次波長金屬光柵之理論研究

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姓名

趙建昌(Chien-Chang Chao) 查詢紙本館藏

畢業系所

光電科學與工程學系

論文名稱

次波長金屬光柵之理論研究
(Theory of Sub-wavelength Metallic Grating)

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摘要(中)

自從1998年T. W. Ebbesen等人分別在Natrue以及Physical Review B期刊上發表次波長金屬孔洞陣列的穿透光異常增強現象，並且引起之後廣泛相關的研究。目前次波長金屬孔洞的穿透光異常增強現象被認為是表面傳播電漿、表面局部電漿以及金屬波導模態的響應所造成。在這些機制中，表面局部電漿以及金屬波導模態都倚賴於金屬波導中的邊界條件。然而，到目前為止還缺乏一個適當數學模型來描述這些局部場形。
這篇論文中，我們使用電磁學理論分析了單一金屬狹縫以及金屬光柵。在單一金屬狹縫中，一個類似表面侷限電磁波的數學模型被提出並且稱呼為Surface modes in waveguide (SMW) 理論。這個SMW理論滿足奈米尺度真實金屬狹縫中的邊界條件。經由分析這個金屬狹縫中的電磁場，可以得到金屬狹縫中的傳播常數以及吸收係數。由SMW理論所得的傳撥常數以及吸收係數都使用Finite Difference Time Domain (FDTD) method 模擬得以驗證其高度的準確度。另外，我們使用SMW理論來修正已知的 Semi-analytical model 並且稱呼此修正後的模型為 Modified semi-analytical model (MSAM)。使用此MSAM模型可以用來分析金屬光柵的光學特性，例如異常的光穿透現象等。

摘要(英)

It has been claimed that part of the mechanism of the transmission enhancement is due to the formation of propagating surface plasmon, localized surface plasmon and slit waveguide mode resonance. For these mechanisms, localized surface plasmon and waveguide mode is analysis rely on a suited boundary condition within the slit waveguide. However, until now, it lacks a suited mathematical expression of the localized fields.
In this thesis, we analyzed both a single metallic slit and metallic grating using electromagnetic theorem. A mathematical expression of the localized field within the slit is assumed to be similar to the form of surface-confined electromagnetic field, called surface modes in waveguide (SMW). This SMW theory is suited for the boundary condition of a nano-scaled metallic slit with a thick thickness. Through analyzing the EM fields inside of the slit, the analytical solutions of the propagating wave vector inside the slit can be solved. It is shown that the SMW has a good agreement with the simulation of the FDTD method. In addition, a semi-analytical model for the analysis of a metallic grating is modified with SMW theory. We call it modified semi-analytical model (MSAM). By using the MSAM, the transmission anomaly of metallic grating can be well-predicted which is more accurate than current analytical theories for a metallic gratings.

關鍵字(中)

★ 次波長
★ 金屬光柵

關鍵字(英)

★ sub-wavelength
★ metallic grating

論文目次

Abstracts II
Contents III
List of Figures V
List of Tables VIII
1. Introductions 1
1-1 Classic Metallic Grating 1
1-2 Extraordinary Transmission Through Metallic Aperture 3
2. Theory Review
2-1 Maxwell Equations 7
2-1-1 Electromagnetic Wave in Free Space 7
2-1-2 Electromagnetic Wave in Real Metal 9
2-1-3 The Energy Flux of Electromagnetic Wave 10
2-1-4 The Boundary Condition of an Interface 10
2-2 Surface Plasmon 11
2-2-1 Solution of Surface-Confined Electromagnetic Waves 12
2-2-2 Dispersion Relation of Surface Plasmon 15
2-3 Thick Metallic Grating 16
2-3-1 Lalanne : Semi-Analyticcal Model 16
2-3-2 Pendry: Transfer Matrix 21
2-3-3 Limitations of Current Theory 25
3. The Eigen Modes Inside Metallic Slit and The Modified Semi-Analytical Model for Metallic grating 27
3-1 Formulation of Eigen Mode in Metallic Slit for TM-Polarized Light 27
3-1-1 Classical Formulation of Fundamental Mode in Metallic Slit 28
3-1-2 The Guessed Surface Mode in Waveguide (SMW) Inside a Metallic Slit for TM-Polarized Light 30
3-1-3 Results and Discussion 35
3-2 Formulation of Eigen Mode in Metallic Slit for TE-Polarized Light 39
3-3 Modified Semi-Analytical Model (MSAM) of Transmission for a TM-Polarized Light 41
3-4 Modified Semi-Analytical Model (MSAM) of Transmission for a TE-Polarized Light 44
4. Analysis of Thick Metallic Grating 47
4-1 Thick Metallic Grating in Silver Film 47
4-1-1 Thickness-Dependent 50
4-1-2 Width-Dependent 53
4-1-3 Angle-Dependent 56
4-2 Discussion 59
5. Conclusion 62
References 64

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指導教授

張正陽(Jenq-Yang Chang)

審核日期

2006-7-14

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