Near-field mapping of complex-valued wavevectors of in-plane hyperbolic phonon polaritons in α-MoO3

Hyperbolic phonon polaritons (HPhPs) in α-phase molybdenum trioxide (α-MoO3) have recently attracted significant attention. They propagate anisotropically along the flake of α-MoO3 and show anomalously concave wavefronts when being excited by a pointlike source. Such anisotropic propagation is governed by the anisotropic wavevectors of HPhPs, which have been studied in different works. However, extracting the complex-valued wavevectors of all HPhP modes directly from the observed anomalous wavefront remains elusive. Here, we theoretically and experimentally demonstrate that the complex-valued HPhP wavevectors can be accurately quantified by fitting the concave wavefront profiles with a modified damped sine-wave function in all allowed directions. To that end, HPhPs are launched by an infrared antenna on a thin flake of α-MoO3 and are imaged in real space by using scanning near-field optical microscope. From the recorded concave wavefronts of HPhPs, we have experimentally retraced both the real part and the imaginary part of polariton wavevectors along different propagation directions. Our results are of fundamental importance for analyzing the optical properties of HPhPs in α-MoO3, which can also be generic to other anisotropic optical/polaritonic systems.