Can transverse plasmonic fields be revealed by differential phase contrast?
Authors: Löffler Stefan , Bellido Edson P , Bicket Isobel C , Botton Gianluigi A. 
Published: December 2016

Surface plasmons give rise to a wide range of applications from molecular sensors [1] over novel circuit designs [2] to the design of meta‐materials with highly unusual optical properties [3]. Of particular importance are localized surface plasmons (LSPs) that are confined to the surface of nanoparticles as they can give rise to a significant enhancement of electromagnetic fields in the vicinity of the nanostructure. Because LSPs typically are confined to the nanometer regime, TEM is ideally suited for mapping those charge oscillations.

So far, the predominant method of studying plasmon oscillations has been EELS, which allows mapping the strength of selected resonance modes by measuring the energy loss probability of the probe beam for different LSP energies. In a non‐relativistic approximation, this energy loss is brought about by the component of the electric field along the optical axis (and, in principle, the magnetic component perpendicular to the optical axis) of the excited plasmon resonance. Thus, it is impossible to gain any information about the electric field in the viewing plane (i.e., perpendicular to the optical axis). Precisely this component can, however, be studied using differential phase contrast (DPC) [4,5].

DPC exploits the fact that electrons subject to an electromagnetic field are deflected according to the Lorentz force. Any deflection along the optical axis gives rise to a change in kinetic energy and, hence, shows up in EELS. Any deflection perpendicular to the optical axis, however, changes the direction of the electron's momentum, but not its magnitude (in first order approximation). This gives rise to a shift in the electron's momentum distribution. The final momentum distribution, after passing the nanostructure, can then conveniently be measured in the TEM's diffraction plane. Compared to a reference measured without field, the displacement of the transmitted beam shows a shift that is proportional to the field integrated along the electron trajectory.

Here, we used the MNPBEM toolbox [6,7] to simulate the plasmonic response of a 200x50x50 nm³ Ag nanorod to the electron beam (see fig. 1). From the data of the surface charges and currents, we then calculated the EELS maps (see fig. 1) and in‐plane deflections along a line parallel to the nanorod (see fig. 2) for different plasmonic modes. The EELS maps show the typical excitation probabilities for the first two modes with two and three maxima. The in‐plane electric field components show a similar behavior in general, although the local extrema are less pronounced. The DPC deflections are found to be in good agreement with the electric field with some small differences close to the center of the rod which can be attributed to the cumulative nature of the DPC deflections as well as retardation effects. The absolute magnitude of the DPC deflections in fig. 2 is of the order of 0.1 µrad at 300 keV which, albeit small, should be measurable with latest generation TEMs when using large camera lengths and/or the LACBED technique. In addition, the deflections can be increased, e.g., by using a lower acceleration voltage.

This work shows that it should be feasible to determine all three components of the electromagnetic field caused by plasmons using a combination of DPC and EELS using state‐of‐the‐art TEMs. This will open up new possibilities for understanding and designing novel plasmonic devices.