二維複式結構光子晶體的能隙

Abstract

光子晶體是一種具有週期性調制介電函數且具有光子能帶及帶隙結構的人工材料, 在光子能隙的頻率波段中電磁波無法在光子晶體內的任何方向傳遞。這種特性具有很多奇特的物理現象及具備應用上的潛力。光子晶體在應用上多數需要具備較寬的光子能隙, 因此, 設計及製造較大寬度能隙的光子晶體是光子晶體研究領域重要課題。再者, 多數研究重心在二維光子晶體上面, 因為它們具有較容易製造以及應用於波導製作方面的諸多優點。因此, 在此論文中, 我們詳細探索多種具有大寬度能隙的二維光子晶體的複式結構, 包括利用在原來晶格中加入額外散射體或移除某部份介質等方式來達成這些目的。 首先, 我們設計了一種可調式光子晶體。此種光子晶體由一組固定方形介質柱套疊另一組具有相同週期可作相對移動的圓形介質柱組成。光子能隙的改變可藉由調整圓柱位置來達成。在此研究中我們主要著重在能隙對各種不同結構參數的敏感度, 尤其是圓柱的位移參數 的效應。我們發現: 當圓柱的位移參數在某些範圍內能隙保持不變, 在這範圍內圓柱位置可以不必要求很高的精確度, 這種性質對製造可調式光子晶體有實質上的重要性。其次, 我們研究二維方形晶格中的方形介質柱內挖去部份介質形成空氣圓柱, 空氣圓柱的位置的改變使得介質重新分佈同時改變了能隙的寬度。我們取得某些參數時可得到極大的能隙,並且在這個條件下能隙邊緣有極平坦的能帶構造, 造成在很寬的k空間群速度為零或很小。這種構造可廣範的應用於今在現今光學設計上。最後, 我們詳細研究了二維方形晶格中的方形介質柱四邊中間位置由其它介質細柱連接, 細柱的長度、寬度、位置及介質常數等因素影響能隙的開或合。而且最大的能隙不一定是細柱完全連接起來時才存在, 完全由細柱與方柱之間介電常數的相對關係來決定。又從能帶結構觀點, 我們得到更明確的規律, 能帶寬度與能帶中心位置跟細柱與方柱間介電常數的相關性。這種規律可提供於設計二維光子晶體能隙。

Photonic crystals (PCs) are artificial materials having the periodical modulation of dielectric structures in space and there exhibit photonic band gaps (PBGs) in which the propagation of electromagnetic (EM) waves in any propagating direction and polarization state is inhibited. This feature leads to various peculiar physical phenomena and provides potential applications. Most proposed applications of PCs rely on large PBGs of PCs, therefore, the design and construction of PCs with large PBGs are a major goal in the PC field. Much attention has been devoted two-dimensional (2D) photonic crystals (i.e., structures with periodic dielectric patterns on a plane and translational symmetry in the perpendicular direction), since they are easier to fabricate (particularly in the optical region) and may be employed in waveguide configuations. In this thesis, we developed several procedures to systematically engineer the 2D PCs with large PBGs, which were scribed into the crystal structure by removing partial composited materials or introducing additional scatterers into unit cell of the prototype lattices. For the first time, we have fabricated a PC with tunable PBGs. The proposed 2D tunable PC structure is realized by inserting a movable circular dielectric rod into a square lattice of square dielectric cylinders in air. The PBGs can be tunable by shifting the position of the circular dielectric rod. In the present work, we mainly concentrate on the subject of sensitivity of the PBGs to the variations of structural parameters of system, especially paying the attention on the effects of the shift s of the position of the circular dielectric rod. We find that there is a region of parameters in which the ratio of the gap width to the midgap is insensitive to the shift of the position of the circular dielectric rod. This property provides the large benefit of relaxing the fabrication tolerance of the tunable PCs. Then, we propose 2D square lattices of square cross-section dielectric rods in air, designed with an air hole drilled into each square rod. By adjusting the shift of the hole position in the square rod in each unit cell, the dielectric distribution of the square rod will be modified. The PC structure proposed here has a sizable complete PBG and exhibits very gently sloped bands near such gap edge, which resulting in a sharp peak of density of state. In addition, the zero or small group velocities are observed in a broad region of k-space. This structure can be fabricated with materials widely used today and opens a facinating area for applications in optoelectric devices.