Microcavities and nanoresonators are characterized by their quality factors Q and mode volumes V. While Q is unambiguously defined, there are still questions on V and in particular on its complexvalued character, whose imaginary part is linked to the non-Hermitian nature of open systems. Helped by cavity perturbation theory and near field experimental data, we clarify the physics captured by the imaginary part of V and show how a mapping of the spatial distribution of both the real and imaginary parts can be directly inferred from perturbation measurements. This result shows that the mathematically abstract complex mode volume in fact is directly observable.This supplementary Material provides complementary results and discussions to the main text, starting with a Section detailing discussing the reliability of the Δ -measurements, followed by a formal comparison of the classical perturbation formula of Eqs. (1) and (2), a study of the accuracy of Eq. (2) for predicting resonance shifts, and by an analytical study of the domain of validity of Eq. (2) that leads to upper bounds for the maximum perturber strength.

We analyse the resonant mode structure and local density of states in high-Q hybrid plasmonic-photonic resonators composed of dielectric microdisks hybridized with pairs of plasmon antennas that are systematically swept in position through the cavity mode. On the one hand, this system is a classical realization of the cooperative resonant dipole–dipole interaction through a cavity mode, as is evident through predicted and measured resonance linewidths and shifts. At the same time, our work introduces the notion of ‘phased array’ antenna physics into plasmonic-photonic resonators. We predict that one may construct large local density of states (LDOS) enhancements exceeding those given by a single antenna, which are ‘chiral’ in the sense of correlating with the unidirectional injection of fluorescence into the cavity. We report an experiment probing the resonances of silicon nitride microdisks decorated with aluminium antenna dimers. Measurements directly confirm the predicted cooperative effects of the coupled dipole antennas as a function of the antenna spacing on the hybrid mode quality factors and resonance conditions.