Observation of a hybrid state of Tamm plasmons and microcavity exciton polaritons

We present evidence for the existence of a hybrid state of Tamm plasmons and microcavity exciton polaritons in a II-VI material based microcavity sample covered with an Ag metal layer. The bare cavity mode shows a characteristic anticrossing with the Tamm-plasmon mode, when microreflectivity measurements are performed for different detunings between the Tamm plasmon and the cavity mode. When the Tamm-plasmon mode is in resonance with the cavity polariton four hybrid eigenstates are observed due to the coupling of the cavity-photon mode, the Tamm-plasmon mode, and the heavy- and light-hole excitons. If the bare Tamm-plasmon mode is tuned, these resonances will exhibit three anticrossings. Experimental results are in good agreement with calculations based on the transfer matrix method as well as on the coupled-oscillators model. The lowest hybrid eigenstate is observed to be red shifted by about 13 meV with respect to the lower cavity polariton state when the Tamm plasmon is resonantly coupled with the cavity polariton. This spectral shift which is caused by the metal layer can be used to create a trapping potential channel for the polaritons. Such channels can guide the polariton propagation similar to one-dimensional polariton wires.


Supplementary Figure S1.
thickness gradient is created in the upper layer of the 11 Here we present the influence of the number of top DBR pairs on the splitting energy between the Tamm plasmon and the cavity mode.  Fig. S2 (b) ). The origin of the second resonance is due to the formation of the T mode at the interface between the metal and DBR Here we present the influence of the number of top DBR pairs on the splitting energy between the Tamm plasmon and the cavity mode. Here we discuss the difference between the bare Tamm plasmon and the hybrid Tamm plasmon-cavity system.
In the calculation it was assumed that the TP structure consists of a DBR and a 40 nm Ag layer, whereas the hybrid structure consists of top DBR, cavity, and bottom DBR with a 40 nm Ag layer on top (as shown in Fig. 1(a)). Fig. S3 shows mode formation of the bare TP structure (red) and the hybrid TP-cavity structure (black line). The upper layer of the top DBR was adjusted so that the TP mode is in resonance with the cavity mode. Two nearly symmetric modes can be observed which further verifies our experimental observation (Fig   2(c) and S2 (c)). One of these modes Q factor is increased by a factor of 2 with respect to the bare TP mode due to the reduction of the metal absorption losses in the hybrid structure. Such an enhancement of the Q factor makes this hybrid system more attractive compared to bare TP system. Figure S4. Simulated microreflectivity spectra of the bare Tamm plasmon structure for different Ag layer thicknesses.

Supplementary
Optimized Ag layer thickness: The TP eigenenergy can be varied by changing either the top layer or the metal layer thickness. However, the metal absorption losses increase by increasing the metal layer thickness. Therefore, altering the DBR top layer thickness would be favorable in order to tune the eigenenergy without reducing the quality of the structure. Fig. S4 shows the calculated reflectivity for different Ag layer thicknesses. The TP mode shifts to higher energies by increasing Ag thickness accompanied by an increase of the Q factor. However, the transmission of the TP mode diminishes by the enhancement of the Ag thickness. Hence, we need an optimum metal layer thickness in order to have sufficient transmission and relatively high Q factor. Ag thickness of 40 nm is an optimum trade-off between the Q factor and the mode transmission. Figure S5. The calculated lower polariton energy shift ∆E at 4K (red) and the cavity Q factor (normalized to the Q factor of the MC with a 10-fold top DBR, blacksymbols) as a function of the number of top DBR pairs. Red and black lines are shown for the guidance of the eye.

Supplementary
Influence of the variation of the number of top DBR pairs on the cavity Q factor as well as on the lower polariton (LP) energy shift ∆E: The LP energy shift ∆E with respect to the LP position of the metal free MC can be varied by changing the number of top DBR pairs as shown in Fig. S5 (red-symbols). In the calculation the structure of the MC was assumed as shown in Fig. 1 (a) and the thickness of the upper layer of the top DBR layer was adjusted so that the heavy-hole exciton (X hh ), cavity, and TP mode are in resonance (E hh = E C = E T ). From the calculation we can observed that the confinement potential ∆E reduces by increasing the number of DBR pairs. The reason for the reduction of ∆E is the same as we have discussed for the bare interaction between the TP and cavity modes (first part of the supplementary information). However, the cavity Q factor enhances by increasing the number of top DBR pairs as expected (Fig S5 (black-symbols)).
Nevertheless, the value of ∆E is still in the meV range when the Q factor is enhanced by a factor of about 3.5. Therefore, this hybrid approach is also suitable for the high Q MC system.