Probing the Photonic Local Density of States with Electron Energy Loss Spectroscopy

Abstract

Electron energy loss spectroscopy performed in transmission electron microscopes is shown to directly render the photonic local density of states with unprecedented spatial resolution, currently below the nanometer. Two special cases are discussed in detail: (i) 2D photonic structures with the electrons moving along the translational axis of symmetry and (ii) quasiplanar plasmonic structures under normal incidence. Nanophotonics in general and plasmonics, in particular, should benefit from these results connecting the unmatched spatial resolution of electron energy loss spectroscopy with its ability to probe basic optical properties such as the photonic local density of states. DOI: 10.1103/PhysRevLett.100.106804 PACS numbers: 73.20.Mf, 78.20.Bh, 79.20.Uv While a plethora of nanophotonic structures is currently being devised for diverse applications like achieving single molecule sensitivity in biosensing [1] or molding the flow of light over nanoscale distances for signal processing [2], no optical characterization technique exists that can render spectroscopic details with truly nanometer spatial resolution. The need for that kind of technique is particularly acute in nanometric plasmonic designs that benefit from sharp edges and metallic surfaces in close proximity to yield large enhancements of the electromagnetic field.Scanning transmission electron microscopes (STEM) can plausibly cover this gap, as they perform electron energy loss spectroscopy (EELS) with increasingly improved energy resolution that is quickly approaching the width of plasmon excitations in noble metals [3] and with spatial resolution well below the nanometer [4]. The connection between EELS and photonics can be readily established when low-energy losses in the sub-eV to a few eV range are considered, compatible with typical photon energies in photonic devices. A formidable amount of information is available in the literature for this so-called valence EELS, including for instance studies of single nanoparticles of various shapes [3,5], interacting nanoparticles [6], thin films [7], composite metamaterials [8], and carbon nanostructures [9]. Many of these reports are relevant to current nanophotonics research, in which the optical response of nanoparticles, nanoparticle assemblies, and patterned nanostructures plays a central role. In this context, EELS has been recently demonstrated to image plasmon modes with spatial resolution better than a hundredth of the wavelength in triangular nanoprisms [3]. However, despite significant progress from the theoretical side [10], no synthetic and universal picture has emerged to explain the spatial modulation of EELS measurements on arbitrary nanostructures.In this Letter, we show that EELS provides direct information on the photonic local density of states (LDOS), and thus it constitutes a suitable tool for truly nanometric characterization of photonic nanostructures. A rigorous derivation of this statement is offered, illustrated by numerical examples for both translationally invariant geomet...

Extremely confined gap surface-plasmon modes excited by electrons

“…7 and Supplementary Note 4). We note that such a direct comparison between EELS measurements and optical response is in general possible but challenging, as electrons and photons excite different linear combinations of plasmonic eigenstates [36][37][38] . Furthermore, complications in carrying out EELS and optical spectroscopy under different environmental conditions can lead to slight energy shifts when confronting the two types of spectra (see ref.…”

Exciton dispersion from first principles

“…Typical examples are intra-atomic d-d excitations in strongly correlated transition-metal oxides [17][18][19] or longitudinal p-like excitons in sp cubic crystals. 2,3,9 In addition, the new electron microscopes are able today to reach very high spatial resolution (well under 1 nm) for the loss spectroscopy, [20][21][22] which, in order to be investigated from the theoretical point of view, requires the knowledge of the dielectric function not at just q = 0, but at many q's, in order to Fourier transform back in real space. Concerning theory, however, ab initio simulations lie a long way behind experiments.…”

Purcell factor for a point-like dipolar emitter coupled to a two-dimensional plasmonic waveguide

“…It is a key quantity to understand spatially and spectrally resolved electron energy loss spectroscopy [19]. Equation (5) makes then a direct link between 2D and 3D LDOS.…”