類週期光子晶體與微型環波導之光傳輸特性

本論文主要研究類週期1維光子晶體、2維光子晶體和環波導的光傳輸特性。對於類週期1維光子晶體，本論文研究圖厄-莫爾斯(Thue-Morse)多層結構中發現有類布拉格反射存在，利用能隙地圖方法可以推導出此類週期結構的類布拉格反射公式。並且在圖厄-莫爾斯結構中的類布拉格反射1/4波長的位置上發現完美穿透，然而在週期結構中的布拉格反射1/4波長的位置上卻會產生高反射。另外在對稱圖厄-莫爾斯結構中，有很強烈的光侷限現象被發現在中間的缺陷層當中。對於類週期2維光子晶體，本論文提出一個新穎的方法來分析較複雜蜂巢結構和阿基米德鑲嵌圖型類週期結構，可以從能帶結構圖型和能隙地圖圖形得到詳細的光學傳播特性，另外可以獲得光子晶體波導2維和3維的場型，從場型圖中可以發現在缺陷區域中會有很強烈的光侷限現象。對於環波導，本論文研究發現比起傳統週期結構的環波導，類週期結構的環波導會有更陡峭的穿透率峰值出現，且因為許多微小的能隙出現，消滅了共振環瓶的現象，因此提高了濾波的品質。另一個特點是在任意的耦合係數和環比例的情況之下，在主要和次要的能帶範圍都會有完美穿透的峰值出現。最後一個特點是提出以-布洛赫餘弦函數來分析和預測圖厄-莫爾斯環波導中全穿透的峰值頻率的位置。

關鍵字

光子能隙結構；布拉格反射；波導；類週期；共振現象；雷射耦合現象

並列摘要

Light propagations in one-dimensional quasiperiodic photonic crystals, two-dimensional quasiperiodic photonic crystals, and microring waveguides, is discussed in this thesis. The quasi-Bragg conditions in the Thue-Morse dielectric multilayers are presented for one-dimensional photonic quasiperiodic crystals based on the gap map. A singular point with complete transmission occurs for a quarter-wave stack in the Thue-Morse dielectric multilayers at the quasi-Bragg condition. However, high reflection occurs for a quarter-wave stack in the periodic bilayers. If a defect layer is introduced into the symmetrical Thue-Morse multilayers, strongly localized modes with high transmission occur at distinct frequencies. For two-dimensional photonic quasiperiodic crystals, a method to analyze honeycomb and quasiperiodic structures such as Archimedean tiling patterns are proposed. Detail information on light propagation is obtained from the band structure and gap map. Moreover, two- and three-dimensional filed diagrams of the photonic waveguide are obtained. Strong localizations are found at the defect region at distinct frequencies. In microring waveguides, three important properties are found for the quasiperiodic systems. First, compared to the periodic microring waveguide, the sharp resonance peaks are obtained in the quasiperiodic systems by eliminating the coupled resonator optical waveguide bottle with mini-gaps. Second, resonance peaks with complete transmission are always obtained by arbitrary coupling and the ratio of the radii in the mini-band and major-band regions of quasiperiodic systems. Lastly, an analytical method is presented to predict the occurrences of resonance peaks with complete transmission based on the gap map at the mini-band regions of a Thue-Morse microring waveguide.

並列關鍵字

Photonic bandgap materials ； Bragg reflectors ； Waveguide ； Quasicrystal ； Resonator ； Laser coupling

參考文獻

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[3] P. J. Pauzauskie, D. J. Sirbuly, and P. Yang, “Semiconductor nanowire ring resonator laser,” Phys. Rev. Lett. 96, 143903 (2006).

[4] B. S. Williams, “Terahertz quantum-cascade lasers,” Nature Photon. 1, 517 (2007).

[6] I. P. Kaminow, “Optical integrated circuits: a personal perspective,” J. Lightwave Technol. 26, 994-1004 (2008).

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類週期光子晶體與微型環波導之光傳輸特性

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