Polaritons in photonic hypercrystals of van der Waals materials

In-plane Hyperbolic Phonon polaritons (HPhPs) are quasiparticles formed via coupling of photons and optical phonons in in-plane hyperbolic materials and offer unique applications in sensing, thermal emitters and high resolution imaging. However, the large momentum mismatch between photons and these in-plane HPhPs has restricted their technological potential as most experimental demonstration rely on sophisticated and expensive near field detection schemes. In this work, using the example of $\alpha-$MoO$_3$, we demonstrate that by constructing photonic hypercrystals of this material, one can not only excite these in-plane HPhPs in the far field but also tune the far field response via twisting the hypercrystal lattice with respect the lattice of $\alpha-$MoO$_3$. Our findings will pave the way for the development of practical in-plane HPhP devices as well as provide access to new fundamental physics of such materials via conventional and well developed far field measurement techniques.