板波於漸變型石英聲子晶體平板聚焦與波導現象之研究

Focusing and Guiding Phenomenon of Lamb Waves in AT-cut Quartz Gradient-Index Phononic Crystal Plates

邱夢禎(Meng-Jhen Chiou)

指導教授 ： 吳政忠

國立臺灣大學/工學院/應用力學研究所/碩士(2013年)

https://doi.org/10.6342/NTU.2013.00847

摘要

聲子晶體(Phononic Crystals)意指一種具週期性的彈性複合材料，其結構為均質填充物週期性地排列於具不同性質的基材中。類比於光子晶體的特性，頻溝(band gap)、負折射(negative refraction)等現象亦存在於聲子晶體中，而這些特性可應用於平面透鏡及耦合器等聲波元件中。
本文主要藉由數值模擬及微製程實驗兩種方式，來分析並驗證板波(Lamb waves)於石英漸變型聲子晶體平板中之聚焦及波導兩種現象。漸變型聲子晶體平板主要由改變聲子晶體的填充率來達成，並進一步與波導結構結合。此外，亦會針對石英之非等向性對於漸變型聲子晶體平板的影響進行探討。並藉由有限元素法(finite element method, FEM)來計算聲子晶體及波導結構之頻散曲線以及觀察漸變型聲子晶體平板中之波傳行為。而文中亦針對漸變係數(gradient coefficient)對於整體波傳行為之影響進行分析及探討。
在實驗方面，漸變型聲子晶體平板以及漸變型聲子晶體平板結合波導兩種結構被製作於石英基板上。而交指叉電極以及高頻振動儀將分別用來作為波源以及量測裝置。最後，與模擬結果相互比較後，實驗的結果成功地驗證了漸變型聲子晶體平板中聚焦及波導兩種現象。

關鍵字

聲子晶體 ； 非等向性 ； 聚焦現象 ； 波導 ； 漸變係數

並列摘要

Phononic crystals (PCs) means a composite structure consists of elastic materials arranged periodically in a background medium. Similar to the characters of photonic crystals, band gap effect and negative refraction also exists in PCs. Moreover, these properties could be applied to flat lenses and acoustic wave couplers.
In this study, focusing and guiding phenomenon of Lamb waves in AT-cut quartz gradient-index phononic crystal (GRIN PC) plate are analyzed numerically and executed experimentally. GRIN PC plate is formed by modulating the filling fractions of PCs and with the combination of waveguide structure. Moreover, the effect of AT-cut quartz’s anisotropic property in GRIN PC plate is discussed. By utilizing finite element method (FEM), dispersion relations of PCs and waveguide structure are calculated and the propagation behaviors of GRIN PC plate are observed. Then, the effect of gradient coefficient in designing GRIN PC plate is also discussed.
In the experiment, GRIN PC plate and GRIN PC plate with waveguide in AT-cut quartz substrates are fabricated. The inter-digital transducer and ultra-high frequency vibrometer are used to be the source and detector, respectively. The measurement results are in good agreement with the calculated results of both devices.

並列關鍵字

phononic crystals ； anisotropic property ； focusing phenomenon ； waveguide ； gradient coefficient

參考文獻

[1] E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett., vol. 58, 2059-2062, 1987

[2] E. Yablonovitch and T. J. Gmitter, “Photonic band structure: The face-centered-cubic case,” Phys. Rev. Lett., vol. 63, 1950-1953, 1989

[3] H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami , “Superprism phenomena in photonic crystals,” Phys. Rev. B, vol. 58, 10096, 1998

[4] M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B, vol. 62, 10696, 2000

[5] C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B, vol. 65, 201104, 2002