Polaritonic non-locality in ultrastrong light-matter coupling

Sub-wavelength electromagnetic field localization has been central in photonic research in the last decade, allowing to enhance sensing capabilities as well as increasing the coupling between photons and material excitations. The ultrastrong light-matter coupling regime in the THz range with split-ring resonators coupled to magnetoplasmons has been widely investigated, achieving successive world-records for the largest light-matter coupling ever achieved. Ever shrinking resonators have allowed to approach the regime of few electrons strong coupling, in which single-dipole properties can be modified by the vacuum field. Here we demonstrate, theoretically and experimentally, the existence of a limit to the possibility of arbitrarily increasing electromagnetic confinement in polaritonic systems. Strongly sub-wavelength fields can excite a continuum of high-momenta propagative magnetoplasmons. This leads to peculiar nonlocal polaritonic effects, as certain polaritonic features disappear and the system enters in the regime of bound-to-continuum strong coupling. Emerging nonlinearities due to the local breaking of Kohn's theorem are also reported.