本論文主要的研究是無序雷射模態的數值模擬，我們使用時域有限差分法(Finite-Difference Time-Domain Method) 從InN奈米圓柱其基本光學性質的分析與探討開始，當奈米金屬圓柱尺寸約為幾十個奈米時，其可見光散射光譜會有一明顯共振的現象，稱為「表面電漿共振」(Surface Plasmon Resonance)，其共振頻率與圓柱大小、形狀、材料以及鄰近物質有關。我們將許多奈米圓柱隨機分佈於無序材料樣品中，光子在樣品中被奈圓柱散射並誘發相長性干涉，而當某些特定波長的光被局限於樣品中時，即可產生特定的頻譜，本論文的目的即是要探討在哪種情況下其光的局限效果最佳，透過改變樣品大小、樣品中奈米圓柱的數目多寡、奈米圓柱的形狀或是核殼奈米圓柱其核半徑與殼厚度比的改變來達到把光局限在樣品中的效果。

In this thesis, we study the random cavity modes formed within the random media by finite-difference time-domain method. Starting from the analysis of the basic optical properties of InN cylindrical nanoparticles, resonant scattering spectra are calculated. When the size of the metal cylindrical nanoparticle is about dozens of nanometers, its scattering spectrum has a resonant peak in the visible wavelength region, called the surface plasmon resonance. Its peak resonant wavelength depends on particle size, shape, its compound dielectric properties, and the dielectric environment. We arrange those cylindrical nanoparticles randomly in space to form a random media. Photons traveling inside the sample will be scattered by those cylindrical nanoparticles and lead to a constructive interference. When photons with particular wavelength are trapped inside the sample, a lasing cavity mode is formed. The purpose of this thesis is to study the light localization condition by changing the sample size, particle filling factors, or the ratio of the core radius and the shell thickness for core-shell InN cylindrical nanoparticles.

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