Tomography of surface phonon polarition fields by electron energy loss spectroscopy

Surface phonon polaritons (SPPs) are coupled photon-phonon excitations that emerge at thesurfaces of dielectric ionic nanostructured materials. Using a highly monochromated electronbeam in a scanning transmission electron microscope (STEM), SPPs can be excited by theelectron beam and mapped by electron energy loss spectroscopy (EELS). A tilt series of EELSspectrum images recorded at a number of tilt angles can be used as the basis for tomographicallyreconstructing the complete three-dimensional (3D) vectorial picture of the local photonic densityof states (LDOS) [1] (Fig. 1). Knowing the full 3D LDOS promises insights into nanoscale physicalphenomena and is invaluable to the design and optimization of nanostructures for fascinating newuses.In this work, we perform a thorough examination of the tomography scheme introduced in [1].Tomographic reconstruction of the LDOS is done by means of minimizing the difference betweenreprojected EELS maps of a reference structure and the simulated (or measured) EELS maps ofthe real structure (Fig. 2). The reprojected maps are calculated based on an eigenmodedecomposition, dependent on the used reference structure. This reference structure is notnecessarily equivalent to the real structure of the system, but may be a simplified representation ofits geometry and ignore changes in the surroundings, such as the substrate.Based on a previous approach used for surface plasmon reconstruction [2, 3], a generalizedscheme, usable for the quasistatic case was performed to deal with mode mixing and symmetrybreaking, which allows for using idealized reference structures in the reconstruction. To validatethis approach, in simulation studies, we consider the impact of the choice of reference structureand the type of eigenmodes used. Finally, we apply these findings to the 3D reconstruction ofexperimental EELS data on more complex structures (Fig. 3).