The realization of strong interactions between light and matter at room temperature at the nanoscale has been a central subject of quantum optics. Surface plasmons(SP), formed on the surface of metal nanostructures, can confine the optical field in the subwavelength space. When the energy exchange between light and matter influences the electromagnetic distribution patterns of their surroundings and the energy levels of the entire system, the system becomes a new hybrid system that realizes strong coupling [1], [2], [3], [4]. It helps advance the basic theory of quantum optics [5], [6], [7] and has wide applications in the fields of quantum-optical devices, quantum communication, and quantum computing [8], [9], [10], [11].

The interaction between light and matter can be divided into weak and strong couplings according to the strength of the energy exchange. When the coupling strength between the exciton and SP is more than half of the sum of their respective losses, the energy level of the hybrid system splits and a new hybrid plasmon–exciton state is formed [12], [13], [14], [15], [16]. The hybrid plasmon–exciton state is called ’plexciton’. Strong coupling has been realized in many different systems [17], [18], [19], [20]. The coupling strength is proportional to (N/V), where N is the effective number of excitons and V is the cavity mode volume. Increasing N [21], [22], [23] and decreasing V [24], [25], [26] are the main methods to increase coupling strength. Strong coupling is easier to realize with the development of nanomaterials such as quantum dots [27], [28], [29] and two-dimensional transition metal dichalcogenides [30], [31], [32]. Therefore, the strong coupling of exciton–SP–exciton systems has rapidly become an emerging research topic. Compared with two-mode coupling, three-mode coupling has more energy-loss channels and a richer modulation capability [33], [34], [35]. The three-mode systems can achieve the two-photon process [36]. The exciton–SP–exciton systems can serve as a research platform for energy transfer processes [20]. The SP–exciton–SP systems can adjust different SPs independently [37], providing a high modulation capability. However, the phenomenon that the peak amplitude of MPB is lower than those of LPB and UPB has not been studied. The coupling mechanism of the middle plexciton state needs further investigation.

In this paper, we develop the Jaynes–Cummings model to investigate the properties of MPB in the excitons–SP–excitons system. First, Hopfield coefficients, which show the composition of the eigenstates, are calculated. The results indicate that the fraction of SP in MPB is relatively low, which reveals that MPB depends more on excitons. Second, the full quantum scattering spectrum is obtained, which agrees with the coupled oscillator model. We also derive an equation for the peak MPB amplitude, which is relevant to the coupling coefficient g and detuning between excitons. Because the coupling strength is larger than the detuning strength under the experimental conditions, the peak MPB amplitude is lower than those of LPB and UPB. Finally, we calculate the average population of eigenstates and find that the average MPB population is relatively low compared to those of LPB and UPB, indicating suppression of MPB. We design a hybrid system of Au nanorods coated with two layers of J-aggregated nanoshells to confirm our theoretical results. The simulation results also show a relatively low peak amplitude of MPB, which fits well with the results of our method.