Abstract
We theoretically describe how fast electrons couple to polaritonic modes in uniaxial materials by analyzing the electron energy loss (EEL) spectra. We show that in the case of an uniaxial medium with hyperbolic dispersion, bulk and surface modes can be excited by a fast electron traveling through the volume or along an infinite interface between the material and vacuum. Interestingly, and in contrast to the excitations in isotropic materials, bulk modes can be excited by fast electrons traveling outside the uniaxial medium. We demonstrate our findings with the representative uniaxial material hexagonal boron nitride. We show that the excitation of bulk and surface phonon polariton modes is strongly related to the electron velocity and highly dependent on the angle between the electron beam trajectory and the optical axis of the material. Our work provides a systematic study for understanding bulk and surface polaritons excited by a fast electron beam in hyperbolic materials and sets a way to steer and control the propagation of the polaritonic waves by changing the electron velocity and its direction.
Highlights
Polar materials have become of high interest in the field of nanophotonics due to their ability to support phonon polaritons, quasiparticles which result from the coupling between electromagnetic waves and crystal lattice vibrations [1,2] with a characteristic wavelength lying in the mid-infrared region
We show that the excitation of bulk and surface phonon polariton modes is strongly related to the electron velocity and highly dependent on the angle between the electron beam trajectory and the optical axis of the material
Our work provides a systematic study for understanding bulk and surface polaritons excited by a fast electron beam in hyperbolic materials and sets a way to steer and control the propagation of the polaritonic waves by changing the electron velocity and its direction
Summary
Polar materials have become of high interest in the field of nanophotonics due to their ability to support phonon polaritons, quasiparticles which result from the coupling between electromagnetic waves and crystal lattice vibrations [1,2] with a characteristic wavelength lying in the mid-infrared region. The crystal layer structure that constitues h-BN, mediated via interlayer van der Waals forces, produces a uniaxial optical response of the material This implies that the dielectric function of h-BN needs to be described by a diagonal tensor ↔ε with two principal axes [12,13]: εx = εy = ε⊥ and εz = ε. Efficient design and utilization of h-BN structures require spectroscopic studies with adequate spatial resolution This can be provided, for instance, by electron energy-loss spectroscopy (EELS) using electrons as localized electromagnetic probes. We further demonstrate that the probing electron traveling above h-BN in aloof trajectories excites volume phonon polaritons (remotely activation) All these findings offer a way to steer and control the propagation of the polaritonic waves and reveal the importance of the anisotropic optical response of the material in the EELS analysis
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