材料與孔洞對於介質波導之光力影響與開口環型共振腔之光力模擬

Abstract

本論文主要研究波導所產生的光力，一共分為4個主題，分別為:平板波導、波導附加超常材料、孔洞波導與開口環型共振腔。我們希望本研究所模擬的光力未來在工程上能有實際的用途。 由於平板介質波導間的光作用力已有數學解析式，且我們已將我們所建構的平板波導模擬模型與理論進行比對，得到吻合的結果後，接著改變系統中其他材料參數來模擬力量的變化。結果顯示當波導間的介質常數大於波導時，力量會由吸引力轉變為排斥力，且電場模態會隨著波導距離以及兩者介質比值的增加而有增高的趨勢。 我們也推導出波導附加超常材料模型中光力的解析式，並模擬改變超常材料的厚度，發現力量會有不連續的變化，以及力量與距離和超常材料厚度的差值有對應關係，都可以由系統色散關係式來進行解釋。另外，增加超常材料的負介電常數，則會使的力量曲線產生偏移的現象。 除了材料參數外，研究結果發現在波導中挖出橢圓孔洞可以增加力量。我們探討橢圓孔洞長短軸比與孔洞數量的增加可以使力量的局部極值增加，同時也發現了入射至結構中電磁波的穿透率、反射率與力量三者間有強烈的對應關係。 最後是開口環型共振腔的模擬，我們在環型共振腔中的環波導上開一小缺口，並利用結構可以侷限電磁波於環中，使環內電磁場增強的特性，成功模擬出當共振腔穿透率最低時，開口作用力即為最強，並且可再藉由調整環波導與長直波導的距離，找出耦合最佳，也就是力量最大的位置。

We analyze the optical force in waveguide. Four topics, which are planar waveguides, waveguides with metamaterial, cavities in waveguide and split optical ring resonator will be discussed. We hope the optical force we simulated can be used in practical way. The analytical solution of optical force in plane dielectric waveguide has been derived. First we compare our FEM simulation with analytical solution, and then we modify the materials except waveguide, studying the effect on force. The result shows as the permittivity of gap between waveguides is larger than that of waveguide, the force turns to repulsive. The higher mode of electric field appears as the distance between waveguides and the ratio of permittivity of gap and waveguide increase. We have also derived the analytical solution of the force in waveguide with metamaterial. We find the force becomes discontinuous with the increasing thickness of metamaterial, and the force is a function of the difference between distance and thickness of metamaterial. These phenomenon could be explained due to the dispersion relation of the system. In addition, negative increasing the permittivity of metamaterial makes the curve of force shift. It is known that ellipse cavities in waveguide make the force stronger. We will study the influence of modifying the geometrical parameters and amount of the ellipse cavities on force. Also we will show the relation between force, transmittance and reflectance of electromagnetic wave in the structure. A new structure named “split optical ring resonator,” which has a split on the ring waveguide of the resonator is built. Because the light could be limited in the ring, the field could be also enhanced. As the transmission of resonator is the lowest, the force on split reaches the maximum. The best coupling location, or the maximum force can be found by modifying the distance between the ring and the straight waveguide.