聲子晶體傳導帶與週期性彈性柱波導之研究

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姓名

許顧鏹(Ku-Chaing Hsu) 查詢紙本館藏

畢業系所

光電科學與工程學系

論文名稱

聲子晶體傳導帶與週期性彈性柱波導之研究
(Study on the conduction band of phononic crystal and periodic elasticity rods waveguide)

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摘要(中)

本論文使用平面波展開法與多重散射法，研究二維聲子晶體中彈性波的行為。由平面波展開法可得出二維聲子晶體中混合波與剪波的頻帶結構，以及無黏滯性流體組成之二維聲子晶體的純縱波頻帶結構，或者是由固體組成的二維聲子晶體之純剪波頻帶結構。我們根據對光子晶體中介電質柱波導之研究，提出與其相似的彈性柱波導結構。藉著引入超晶格，其頻帶結構可被計算，並可找出可傳播模態。我們也對彈性柱波導做彎曲角度變化以及無序排列，以研究其對於穿透率的影響。相信在將來，對於彈性波的應用上，此形式之波導能成為一有用的元件。

摘要(英)

In this thesis, we use plane wave expansion method (PWEM) and multiple scattering method to study the propagation behavior of elastic waves in the two-dimensional phononic crystals. The band structure of mixed (longitudinal-transverse) polarization mode and transverse polarization mode can be calculated using PWEM. The band structure for longitudinal polarization mode of two-dimensional phononic crystal composed of non-viscous fluid, and the band structure of transverse polarization mode of two-dimensional phononic crystal of solid can also be calculated. Inspired by the research of dielectric rods waveguide for guiding light, we propose elastic rods waveguide for guiding sound. The band structure of elastic rods waveguide is calculated using super-cell method, and the propagating mode can be obtained. We also consider the effect of bends and disorder on the transmission of the elastic rods waveguide. We believe that this kind of acoustic waveguide can useful in the future.

關鍵字(中)

★ 聲子晶體
★ 彈性柱波導
★ 介電質柱波導

關鍵字(英)

★ phononic crystal
★ periodic elasticity rods waveguide

論文目次

中文摘要 --------------------------------------------- Ⅰ
英文摘要 --------------------------------------------- Ⅱ
致謝 --------------------------------------------- Ⅲ
目錄 --------------------------------------------- Ⅳ
圖目錄 --------------------------------------------- Ⅴ
表目錄 --------------------------------------------- Ⅶ
第一章序論----------------------------------------- 1
第二章理論分析------------------------------------- 3
2-1 平面波展開法應用在聲子晶體------------------- 4
2-2 二維聲子晶體混合波、純剪波、純縱波頻帶結構--- 10
2-2-1 二維聲子晶體混合波頻帶結構------------------- 10
2-2-2 二維聲子晶體純縱波或純剪波頻帶結構----------- 11
2-3 二維聲子晶體超晶格--------------------------- 14
2-4 多重散射法----------------------------------- 16
2-5 多重散射法中能流計算------------------------- 22
第三章數值模擬------------------------------------- 27
3-1 二維聲子晶體混合波與剪波頻帶結構------------- 27
3-2 二維聲子晶體純縱波與純剪波頻帶結構----------- 31
3-3 超晶格於缺陷態頻帶結構----------------------- 34
第四章彈性柱波導研究與討論------------------------- 39
4-1 純縱波之彈性柱波導--------------------------- 40
4-2 純剪波之彈性柱波導--------------------------- 46
4-3 無序之分析與討論----------------------------- 56
4-3-1 無序對於純縱波之彈性柱波導其波導效應的影響--- 57
4-3-2 無序對於純剪波之彈性柱波導其波導效應的影響--- 61
第五章結論與未來展望------------------------------- 65
參考資料 --------------------------------------------- 67

參考文獻

[1] F. Garcia-Santamaria, C. Lopez, F. Meseguer, F. Lopez-Tejeira, J. Sanchez-Dehesa, H. T. Miyazaki, “Opal-like photonic crystal with diamond lattice,” Appl. Phys. Lett., 79, 2309, 2001.
[2] Y. Fink, N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679, 1998.
[3] Chiyan Luo, Steven G. Johnson, and J. D. Joannopoulos, “All-angle negative refraction without negative effective index,” Phys. Rev. B, Vol65, 201104, 2002.
[4] J. D. Joannopoulos, R. D. Meade, J. N. Winn, “Photonic crystals-molding the flow of light,” Princeton University Press, 1995.
[5] K. Sakoda, “Optical properties of photonic crystals,” Springer, Berlin, 2001.
[6] M. Plihal, A. A. Maradudin, “Photonic band structure of two-dimensional systems : The triangular lattice,” Phys. Rev. B, 44, 8565, 1991.
[7] Bikash C. Gupta, Chao-Hsien Kuo, and Zhen Ye, “Propagation inhibition and localization of electromagnetic waves in two-dimensional random dielectric systems,” Phys. Rev. E, 69, 066615, 2004.
[8] Lie-Ming Li, Zhao-Qing Zhang, “Multiple-scattering approach to finite-sized photonic band-gap materials,” George B. Arfken and Hans J. Weber, Mathematical Methods for Physicists, 5th Ed, Academic Press, 2000.
[9] A. Yariv, P. Yeh, “Optical waves in crystals,” John Wiley & Sons, New York, 1984.
[10] Y. Fink, J. N. Winn, Shanhui Fan, Chiping Chen, J. Michel, John D. Joannopoulos, E. L. Thomas, “A dielectric omnidirectional reflector,” Science, 282, 1679, 1998.
[11] M. M. Sigalas and E. N. Economou, “ Elastic and Acoustic Wave Band Structure,” Journal of Sound and Vibration, Vol. 158, No. 2, 377-382, 1992.
[12] M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, “Acoustic band structure of periodic elastic composites,” Phys. Rev. Lett., Vol. 71, No. 13, 2022-2025, 1993.
[13] 欒丕綱, 陳啟昌, “光子晶體-從蝴蝶翅膀到奈米光子學,” 五南出版社, 台灣, 2005.
[14] J. V. Sanchez-Perez, D. Caballero, R. Martinez-Sala, C. Rubio, J. Sanchez-Dehesa, F. Meseguer, J. Llinares, and F. Galvez, “Sound attenuation by a two-dimensional array of rigid cylinders,” Phys. Rev. Lett., Vol. 80, No. 24, 5325-5328, 1998.
[15] M. S. Kushwaha, P. Halevi, and G. Martinez, “Theory of acoustic band structure of periodic elastic composites,” Phys. Rev. B, Vol. 49, No. 4, 2313-2322, 1994.
[16] J. O. Vasseur, B. Djafari-Rouhani, L. Dobrzynski, M. S. Kushwaha, and P. Halevi, “Complete acoustic band gaps in periodic fibre reinforced composite materials: the carbon/epoxy composite and some metallic systems,” J. Phys.: Condens. Matter, Vol. 6, No. 42, 8759-8770, 1994.
[17] Pi-Gang Luan, Tzong-Jer Yang, “Unified treatment for classical waves in two-dimensional inhomgeneous media,” E-print
[18] Fugen Wu, Zhilin Hou, Zhengyou Liu, Youyan Liu, “Point defect states in two-dimensional phononic crystals,” Phys. Lett. A, 292, 198-202, 2001.
[19] 溫熙森, “光子/聲子晶體理論與技術,” 科學出版社, 北京, 2006.
[20] M. Kafesaki, M. M. Sigalas, and N. Garcia, “Frequency modulation in the transmittivity of wave guides in elastic-wave band-gap materials,” Phys. Rev. Lett., Vol. 85, No. 19, 4044-4047, 2000.
[21] M. Kafesaki, M. M. Sigalas, and N. Garcia, “Wave guides in two-dimentional elastic wave band gap materials,” Phys. B, Vol. 296, 190-194, 2001.
[22] Shanhui Fan, Joshua N. Winn, Adrian Devenyi, J. C. Chen, Robert D. Meade, and J. D. Joannopoulos, “Guided and defect modes in periodic dielectric waveguides,” J. Opt. Soc. Am. B,Vol. 12, 1267-1272, 1995.
[23] Pi-Gang Luan, Kao-Der Chang, “Transmission characteristics of finite periodic dielectric waveguides,” Optics Express, Vol. 14, No. 8, 3263-3272, 2006.
[24] Sheng Li, Thomas F. George, Liang-Shan Chen, Xin Sun, and Chao-Hsien Kuo, “Disorder effect on the focus image of sonic crystals in air,” Phys. Rev. E, Vol. 73, 056615, 2006.
[25] Jia-Hong Sun, and Tsung-Tsong Wu, “Propagation of surface acoustic waves through sharply bent two-dimensional phononic crystal waveguides using a finite-difference time-domain method,” Phys. Rev. B, Vol.74, No.174305, 2006.
[26] Khelif A et al., “Trapping and guiding of acoustic waves by defect modes in a full-band-gap ultrasonic crystal,” Phys. Rev. B, Vol 68, No. 21, 174301, 2003.
[27] Khelif A et al., “Guiding and bending of acoustic waves in highly confined phononic crystal waveguides,” Appl. Phys. Lett., Vol. 84, No.22, 4400-4402, 2004.
[28] M. S. Kushwaha, P. Halevi, “Giant acoustic stop bands in two-dimensional periodic arrays of liquidcykinders,” Appl. Phys. Lett., Vol69, 31, 1996.

指導教授

欒丕綱(Pi-Gang Luan)

審核日期

2007-7-13

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