臺灣博碩士論文加值系統

在多模干涉(Multimode interference, MMI)耦合器與對稱曲線錐形波導相結合製作在絕緣層上覆矽(Silicon-on-insulator, SOI)上，具有最佳絕熱模態轉換(adiabatic mode conversion)並且有最大輸出功率。從單模波導傳輸到臨界線性錐形波導與多模波導結合的TE0模態為絕熱模態轉換，TE0模態成分比例為97.87%以上，TE2和其他模態成分比例低於2.13%，此時的線性錐形波導具有最大發散角θmax。1x1 MMI耦合器與該線性錐形波導組合下，最大發散角經驗方程式為 θmax = 2tan-1 [(0.35 Wmmi - Ws) / (0.172 Lmmi)]，且通過1x1 MMI耦合器三種不同多模波導寬度Wmmi為4 m / 8 m / 12 m且多模波導寬度Lmmi為28.7 um / 113.0 um / 257.2 um與設計的線性錐形波導相結合，並證明其元件輸出功率必定為0.95以上，則1x1 MMI耦合器三種不同多模波導寬度的最大發散角θmax 為 16 / 14 / 8，一對的線性錐形波導損耗分別為0.022dB / 0.172dB / 0.158dB。線性錐形波導最大發散角θmax與發散角θ為1時的線性錐形波導長度Lt相比較，各別縮短93.7% / 92.9% / 87.5%。
反向拋物線錐形波導被證明具有高效率模態耦合，TE0模態輸出成分比例在反向拋物線錐形波導中為99.13%，相較於線性錐形波導輸出97.87%增加1.26%，提供最佳絕熱模態轉換。1x1 MMI耦合器與反向拋物線錐形波導相結合的輸出功率為0.96；相較於1x1 MMI耦合器沒有錐形波導的輸出功率為0.41增加134.15%。該反向拋物線錐形波導的最短長度Lt為20.2 m，比線性錐形波導長度為27.2 m縮短25.73%。

A multimode interference (MMI) coupler is combined with a symmetrically curved tapered waveguide on a silicon-on-insulator (SOI) chip for optimal adiabatic mode conversion and maximum output power. When TE0 mode is a critical adiabatic mode conversion from a single-mode waveguide to an extreme linear tapered waveguide combined with a MMI coupler, so this linear tapered waveguide is achieved to the maximum divergence angle. The TE0 mode component ratio is 97.87% above, and the TE2 and other mode component ratios are 2.13% below. The maximum divergence angle is expressed byθmax  2tan-1[(0.35 Wmmi - Ws) / (0.172 Lmmi)] under a 1x1 MMI coupler combined with this linear tapered waveguide. The expression formula is demonstrated by three different widths of multimode waveguide Wmmi of 4 m / 8 m / 12 m and length of multimode waveguide Lmmi of 28.7 m / 113.0 m / 257.2 m combined with the designed linear tapered waveguide. So the maximum divergence angle is obtained atθmax  16 / 14 / 8, respectively with respect to a pair of linear tapered waveguide loss of 0.022 dB / 0.172 dB / 0.158 dB and this linear tapper length is reduced by 93.7% / 92.9% / 87.5% than the divergence angle  = 1. The output power of a 1x1 MMI coupler combined with a critical linear tapered waveguide is at least 0.95.
An inverse parabolic tapered waveguides have been demonstrated to have high efficiency modal coupling. In the inverse parabolic tapered waveguide, the TE0 mode component ratio is 99.13%, which is an increase of 1.26% compared to 97.87% of the linear tapered waveguide output, provides the best adiabatic mode conversion. The output power of a 1x1 MMI coupler combined with this inverse parabolic tapered waveguide is 0.96, which is 134.15% more than a basic MMI coupler without tapered waveguide output power 0.41. The shortest length Lt of this inverse parabolic tapered waveguide is 20.2 m, which is 25.73% smaller than a linear tapered waveguide length 27.2 m.

中文摘要 i
英文摘要 iii
致謝 v
目錄 vi
圖目錄 ix
表目錄 xii
符號說明 xiii
第一章 緒論 1
1.1 研究動機 1
1.2 論文架構 4
第二章 基本理論及模擬方法 7
2.1 絕緣層上覆矽波導結構 7
2.1.1 有效折射率法 (Effective index method) 8
2.1.2 特徵模態擴展方法 (Eigenmode expansion method) 11
2.2 多模干涉基本理論 15
2.3 多模干涉模態傳輸分析 21
2.4 一般干涉(General interference) 24
2.4.1 單一成像(Single images) 25
2.4.2 多重成像(Multiple images) 27
2.5 限制干涉(Restricted interference) 28
2.5.1 成對干涉(Paired interference) 28
2.5.2 對稱干涉(Symmetric interference) 30
第三章 最大發散角經驗方程式建立 34
3.1 基本1x1多模干涉耦合器 34
3.2 線性錐形波導之絕熱模態轉換 39
3.3 線性錐形波導之最大發散角經驗方程式 43
第四章 最佳曲線錐形波導分析 56
4.1 曲錐形波導幾何結構 56
4.2 直線錐形波導分析 59
4.3 凹彎曲錐形波導分析 63
4.4 凸彎曲錐形波導分析 67
4.5 最佳曲線錐形波導 72
第五章 結論 74
未來工作 77
參考文獻 78
研究著作 82

[1] R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quant., vol. 12, no. 6, pp. 1678-1687, 2006.
[2] M. Lipson, “Guiding, modulating, and emitting light on silicon-challenges and opportunities,” J. Lightwave Technol., vol. 23, no. 12, pp. 4222-4238, 2005.
[3] Kevin Kruse and Christopher T. Middlebrook, “Polymer taper bridge for silicon waveguide to single mode waveguide coupling,” Opt. Commun., vol. 362, pp. 87-95, 2016.
[4] J. Guo and Y. Zhao, “Analysis of Mode Hybridization in Tapered Waveguides,” IEEE Photonic. Tech. L., vol. 27, no. 23, pp. 2441–2444, 2015.
[5] C. Sun, Y. Yu, G. Chen and X. Zhang, “A Low Crosstalk and Broadband Polarization Rotator and Splitter Based on Adiabatic Couplers,” IEEE Photon. Tech. Lett., vol. 28, no. 20, pp. 2253-2256, 2016.
[6] Daoxin Dai and Ming Zhang, “Mode hybridization and conversion in silicon-on-insulator nanowires with angled sidewalls,” Opt. Express, vol. 23, no. 25, pp. 32452-32464, 2015.
[7] Yunfei Fu, Tong Ye, W. Tang and Tao Chu, “Efficient adiabatic silicon-on-insulator waveguide taper,” Photon. Res., vol. 2, no. 3, pp. A41-A44, 2014.
[8] E. H. Khoo, A. Q. Liu and J. H. Wu, “Nonuniform photonic crystal taper for high-efficiency mode coupling,” Opt. Express, vol. 13, no. 20, pp. 7748-7759, 2005.
[9] S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis and J. D. Joannopoulos, “Adiabatic theorem and continuous couple-mode theory for efficient taper transition,” Phys. Rev., vol. E 66, no. 6, pp. 066608, 2002.


[10] H. Zhou, J. Song, C. Li, H. Zhang and P. G. Lo, “A library of ultra-compact multimode interference optical couplers on SOI,” IEEE Photon. Tech. L., vol. 25, no. 12, pp. 1149-1152, 2013.
[11] Jijiang Wu, Bangren Shi and Mei Kong, “Exponentially tapered multimode interference couplers,” Chin. Opt. Lett., vol. 4, no. 3, pp. 167-169, 2006.
[12] Wim Bogaerts, Pieter Dumon, Dries Van Thourhout and Roel Baets, “Low-loss, low-cross-talk crossings for silicon-on-insulator nanophotonic waveguides,” Opt. Lett., vol. 32, no. 19, pp. 2801-2803, 2007.
[13] D. J. Thomson, Y. Hu, G. T. Reed and J. Fedeli, “Low Loss MMI Couplers for High Performance MZI Modulators,” IEEE Photon. Tech. L., vol. 22, no. 20, pp. 1485-1487, 2010.
[14] Z. Sheng et al., “A Compact and Low-Loss MMI Coupler Fabricated With CMOS Technology,” IEEE Photonics J., vol. 4, no. 6, pp. 2272-2277, 2012.
[15] W. P. Huang and C. L. Xu, “Simulation of three-dimensional optical waveguides by a full-vector beam propagation method,” IEEE Journal of Quantum Electronics, vol. 29, no. 10, pp. 2639-2649, 1993.
[16] D. F. G. Gallagher and T. P. Felici, “Eigenmode expansion methods for simulation of optical propagation in photonics: pros and cons,” Proc. SPIE, vol. 4987, pp. 69-82, 2003.
[17] A. M. Prabhu, A. Tsay, Z. Han, and V. Van, “Ultracompact SOI microring add-drop filter with wide bandwidth and wide FSR,” IEEE Photonics Technology Letters., vol. 21, no. 10, pp. 651-653, 2009.
[18] P. K. Bhattacharya, Semiconductor Optoelectronic Devices, Englewood Cliffs, Prentice Hall, NJ, USA, 1998.
[19] O. Bryngdahl, “ Image formation using self-imaging techniques,” J. Opt. Soc. Am., vol. 63, no. 4, pp.416-419, 1973.
[20] R. Uleich and G. Ankele, “Self-imaging in homogenoous planar optical waveguides,” Appl. Phys. Lett., vol. 27, no. 6, pp.337-339, 1975.
[21] L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: Principles and applications,” J. Lightwave Technol., vol. 13, no. 4, pp. 615-627, 1995.
[22] Ricky W. Chuang, Zhen-Liang Liao, and Chih-Kai Chang,” Integrated optical beam splitters employing symmetric mode mixing in SiO2/SiON/SiO2 multimode interference waveguides,” Japan. J. Appl. Phys., vol. 46, no. 4B, pp.2440-2444, 2007.
[23] D. C. Chang and E. F. Kuester, “A hybrid method for paraxial beam propagation in multimode optical waveguides,” IEEE Trans. Microwave Theory Tech., vol.29, no. 9, pp.923-933, 1981.
[24] M. Bachmann, P.A.Besse, and H. Melchior, “General self-imaging properties in NxN multi-mode interference couplers including phase relations,” Appl. Opt., vol. 33, no. 18, pp.3905-3911, 1994.
[25] R. M. Jenkins, R.W. J. Deveraux, and J. M. Heaton, “Waveguide beam splitters and recombiners based on multimode propagation phenomena,” Opt. Lett., vol. 17, no. 14, pp.991-993, 1992.
[26] J. M. Heaton, R. M. Jenkins, D. R. Wight, J. T. Parker, “A novel waveguide Mach-Zehnder interferometer based on multimode interference phenomena,” Optics Commun., vol. 109, no. 3, pp.410-424, 1994.
[27] R. Ulrich and T. Kamiya, “Resolution of self-images in planar optical waveguides,” J. Opt. Soc. Amer., vol. 68, no. 5, pp. 583-592, 1978.
[28] Integrated Optics Software FIMMWAVE 5.2, Photon Design, Oxford, U.K. [Online]. Available:http://www.photond.com
[29] A. S. Sudbo, “Film mode matching- a versatile numerical method for vector mode field calculations in dielectric waveguides,” Pure Appl. Opt., vol. 2, no. 3, pp. 211-233, 1993.
[30] M. Bachmann, P. A. Besse and H. Melchior, “Overlapping-image multimode interference couplers with a reduced number of self-images for uniform and nonuniform power splitting,” Appl. Opt., vol. 34, no. 30, pp. 6898-6910, 1995.
[31] Y. Liu, W. Sun, H. Xie, N. Zhang, K. Xu, Y. Yao, S. Xiao and Q. Song, “Adiabatic and ultra-compact waveguide tapers based on digital metamaterials,” IEEE J. Sel. Top. Quant., vol. 25, no. 3, pp. 1-6, 2018.
[32] P. P. Sahu, “Parabolic tapered structure for an ultracompact multimode interference coupler,” Appl. Opt., vol. 48, no. 2, pp. 206-211, 2009.
[33] P. Sethi, A. Haldar, and S. K. Selvaraja, “Ultra-compact low-loss broadband waveguide taper in silicon-on-insulator,” Opt. Express, vol. 25, no. 9, pp. 10196-10203, 2017.
[34] J. Zhang, Y. Yang, H. Xin, J. Huang, D. Chen, and Z. Zhang, “Ultrashort and efficient adiabatic waveguide taper based on thin flat focusing lenses,” Opt. Express, vol. 25, no. 17, pp. 19894-19903, 2017.
[35] Jing Wang, Minghao Qi, Yi Xuan, Haiyang Huang, You Li, Ming Li, Xin Chen, Qi Jia, Zhen Sheng, Aimin Wu, Wei Li, Xi Wang, Shichang Zou and Fuwan Gan. “Proposal for fabrication-tolerant SOI polarization splitter-rotator based on cascaded MMI couplers and an assisted bi-level taper,” Opt. Express, vol. 22, no. 23, pp. 27869-27879, 2014.
[36] Y. Zhang et al., “A CMOS-Compatible, Low-Loss, and Low-Crosstalk Silicon Waveguide Crossing,” IEEE Photon. Tech. L., vol. 25, no. 5, pp. 422-425, 2013.
[37] Daoxin Dai, Yongbo Tang and John E Bowers, “Mode conversion in tapered submicron silicon ridge optical waveguides,” Opt. Express, vol. 20, no. 12, pp. 13425-13439, 2012.
[38] C. Chen and C. Chiu, “Taper-integrated multimode interference based waveguide crossing design,” IEEE J. Quantum. Elect., vol. 46, no. 11, pp. 1656-1661, 2010.