近年來，透過破壞晶體結構的對稱性，操縱光束的頻率(Frequency)、波向量(Wave vector)、偏振(Polarization)以及相位(Phase)為目前奈米光子學主要的研究方向之一，這種方式為奈米光子學衍生出多樣化的領域分支以及應用，例如:連續譜束縛態(Bound states in the continuum)、偏振渦漩(Polarization vortex)、手性光子學(Chiral photonics)。本文我們將連結電漿子晶體中的結構對稱性與動量空間中的偏振渦漩，透過改變結構面內反置對稱(In-plane inversion symmetry)的方式，使材料對於左旋和右旋偏振光的吸收程度產生差異，以此討論輻射電場中圓二色性的行為(Circular dichroism, CD)。
首先，本文將從表面電漿子的工作原理出發，透過分析表面電漿極化子(Surface Plasmon Polaritons, SPPs)以及局域性表面電漿子(Localized Surface Plasmons, LSPs)的行為模式，以理解調控晶體的基礎機制。緊接著，我們將介紹本文所調控的晶體對稱性，並引入龐加萊球來幫助理解動量空間中偏振態的行為模式，並透過時間耦合模式理論(Temporal Coupled-Mode Theory, TCMT)所建構的理論模型，描述破壞結構面內反置對稱前與破壞後在動量空間中偏振態的分布行為。最後使用實驗室所搭建的動量空間成像光譜(Momentum-space imaging spectroscopy)，分別針對不同對稱性的結構量測反射率能譜與等頻輪廓(iso-frequency contour)， 將數據結果透過[(R_LCP-R_RCP)/(R_LCP+R_RCP)]的方式將數據轉換成圓二色性訊號，以便討論不同參數所設計的結構對於左旋和右旋偏振光吸收程度的差異，並與理論結果進行比對。
在結構的選擇上我們選用蜂巢晶格當作設計的基礎，並探討了兩種結構調控方式。第一種是基於孔徑直徑差的結構調控，藉由調控孔徑大小的方式，來破壞inversion symmetry，同時透過調控結構不對稱性的方式，以討論圓二色性強度差異。第二種方式是基於孔徑直徑的結構調控，將孔徑的直徑差固定為60 nm，以同時增加兩個孔徑的大小的方式，探討局域表面電漿子對偏振態的分布行為的影響。實驗結果表明，對於不對稱性為0.8的結構擁有最大的CD (63%)，且隨結構參數的調控，動量空間中偏振態的演變行為與理論模型相符。因此我們得以驗證，結構對稱性決定偏振渦漩的生成，這奠定了往後奈米光子學應用的基礎。

In recent years, manipulating the frequency, wave vector, polarization, and phase of light beams by disrupting the symmetry of crystal structures has become a prominent research direction in the field of nanophotonics. This approach has given rise to a diverse range of subfields and applications, including bound states in the continuum, polarization vortices, and chiral photonics. In this paper, we establish a connection between the structural symmetry in plasmonic crystals and polarization vortices in momentum space. By altering the in-plane inversion symmetry of the material, we induce differential absorption of left-handed and right-handed polarized light, allowing us to explore the behavior of circular dichroism in the radiative field.
First, we will begin by elucidating the principles of surface plasmon resonance, analyzing the behaviors of surface plasmon polaritons (SPPs) and localized surface plasmons (LSPs) to understand the fundamental mechanisms behind manipulating crystals. Next, we will introduce the modified crystal symmetry in our study and employ Poincaré spheres to aid in comprehending the behavior of polarization states in momentum space. Using a theoretical model constructed through Temporal Coupled-Mode Theory (TCMT), we will describe the distribution of polarization states in momentum space before and after breaking the in-plane inversion symmetry.
Finally, we will employ momentum-space imaging spectroscopy, an experimental technique developed in our laboratory, to measure reflectance spectra and iso-frequency contours for structures with different symmetries. We will transform the data into circular dichroism signals using [(R_LCP-R_RCP)/(R_LCP+R_RCP)] to discuss the differences in absorption of left-handed and right-handed polarized light for structures designed with different parameters, comparing the results with our theoretical predictions.
For our structural design, we have chosen a honeycomb lattice as the foundation and explored two methods of symmetry manipulation. The first method relies on varying the pore diameters to break inversion symmetry, generating differences in circular dichroism intensity through asymmetry control. The second method involves keeping the pore diameters fixed at 60 nm while simultaneously increasing the sizes of two pores to further investigate the impact of localized surface plasmons on the distribution of polarization states. Experimental results demonstrate that structures with an asymmetry factor of 0.8 exhibit the highest CD (63%), and the evolution of polarization states in momentum space aligns with the theoretical model. Therefore, we have verified that structural symmetry determines the generation of polarization vortices, laying the foundation for future applications in nanophotonics.

一、 摘要 i
二、 Abstract ii
三、 致謝 iv
四、 目錄 v
五、 圖目錄 vii
一、 基本原理介紹 1
1.1表面電漿子的歷史與背景 1
1.1.1局域性表面電漿子(Localized Surface Plasmons, LSPs) 3
1.1.2表面電漿極化子(Surface Plasmon Polaritons, SPPs) 5
1.1.3表面電漿子的品質因子(Quality factor, Q) 7
1.2電漿子晶體 (Plasmonic crystals) 9
1.2.1晶體中的對稱性 10
1.2.2動量空間中的偏振態 12
1.2.3時間耦合模式理論（Temporal Coupled-Mode Theory, TCMT） 19
二、 儀器及原理介紹 25
2.1 樣品製程方法 25
2.1.1熱蒸鍍(Thermal evaporator) 25
2.1.2雙聚焦離子束(Dual-Beam Focused ion beam, DB-FIB) 26
2.1.3原子層沉積(Atomic layer deposition, ALD) 27
2.2光學量測 29
2.2.1動量空間成像光譜(Momentum-space imaging spectroscopy) 29
2.2.2傅立葉光學(Fourier Optics) 30
2.2.3實驗設置 31
2.3模擬原理介紹 32
2.3.1時域有限差分法(Finite difference time domain method, FDTD) 32
三、 實驗流程 34
3.1樣品製備過程 34
3.2蜂巢晶格結構設計 35
四、 實驗與模擬結果分析 36
4.1蜂巢晶格(C6" symmetry)" 37
4.2蜂巢晶格(C3" symmetry)" 40
4.2.1基於孔徑直徑差的結構調控 40
4.2.2基於孔徑直徑的結構調控 44
五、 結論 44
六、參考資料 48

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