Quantization of optical quasinormal modes for spatially separated cavity systems with finite retardation

A multicavity quantization scheme is developed using quasinormal modes (QNMs) of optical cavities embedded in a homogeneous background medium for cases where retardation is significant in the intercavity coupling. Using quantities that can be calculated in computational optics with numerical Maxwell solvers, we extend previous QNM quantization schemes and define a quantitative measure to determine if a separate quantization of QNM cavities is justified or if a joint quantization of the system is necessary. We test this measure for the examples of two coupled one-dimensional dielectric slabs and a three-dimensional dimer consisting of metal nanorods acting as QNM cavities. For sufficiently large separations, the new scheme allows for an efficient treatment of multicavity phenomena using parameters defined for the individual cavities. Formulating the Hamiltonian in a familiar system-bath form, the scheme connects the rigorous QNM theory and widespread phenomenological models of open cavities coupled to a shared photonic bath with parameters obtained directly from Maxwell calculations.