Photon-induced near-field electron microscopy: Mathematical formulation of the relation between the experimental observables and the optically driven charge density of nanoparticles

Abstract

Photon-induced near-field electron microscopy (PINEM) enables the visualization of the plasmon fields of nanoparticles via measurement of photon-electron interaction [S. T. Park et al., New J. Phys. 12, 123028 (2010)]. In this paper, the field integral, which is a mechanical work performed on a fast electron by the total electric field, plays a key role in understanding the interaction. Here, we reexamine the field integral and give the physical meaning by decomposing the contribution of the field from the charge-density distribution. It is found that the "near-field integral" (the near-field approximation of the field integral) can be expressed as a convolution of the two-dimensional projection of the optically driven charge-density distribution in the nanoparticle with a broad radial response function. This approach, which we call the "convolution method," is validated by applying it to Rayleigh scattering cases, where previous analytical expressions for the field integrals in near-field approximations are reproduced by the convolution method. The convolution method is applied to discrete dipole approximation calculations of a silver nanorod, and the nature of the induced charge-density distributions of its plasmons is discussed.

Electron energy losses and cathodoluminescence from complex plasmonic nanostructures: spectra, maps and radiation patterns from a generalized field propagator

“…Its numerical implementation is fast and does not rely on numerical libraries. An extension of this approach would be adequate for the computation of the optical forces exerted on metallic nanoparticles or to more complex experiments such as electron energy gain spectroscopy experiments (García de Abajo and Kociak 2008b, Yurtsever et al 2012, Talebi et al 2013, Park and Zewail 2014. We consider an electron traveling in a medium of dielectric constant ε 2 with a velocity = −v v e z ( > v 0) towards a substrate located in the < z 0 region and characterized by a dielectric constant ε 1 (see figure 1).…”

“…The connection of the electron energy loss probability with the local density of electromagnetic modes of metallic particles has been analyzed in detail (García de Abajo and Kociak 2008a, Hohenester et al 2009, Boudarham and Kociak 2012. Recent advances in combined electron/optical spectroscopy techniques such as electron energy gain spectroscopy demonstrated in ultrafast transmission electron microscopes (TEM) or surface plasmon threedimensional (3D) imaging push forward the need and development of novel simulation techniques (Hohenester et al 2009, Nicoletti et al 2013, Hörl et al 2013, Rivacoba and Zabala 2014, Park and Zewail 2014.…”

Simultaneous observation of the quantization and the interference pattern of a plasmonic near-field

“…Alternatively, photoexcitation and subsequent EELS imaging of SPPs using the time-resolved photon-induced near-field electron microscopy (PINEM) technique has recently demonstrated additional control of the SPP properties, as well as the possibility to film their evolution in the femtosecond (fs) time domain 19 20 . These experiments allow the observation of SPPs in multiple dimensions; space, energy and time, yielding unprecedented insight into their fundamental properties.…”

Photon gating in four-dimensional ultrafast electron microscopy

“…The use of femtosecond lasers to generate the electron probe and excite the specimen has made it possible to achieve temporal resolution on the femtosecond time scale, as determined by the cross-correlation of the optical and electron pulses. One important method in the UEM repertoire is photon-induced near-field electron microscopy (PINEM) (4,5), in which the dynamic response detected by the electron probe is the pump-induced charge density redistribution in nanoscale specimens (6).…”