Enhanced emission near exceptional points shaped by Riemann surface topology

The Purcell effect describes how the spontaneous emission of an emitter can be modified by placing it in a resonant cavity. The degree of Purcell enhancement is controlled by the Q-factor and the local density of states (LDoS) profile of the resonant cavity. Recently, research has examined cases of non-Purcell enhancement in resonant cavities by utilizing non-Hermitian spectral degeneracies in parameter space known as exceptional point degeneracies (EPDs). At an EPD of Nth order, N eigenfrequencies and their corresponding eigenvectors coalesce. The detuned resonances from the EPD due to a small perturbation follow a fractional series expansion which affects the shape of the eigenfrequency Riemann surfaces. We experimentally demonstrate, using two coupled RLC cavities at EPD-2 conditions, an anomalous Purcell physics characterized by a three-fold enhanced emissivity near EPDs. When the order of EPD is further increased, e.g. to an EPD-3, we identify two types of perturbations that lead to a completely different fractional series eigenvalue expansion and show, theoretically and experimentally, that their dominant fractional power term influences the scaling of the non-Purcell emissivity enhancement near the EPD-3 by altering the LDoS profiles.