Ultralong‐Range Polariton‐Assisted Energy Transfer in Organic Microcavities

Abstract Non‐radiative energy transfer between spatially‐separated molecules in a microcavity can occur when an excitonic state on both molecules are strongly‐coupled to the same optical mode, forming so‐called “hybrid” polaritons. Such energy transfer has previously been explored when thin‐films of different molecules are relatively closely spaced (≈100 nm). In this manuscript, we explore strong‐coupled microcavities in which thin‐films of two J‐aggregated molecular dyes were separated by a spacer layer having a thickness of up to 2 μm. Here, strong light‐matter coupling and hybridisation between the excitonic transition is identified using white‐light reflectivity and photoluminescence emission. We use steady‐state spectroscopy to demonstrate polariton‐mediated energy transfer between such coupled states over “mesoscopic distances”, with this process being enhanced compared to non‐cavity control structures.


Conventional (N+2) Hamiltonian model Vs. New 3N Hamiltonian model
Our approach, recently proposed in a theoretical work by Balasubrahmaniyam et al. [1] and experimentally confirmed by Georgiou et al. [2] is different from the (N+1) x (N+1) Hamiltonian that we have used previously to describe multimode optical cavities [3] . Here, the model is based on a 3N x 3N Hamiltonian shown in matrix Equation (1) [1] . S4 We show in Figure S3a-d that the use of this 3N x 3N Hamiltonian results in an improved fit compared to a model based on a conventional (N+2) x (N+2) Hamiltonian in which simultaneous interactions occur between the two excitons and all N optical states.
Specifically, we plot the same experimental reflectivity maps shown in the paper (Figure 2a and c) however we plot data over a reduced spectral range (550 -700 nm) and overlay it with the polariton energies extracted from the two different models. This is shown in Figure S3a and c, where we overlay data with a photon-decoupled 3N Hamiltonian model described in Equation (1), while Figure S3b and d shows the same data that is instead modelled using a conventional N+2 Hamiltonian described in Equation (S1). Note that we have used the same interaction potential values (g) and dispersive optical modes Γ1,2,3… in both models.
Although we find that the "conventional" N+2 Hamiltonian model shown in Figure S3b and d fits the experimental data relatively well, we observe a small deviation between experimental and simulation polariton modes, particularly at energetic regions around the exciton energies. For instance, in Figure S3b, polariton mode P5 crosses the TDBC exciton (vertical white dashed line) at a wavelength of 588 nm and an angle of 35°. At this point, it is apparent from the experimental data that there is a splitting of the polariton mode which is only correctly described by the 3N Hamiltonian model used in Figure S3a (splitting between modes MP4 and UP3). This deviation between the experimental data and the N+2 Hamiltonian model of Equation (S1) can also be seen for polariton modes P4-7 in Figure S3d at the points where the polariton modes cross the energy of the NK-2707 and TDBC excitons (white horizontal dashed lines). In all cases the new model shown in Figure S3c describes the mode splitting observed in the experimental data resulting in an improved fit.
(S1) For completeness, in Figure S4a-d we also re-plot the angle-resolved white-light reflectivity and PL data shown in Figure 2 of the manuscript. Here we plot the figure over a more extended wavelength range (between 530 nm to 805 nm), allowing photon mode Γ1 and polariton branch LP1 to be seen.  Figure S5 plots the Hopfield coefficients for LP3, MP3 and UP3 of Cavity-A. As it can be seen, middle branch MP3 is a mixture of the Γ3 photon-mode, with NK-2707 and TDBC excitons, with mixing being maximised at an angle of ~43°. Figure S6 shows the Hopfield coefficients of Cavity-B for polariton branches LP5, MP5 and UP5 with MP5. Here a high degree of mixing is observed between photon-mode Γ5 and NK-2707 and TDBC excitons at an angle of ~35°.

S9
In Figure S8 we plot a cross-section of PL emission from Cavity-A at an angle corresponding to a maximum mixing between photons and the two excitons at θ = 43º, along with PL emission from the Multilayer-A control film that was also collected at the same angle.
Here, it can be clearly seen that at this angle of maximum hybridisation between the two excitons, a redistribution of energy occurs between the molecular donor species to the acceptor species which is positioned at lower energy. Here the angle of maximum mixing (θ = 43º) was identified using the Hopfield coefficients plotted in Figure S5 of the Supporting Information. Figure S8. PL data from Multilayer-A (black) and Cavity-A (red). PL was collected at an angle of 43º for both the cavity and the film. This angle corresponds to a maximum hybridisation between the two excitons in Cavity-A. S10

Materials and Methods
Organic molecule solutions and films. TDBC (supplied by FEW Chemicals GmbH) and NK-2707 (supplied by Hayashibara Biochemical) were dissolved at 10% and 5% by mass in a DI water / gelatine solution (20 mg mL -1 ), respectively. Films were spin-coated from 100 μL of the solution held at a temperature of 65°C. PS (supplied by Sigma-Aldrich) of molecular weight Mw ~ 350,000 was dissolved in toluene at 100 mg mL -1 and spin-coated using 200 μL of solution held at room temperature. The thickness of the various layers was controlled by changing the rotation speed of the substrate during spin-coating and was determined using a Bruker Dektak XT profilometer. Reflected light was collected through a series of lenses mounted on the second arm and directed into an Andor Shamrock SR-303i-A CCD spectrometer using an optical fibre. For angle-resolved PL measurements, samples were excited close to normal incidence using a 405 nm CW laser diode. PL was collected through the same motorised arm used to collect light in reflectivity measurements. PLE measurements. Laser excitation was performed using a Fianium Supercontinuum laser with 6 ps pulse and 40 MHz repetition rate. Broadband laser light was filtered through a SPEX 270M monochromator to tune the excitation wavelength. The same goniometer setup described above was used for the excitation of the sample at different angles, with two photodiodes (SM1PD1A) added in the excitation and collection paths to measure the intensity of the incident and reflected excitation light. PL from the sample was collected at normal S11 incidence using lenses mounted on a third arm and then directed into an Andor Shamrock SR-303i-A CCD spectrometer.
Femtosecond pump-probe measurements. Excitation of the sample was performed using a 400 nm frequency-doubled Ti:Sapphire laser amplifier having a 1 kHz repetition rate and a pulse width of 100 fs. The white-light continuum probe was generated using a few microjoules of the amplified pulse at 800nm which was focused on a sapphire glass plate. Different delays were achieved using a retroreflector configuration mounted onto a motorised stage. The femtosecond pump-probe experiment was performed using a typical non-collinear setup where the excitation beam was directed onto the sample close to normal incidence while the probe beam was incident onto the sample at an angle of ~5°. The signal was either collected through a fibre bundle and then imaged into a spectrometer, or filtered through a 10 nm band-pass filter and then sent to a lock-in amplifier.