Strongly Coupled Plasmon and Phonon Polaritons as Seen by Photon and Electron Probes

The ability to control and modify infrared excitations in condensed matter is of both fundamental and applied interest. Here we explore a system supporting low-energy excitations, in particular, mid-infrared localized plasmon modes and phonon polaritons that are tuned to be strongly coupled. We study the cou-pled modes by using far-field infrared spectroscopy, state-of-the-art monochromated electron energy-loss spectroscopy, numerical simulations, and analytical modeling. We demonstrate that the electron probe facilitates a precise characterization of polaritons constituting the coupled system, and enables an active control over the coupling and the resulting sample response both in frequency and space. Although far -field optical spectra can be substantially different from near-field electron energy-loss spectra, we show that a direct comparison is possible via postprocessing and right positioning of the electron beam. The resulting spectra allow us to evaluate the key parameters of the coupled system, such as the coupling strength, which we demonstrate to be probe independent. Our work establishes a rigorous description of the spectral features observed in light-and localized electron-based spectroscopies, which can be extended to the analysis of analogous optical systems with applications in heat management and electromagnetic field concentration or nanofocusing.