Superemitters in hybrid photonic systems: A simple lumping rule for the local density of optical states and its breakdown at the unitary limit

We theoretically investigate how the enhancement of the radiative decay rate of a spontaneous emitter provided by coupling to an optical antenna is modified when this ``superemitter'' is introduced into a complex photonic environment that provides an enhanced local density of optical states (LDOS) itself, such as a microcavity or stratified medium. We show that photonic environments with increased LDOS further boost the performance of antennas that scatter weakly, for which a simple multiplicative LDOS lumping rule holds. In contrast, enhancements provided by antennas close to the unitary limit, i.e., close to the limit of maximally possible scattering strength, are strongly reduced by an enhanced LDOS of the environment. Thus, we identify multiple scattering in hybrid photonic systems as a powerful mechanism for LDOS engineering.