光子晶體及表面電漿子共振腔之模擬研究

Abstract

本論文以利用數值上時域有限差分法和耦合波法相互配合去探討光子晶體和表面電漿子共振腔的特性。光子晶體是由二到三個介質作一維，二維，或三維的週期性排列組成。光子晶體的特性可以應用在提升發光二極體的光萃取率。更進一步的，我們結合時域有限差分法和傅立葉轉換分析光子晶體共振腔的品質係數和Purcell係數。很大的品質係數和很小的等效體積是造成很大Purcell係數的主因。共振模態場形的高對稱性是造成高品質係數的主要原因之一。 此外，表面電漿子造成金屬光柵的異常穿透或反射的現象也被討論。之後藉由一維金屬光柵形成表面電漿子共振腔。由數值結果顯示表面電漿子會在共振腔內形成駐波。最後，我們比較兩種金屬光柵結構讓表面電漿子和量子井耦合的特性並且指出金屬光柵在半導體裡面的有機會讓量子井和表面電漿子的共振腔或耦合模態相互耦合。但是另外一種金屬光柵在空氣中的結構，只有水平的表面電漿子模態才有可能和量子井耦合。所以，金屬光柵朝下的結構會是比較好的選擇。

The objective of this thesis is to investigate numerically the properties of photonic crystal and surface plasmon cavities by corporately using finite-difference time domain (FDTD) and coupled-wave methods. A photonic crystal generally consists of two or more materials with different dielectric constants. It can be applied to enhance the light extraction of LED. In addition, a single-defect cavity can be formed by removing a cell in a photonic crystal. We study the photonic crystal cavity with FDTD and Fourier transform. From the results, by combining a high quality factor with a wavelength-size small-mode volume, a very high Purcell factor is achieved. A surface plasmon polariton (SPP) is an electromagnetic excitation existing on the metal surface. The physical properties of extraordinary transmission/reflection are also investigated. Surface plasmon on a periodic metal grating will form certain band structures. A band gap often opens up at the boundary of the band edge. In this frequency region, surface plasmon will bounce in the single-defect cavity. From the results, they display a standing wave is formed by the reflectors on either side of the cavity. Besides, we discuss two different SPP-QWs coupling structures. They are both comprised of a silver thin film textured by a one-dimensional grating. Square ridges of one structure are in the air, but the other’s are in the GaN. Through various numerical studies, we reveal that the latter is the better choice.