Organic-based microcavities with vibronic progressions: Photoluminescence

We theoretically study the photoluminescence properties of organic-based microcavities with vibronic progressions. We analyze the relaxation from the exciton reservoirs to the polariton anticrossing region; the presence of vibronic levels qualitatively enriches the physics of the system with the appearance of new decay channels. The relaxation dynamics is studied with a master equation and the cavity photoluminescence is obtained from the polariton stationary population. We show that the exciton radiative recombination in which a molecule ends up in a vibrationally excited level of the electronic ground state can lead to qualitatively new features in the cavity luminescence spectrum.

Figure 1

(Color online) Sketch representing the energy levels of the molecule composing the organic crystal. Usually $E_{10}⪢E_{01}$ and $E_{11}-E_{10}\sim E_{01}$.

Figure 2

(Color online) Sketch representing the interaction of the molecule with light. The interaction of photons with $|00⟩\leftrightarrow |10⟩$ and $|00⟩\leftrightarrow |11⟩$ transitions gives rise to polaritons [(a) and (b)]. Since the absorption from the $|01⟩$ level is almost immaterial, the photoemission from the $|10⟩\to |01⟩$ and $|11⟩\to |01⟩$ transitions works as a polariton relaxation channel [(c) and (d)].

Figure 3

(Color online) Dispersion relations of the normal propagating modes for the microcavity considered in the numerical simulation. The organic active layer is constituted by molecules with one vibronic replica both at the electronic ground and excited states, as depicted in Fig. 1. Photons whose polarization is parallel to the dipole interact with excitons and give rise to three polariton branches, the third arising from the interaction with the vibronic level $|11⟩$. The middle photonlike dispersion relation represents the other photon polarization.

Figure 4

(Color online) Stationary polariton populations of the simulated system. The lower polariton features $e$ population peak at around $5\times {10}^{-4}{\text{Å}}^{-1}$.

Figure 5

(Color online) Pictorial representation of the photoluminescence coming from the simulated microcavity. The luminescence features a peak in the lower polariton branch that is due to the radiative recombination of the excitons in the lower reservoir. An explicit signature of such a process is the energy difference between the peak and the reservoir, that must be equal to a vibronic quantum $E_{01}$.

Figure 6

Pictorial representation of the photoluminescence coming from the simulated microcavity. Each solid line represents the luminescence spectrum at definite $\mathbf{k}$ vector. The darkest one is taken at $\left|\mathbf{k}\right|\sim 0{\text{Å}}^{-1}$ whereas the lightest one is taken at $\left|\mathbf{k}\right|\sim 0.001{\text{Å}}^{-1}$. It is possible to recognize light coming from middle polariton branch, as well as the peak from the lower polariton.