二維金屬奈米粒子的表面電漿子現象研究

Abstract

根據Maxwell電磁理論，探討二維銀奈米粒子受到電偶極波源激發下表面電漿子現象，以及於半平面中TE wave與電偶極波源所造成的二維銀奈粒子表面電漿現象。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，並以奇異值拆解法求得展開係數。 本研究首先推導無限域中電偶極所輻射的電磁場，並以級數展開的方式求得單一電偶極與一圓柱奈米粒子的電磁散射問題，考慮不同電偶極位置與方向造成銀橢圓奈米粒子、核-殼奈米粒子及兩顆銀奈米粒子在共振時的表面電漿子現象。由數值模擬結果可以看出：考慮一圓形的銀奈米粒子，改變電偶極位置與方向，並不影響其共振波長；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；而不同方向的電偶極波源可分別在奈米粒子鏈上激發出橫向與緃向模態。 本研究並推導滿足半平面上直線邊界的散射基函數，用以展開半平面中問題中，銀奈米粒子所造成的散射場。並模擬不同奈米粒子受到TE wave與電偶極波源於共振時，所造成於基材上的表面電漿子現象。並發現基材的存在會使金屬奈米粒子的表面電漿現象出現高階的模態，並在奈米粒子接近基材的區域有較強的電磁場增益現象。

Surface plasmon resonances of two-dimensional silver nanoparticles under the electrical dipole source and TE wave are investigated. By using Maxwell’s equations 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 far field responses are estimated by calculating the scattering cross section. An electromagnetic field radiated by a two-dimensional electric dipole source in the infinite domain is first derived. Then, an analytical series expansion solution of the scattering between an electrical dipole and a cylinder is presented. Numerical results of single, solid/core-shell and two solid cylindrical nanoparticles under the electrical dipole source with resonance frequency are presented. It is demonstrated from numerical results that the resonances wavelength of core-shell nanoparticles strongly depends on the shell thickness. It is also observed that different positions and orientations of the electric dipole source do not change the resonance peak of a single metal nanocylinder. In order to solve the half-plane problem, a scattering base function which satisfies boundary conditions of the interface is derived. Incident field of TE wave or electrical dipole source is modified to satisfy the boundary conditions of the interface. Numerical results of varied nanoparticles lie on the dielectric substrate under the electromagnetic source are presented. Compare with infinite domain problem, the dielectric substrate changes the surface plasmon mode and the enhanced electromagnetic field on the nanoparticles.