The Reststrahlen Effect in the Optically Thin Limit: A Framework for Resonant Response in Thin Media

Sharp resonances can strongly modify the electromagnetic response of matter. A classic example is the Reststrahlen effect - high reflectivity in the mid-infrared in many polar crystals near their optical phonon resonances. Although this effect in bulk materials has been studied extensively, a systematic treatment for finite thickness remains challenging. Here we describe, experimentally and theoretically, the Reststrahlen response in hexagonal boron nitride across more than 5 orders of magnitude in thickness, down to a monolayer. We find that the high reflectivity plateau of the Reststrahlen band evolves into a single peak as the material enters the optically thin limit, within which two distinct regimes emerge: a strong-response regime dominated by coherent radiative decay and a weak-response regime dominated by damping. We show that this evolution can be explained by a simple two-dimensional sheet model that can be applied to a wide range of thin media.