以高斯光束及平面波模擬二維金屬奈米粒子之散射現象

Abstract

根據Maxwell電磁理論，探討二維奈米粒子受到高斯光束(Gaussian beam)波源激發下所引起的表面電漿子現象，在此以多重中心展開法為理論架構，以多個展開中心展開的內域場及散射場，並在散射體邊界上取點以滿足邊界條件，以奇異值拆解法求得其係數解。接著討論以平面波(Plane wave)波源，以有限時域差分法去計算二維奈米粒子的表面電漿現象，在此以精確二維有限時域差分法為計算架構，以便處理金屬介質的問題。 本研究首先推導無限域中高斯光束的電磁場現象，並以級數展開的形式表現其電磁場現象，接著考慮核-殼奈米粒子及橢圓實心奈米粒子的表面電漿現象。 本研究並推導出利用有限時域差分法計算奈米粒子受到平面電磁波(TE wave)入射時，其所造成的電磁場現象，同時計算不同形狀時的電磁場現象。 並將其結果與多重中心展開法計算之結果做比較其正確性，以便對表面電漿之現象有更深一層之認識。

Surface plasmon resonance of two-dimensional silver nanoparticles under the electrical Gaussian beam source and TE wave are investigated. Based on Maxwell Equation and multi-multipole method, we first calculate the cofficients by satisfying boundary conditions. Singular value decomposition is also used to solve the overdetermined linear equations. The electromagnetic field radiated by the Gaussian beam in two-dimensional in the infinite domain is first derived, then the analytic solution is also presented. Numerical results of a solid/core-shell and elliptical cylindrical nanoparticle with Gaussian beam source under resonance frequency are presented. We use the compact 2D-FDTD Method to solve the silver nanoparticles. The electromagnetic field is derived by using the FDTD method. We also compare the numerical results between analytic solutions and FDTD results, then we also compare the electromagnetic field by using the MMP method and FDTD method.