本研究主要的內容是藉由數值模擬來分析光在奈微米光學元件中傳播的特性。在本論文中，我們利用光子晶體結構，將介電質材料以週期性的方式排列，來產生所謂的光侷限效應。然而光在波導中傳播時，會存在光耗損，因此本論文的第一個部分是研究如何以三維光子晶體結構降低二維光子晶體波導之傳播光耗損。我們使用有限時域差分法，將奈米小球所排列的三維光子晶體放置於二維光子晶體波導上，來達到有效減少垂直方向上的能量損耗。結果顯示TM模態光波穿透率可有效提升2.25倍。本論文的第二部份，我們利用光子晶體建構透鏡，結合角錐狀波導，將光由寬波導耦合進入窄波導之中，其耦合效率達到87%。
本論文的第三部分研究週期性排列的甜甜圈波導，此一新型的光子晶體波導能夠有效地將光的能量侷限在其中空結構當中，而且波導的中心為空氣，更是降低了因介質的因素所造成的能量損耗。我們以圓柱座標的有限時域差分法來探討甜甜圈波導的結構，計算出結構所產生的光子能隙，找到能夠將能量完全侷限在波導的條件。另一個特性則是，甜甜圈波導的在部分光子能隙(partial band gap) 的條件下，能夠找到讓光場在出光時不易繞射(diffractionless)的效果。利用Bessel節點的方式位置甜甜圈的條件之下，其出光的繞射角可由?????縮減至????? 。利用此結構在雷射上，能夠提升光束集中的效果。
本論文的第四部分是共振波導元件。傳統上要製作窄頻的光濾波器需要靠多層的光學薄膜，而共振波導元件則是以次波長光柵加上平面波導的結構亦能達到相同的效果。我們以嚴格耦合波理論來進行計算，在製作方面，以化學沉積法在共振波導薄膜元件上成長SiO2薄膜，共振波長的頻寬會隨著薄膜厚度的增加而呈現震盪的效果，當薄膜厚度超過一臨界值時頻寬便不再震盪。本論文的第五部分，我們利用單層排列的奈米小球與乾蝕刻技術，製作二維的共振波導元件。此一製程過程簡化了製作次波長光柵所需的電子束微影法之曝光顯影製程，此元件可應用於提升太陽電池之光萃取效應。

Nanophotonics has attracted most of researchers’ interests owing to its plenty of promising purposes such as integrated optics, plasmonics, photonic bandgap for light manipulation, near-filed scanning optical microscopy, ultra-high-resolution lithography, bio-medical sensing, high-density data storage, and etc. With the rapid growing fabrication technology of nano structure, previously proposed applications which were limited to merely theoretical investigation have become feasible. In this thesis, several concepts associated with nanophotonics are investigated and demonstrated including photonic crystal waveguide, novel photonic structures, and subwavelength grating resonance.
In waveguide application, we present a SOI rib waveguide embedded with two-dimensional photonic crystal structure for making photonic bandgap yielding filter characteristics between 1.3?m and 1.55?m wavelength. Additional added three-dimensional photonic crystal structure is also showing to reduce the propagation loss of the guided mode. In addition, we present a structure of tapered waveguide to improving the coupling efficiency for coupling application. The equivalent microlens structure consists of two-dimensional photonic crystal structure shows that the transmission efficiency of coupled mode can approach 87.5%. The photonic-crystal based telescopic structure is feasible of embedded to integrated optics for practical application.
We propose a novel donut-like waveguide, which has a photonic crystal structure to improve its directional characteristics. This device is able to reduce the diffraction angle of outward beam from a waveguide. The photonic band gap of the structure associated with concentric tori with linearly increased distance is designed and analyzed. The result of field distribution shows the energy is combined in the hollow region inside the waveguide. In the partial band gap, the output from the donut waveguide can cause diffractionless output beam that is capable of functioning as a highly efficient beam shaper.
For subwavelength grating resonance, two approaches of manipulating the resonance behavior are demonstrated to increase its quality factor Q. By using a novel air-bridged resonant grating-waveguide structure, we demonstrate that it is capable of modifying the resonance wavelength and spectral width under normal incidence with a post process which is unachievable in previous resonant grating structures. For two-dimensional resonant grating structure, we develop an easy approach by using single-layered polystyrene microspheres of triangular array that can replace the complex process of e-beam lithography. A following etching process is used to fabricate the resonant structure. The resultant transmittance shows a very wide angular response over 20 degrees which is suitable of trapping the light of oblique incidence for BIPV application.

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