Revisit Cherenkov Radiation in the Hyperbolic Metamaterials

Cherenkov radiation refers to the physical phenomenon that a moving charged particle emits coherent photons, when the particle velocity is larger than the phase velocity of light in the medium. Interestingly, recent experiments have reported that hyperbolic metamaterials enable Cherenkov radiation without any velocity cutoff, owing to the extremely large photonic density of states. In this work, we revisit the radiation features of Cherenkov radiation in hyperbolic metamaterials constructed by periodic metallodielectric structures. We found that the nonlocal effects have strong impacts on Cherenkov radiation in this configuration. On the one hand, the spatial dispersion from the finite structural size truncates the large wavevector of bulk Bloch modes, giving rise to finite photonic density of states. As a result, a nonzero velocity threshold appears. On the other hand, the nonlocal charge screening in metals results in an ultimate velocity threshold in the quantum size regime, where the velocity threshold can no longer be reduced by decreasing the structural size. Although the nonlocal Cherenkov threshold deteriorates the performance of freeelectron sources in the low energy regime, the additional longitudinal modes resulting from spatial nonlocality can enhance the photon emission at epsilon-near-zero frequencies. Our work not only completes the theory of Cherenkov radiation in the hyperbolic metamaterials, but also provides significant guidance for the future experiments in this area.