Multimode Organic Polariton Lasing

We present a beyond-mean-field approach to predict the nature of organic polariton lasing, accounting for all relevant photon modes in a planar microcavity. Starting from a microscopic picture, we show how lasing can switch between polaritonic states resonant with the maximal gain, and those at the bottom of the polariton dispersion. We show how the population of nonlasing modes can be found, and by using two-time correlations, we show how the photoluminescence spectrum (of both lasing and nonlasing modes) evolves with pumping and coupling strength, confirming recent experimental work on the origin of blueshift for polariton lasing.

Figure 1

(a) Organic molecules are placed inside a microcavity that supports multiple photon modes. (b) Molecular level structure and processes: Incoherent electronic pumping has rate ${\mathrm{\Gamma }}_{\uparrow }$, electronic decay ${\mathrm{\Gamma }}_{\downarrow }$, and dephasing ${\mathrm{\Gamma }}_z$. The thermal (de)excitation rates of the vibrational modes are ${\gamma }_{\uparrow (\downarrow )}$. (c) Discretized photon dispersion. Integer $k$ labels modes. Light-matter coupling hybridizes the photon (${\omega }_k$) and exciton ($ϵ$) into polariton modes. Figure plotted for ${\omega }_0=ϵ$. We truncate the photon modes at $K=N_{\text{modes}}$ where the hybridization becomes weak.

Figure 2

Phase diagrams for the system at two values of the Rabi splitting ${\mathrm{\Omega }}_R$. The top row shows total photon occupation vs external pump rate (vertical) and the detuning of the photon dispersion from the zero vibron transition (horizontal). The white line is the single mode, MF linear stability result. The bottom row shows the $K$ index of the highest occupied photon mode. The white dashed line indicates the parameters used in Figs. 3. The parameters used here are $S=0.1$, ${\omega }_v=0.2$, ${\mathrm{\Gamma }}_{\downarrow }=\kappa ={10}^{-4}$, ${\mathrm{\Gamma }}_z=0.03$, ${\gamma }_v=0.02$, and $k_b{T}_v=0.025\mathrm{eV}$.

Figure 3

Lasing mode switching for two different Rabi splittings ${\mathrm{\Omega }}_R$. The top row shows photon occupation as a function of external pump when ${\omega }_0$ falls in between the (1-0) and (2-0) transitions (${\omega }_0-ϵ=-1.5{\omega }_v$). (a) For Rabi splitting of ${\mathrm{\Omega }}_R=0.1\mathrm{eV}$, the nonzero vibron transitions (vibronic sidebands) are outside of the range of strong coupling. There is clear switching between two lasing modes, one close to (1-0) and the other at $K=0$. Each mode that lases behaves linearly (a linear fit is shown by the thinner, fainter lines), similarly to textbook weak-coupling single-mode models. Reference [37] shows the threshold behavior on logarithmic scale. (b) For Rabi splitting of ${\mathrm{\Omega }}_R=0.4\mathrm{eV}$ the lasing behavior is strongly influenced by the light-matter coupling, and the curves are no longer linear. The bottom row shows the occupation of all photon modes vs bare photon frequency ${\omega }_k$, for the same values of ${\omega }_0$ and ${\mathrm{\Omega }}_R$ as in (a),(b), and pump strengths as marked by the gray vertical lines in panels (a),(b). Other parameters are the same as in Fig. 2.

Figure 4

(a)–(b) Photoluminescence spectra of the system for (a) ${\mathrm{\Gamma }}_{\uparrow }=0.1{\mathrm{\Gamma }}_{\downarrow }$ and (b) ${\mathrm{\Gamma }}_{\uparrow }={\mathrm{\Gamma }}_{\downarrow }$. (c) The energy of the lower polariton branch ${\nu }_0^{\mathrm{LP}}$ (purple, solid line, left axis) and $⟨{\sigma }^z⟩$ (dashed, orange line, right axis) vs pump strength. The black dots correspond to the pump values in panels (a)–(b) above, and the gray line marks the lasing threshold.