一維光柵陣列結構的特性及應用研究-以Helmholtz resonator 陣列及Morpho 蝴蝶翅膀結構為例

Study and Applications of the One-Dimensional Grating Structures- Helmholtz Resonator Array and Morpho Butterfly Wing.

盧俊宏(Jyun-Hong Lu)

指導教授 ： 陳啟昌 ； 蕭輔力

國立中央大學/理學院/光電科學與工程學系/博士(2015年)

摘要

本文研究關於一維亥姆霍茲共鳴器陣列及Morpho 蝴蝶翅膀微結構的特性。
藉由共振腔的共振(局域共振)，亥姆霍茲共鳴器陣列可以在特定頻率產生很大的吸收。調整亥姆霍茲共鳴器的結構參數可以觀察到不同結構的共振波長位移的情形。而彈簧質量模型的近似，可以幫助我們更進一步的了解聲波在亥姆霍茲共鳴器中的共振行為。在模擬的過程中我們發現亥姆霍茲共鳴器陣列在特定頻率會有類似Fabry–Pérot干涉的效應，且其頻率與底板厚度相關。由穩態場圖可以觀察到此效應是由底板和亥姆霍茲共鳴器陣列的共振所產生。在應用方面，由測試的結果發現，亥姆霍茲共鳴器陣列對於液體參數變化的感應非常靈敏，因此很適合拿來量測混和溶液的濃度變化。
在聲學的量測系統上我們採用了Ultrasonic immersion transmission technique來量測亥姆霍茲共鳴器陣列。並且在結構特性量測及濃度量測的兩個階段分別採用了不同的量測架構。量測結果顯示在高低頻的信號對比度都超過20dB，且結構對濃度變化的靈敏度高達1757 kHz/Molar ratio unit(Molar ratio 0-0.035)。
Morpho蝴蝶翅膀結構的部分，我們採用嚴格耦合波理論和平面波展開法來分析此結構的特性。我們發現其lamella間的錯位是造成斜向入射時反射光不會有色偏的主因。此外，我們也發現調整結構的垂直方向週期可以等比例的調整反射光顏色。我們也嘗試把蝴蝶翅膀結構視為一個二維的光子晶體結構，並且使用二維的平面波展開法和計算態密度來分析翅膀結構。計算結果顯示翅膀結構在垂直方向藍光區域並不一定會有相對應的partial band gap。在態密度的結果中，在藍光區域會有明顯的強度下降情形。我們改進了態密度的計算方式，使它可以顯示入射角度及反射光頻率的資訊。與嚴格耦合波理論的結果相比較，雖然反射行為不會完整的相符，不過改良後的態密度的結果所顯示出來的反射特徵與嚴格耦合波的結果一致。這也代表Morpho蝴蝶翅膀結構可以被視為一個二維的光子晶體結構。經由改良後的態密度計算法，可以讓平面波展開法分析斜向入射光的反射行為。

關鍵字

有限差分時域法 ； 亥姆霍茲共鳴器 ； 聲子晶體 ； 彈簧質量模型 ； 光子晶體 ； Morpho 蝴蝶翅膀 ； 嚴格耦合波理論 ； 平面波展開法 ； 態密度

並列摘要

In this thesis, we studied the one-dimensional (1D) grating structures of the Helmholtz resonator (HR) array and the Morpho butterfly wing. The HR array can absorb sound waves in specific frequencies by the locally resonant effect. By adjusting the structural parameters of the HR array, we can observe the behavior of the resonant frequency shift. The mapping between the two-spring-mass model and the finite-difference time-domain results can help us to understand the acoustic resonance inside the HR structure. Furthermore, we discover that the Fabry–Pérot-type interference occurs in this structure, and that the resonant frequencies are proportional to the thickness of the substrate. This resonant effect can be obviously observed in the field pattern of the quasi-steady state, and it resonates from the HR and substrate structure. Besides, HR array is rather sensitive to the variation of the liquid parameters. Therefore, this kind of structure is suitable for sensing the liquid concentration.
In the acoustic measurement system, we adopt the ultrasonic immersion transmission technique in our experimental setup. In the two experimental stages of the structural parameters and liquid concentration sensing, we set the two different types of the experimental setups. The measured results show that the extinction ratio is larger than 20dB, and the sensitivity to the variation of the liquid concentration is up to 1757 kHz/Molar ratio unit during the Molar ratio 0-0.035.
We adopt the rigorous coupled-wave analysis algorithm (RCWA) and plane wave expansion (PWE) method to investigate the optical properties of wing structure of the Morpho butterfly. The results show that the displacement between the lamellae is the main condition for reflected the stable wavelength (color) in the oblique incidence. Besides, adjusting the period in the vertical direction can linearly modify the reflection (wavelength) color. The wing structure can be regarded as a two dimensional photonic crystal (2D PC) structure and we analyze the optical behavior by using the plane wave expansion (PWE) method and the photonic density of states (PhDOS). The results show that the partial band gap does not usually exist in the direction of the normal incidence. Furthermore, we improve the calculation of the PhDOS for the condition in the oblique incident light. The property of the reflection light can be observed in the results obtained from the modified PhDOS results which consist with that of the RCWA. The consistency between the two methods also implies that the wing structure can be regarded as a 2D periodic structure.

並列關鍵字

Finite-difference time-domain method ； Helmholtz resonator ； Phononic crystals ； Spring-mass model ； Photonic crystals ； Morpho butterfly wings ； Rigorous coupled wave theory ； Plane wave expansion method ； Density of states

參考文獻

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