電磁波包於色散介質中的傳播行為｜國立中央大學博碩士論文系統

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研究生：	吳杰倫 Jie-Luen Wu
論文名稱：	電磁波包於色散介質中的傳播行為
指導教授：	欒丕綱 Pi-Gang Luan
口試委員:
學位類別：	碩士 Master
系所名稱：	理學院 - 光電科學與工程學系 Department of Optics and Photonics
論文出版年：	2013
畢業學年度：	101
語文別：	中文
論文頁數：	74
中文關鍵詞：	超材料、負折射、有限時域差分法、色散介質、Z轉換、能量速度
外文關鍵詞：	Metamaterials, Negative refraction, FDTD, dispersion medium, Z-transform, energy velocity
相關次數：	點閱：15 下載：0
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本論文採用以 Z-轉換輔助的有限時域差分法 (Z-transform assisted finite-difference time-domain method 或 Z-transform assisted FDTD method) 來模擬電磁波包在細金屬線陣列 (Wire Array) 和裂環共振器陣列 (Split-Ring Resonator Array) 所構成的複合式人工構造 (Wire-SRR Array) 中的傳播行為。此種複合介質具有類似於 Drude 模型形式的色散型介電係數 (permittivity) 以及類似於 Lorentz 模型的色散型磁導率 (permeability)，並在某一段頻率範圍內具有負折射率 (negative refractive index)。本研究主要探討電磁波在負折射頻段於介質中的傳播行為，具體內容包括：波包在介質中的移動速度、群速度、能量速度在介質強吸收以及弱吸收的情況下的行為比較，以及波包在空氣與Wire-SRR介質介面處的能量穿透情形。最後探討波包在Wire-SRR進入介質中的折射行為，並將其結果和單頻的折射定率做比較。

In this thesis we adopt the Z-transform assisted Finite-difference time domain (FDTD) method to simulate the wave packet propagating behavior in the artificial structure which composed with periodically arranged thin metallic wires and spilt-ring resonators (SRRs). This artificial medium has dispersive permittivity like that of Drude model and dispersive permeability like that of Lorentz model, and has negative refractive index in a range of frequency. The main theme of our study is about the propagating behaviors of electromagnetic waves in this medium in the negative refraction frequency range. We study and discuss the differences among wave packet velocity, group velocity, and energy velocity in lossless and absorptive medium respectively. Finally, we compare the energy transmittance and refractive performance of wave packet with that of the monochromatic waves.

摘要    I
誌謝    III
目次    IV
圖目錄    VI
表目錄    VIII
一、緒論    1
1-1 負折射與等效介質    1
1-2 波包在等效介質中的傳播    2
二、負折射與色散性的等效介質    3
2-1  色散模型    3
2-1-1  Drude Model    3
2-1-2  Lorenz Model    4
2-1-3  色散介質中的能量密度    5
2-1-4  吸收性色散介質中的能量密度    7
2-2  負折射材料的實現與等效模型    10
2-2-1  細金屬線陣列-等效電漿模型    10
2-2-2  裂環共振器(split-ring resonator , SRR)    14
三、時域有限差分法（Finite Difference Time Domain，FDTD）於電磁波之應用    17
3-1　FDTD架構    17
3-1-1　Maxwell's Equation    19
3-1-2　FDTD中電磁場的遞迴關係    20
3-2　完美匹配的吸收邊界    22
3-3  Z轉換(Z-Transform)在色散介質中的應用    26
3-3-1  Z轉換(Z-Transform)的基本定義    26
3-3-2  FDTD中Z 轉換於Drude Model之應用    27
3-4　FDTD數值模擬的穩定性    31
四、波包在等效介質中的模擬與分析    32
4-1　模擬參數設定    32
4-2　金屬線-裂環共振器陣列(Wire-SRR )    35
4-2-1　波包正向入射之群速度    35
4-2-2　波包正向入射之穿透率以及反射率    40
4-2-3　波包斜向入射之折射角    46
4-3　波包的能量耗散以及介質的吸收    53
4-4  數值積分的時間間隔對於誤差之影響    57
五、結論與未來展望    59
5-1 結論    59
5-2 未來展望    60
參考文獻    61

                                

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