光學倒易對稱性和存在於電漿子與超穎物質之侷部源的交互作用之研究

Abstract

在這篇論文裡，首先用格林函數方法去描述光學和量子力學的倒易性質，並發現在電充係數和磁透係數皆滿足對稱條件的時候，光學倒易性質是成立的；而在量子力學裡也有相同的電位對稱條件，並同時觀察到若電子在有磁場的環境下運動，倒易性質會被破壞。另外，我們亦提供平面波的方法去解釋光學和量子力學的倒易性質。最後我們進一步應用格林函數方法去處理在近場光學裡的問題，並考慮源為電雙極的型式，且討論兩種不同的系統。首先考慮一個電雙極在近兩種不同的超穎物質，分別為在一個介質裡加了奈米金屬棒陣列、一個金屬層和一個介質層所交錯構成的多層結構。對於前者，我們發現分子的生命期在介質裡負折射發生的時候會變的很小和分子的發射頻譜會有很大的藍移現象；對於後者，我們可以發現類似於前者的物理現象，且在文獻中較少被注意；這些重要的特徵提供我們用表面螢光的實驗去觀測到不同於一般的光學性質。再來考慮兩個分子在近金屬奈米球殼之間的能量轉移率，並且考慮非定域效應。而這兩個分子分佈情形為：兩個分子在球殼外、兩個分子在球殼內和一個分子在球殼內但另一個分子在球殼外。因為在奈米金屬球殼上的自由電子的集體震動行為，也就是表面電漿效應；金屬的非定域效應；施體分子的發射頻率等等，分子間的螢光共振能量轉移增強的倍率會有一些有趣的變化。數值結果顯示，分子間螢光共振能量轉移增強的倍率會達到共振主要是因為多極鍵結和反鍵結的金屬奈米球殼的耦合電漿模態；在低頻時，金屬的非定域效應會減弱分子間的螢光共振能量轉移增強的倍率並且會有藍移的現象，利用很小尺寸的金屬粒子，我們可以發現這些訊息在分子之間的螢光共振能量轉移增強效應上是很有用的。

In this thesis, first we use the Green function methods to describe the optical reciprocity and extend to quantum-mechanical reciprocity. We find that optical reciprocity is valid under the condition when both the permittivity and permeability tensors are symmetric and a similar condition in quantum mechanics with the potential replacing the roles of both permittivity and permeability tensors. We also observe reciprocity to break down in the system with an electron moving in a magnetic field. In addition, we use plane wave method to describe the reciprocal symmetry in both optics and quantum mechanics. Finally, we apply the Green function method to near field optics involving dipolar sources. We have studied two different systems. One problem has the dipole near two kinds of metamaterials. For the first kind which consists of a composite of metallic nanowires and a dielectric host, the results show that the molecular lifetimes become exceedingly short when negative refraction occurs within the medium, and large blue-shifts can occur for the emission frequencies of the admolecues. For the stratified layered system, abrupt changes in both the emission lifetimes and frequencies can also take place upon negative refraction, although to a much less extent. These abrupt changes thus provide signatures for probing the transition to such unusual optical property for the medium via surface-fluorescence experiments. The other problem deals with the energy transfer between two dipoles near a metallic nanoshell with nonlocal dielectric response. Two molecules can be located both outside, both inside, or one inside and one outside the shell. Particular focus will be on the enhancement of the fluorescence resonance energy transfer (FRET) process due mainly to the surface plasmon excitation of the free metallic electrons, and the nonlocal effects on this will be studied with reference to a number of factors including the molecular locations and orientations, the emission frequency of the donor, etc. Numerical results show that the resonances in the enhanced FRET rate will be dominated by the multipolar bonding and antibonding cross-coupled plasmonic modes of the nanoshell; and that the nonlocal effects will generally lead to blue-shifted resonances, as well as diminution of the enhancement for the low-frequency portions of both modes. Such information will be useful for future application of plasmonic enhanced FRET using metallic particles of ultrasmall sizes.