Full Three-Dimensonal Reconstruction of the Dyadic Green Tensor from Electron Energy Loss Spectroscopy of Plasmonic Nanoparticles

Anton Hörl,Andreas Trügler,Ulrich Hohenester

doi:10.1021/acsphotonics.5b00256

Anton Hörl, Andreas Trügler + Show 1 more

Open Access

https://doi.org/10.1021/acsphotonics.5b00256

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Journal: ACS photonics	Publication Date: Sep 11, 2015
Citations: 37	License type: cc-by

Affiliation: University of Graz

Abstract

Electron energy loss spectroscopy (EELS) has emerged as a powerful tool for the investigation of plasmonic nanoparticles, but the interpretation of EELS results in terms of optical quantities, such as the photonic local density of states, remains challenging. Recent work has demonstrated that, under restrictive assumptions, including the applicability of the quasistatic approximation and a plasmonic response governed by a single mode, one can rephrase EELS as a tomography scheme for the reconstruction of plasmonic eigenmodes. In this paper we lift these restrictions by formulating EELS as an inverse problem and show that the complete dyadic Green tensor can be reconstructed for plasmonic particles of arbitrary shape. The key steps underlying our approach are a generic singular value decomposition of the dyadic Green tensor and a compressed sensing optimization for the determination of the expansion coefficients. We demonstrate the applicability of our scheme for prototypical nanorod, bowtie, and cube geometries.

Highlights

Electron energy loss spectroscopy (EELS) has emerged as a powerful tool for the investigation of plasmonic nanoparticles, but the interpretation of EELS results in terms of optical quantities, such as the photonic local density of states, remains challenging
This leads to a nonlocal response function, which allows for a tomographic reconstruction only under restrictive assumptions, such as the applicability of the quasistatic approximation or a plasmonic response governed by a single mode
To prove the applicability of our reconstruction scheme, we generate the “experimental” EELS data Γexp using the simulation toolbox MNPBEM for plasmonic nanoparticles.[20,21]

Summary

Introduction

Electron energy loss spectroscopy (EELS) has emerged as a powerful tool for the investigation of plasmonic nanoparticles, but the interpretation of EELS results in terms of optical quantities, such as the photonic local density of states, remains challenging. The problem with EELS tomography is that the measurement signal (the loss probability) is not the integral of local losses along the electron trajectory but involves a two-step process where the swift electron first excites a particle plasmon and performs work against the induced particle plasmon field This leads to a nonlocal response function, which allows for a tomographic reconstruction only under restrictive assumptions, such as the applicability of the quasistatic approximation or a plasmonic response governed by a single mode. We develop a rather generic model for the EELS probabilities, which depends on a few parameters, and determine the parameters such that the model data match as closely as possible the measured data Within this approach we are able to obtain the most accurate reconstructions of the dyadic Green tensor, which, in turn, allows us to extract the three-dimensional photonic LDOS from a collection of tilted EELS maps. Bulk losses are due to Cherenkov radiation and electronic excitations,[1] and the loss probability is obtained by multiplying the loss probability per unit length γbj ulk(ω), inside

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Conclusion