Observed enhanced emission at higher-order exceptional points in RF circuits

The Purcell effect -- stemming directly from the celebrated Fermi's Golden Rule -- links the enhanced emissivity of an emitter to the local density of states (LDoS) of a surrounding cavity. Under typical circumstances the LDoS is assumed to have a Lorentzian lineshape. Here, we go beyond the traditional Purcell framework by designing RF cavities with non-Lorentzian LDoS caused by higher-order non-Hermitian exceptional point degeneracies (EPDs) where $N\geq 2$ eigenfrequencies and their associated eigenmodes coalesce. We experimentally demonstrate a non-conventional emissivity enhancement (as compared to the isolated resonance regime) that increases with the EPD order $N$. The theoretical analysis traces its origin to an $N$-th power Lorentzian LDoS line shape that dominates under judicious spatially designed cavity losses. Our results reveal a new route to design cavities that do not rely on ultrahigh $Q$-factor resonators or small modal volumes.