線性和非線性波在一維無序晶格的散射與局域

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研究生：	王暄淯 Wang, Hsuan-Yu
論文名稱：	線性和非線性波在一維無序晶格的散射與局域 Scattering and localization of linear and nonlinear waves in one-dimensional disordered lattices
指導教授：	李瑞光 Lee, Ray-Kuang
口試委員:	蔡雅芝許佳振李柏璁
學位類別：	碩士 Master
系所名稱：	電機資訊學院 - 光電工程研究所 Institute of Photonics Technologies
論文出版年：	2013
畢業學年度：	101
語文別：	英文
論文頁數：	31
中文關鍵詞：	局域波、無序晶格
外文關鍵詞：	Anderson localization, disordered lattices, disordered lattice solitons
相關次數：	點閱：2 下載：0
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在這個研究中，我們用數值方法spectral method計算了馬克士威爾方程式和薛丁格方程式，討論了電磁波和電子波在不同種類的一維無序晶格的散射與局域，我們也計算Lyapunov exponent和層數不同的無序晶格的平均穿透率來分析波長在能帶和能帶邊緣的電磁波在不同無序程度的晶格的局域程度，我們也分析了因為無序而產生的能隙模態的局域特性，然後，我們也用牛頓法在位能是無序晶格的非線性薛丁格方程式找到一些無序晶格能隙孤立子。

There have been numerical investigations for electron and electromagnetic waves in the one-dimensional disordered lattice. The electron eigenmodes of one-dimensional disordered lattice are investigated for three different models. The electromagnetic eigenmodes of one-dimensional disordered lattice are also investigated. The degree of localization of the wavelength at the band, gap edge and gap are studied. Finally, the disordered lattice solitons are presented.

Table of Contents

List of Figures     vi
List of Symbols     viii
Chapter 1: Introduction
1.1  Overview    1
1.2  Description of the work    2

Chapter 2: Schrödinger equation in one-dimensional disordered lattices
2.1  Electron wave dynamic in 1D random potential    3
2.2  Randomness in the width and position of the barriers    4
2.3  Randomness in the width and position of the wells    6
2.4  Randomness in the width and position of barriers and wells    8

Chapter 3: Maxwell’s equations in one-dimensional disordered lattices 
3.1  Electromagnetic wave dynamic in 1D dielectric lattices    9
3.2  Randomness in the layer thickness      11

Chapter 4:  Propagation of electromagnetic wave through a 1D disordered lattice: Transmittance, Lyapunov exponent, and its Variance
4.1  The transfer matrix method for a multilayered structure     14
4.2  Anderson localization in disordered lattice    19

Chapter 5:  Nonlinear Schrödinger equation in one-dimensional disordered lattices 
5.1  Disordered lattice solitons    26

Chapter 6:  Conclusion    30

Bibliography    31

                                

[1] Mordechai Segev, Yaron Silberberg and Demetrios N. Christodoulides. Anderson localization of light. Nature photon 7, 197-204 (2013).
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localization in disordered two-dimensional photonic lattices. Nature 446,
52–55 (2007).
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[6] Pi-Gang Luan and Zhen Ye. Statistics of Lyapunov exponent in one-dimensional layered systems. Phys. Rev. E. 64, 066609 (2001).
[7] Yoav Lahini, Assaf Avidan, Francesca Pozzi, Marc Sorel, Roberto Morandotti, Demetrios N. Christodoulides, and Yaron Silberberg. Anderson Localization and Nonlinearity in One-Dimensional Disordered Photonic Lattices. Phys.Rev.Lett. 100, 013906 (2008).
[8] Nikolaos K. Efremidis and Kyriakos Hizanidis. Disordered Lattice Solitons. Phys.Rev.Lett. 101, 143903 (2008).
[9] D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg. Gap Solitons inWaveguide Arrays. Phys.Rev.Lett. 92, 1093904 (2004).
[10] 黃孟傑，波在一維系統中的傳播與局域化，中央大學碩士論文(民國94年)

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