進階搜尋


下載電子全文  
系統識別號 U0026-2008201912403500
論文名稱(中文) 一維週期性介電質奈米結構的連續體束縛態之FDTD模擬分析
論文名稱(英文) Bound States in Continuum for 1D Periodic Dielectric Nanostructures analyzed by Finite Difference Time Domain method
校院名稱 成功大學
系所名稱(中) 光電科學與工程學系
系所名稱(英) Department of Photonics
學年度 107
學期 2
出版年 108
研究生(中文) 陳奇葆
研究生(英文) Chi-Pao Chen
學號 L76061210
學位類別 碩士
語文別 中文
論文頁數 40頁
口試委員 指導教授-張世慧
口試委員-張亞中
口試委員-陳宣燁
口試委員-吳品頡
中文關鍵字 有限差分時域法  週期性邊界條件  光子晶體  連續體束縛態 
英文關鍵字 FDTD  periodic boundary conditions  photonic crystal  bound state in continuum 
學科別分類
中文摘要 光子晶體因為其中週期性的介電係數,能夠產生許多特殊的現象,例如當光在晶體中傳播時,會因為每層結構之間的交互作用而出現破壞性干涉,這些破壞性干涉會導致某些頻率無法在其中傳播,而這些頻率所覆蓋的區域便稱為光子能隙,光子晶體的能帶結構也因此被分為上下兩部分。由光子晶體所組成的波導,其中可以發現連續體中的束縛態(BIC),這些特殊的模態由波源連續頻譜外的束縛態所引起,並且在連續頻譜中它的能量會持續疊加,因此它具有很高的品質因數而被廣泛的應用。連續體束縛態出現的原因有很多,在Fabry-Pérot中可以利用來回的相位差,使共振腔兩側變為完美反射鏡,如此一來電磁波便會被限制在其中而產生BIC。在光子晶體波導中,由於週期性排列而具有很好的對稱性,因此其中電磁場的水平波向量有機會疊加在一起,若是這樣的情形發生在連續頻譜中則可形成BIC。在本篇論文中,我們利用FDTD加上週期性邊界條件來模擬光子晶體波導,並且在其中成功找到連續體束縛態的特徵,之後分析BIC出現的條件做出電場分布圖,用以討論BIC模態的組成分布,最後改變結構的形狀,來觀察不同結構下所產生的BIC情形。
英文摘要 Photonic crystals can produce many special phenomena because of its periodic dielectric structure. For example, when light travels through a photonic crystal, it can cause destructive interference due to the interaction between each layer of structure. These destructive interferences can prohibit the propagation of some frequencies, and the areas covered by these frequencies are called photonic band gaps. The band structure of photonic crystals is therefore divided into upper and lower parts. Bound states in the continuum (BICs) are found in the waveguide composed of photonic crystals. These special modes are caused by bound states outside the continuous spectrum of the wave source. And its energy is continuously rises in the continuous spectrum, so it has very high Q-factor. This makes them useful for many optical and other application. There are many reasons for the occurrence of continuum bound states. In the Fabry-Pérot cavity, the round-trip phase shifts can be used to make the two sides of the resonant cavity become perfect mirrors, so that electromagnetic waves are confined to generate BICs. In a photonic crystal waveguide, its periodic arrangement can provide good symmetry, so the horizontal wave vector of the electromagnetic field has the opportunity to be superimposed. If such a situation occurs in the continuous spectrum, BICs can be formed. In this article, we use FDTD with periodic boundary conditions to simulate the photonic crystal waveguide, and successfully find the BICs. Then we analyze the conditions of BICs to make electric field patterns to discuss the composition distribution of BIC modes. We also changed the shape of the structures to observe the BICs generated under different structures.
論文目次 口試委員審定書 I
中文摘要 II
Abstract III
致謝 VIII
目錄 IX
圖目錄 XI
第一章 緒論 1
1-1 前言 1
1-2 研究動機 2
1-3 本文內容 2
第二章 相關理論介紹 3
2-1 光子晶體 3
2-2 連續體束縛態 5
2-3 布里淵區 7
第三章 數值模擬方法 8
3-1 有限差分時域法(FDTD) 8
3-2 摺積完美匹配層(CPML) 11
3-3 週期性邊界條件 13
第四章 模擬結果與討論 15
4-1 Fabry-Pérot 15
4-2 週期性光子晶體 17
4-2-1完整介電質結構 17
4-2-2十字切割介電質結構 23
4-2-3十字形介電質結構 27
4-2-3 x對稱和y對稱介電質結構 31
第五章 結論與未來展望 37
5-1 結論 37
5-2 未來展望 38
參考資料 39
參考文獻 [1] John, Sajeev, "Strong localization of photons in certain disordered dielectric superlattices," Physical review letters 58(23), 2486.(1987)
[2] Krauss, Thomas F., M. Richard, and Stuart Brand, "Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths," Nature 383(6602), 699.(1996)
[3] Lepetit, Thomas, et al., "Resonantly trapped bound state in the continuum laser," arXiv preprint arXiv 1508(05164).(2015).
[4] John D. Joannopoulos, Steven G. Johnson, Joshua N. Winn, Robert D. Meade, Photonic Crystals: Molding the Flow of Light(2nd ed.), New Jersey: Princeton University Press pp.4.(2007)
[5] John D. Joannopoulos, Steven G. Johnson, Joshua N. Winn, Robert D. Meade, Photonic Crystals: Molding the Flow of Light(2nd ed.), New Jersey: Princeton University Press pp.51. (2007)
[6] Hsu, Chia Wei, et al., "Bound states in the continuum," Nature Reviews Materials 1(9), 16048.(2016)
[7] J. von NeumannE. P. Wigner, " Uber merkwürdige diskrete Eigenwerte. Uber das Verhalten von Eigenwerten bei adiabatischen Prozessen," Physikalische Zeitschrift 30, 465.(1929)
[8] Parker, R., "Resonance effects in wake shedding from parallel plates: some experimental observations," Journal of Sound and Vibration 4(1), 62.(1966)
[9] Cumpsty, Nicholas Alexander, and D. S. Whitehead, "The excitation of acoustic resonances by vortex shedding", Journal of Sound and Vibration 18(3), 353. (1971)
[10] Koch, W., "Resonant acoustic frequencies of flat plate cascades", Journal of Sound and Vibration 88(2), 233.(1983)
[11] Parker, R., and S. A. T. Stoneman, "The excitation and consequences of acoustic resonances in enclosed fluid flow around solid bodies", Proceedings of the Institution of Mechanical Engineers, Part C: Mechanical Engineering Science 203(1), 9.(1989)
[12] Evans, D. V., C. M. Linton, and F. Ursell, "Trapped mode frequencies embedded in the continuous spectrum", The Quarterly Journal of Mechanics and Applied Mathematics 46(2), 253.(1993)
[13] Davies, E. B., and L. Parnovski, "Trapped modes in acoustic waveguides", The Quarterly Journal of Mechanics and Applied Mathematics 51(3), 477.(1998)
[14] Hsu, Chia Wei, et al., "Bound states in the continuum," Nature Reviews Materials 1(9), 16048.(2016)
[15] Fan, Shanhui, Wonjoo Suh, and John D. Joannopoulos, "Temporal coupled-mode theory for the Fano resonance in optical resonators," Journal of the Optical Society of America A 20(3), 569.(2003)
[16] Haus, H. A., Waves and Fields in Optoelectronics, New Jersey: Prentice Hall, Incorporated.(1984)
[17] Manolatou, C., et al., "Coupling of modes analysis of resonant channel add-drop filters," IEEE journal of quantum electronics 35(9) 1322.(1999)
[18] Wang, Zheng, and Shanhui Fan., "Compact all-pass filters in photonic crystals as the building block for high-capacity optical delay lines," Physical Review E 68(6) 066616.(2003)
[19] Yanik, Ahmet A., et al., "Seeing protein monolayers with naked eye through plasmonic Fano resonances," Proceedings of the National Academy of Sciences 108(29) 11784.(2011)
[20] Zhen, Bo, et al., "Enabling enhanced emission and low-threshold lasing of organic molecules using special Fano resonances of macroscopic photonic crystals," Proceedings of the National Academy of Sciences 110(34) 13711.(2013)
[21] 陳楠,「計算分析變化單位晶格角度下二維光子晶體的最大完全能隙」,臺灣大學應用力學研究所學位論文,頁18。(2011)
[22] John D. Joannopoulos, Steven G. Johnson, Joshua N. Winn, Robert D. Meade, Photonic Crystals: Molding the Flow of Light(2nd ed.), New Jersey: Princeton University Press pp.38. (2007)
[23] Plihal, M., and A. A. Maradudin, "Photonic band structure of two-dimensional systems: The triangular lattice," Physical Review B 44(16), 8565.(1991)
[24] Yee, K. S., "Numerical Solution of Initial Boundary Value Problems Involving Maxwell’s Equations in Isotropic Media,' IEEE Trans. Nucl. Sci 27, 1829.(1966)
[25] Mur, Gerrit, "Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations," IEEE transactions on Electromagnetic Compatibility 4, 377.(1981)
[26] Berenger, Jean-Pierre, "A perfectly matched layer for the absorption of electromagnetic waves," Journal of computational physics 114(2), 185.(1994)
[27] Roden, J. Alan, and Stephen D. Gedney, "Convolution PML (CPML): An efficient FDTD implementation of the CFS–PML for arbitrary media," Microwave and optical technology letters 27(5), 334.(2000)
[28] Yang, Fan, et al., "A simple and efficient FDTD/PBC algorithm for scattering analysis of periodic structures," Radio Science 42(04), 1.(2007)
論文全文使用權限
  • 同意授權校內瀏覽/列印電子全文服務,於2019-08-23起公開。
  • 同意授權校外瀏覽/列印電子全文服務,於2019-08-23起公開。


  • 如您有疑問,請聯絡圖書館
    聯絡電話:(06)2757575#65773
    聯絡E-mail:etds@email.ncku.edu.tw