Exploitation of strong light-matter interactions in plasmonic systems is vital for both fundamental studies and the development of new applications, which enables exceptional physical phenomena and promotes potential applications in nanophotonics, information communication, and quantum information processing. Here, we present an analytic model of the interaction between localized surface plasmon resonances and excitons, where a semiclassical method is utilized. Two kinds of metal nanoparticles (nanosphere and nanoellipsoid) are considered in our study. We derive the relations between the plasmon-exciton coupling strength and the geometry and material parameters of the coupled systems when the nanoparticles are put in an excitonic medium, which give an important guide to achieve strong plasmon-exciton coupling. Rabi splittings and anticrossing behavior are also demonstrated in the calculated extinction spectra. Furthermore, we propose an analytic model to describe the strong coupling between excitons and plasmon in a core-shell nanorod structure which is widely used in experiments. Our study provides a simple yet rigorous prescription to both analyze and design plexcitonic systems aiming at strong light-matter interactions.
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