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

王暄淯(Hsuan-Yu Wang)

指導教授 ： 李瑞光

國立清華大學/電機資訊學院/光電工程研究所/碩士(2013年)

https://doi.org/10.6843/NTHU.2013.00272

摘要

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。

關鍵字

局域波 ； 無序晶格

並列摘要

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.

並列關鍵字

Anderson localization ； disordered lattices ； Lyapunov exponent ； disordered lattice solitons

參考文獻

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localization in disordered two-dimensional photonic lattices. Nature 446,

52–55 (2007).

[3] Ad Lagendijk, Bart van Tiggelen, and Diederik S. Wiersma. Fifty years of Anderson localization. Physics Today 62, 24-29 (2009).