The Purcell effect—stemming directly from the celebrated Fermi 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 line shape. Here, we go beyond the traditional Purcell framework by designing rf cavities with non-Lorentzian LDOS line shapes caused by higher-order non-Hermitian exceptional-point degeneracies (EPDs) where $N\ge 2$ eigenfrequencies and their associated eigenmodes coalesce. We experimentally demonstrate a nonconventional emissivity enhancement (as compared with the isolated resonance regime) that increases with the EPD order $N$. The theoretical analysis traces its origin to an $N\mathrm{th}$-power Lorentzian LDOS line shape that dominates under judicious spatially designed cavity losses. Our results reveal a route to design cavities that do not rely on ultrahigh-$Q$-factor resonators or small modal volumes.

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• Local density of states
• Optoelectronics
• Photonics
• Spontaneous emission
• Coupled oscillators
• Exceptional points
• Cavity resonators
• Room temperature RF