Tuning the Coherent Propagation of Organic Exciton-Polaritons through Dark State Delocalization

Abstract

While there have been numerous reports of long-range polariton transport at room-temperature in organic cavities, the spatiotemporal evolution of the propagation is scarcely reported, particularly in the initial coherent sub-ps regime, where photon and exciton wavefunctions are inextricably mixed. Hence the detailed process of coherent organic exciton-polariton transport and, in particular, the role of dark states has remained poorly understood. Here, femtosecond transient absorption microscopy is used to directly image coherent polariton motion in microcavities of varying quality factor. The transport is found to be well-described by a model of band-like propagation of an initially Gaussian distribution of exciton-polaritons in real space. The velocity of the polaritons reaches values of ≈ 0.65 × 10⁶ m s^-1 , substantially lower than expected from the polariton dispersion. Further, it is found that the velocity is proportional to the quality factor of the microcavity. This unexpected link between the quality-factor and polariton velocity is suggested to be a result of varying admixing between delocalized dark and polariton states.

Keywords: Q-factor; TA microscopy; coherent transport; dark states; energy transport; exciton-polaritons.

Figure 1

Optical characterization of BODIPY‐R microcavities. a) Absorption spectrum of a bare film of BODIPY‐R molecules in polystyrene matrix (red) and reflectivity of a DBR with n = 7.5 (blue), with superimposed fits (lines) used for transfer matrix simulations. b) Schematic of DBR microcavity, consisting of pairs of Nb₂O₅/SiO₂ alternating layers. BODIPY‐R molecules in a polystyrene matrix are sandwiched in the center of the cavity. c) Angle‐resolved reflectivity of a reference TiO₂/SiO₂ n = 5.5 microcavity with lower (LP) and upper (UP) polariton branches marked. Circles denote LP and UP dispersions obtained from transfer matrix simulation. The corresponding uncoupled cavity mode and exciton positions are indicated as solid lines. Dashed box shows range of wavelengths covered by pump pulse in fs transient absorption microscopy experiment and range of wavevectors pumped by the high numerical aperture objective (total range of 128.4°). d) Simulated transmission spectra of model (empty) Nb₂O₅/SiO₂ cavities showing the narrowing of spectra with increasing Q‐factor. e) Transient absorption of BODIPY‐R dispersed in polystyrene film and microcavities with Q‐factors ranging from 66 to 479 (n = 3.5 to n = 6.5), excited with a ≈10 fs broadband pump pulse (FWHM ≈60 nm) centered at 550 nm. In the film the positive feature at 640 nm corresponds to the bleach. In the microcavities, the positive features at 620 to 660 nm match the position of the UP and LP at ≈0°. f) Decay of UP bleach (unshaded) and rise times of LP bleach (purple shading) extracted from exponential fit of the transient absorption kinetics.

Figure 2

Transient absorption microscopy images of BODIPY‐R molecules in microcavity for n = 3.5 (top) and n = 6.5 (bottom) mirror pairs. a) Transient absorption microscopy images showing initial expansion up to 125 fs and subsequent contraction. The dotted line indicates the radial Gaussian standard deviation. The scale bar in the images is 500 nm. b) Kinetic extracted from center of spatial pump probe signal for the full cavity series. Stars indicate the signal maximum used to calculate t ₀ for each cavity. c) Mean‐square displacement of signal as a function of time. Circles are raw data and solid line shows fit to Equation (5). d) Coherence loss time (circles) extracted from Equation (5) as a function Q‐factor. Error bars are derived from a minimum of five repeat experiments. Squares indicate the corresponding photon lifetime for the cavity. e) Exciton‐polariton velocity (circles) extracted from fitting equation (5) to MSD, as a function of Q‐factor. Experimental error bars are derived from a minimum of five repeat experiments at different sample locations. Triangles show expected group velocity of UP (filled) and LP states (open), calculated as described in the main text and scaled for ease of comparison. Error bars reflect standard deviation for cavity thicknesses 200–215 nm.

Figure 3

Summary of proposed mechanism for Q‐factor dependence of transport. (Left) Rapid population exchange between bright polaritons and dark states occurs at a rate k _exchange. Until decoherence, these states transport together. (Center) The Q‐factor directly impacts the photonic density of states (Gaussians) and thus indirectly impacts the energetic distribution of coupled versus uncoupled molecules (circles), though the same proportion of molecules is strongly coupled in every case. The resulting dark states exhibit Q‐factor‐dependent bandwidth. (Right) This effect leads to correspondingly Q‐factor‐dependent delocalization of the dark states (black, blue, red). As the spatial extent of the bright polaritons (green) is large and approximately constant, this alteration of dark states is the principal means to alter the wavefunction overlap (outlines) and thus rate of exchange between polaritons and dark states.