本論文研究光在矩形截面光子晶體環形波導運行的特性。環形波導形狀設定為矩形是為了易於後續以電路板進行製程。我們利用圓柱座標有限時域差分法計算光在結構中的運行，改變矩形截面的寬度與厚度，找出讓光能量能夠侷限在結構之中的參數。我們改變環形波導中心寬度，利用快速傅立葉轉換觀察模態有效折射率的變化。接著我們將中心寬度固定，改變連續波射入波導之中，並研究光波頻率與色散的關係。在優化光運行的特性之後，矩形截面的厚度定為電路板的2倍，矩形截面寬度為0.45a (a為光子晶體晶格常數)。當矩形厚度為電路板的3倍時，矩形寬度為0.33a的參數進行模擬。經波導傳播耗損的計算，兩種結構的波導傳播耗損分別為-0.746 dB⁄cm以及-0.736 dB⁄cm。我們觀察到兩結構最低的背向散射光強度僅有-28.56 dB。;This study explores the properties of light propagation in periodically arranged torus photonic crystal waveguides, designed with rectangular cross-sections to simplify fabrication processes. Using the cylindrical-coordinate finite-difference time-domain method, we systematically varied the width and thickness of the rectangular cross-section to obtain a higher energy confinement within the structure. Two configurations were selected for further simulation. 1. The thickness of the rectangular cross-section is twice that of the PCB. The width of the rectangular cross-section is 0.45a where a is the lattice constant of the photonic crystal structure. 2. The thickness of the rectangular cross-section is three times that of the PCB. The width of the rectangular cross-section is 0.33a. The effective index neff of the waveguide was analyzed using fast Fourier transform while varying the width of the central waveguide. We studied the dispersion relation of the waveguide. The propagation loss calculations were investigated for both configurations. The simulated propagation losses were -0.746 dB⁄cm, and -0.736 dB⁄cm, respectively. Additionally, the minimum Back scattering was as low as -28.56 dB.
