), pp. 1622-1631 (2004).
4. Jason S. Orcutt, Benjamin Moss, Chen Sun, Jonathan Leu, Michael Georgas, Jeffrey Shainline, Eugen Zgraggen, Hanqing Li, Jie Sun, Matthew Weaver, Stevan Urošević, Miloš Popović, Rajeev J. Ram, and Vladimir Stojanović, "Open foundry platform for high-performance electronic-photonic integration", Optics Express 20(11), pp. 12222-12232 (2012).
5. Xia Chen, Stevan Stanković, Scott Reynolds, Thalía Domínguez Bucio, Ke Li, David J. Thomson, Frederic Gardes, Graham T. Reed, "The Emergence of Silicon Photonics as a Flexible Technology Platform", Proceedings of the IEEE 106(12), pp. 2101-2116 (2018).
6. Benjamin G. Lee, and Nicolas Dupuis, "Silicon Photonic Switch Fabrics: Technologyand Architecture", Journal of Lightwave Technology 37(1), pp. 6-20 (2019).
7. Sarvagya Dwivedi, "Calibration-free Si-SiN Optical Phased Array", OSA Advanced Photonics Congress (IPR, Networks, NOMA, PVLED, SPPCom), Paper IM4A.3 (2019).
8. Tsutomu Kitoh, Norio Takato, Mitsuho Yasu, and Masao Kawachi, "Bending Loss Reduction in Silica-Based Waveguides by Using Lateral Offsets", Journal of Lightwave Technology 13(4), pp. 555-562 (1995).
9. Jeong Hwan Song, Tangla D. Kongnyuy, Andim Stassen, Vignesh Mukund, and Xavier Rottenberg, "Adiabatically Bent Waveguides on Silicon Nitride Photonics for Compact and Dense Footprints", IEEE Photonics Technology Letters 28(20), pp. 2164-2167 (2016).
10. Takeshi Fujisawa, Shuntaro Makino, Takanori Sato, and Kunimasa Saitoh, "Low-loss, compact, and fabrication-tolerant Si-wire 90° waveguide bend using clothoid and normal curves for large scale photonic integrated circuits", Optics Express 25(8), pp. 9150-9159 (2017).
11. Florian Vogelbacher, Stefan Nevlacsil, Martin Sagmeister, Jochen Kraft, Karl Unterrainer, and Rainer Hainberger, "Analysis of silicon nitride partial Euler waveguide bends", Optics Express 27(22), pp. 31394-31406 (2019).
12. Robert N. Sheehan, Steven Horne, Frank H. Peters, "The design of low-loss curved waveguides", Optical and Quantum Electronics volume 40, pp. 1211-1218 (2008)
13. Matteo Cherchi, Sami Ylinen, Mikko Harjanne, Markku Kapulainen, and Timo Aalto, "Dramatic size reduction of waveguide bends on a micron-scale silicon photonic platform", Optics Express 21(15), pp. 17814-17823 (2013).
14. Wim Bogaerts, Shankar Kumar Selvaraja, "Compact Single-Mode Silicon Hybrid Rib/Strip Waveguide With Adiabatic Bends", IEEE Photonics Journal 3(3), pp. 422-432 (2011).
15. Christian Koos, Christopher G. Poulton, Lars Zimmermann, Lenin Jacome, Juerg Leuthold, Wolfgang Freude, "Ideal Bend Contour Trajectories for Single-Mode Operation of Low-Loss Overmoded Waveguides", IEEE Photonics Technology Letters 19(11), pp. 819-821 (2007).
16. Jeong Hwan Song, Tangla D. Kongnyuy, Peter De Heyn, Sebastien Lardenois, Roelof Jansen, and Xavier Rottenberg, "Low-Loss Waveguide Bends by Advanced Shape for Photonic Integrated Circuits", Journal of Lightwave Technology 38(12), pp. 3273-3279 (2020).
17. Jeong Hwan Song, T.D. Kongnyuy, N. Hosseini, A. Stassen, R. Jansen, X. Rottenberg, "Advanced waveguide bends for photonic integrated circuits", 45th European Conference on Optical Communication, P53/SC2, Dublin, Ireland (2019).
18. Kane Yee, "Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media", IEEE Transactions on Antennas and Propagation 14(3), pp. 302-307 (1966).
19. Meisam Bahadori, Mahdi Nikdast, Qixiang Cheng, Keren Bergman, "Universal Design of Waveguide Bends in Silicon-on-Insulator Photonics Platform", Journal of Lightwave Technology 37(13), pp. 3044-3054 (2019).
20. Philippe P. Absil, Peter De Heyn, Hongtao Chen, Peter Verheyen, Guy Lepage, Marianna Pantouvaki, Jeroen De Coster, Amit Khanna, Youssef Drissi, Dries Van Thourhout, Joris Van Campenhout, "Imec iSiPP25G silicon photonics: a robust CMOS-based photonics technology platform", Proc. of SPIE 9367, 93670V (2015).