Simulation of surface plasmon resonance of metallic nanoparticles by the boundary-element method

Abstract

A set of new surface integral equations (Fredholm equations of the second kind) has been systematically derived from the Stratton-Chu formulation of Maxwell's equations for a two-dimensional TM mode to investigate the interactions of an incident electromagnetic wave with nanostructures, especially metals. With these equations, the surface components (the tangential magnetic field, the normal displacement, and the tangential electric field) on the boundary are solved simultaneously by the boundary-element method numerically. For nanometer-sized structures (e.g., dimension of 10 nm), our numerical results show that surface plasmon resonance causes a strong near-field enhancement of the electric field within a shallow region close to the interface of metal and dielectric. In addition, the corresponding pattern of the far-field scattering cross section is like a dipole. For the submicrometer-sized cases (dimension of several hundreds of nanometers), the numerical results indicate the existence of a standing wave on the backside surface of metals. This phenomenon could be caused by two surface plasmon waves that creep along the contour of metals clockwise and counterclockwise, respectively, and interfere with each other.

The analysis of TM-mode and TE-mode optical responses of metallic nanostructures by new surface integral equations

“…These surface integral equations [2] are in terms of the surface components of the tangential magnetic field H z , the normal displacement field D n , and the tangential electric field E t . Here, the Green functions G j of medium j, j=1, 2, are written as…”

“…If an incident EM plane wave is in TM-mode (the polarization of the electric field is in-plane) to impinge upon the scatterer, Eqns. (1) to (3) are used to calculate the surface components along the boundary, and then the corresponding integral representations [2] are used to obtain the field values in the exterior and interior domains. Take a typical case as an example; an incident wave of TM-mode propagates from the left to the right hand side at ω=4.558×10 15 rad/s (3eV) to impinge upon a silver cylinder (r=200nm).…”

“…1 and 2. Since the surface plasmon wave exists only in TM mode [2], the scattering responses of an EM wave in the near field of a metallic nanoscatterer are totally different in the TM and TE modes. The total electric field distribution in the vicinity of a silver cylinder with r=200nm irradiated by a TE-mode plane wave at ω=4.558×10…”

“…Since the behaviors of a nanometer-sized scatterer (e.g. several tens nanometers) are intensively investigated in lots of papers [1][2][3][4], we focus on the studies of a 2D metallic nanoscatterer with a size of several hundreds nanometers in this paper to demonstrate the difference of the TM-mode and TEmode responses. In this paper, two sets of surface integral equations derived from the Stratton-Chu formulation [5] are used and implemented by BEM to simulate the interactions of an EM wave in TM-mode and in TE-mode with a 2D metallic nanoscatterer, respectively.…”

Improved performance of numerical simulation algorithms for nanoscale electromagnetics

“…While dielectrics and semiconductors are already well understood and implemented in integrated optical devices, metals, in particular silver and gold, offer promising possibilities due to a rich variety of fascinating and often unexpected electromagnetic effects at optical frequencies [2][3][4][5][6]. The light illumination of metallic particles with dimensions in the submicron range may cause an excitation of a Surface Plasmon Polariton (SPP) resonance.…”