Space-time duality in polariton dynamics

The spatial and temporal dynamics of wave propagation are intertwined. A common manifestation of this duality emerges in the spatial and temporal decay of waves as they propagate through a lossy medium. A complete description of the non-Hermitian wave dynamics in such a lossy system, capturing temporal and spatial decays, necessitates the use of complex-valued frequency and/or wavenumber Eigen-values. Here, we demonstrate that the propagation of polaritons - hybrid light-matter quasiparticles - can be broadly controlled in space and time by temporally shaping their photonic excitation. Using time-domain terahertz near-field nanoscopy, we study plasmon polaritons in bilayer graphene at sub-picosecond time scales. Suppressed spatial decay of polaritons is implemented by temporally engineering the excitation waveform. Polaritonic space-time metrology data agree with our dynamic model. Through the experimental realization and visualization of polaritonic space-time duality, we uncover the effects of the spatio-temporal engineering of wave dynamics; these are applicable to acoustic, photonic, plasmonic, and electronic systems.