Fabrication and Optical Properties of Photonic Crystals with Face-Centered Structures

本論文主要著重在三維空間的光子晶體，利用理論計算與實驗量測，研究面心長方結構與面心立方結構的光學性質。我們藉著直徑兩百五十微米的光纖，當作基本元素，來排列出工作區域落在十億赫茲，含有面心長方結構的光子晶體。這些光纖先被排列成雙層的最密堆積，再以蝕刻的方式令其變細，接著把兩片蝕刻過的雙層光纖單元，以層層交叉的方式堆疊，即可組成一個擁有四層結構的面心長方光子晶體。最後透過有限差分時域法的理論計算，我們發現此面心長方結構具有一個光學吸收峰，而這可能是所有面心長方光子晶體的共同特性。 另一方面，由於自然界中存在著自我組裝的現象，漂浮在水中的聚苯乙烯奈米球，即可藉此凝聚成一個面心立方結構的光子晶體。藉由選取直徑一百九十九至兩百九十九奈米的奈米球，再加上平面波展開法的計算，以及顯微鏡量測系統的光學測量，我們已經成功地製作出，可調控光子能隙之面心立方結構的光子晶體，其工作範圍可涵蓋整個可見光波段。在本論文中，除了研究面心長方結構，於光子能隙附近的吸收性質之外，也研究了面心立方結構在光子能隙中的反射特性；並且包含了理論計算與實驗量測之間的精細比較。Three-dimensional photonic crystals formed with face-centered-tetragonal (FCT) and face-centered-cubic (FCC) structures were researched by theoretical calculation and experimental measurement. We used optical fibers with diameter of 250 µm to construct photonic crystals in the terahertz region. The fibers were arranged in two close-packed layers and etched thinner for crossing layer by layer, and then an FCT structure with four layers was fabricated. By the computation with the finite-difference time-domain (FDTD) method, we found an absorption peak in our FCT specimen, and it may be the common behavior of FCT. Furthermore, due to the self-assembling behavior, polystyrene nanospheres (PSNS) could congregate to a photonic crystal with FCC structure. By choosing the diameter of PSNS ranging from 199 nm to 299 nm, plus the computation of the plane-wave expansion (PWE) method and the measurement of the microscopic measurement system, we were successful to create photonic crystals whose tunable photonic bandgaps (PBG) covered the visible region. In this thesis, the absorption and reflection properties have been investigated near the photonic bandgap in FCT and FCC structures, respectively. A detailed compassion between theoretical calculation and experimental measurement will be included.1. Introduction.........................................01 1.1 Papers Review.....................................01 1.2 The Highlight of Photonic Crystals................02 1.3 Motivations to this Thesis........................03 2. Theoretical Computation of Photonic Crystals.........04 2.1 Maxwell Equations to Electromagnetic Waves........04 2.2 The Finite-Difference Time-Domain (FDTD) Method...06 2.3 The Plane-Wave Expansion (PWE) Method.............12 3. Face-Centered-Tetragonal Structure...................21 3.1 Fabrication of Terahertz Photonic Crystals with Optical Fibers....................................21 3.2 Accuracy of the Software We Used..................23 3.3 Computation by the FDTD Method....................25 3.4 Results and Discussion............................27 4. Face-Centered-Cubic Structure........................37 4.1 Fabrication of Photonic Crystals with Polystyrene Nanospheres...........................37 4.2 Computation by the PWE Method.....................39 4.3 Measurement in the Visible Region.................40 4.4 Results and Discussion............................41 5. Conclusion...........................................53 References..............................................5