本文研究受激輻射表面電漿子放大器，如金奈米殼球和金核殼球等結構，通過增益介質如染料分子或量子點摻入二氧化矽所在之核或殼層。我們通過使用Mie理論求解在平面波照射下的響應來研究奈米殼結構的超共振，此外又使用並矢Green’s函數研究由電偶極子激發奈米殼結構的響應。增益介質其與波長相關的相對介電係數則由Lorentz模型建立。由奈米殼結構的平面波響應，如散射和吸收截面積，可以確立其超共振現象，也代表此受激輻射表面電漿子放大器可以應用於奈米雷射。

In the paper, a spaser (surface plasmon amplification by stimulated emission of radiation) has been proposed. For example, Au nanoshells containing gain medium (e.g. dyes or quantum dots) embedded in the silica core or coreshells coated by a gain medium. We study the super-resonance of nanoshell by using the Mie theory for their responses under the irradiation of plane wave. Moreover, the responses of these nanostructures excited by an electric dipole will be studied using the dyadic Green’s functions. The wavelength-dependent permittivity of the gain medium is modelled by Lorentz model. From the plane-wave responses (scattering and absorption cross sections) of the nanostructure, we can determine the super-resonance behavior. It implies that this spaser can be used for the application of nanolaser.

誌謝 i
摘要 ii
Abstract iii
目錄 iv
圖目錄 vi
表目錄 1
第一章 緒論 4
1.1 前言 4
1.2 文獻回顧 5
1.3 本文內容 10
第二章 介質參數之假設與建立 12
2.1 摻入增益介質之介電係數的假設 12
2.2 Lorentz模型擬合發射光譜與建立摻入增益介質之介電係數 14
2.3 散射截面積效率、吸收截面積效率 15
2.4 輻射效率 17
第三章 數值結果與分析討論 19
3.1 奈米殼散射體 21
3.1.1 金奈米殼球 22
3.1.1.1 平面波波源 22
3.1.1.2 電偶極波源 56
3.1.2 三層(three-layer)金奈米殼球 59
3.2 殼核散射體 64
3.2.1 金核殼球 65
3.2.1.1 平面波波源 65
3.2.1.2 電偶極波源 90
3.2.2 金核殼桿 93
第四章 結論與未來展望 99
4.1 結論 99
4.2 未來展望 100
附錄A Lorentz模型參數 101
附錄B MMP擺點 110
參考文獻 111

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