三維金屬奈米粒子於電磁場中之電漿子現象

摘要

根據麥克斯威爾電磁理論，探討三維銀奈米粒子受到橫電磁波入射後的表面電漿子現象。在多重中心展開法的理論架構下，以多個展開中心展開散射體的散射場及內域場，透過在散射體邊界上取點及滿足邊界條件以建立一係數矩陣方程組，並以奇異值拆解法求解矩陣。
本研究考慮三維與二維銀奈米粒子在表面電漿共振時的比較，同時並模擬銀橢球奈米粒子、核-殼奈米粒子及兩顆銀球奈米粒子在入射共振波長時的表面電漿子現象。由數值模擬結果可以看出：當銀橢球奈米粒子的細長比愈大時，所引致的電場增強幅度愈大；對於核-殼奈米粒子，改變殼層的厚度可達到調變共振波長的目的，當考慮介質 核心半徑為10nm時，改變銀殼層的厚度為20nm、15nm、10nm、5nm時，其較長的共振波長分別為385nm、390nm、406nm、461nm。

Abstract

Surface plasmon resonances of silver nanoparticles under the transverse electromagnetic wave incident are investigated. By using Maxwell’s equation and multi-multipole method, a set of linear equations of expansion coefficients is first constructed by satisfying boundary conditions pointwisely. Singular value decomposition is then used to solve the overdetermined linear equations. The field responses as well as the scattering cross section are calculated.
Numerical results of single, solid/core-shell (both spherical and spheroidal) and two solid spherical nanoparticles under incident resonance wave are presented. It is demonstrated from numerical results that for core-shell nanoparticles the resonances wavelength strongly depend on the thickness of the shell.It is also observed that for spheroidal nanoparticles with sharper shape, the field magnitudes can be extremely large, sometimes even up to hundred times to the magnitudes of the incident waves.