本研究利用具凸透反射鏡之全像干涉曝光系統，在基板上形成連續漸變週期光柵結構，最終將該結構應用於波導模態共振及啁啾布拉格光柵兩種光學元件上。波導模態共振元件是在連續漸變週期光柵上蒸鍍上一層Ta2O5材料形成波導光柵結構，當入射光波長滿足相位匹配條件時便會產生高反射的現象，為了滿足漸變週期光柵在各個位置的相位匹配條件，我們利用金屬遮罩輔助電子束蒸鍍，成功在波導模態共振元件上形成厚度連續漸變的Ta2O5薄膜並幾乎滿足各個位置的相位匹配條件，最終實現波長範圍500 ~ 700 nm的窄線寬濾波器，在垂直極化及水平極化下線寬僅有4.2及0.78 nm，且連續漸變的結構使得該元件同時具備光譜重現的特性，作為光譜儀亦有相當好的特性。
此外，本研究也將連續漸變週期光柵結構應用於啁啾布拉格光柵上，由於波導上各處的光柵週期不同，因此反射的布拉格波長具有群體延遲的特性，這使得該元件具有色散補償或脈衝壓縮的效果。在該項目中光柵材料為氧化石墨烯，光柵週期在1 cm的長度下僅有8.29 nm的變化，而後利用基板轉移技術將週期變化緩慢的光柵結構覆蓋在矽波導上，形成啁啾布拉格光柵元件，在O band的工作波段內有超過20 nm的反射頻寬，最高E/R值約為20 dB，未來若將該技術應用於C band的工作範圍上，應能實現相當有效的色散補償器。

In this work, continuously-chirped grating structures are formed on the substrate by utilizing the laser interference lithography system equipped with a convex mirror. As-formed chirped grating structures are applied to implement guided mode resonance (GMR) filters and the on-chip chirped Bragg gratings. The GMR filter is formed by depositing a high-refractive-index Ta2O5 film atop continuously-chirped gratings. To fulfill the phase-matching condition of the grating at each position, we utilized metal-mask to assist e-beam evaporation and successfully form a continuously-gradient Ta2O5 film on the GMR filter. As a result, we successfully demonstrated narrow bandwidth filters with an operating wavelength range of 500~700 nm. The bandwidth of the transmission dips is 4.2 and 0.78 nm for vertical and horizontal polarization direction, respectively. The proposed chirped GMR filter can serve as a dispersive element for on-chip spectroscopy with superior resolution.
In this study we also implement chirped waveguide Bragg gratings using continuously gradient-period grating structures. Chirped gratings provide spatially varied grating period that enables linear group delay response, thus enables applications in dispersion compensation or pulse compression. Gradient-period graphene oxide (GO) gratings (ΔP = 8.29 nm/cm) are implemented for the following transfer onto a silicon strip waveguide using PMMA-assisted transfer process. The resulting device provides a broad reflection bandwidth of over 20 nm and an extinction ratio of up to 20 dB for 1-cm-long GO/silicon hybrid chirped gratings in the O band wavelengths.

中文審定書. i
英文審定書 ii
致謝 iii
中文摘要. iv
Abstract v
圖目錄. ix
表目錄 xiii
第一章 緒論 1
1-1 研究背景 . 1
1-2 研究動機 . 2
第二章 漸變週期光柵 7
2-1 文獻回顧 . 7
2-2 次波長光柵製程 . 10
2-2.1 平坦化光場全像干涉系統 . 10
3-1.2 漸變週期光柵曝光系統 . 12
2-3 光柵檢測系統 . 14
2-3.1 掃描式電子束顯微鏡(Scanning electron microscope, SEM) 14
2-3.2 原子力顯微鏡(Atomic force microscope, AFM) . 15
2-3.3 光柵繞射系統(Diffraction system) . 17
第三章 波導模態共振元件 24
3-1 文獻回顧 . 24
3-1.1 高對比折射率光柵 . 24
3-1.2 漸變式波導模態共振濾波器 . 26
3-1.3 波導模態共振頻譜儀 . 28
3-2 波導模態共振原理 29
3-3 波導模態共振原理之特性 31
3-3.1 極化選擇性 . 31
3-3.2 共振線寬 . 31
3-4 嚴格耦合波分析 33
3-4.1 嚴格耦合波分析原理 . 33
3-4.2 弱調制波導光柵 . 36
3-5 波導模態共振濾波器模擬 38
3-6 波導模態共振濾波器製程 41
3-6.1 漸變週期光柵製程 . 41
3-6.2 波導模態共振濾波器製程 . 42
3-7 波導模態共振元件製程結果 45
3-7.1 漸變週期光柵檢測 . 45
3-7.2 Ta2O5 漸變厚度 46
3-8 波導模態共振元件量測 47
3-8.1 量測系統 . 47
3-8.2 可見光濾波器量測 . 48
3-8.3 單波長雷射濾波器量測 . 50
3-8.4 光譜重建 . 52
第四章 啁啾布拉格光柵 54
4-1 文獻回顧 . 54
4-2 布拉格光柵原理 54
4-3 數值分析 58
4-3.1 轉移矩陣法 . 58
4-3.2 特徵模態展開法 . 61
4-4 啁啾布拉格光柵製程 62
4-4.1 氧化石墨烯介紹 . 62
4-4.2 氧化石墨烯製備 . 63
4-4.3 氧化石墨烯光柵製程 . 64
4-4.4 光柵基板轉移技術 . 65
4-5 氧化石墨烯光柵檢測 66
4-5.1 拉曼光譜學 . 66
4-5.2 大面積氧化石墨烯微結構製程 . 68
4-6 啁啾布拉格光柵製程結果 70
4-7 啁啾布拉格光柵量測 72
4-7.1 矽波導晶片量測系統 . 72
4-7.2 啁啾布拉格光柵量測 . 73
第五章 結論及未來工作 74
5-1 結論 74
5-1.1 波導模態共振元件 . 74
5-1.2 啁啾布拉格光柵 . 75
5-2 未來工作 76
5-2.1 二維波導模態共振元件 . 76
5-2.2 全頻譜波導模態共振元件 . 77
5-2.3 優化啁啾布拉格光柵 . 77
第六章 參考文獻 79

[1] Lee, K. J., et al. "Silicon-layer guided-mode resonance polarizer with 40-nm bandwidth." IEEE Photonics Technology Letters 20.22 (2008): 1857-1859.
[2] Lin, Hsin-An, and Cheng-Sheng Huang. "Linear variable filter based on a gradient grating period guided-mode resonance filter." IEEE Photonics Technology Letters 28.9 (2016): 1042-1045.
[3] Triggs, Graham J., et al. "Chirped guided-mode resonance biosensor." Optica 4.2 (2017): 229-234.
[4] Saleem, M. R., et al. "Bio-molecular sensors based on guided mode resonance filters." IOP Conference Series: Materials Science and Engineering. Vol. 146. No. 1. IOP Publishing, 2016.
[5] Boonruang, Sakoolkan, and Waleed S. Mohammed. "Multiwavelength guided mode resonance sensor array." Applied Physics Express 8.9 (2015): 092004.
[6] Lv, Changwu, et al. "Angle-resolved diffraction grating biosensor based on porous silicon." Journal of Applied Physics 119.9 (2016): 094502.
[7] Tabassum, Shawana, Ratnesh Kumar, and Liang Dong. "Nanopatterned optical fiber tip for guided mode resonance and application to gas sensing." IEEE Sensors Journal 17.22 (2017): 7262-7272.
[8] Fortin, Gilles, and Nathalie McCarthy. "Chirped holographic grating used as the dispersive element in an optical spectrometer." Applied optics 44.23 (2005): 4874-4883.
[9] Katzir, A., et al. "Chirped gratings in integrated optics." IEEE Journal of Quantum Electronics 13.4 (1977): 296-304.
[10] Liu, Ke, et al. "One‐Step fabrication of graded rainbow‐colored holographic photopolymer reflection gratings." Advanced Materials 24.12 (2012): 1604-1609.
[11] 高子杰,連續漸變週期光柵的實現與應用,中山大學光電工程學系研究所學位碩士論文, 2017.
[12] http://lifeng.lamost.org/courses/astrotoday/CHAISSON/AT304/HTML/AT30401.HTM.
[13] http://physexp.thu.edu.tw/~kuan/OE_LAB/index-2-1-7.html
[14] Tan, Dawn TH, Pang C. Sun, and Yeshaiahu Fainman. "Monolithic nonlinear pulse compressor on a silicon chip." Nature communications 1 (2010): 116.
[15] Zou, Zhi, et al. "Channel-spacing tunable silicon comb filter using two linearly chirped Bragg gratings." Optics express 22.16 (2014): 19513-19522.
[16] Ouellette, Francois. "Dispersion cancellation using linearly chirped Bragg grating filters in optical waveguides." Optics letters 12.10 (1987): 847-849.
[17] 施峻富,可圖案轉移之氧化石墨烯光柵薄膜的實現與應用,中山大學光電工程學系研究所學位碩士論文,2016.
[18] Chou, Stephen Y., Peter R. Krauss, and Preston J. Renstrom. "Imprint of sub‐25 nm vias and trenches in polymers." Applied physics letters 67.21 (1995): 3114-3116.
[19] Gabor, Dennis. "A new microscopic principle." (1948): 777.
[20] Byun, Ikjoo, and Joonwon Kim. "Cost-effective laser interference lithography using a 405 nm AlInGaN semiconductor laser." Journal of Micromechanics and Microengineering 20.5 (2010): 055024.
[21] Ohira, T., et al. "InP 2D nano-structures fabricated by two-time laser holography." Indium Phosphide and Related Materials, 2001. IPRM. IEEE International Conference On. IEEE, 2001.
[22] Mao, Weidong, Ishan Wathuthanthri, and Chang-Hwan Choi. "Tunable two-mirror laser interference lithography system for large-area nano-patterning." Alternative Lithographic Technologies III. Vol. 7970. International Society for Optics and Photonics, 2011.
[23] 張漢榮,利用勞氏鏡干涉架構搭配光場強度均勻器製作晶圓級奈米圖案,中山大學光電工程學系研究所學位碩士論文, 2016
[24] https://www.materialsnet.com.tw/AD/ADImages/AAADDD/MCLM100/download/equipment/EM/FE-SEM/FE-SEM005.pdf
[25] http://web1.knvs.tp.edu.tw/AFM/ch4.htm
[26] http://www.teo.com.tw/prodDetail.asp?id=1344
[27] Rao, Yi, et al. "Long-wavelength VCSEL using high-contrast grating." IEEE Journal of Selected Topics in Quantum Electronics 19.4 (2013): 1701311-1701311.
[28] Karagodsky, Vadim, and Connie J. Chang-Hasnain. "Physics of near-wavelength high contrast gratings." Optics express 20.10 (2012): 10888-10895.
[29] Ferrara, James, et al. "Heterogeneously integrated long-wavelength VCSEL using silicon high contrast grating on an SOI substrate." Optics express 23.3 (2015): 2512-2523.
[30] Magnusson, Robert, and Mehrdad Shokooh-Saremi. "Physical basis for wideband resonant reflectors." Optics express 16.5 (2008): 3456-3462.
[31] Magnusson, Robert, Mehrdad Shokooh-Saremi, and Xin Wang. "Dispersion engineering with leaky-mode resonant photonic lattices." Optics Express 18.1 (2010): 108-116.
[32] Mateus, Carlos FR, et al. "Ultrabroadband mirror using low-index cladded subwavelength grating." IEEE Photonics Technology Letters 16.2 (2004): 518-520.
[33] Zheng, Gaige, et al. "Angle-insensitive and narrow band grating filter with a gradient-index layer." Optics letters 39.20 (2014): 5929-5932.
[34] Lin, Hsin-An, and Cheng-Sheng Huang. "Linear variable filter based on a gradient grating period guided-mode resonance filter." IEEE Photonics Technology Letters 28.9 (2016): 1042-1045.
[35] Lin, Hsin-An, et al. "Compact spectrometer system based on a gradient grating period guided-mode resonance filter." Optics Express 24.10 (2016): 10972-10979.
[36] Lin, Hsin-An, Hsin-Yun Hsu, and Cheng-Sheng Huang. "Compact wavelength detection system based on a gradient grating period guided-mode resonance filter." Lasers and Electro-Optics (CLEO), 2016 Conference on. IEEE, 2016.
[37] Fang, Chaolong, et al. "Tunable guided-mode resonance filter with a gradient grating period fabricated by casting a stretched PDMS grating wedge." Optics letters 41.22 (2016): 5302-5305.
[38] Dobbs, Dennis W., Irena Gershkovich, and Brian T. Cunningham. "Fabrication of a graded-wavelength guided-mode resonance filter photonic crystal." Applied physics letters 89.12 (2006): 123113.
[39] Ganesh, Nikhil, et al. "Compact wavelength detection system incorporating a guided-mode resonance filter." Applied physics letters 90.8 (2007): 081103.
[40] Liu, Longju, et al. "Fabricating a linear variable filter using nanoreplica molding." Lasers and Electro-Optics (CLEO), 2016 Conference on. IEEE, 2016.
[41] Wood, Robert Williams. "XLII. On a remarkable case of uneven distribution of light in a diffraction grating spectrum." The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 4.21 (1902): 396-402.
[42] Hessel, A., and A. A. Oliner. "A new theory of Wood’s anomalies on optical gratings." Applied optics 4.10 (1965): 1275-1297.
[43] Moharam, M. G., and T. K. Gaylord. "Rigorous coupled-wave analysis of planar-grating diffraction." JOSA 71.7 (1981): 811-818.
[44] 周柏仰, 波導共振模態濾波器的製作與模擬, 交通大學電子工程學系研究所學位碩士論文, 2010.
[45] 賴國偉, 波導模態共振之元件應用, 交通大學電子工程學系研究所學位碩士論文, 2011.
[46] Inoue, Junichi, et al. "Reflection characteristics of guided-mode resonance filter combined with bottom mirror." Optics letters 39.7 (2014): 1893-1896.
[47] Wang, S. S., et al. "Guided-mode resonances in planar dielectric-layer diffraction gratings." JOSA a 7.8 (1990): 1470-1474.
[48] Shin, DongHo, et al. "Thin-film optical filters with diffractive elements and waveguides." Optical Engineering 37.9 (1998): 2634-2647.
[49] Uchida, Naoya. "Calculation of diffraction efficiency in hologram gratings attenuated along the direction perpendicular to the grating vector." JOSA 63.3 (1973): 280-287.
[50] D. K. Cheng, Field and wave electromagnetic, Tsinghuna University Press, 1989.
[51] Moharam, M. G., et al. "Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings." JOSA A 12.5 (1995): 1068-1076.
[52] https://www.samcointl.com
[53] http://opto-equipment.etrading.com.tw
[54] Hill, K. O., et al. "Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication." Applied physics letters 32.10 (1978): 647-649.
[55] Kawasaki, Brian S., et al. "Narrow-band Bragg reflectors in optical fibers." Optics Letters 3.2 (1978): 66-68.
[56] Capmany, José, David Domenech, and Pascual Muñoz. "Silicon graphene Bragg gratings." Optics Express 22.5 (2014): 5283-5290.
[57] http://psroc.org.tw/bimonth/download.php?d=1&cpid=184&did=4
[58] Pramanik, Avijit, et al. "Extremely high two-photon absorbing graphene oxide for imaging of tumor cells in the second biological window." The journal of physical chemistry letters 5.12 (2014): 2150-2154.
[59] Yavuz, S., et al. "Graphene oxide as a p-dopant and an anti-reflection coating layer, in graphene/silicon solar cells." Nanoscale 8.12 (2016): 6473-6478.
[60] Szabó, Tamás, Anna Szeri, and Imre Dékány. "Composite graphitic nanolayers prepared by self-assembly between finely dispersed graphite oxide and a cationic polymer." Carbon 43.1 (2005): 87-94.
[61] Park, Sungjin, and Rodney S. Ruoff. "Chemical methods for the production of graphenes." Nature nanotechnology 4.4 (2009): 217.
[62] Chen, Chun-Hu, et al. "Effective Synthesis of Highly Oxidized Graphene Oxide That Enables Wafer-scale Nanopatterning: Preformed Acidic Oxidizing Medium Approach." Scientific reports 7.1 (2017): 3908.
[63] Hsu, Hsin-Yun, Yi-Hsuan Lan, and Cheng-Sheng Huang. "A Gradient Grating Period Guided-Mode Resonance Spectrometer." IEEE Photonics Journal 10.1 (2018): 1-9.
[64] Li, Erwen, et al. "Broadband on-chip near-infrared spectroscopy based on a plasmonic grating filter array." Optics letters 41.9 (2016): 1913-1916.