MMP Simulation of Plasmonic Particles on Substrate Under E-Beam Illumination

Abstract

A novel numerical approach to investigate the resonance behavior of plasmonic particles on a substrate under e-beam illumination is presented. The method is based on the Multiple Multipole Program (MMP), a generalized point matching technique, and is augmented by the ability to compute layered media and electron energy loss spectroscopy (EELS) measurements. Furthermore, the whole framework is complemented by a mesh-based method that automatically places the multipole expansions and matching points for arbitrary three-dimensional geometries. The performance of our technique is analyzed by a series of numerical experiments. The EELS responses of a plasmonic split-ring resonator in free space and a plasmonic disk dimer on a membrane, as well as the resonant modes, are simulated. Finally, our implementation is compared to the established discontinuous Galerkin time domain (DGTD) method with respect to its computational efficiency. We show significantly improved performance especially for the computation of EELS resonance maps.

Dielectric Sphere Oligomers as Optical Nanoantenna for Circularly Polarized Light

“…To describe this situation, we show the field mapping in the SI along with the extracted ED components using MMP simulations. 29 At an energy of 3.1 eV and an angle of 130°in the CPL mapping in Figure 3d, two-color features with RCP in the entire left sphere and LCP in the entire right sphere are found, which are similar to the electric dipole rotation discussed above. However, in this case, each sphere displays a donut pattern with the center of the sphere having no signal.…”

“…To map the field distribution for visualization of the dipole rotation, we utilized a multiple multipole program (MMP) with an e-beam excitation, which also allowed extracting a certain multipole mode. 29,30 Like in experiment, the e-beam energy was set to 80 keV for all the simulations.…”

Coupling finite elements and auxiliary sources for electromagnetic wave propagation

“…, respectively. On the bounded MMP domain Ω 1 m we define an auxiliary volume mesh for the numerical quadrature of the error (38). However, on top of ℳ f , only a mesh on the two-dimensional hypersurface Γ 01 is really necessary for the coupling, in order to compute the numerical integrals on that interface.…”

“…We therefore use layered dipoles , 38 p. 128, Section 4.3.2, which rely on the layered‐media Green ' s functions reported in Reference 12. Their implementation includes Sommerfeld integrals, which present singularities that require integration over complex contours.…”

“…Winkelmann (ABB Corporate Research Center): we gratefully acknowledge their contribution. We also acknowledge U. Koch, researcher at the Institute of Electromagnetic Fields of ETH Zurich (D‐ITET), for his C++ implementation of layered dipoles, 38 p. 128, section 6.3.2.…”