聲子晶體是由兩種或兩種以上的彈性材料週期性排列而成的結構，聲子晶體能隙之現象，可以阻絕特定頻率的聲波於結構中傳遞，而當破壞聲子晶體完美的週期性結構時，在能隙中會產生缺陷模態，利用缺陷模態可加以設計成共振腔或缺陷波導，因此許多聲學元件以聲子晶體設計成濾波器、分波器等聲學元件。
拓樸絕緣體以量子霍爾效應、量子自旋霍爾效應與量子能谷霍爾效應為基礎，其邊緣模態因受到拓樸保護之影響，對於亂序與缺陷免疫，且可避免後向散射之干擾，具有強大的波傳行為，在電磁波、聲波與彈性波領域都有許多學者研究。
拓樸波導具有強大的傳播能力，與一般線缺陷波導相比其傳播損耗較低，本文利用拓樸波導結合聲子晶體共振腔設計聲學之波長多工器，因阿基米德晶格為具有高度圓對稱性之結構，共振態易形成迴音廊模態，因此以Archimedean(3,4,6,4)晶格聲子晶體為模型。基於量子能谷霍爾效應之理論，破壞晶格對稱性得到拓樸不等價之結構，建立拓樸波導，於拓樸波導頻率範圍內選定一頻率，再設計聲子晶體共振腔，透過改變共振腔散射柱大小獲得不同共振頻率的共振腔，並分析所形成環形共振之迴音廊模態的高品質因子。接著將拓樸波導耦合至共振腔觀察其效能，並設計通道，將聲波從共振腔導出，達到通道濾波器之功用。最後建構四通道的波長多工器，成功地藉由波長多工器將特定頻率的聲波透過通道導出，其穿透率介於47 ~ 68%之間，約為利用線缺陷波導結合共振腔之波長多工器的2倍高，全文使用有限元素軟體COMSOL Multiphysics®進行模擬。

The topological waveguide has the characteristic of robust wave propagation, and low-loss of energy compared with the line defect waveguide. In this work, a 4-channel acoustic wavelength division demultiplexer based on the topological waveguide coupling to phononic crystal ring cavities is proposed. The Archimedean(3,4,6,4) tiling phononic crystals are studied because of its high degree of circular symmetry. According to quantum valley Hall effect, we destroy the spatial inversion symmetry and investigate its topologically inequivalent structure, so the topological waveguide can be constructed. In order to study the coupling between the topological waveguide and the ring cavity, we design cavities with specific resonant frequencies in the phononic crystal by modulating the size of the scatter in cavity. Also, we observe that the whispering-gallery-mode with high quality factor appears in the cavity at specific resonant frequency. To achieve the function of acoustic channel filter, the topological waveguide and the ring resonator are used to separate the sound wave of different frequencies. Finally, a 4-channel acoustic wavelength division demultiplexer is realized by using a Archimedean(3,4,6,4) tiling phononic crystals. The efficiency of the demultiplexer is successfully demonstrated. The transmission is between 47 ~ 68% and is better more than twice as that of the demultiplexer which based on the line defect waveguide.

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