Active control of polariton-enabled long-range energy transfer

Abstract Optical control is achieved on the excited state energy transfer between spatially separated donor and acceptor molecules, both coupled to the same optical mode of a cavity. The energy transfer occurs through the formed hybrid polaritons and can be switched on and off by means of ultraviolet and visible light. The control mechanism relies on a photochromic component used as donor, whose absorption and emission properties can be varied reversibly through light irradiation, whereas in-cavity hybridization with acceptors through polariton states enables a 6-fold enhancement of acceptor/donor contribution to the emission intensity with respect to a reference multilayer. These results pave the way for synthesizing effective gating systems for the transport of energy by light, relevant for light-harvesting and light-emitting devices, and for photovoltaic cells.

In the strong light-matter coupling regime, photons confined within an optical cavity interact with material emitters, thus changing the fundamental physical properties of the coupled system and creating hybrid light-matter states 1,2 . Excitations of these states are quasiparticles named polaritons, carrying features of both photons and excitons. One consequence of polariton formation is that the energy spectrum of the system changes, featuring two peaks separated, at zero cavity-transition detuning, by the Rabi splitting. The potential to modify material properties and chemistry underneath through strong light-matter coupling has stimulated enormous interest from the scientific community, both at the fundamental level and for its potential technological applications [3][4][5] . Organic materials provide relevant opportunities in this context, due to their large oscillator strengths that can lead to the achievement of large Rabi splitting values. Frenkel excitons 6 might strongly localize in organics at single-molecule level, with binding energies of the order of 1 eV 7 , and Rabi splittings of hundreds of meV might enable the observation of macroscopic quantum phenomena at room temperature. In this framework, some remarkable achievements include room temperature Bose-Einstein condensation 8 , polariton lasing 9,10 , tunable third harmonic generation 11 , and increased efficiency in organic photovoltaics (OPVs) 12 . Indeed, one of the main challenges in OPVs is the improvement of the power conversion efficiencies (PCE) 13,14 , that suffer from the relatively large non-radiative decay rates and the typically incoherent, diffusive nature of exciton transport. The formation of delocalized polaritons in the collective strong coupling regime, which originates from the photonic component, has the potential to enhance energy transfer efficiencies overcoming low exciton transport and charge carrier mobility, thus effectively leading to an improvement of the overall efficiency of light harvesting 12 . The long-range energy transfer offered by polariton states already led to a promising outlook for the enhancement of the PCE 15 .
In conventional Förster-type energy transfer processes, energy transport is based on exciton dipole-dipole interactions between a donor and an acceptor molecule, with a low effective range of a few nm 7 . This usually requires physical blending of different molecular components to enable energy transport. Instead, in the strong coupling regime the quantum-mechanical entanglement of the donor and acceptor molecules within the polaritonic states enables a new energy transport mechanism that is no longer dependent on the spatial distance 16,17 . Several reports indicate that mixed exciton-polariton states serve as fast pathways for the energy transfer from the donor molecules to the acceptor ones [18][19][20] and, consequently the spatial range of transfer has been extended from 10 nm 21 to a few micrometers 16,22 . These results have been obtained by physically separating the donor and acceptor molecules by embedding them in layered systems with a transparent spacer 23 . However, such systems are basically static. While the coupling parameters are traditionally permanently defined by a given cavity design (i.e. layer composition, thickness, and topology), dynamic systems where external stimuli might activate or deactivate polariton states [24][25][26] would open much more exciting perspectives for precisely controlling energy flows in intelligent resonant photonics.
Here we propose a new class of optical cavities based on a photogateable donor-acceptor system, in which UV-light driven photoisomerization directly affects the energy transfer mechanism. A microcavity architecture is developed by two different dye layers, sequentially deposited from orthogonal solvents to form the donor-acceptor system. UV light irradiation activates the photoisomerization process of the donor, thus controlling the concentration of transfer-available components in the cavity. As the concentration increases, polariton states are formed and the energy transfer process to the acceptor is activated. Furthermore, irradiation with visible light switches back the energy levels to the initial uncoupled conditions, thus deactivating the polariton-assisted energy transfer process. The capability to control complex energy flows in photonic devices by means of external light provides additional functionalities and opportunities in light harvesting based on strong light-matter coupling.

Results and Discussion
The microcavity architecture, schematised in Fig. 1a, consists of two Ag films as mirrors, sandwiching two spatially separated photoactive layers. Fig. 1: Device architecture and molecular system. a Schematics of the cavity before and after photochromic donor conversion. The donor molecule, initially transparent in the visible range in its SP form, is converted to a colored MC form by irradiation with UV light (violet arrow), whereas the back-conversion can occur by irradiation with green light (green arrow) or by thermal relaxation. The vertical bent arrows represent the donor-acceptor energy transfer in the two configurations. b Absorption spectrum of a PMMA film with SP (black dashed lines) and MC (black continuous line) and corresponding PL spectrum of the SP (×5 intensity, red dashed line) and MC form (converted by UV exposure for 5 s, red continuous line). c Absorption (black line) and emission (red line) of a film of PVA doped with BRK. The excitation wavelength for the emission measurements is 532 nm.
The absorption and emission of the donor layer, which is based on the photochromic 1,3,3-Trimethylindolino-6'-nitrobenzopyrylospiran (SP) 24 in a host matrix of poly(methyl methacrylate) (PMMA), are reversibly varied by UV and green light irradiation. The SP film is transparent in the 450-800 nm range (Fig. 1b) and exhibits a highly uniform morphology (root mean square roughness = 0.3 nm, Fig. S1a,b). Upon irradiation with UV light (UV = 365 nm), SP converts to merocyanine (MC). For each value of the duration of the UV exposure, a mixture of SP and MC is obtained, with relative content depending on the specific irradiation conditions and only the MC component being coupled to the cavity mode. MC features a strong absorption peaked at 554 nm, while its photoluminescence (PL), measured with a pump laser at 532 nm, is peaked at 663 nm (Fig. 1b). The PL from the PMMA-SP film under the same excitation conditions features only a very weak peak at 600 nm (Fig. 1b), in agreement with previous reports 27 .
The controlled photochromic conversion is exploited to activate/deactivate the coupling to the microcavity, and the resulting excited state energy transfer to the acceptor molecules. The length of the active region is chosen to have the second-order resonant mode at about 620 nm at normal incidence (inter-mirror distance = 355 nm), a configuration that is expected to enhance the lightmatter coupling for both the donor and acceptor molecules 16,23 (Fig. S2). The J-aggregate 28 form of 3,3'-Bis(3-sulfopropyl)-4,5:4',5'-dibenzo-9-ethylthiacarbocyanine betaine thiethylammonium salt (BRK) 16,19 is used as acceptor, embedded in a host matrix of polyvinyl alcohol (PVA). BRK absorbs at 655 nm, whereas its emission shows peaks at 612 nm and 659 nm, respectively (Fig. 1c). The most intense peak is attributed to fully formed J-aggregates, while the smaller and blue-shifted one is traceable to some BRK molecules which do not aggregate in the fabrication process (see Supplementary Information -SI-, Fig. S3). While contributing to BRK absorption broadening, nonaggregated molecules do not interfere severely with the polariton formation since their number, and thus their coupling to the cavity field, is sufficiently small compared to the fully formed aggregates.
The kinetics of the SP-to-MC photochromic conversion upon exposure to 365 nm light is shown in  performed on reference first-order cavities embedding either BRK-doped PVA or MC-doped PMMA, respectively (details in Section 4 of SI, Fig. S7 and S8). In pristine devices (UV exposure time = 0 s), only the BRK aggregates couple to the cavity field at visible wavelengths. Since the BRK absorption is off resonance to the cavity dispersion, we observe only a slight shift with respect to the uncoupled bands (the resulting light-matter coupling constant for BRK is = 117 meV). Once MC is introduced in the system by means of UV irradiation, two exciton species can participate in the polariton formation and three polaritonic branches appear (Fig. 2), i.e., the upper polariton branch (UPB) at about 503 nm, the middle polariton branch (MPB) at 612 nm and the lower polariton branch (LPB) at 675 nm (all wavelengths at normal incidence). A fit of the polaritonic dispersions is also performed using a coupled oscillator model 30 , which allows the Hopfield coefficients to be retrieved for each polariton branch (see Fig. S9, S10, and S11). The results of this analysis at 0° are shown in evidences the possibility to control the degree of hybridization between the donor and acceptor molecules by an external light signal. We also mention that in between the polaritonic branches visible in the transmission spectra, the system also contains "dark states" or "exciton reservoirs" corresponding to the excitonic transitions of the donor and acceptor molecules that are not coupled to the cavity field.
The light-matter coupling strength is known to depend on the square root of number of emitters interacting with the cavity field 31,32 . Since we are actively changing the concentration of donors available to energy transfer (MC), we expect the light-matter coupling constant to The system can be back-switched 33 by irradiation with green laser light (532 nm, intensity ∼ 275 mW cm -2 ), which reverses the SP-MC photoisomerization (Fig. 4). The transmission maps for various times of green light exposure are reported in Fig. S13 and S14.
Ultimately obtained bands are largely comparable to those of the pristine device, with minor changes of signal intensity and broadening of the photonic mode most likely due to the residual MC component. The complete set of polariton branches can be observed in the system for up to four consecutive UV-green irradiation cycles (Fig. S15). Fatigue effects, attributed to photo-oxidation 34   The angle-resolved emission from cavities after different UV exposure times and then shortly excited by a 532 nm laser are shown in Fig. 5. The corresponding emission spectra are reported in Fig. S16. The emission spectrum of the cavity before irradiation with UV light shows two bands peaked at 600 nm and 668-671 nm, respectively. As soon as the UV light is switched on, the upper band intensity decreases and finally disappears while the lower one red-shifts and its intensity increases. In agreement with the transmission data, a back-conversion of the PL signal is found upon longer (5-90 min) irradiation with green light (Fig. S17 and S18).
This behavior can be rationalized from a simple model that assumes that the polaritonic modes behave as a filter for the emission from the molecular reservoir. Although the emitted light is transmitted from the center of the cavity to the outside, the corresponding emission can be determined by means of a conventional cavity transmission function (see Section 9 and Fig. S19 in SI). Thus, we represent the emission as the PL signal of the bare molecules modulated by the cavity transmission: where is the cavity transmission of the hybrid system, , are the emission intensities of the molecules outside the cavity, and , are phenomenological weight coefficients. The coefficients effectively represent the contributions of both molecular species to the emission of the hybrid system.
For the simulation of the emission maps, we fit (Eq. 1) to the experimental PL intensity from the cavity, using the weight coefficients , as free parameters. This approach for the simulation of the emission properties of the cavity is equivalent to a rate equation model, which has been successfully applied for the interpretation of the emission measurements in similar systems 30,39,40 under the assumption that radiative pumping 41 is the dominant population mechanism for the LPB, i.e., the vibrational scattering from the acceptor excitonic reservoir is negligible (see Section 10 and Fig. S20 of SI for details). In our hybrid system, the used approximation is valid since radiative pumping occurs not only from the acceptor reservoir, but also from the donor one, due to the fact that the MC emission has a significant overlap with the LPB. The results of the simulations are shown in the bottom of Fig.   5. As an example of validity of the model, we report in Fig. 6a the comparison between the measured and simulated integrated emission intensity of the LP at a fixed angle (in this case 0°) as a function of the UV exposure time.
The simulated data reproduces the experimental measurements well. They demonstrate that the increase in the number of MC molecules not only dramatically changes the absorption properties of the system but also its emission, with a direct impact on the energy transport from We explain this behavior through the level scheme in Fig. 6f. Firstly, the green laser pumps both the donor and acceptor excitonic reservoirs, then the molecules emit into the lower polariton state through its photonic component (radiative pumping mechanism corresponding to arrows 1 and 2 in the scheme). The lower polaritonic state has two main loss mechanisms: the dominant one is radiative decay through the cavity mirrors (arrow 4), which occurs on femtosecond timescales, while the second one is non-radiative decay to the acceptor excitonic reservoir (arrow 3), with efficiency proportional to acceptor fraction in LP. While this process is expected to be slower than radiative decay 30,39,40,42 , its appearance significantly affects the excitation transfer pathways due to pumping of the acceptor excitonic reservoir. In particular, it provides transfer of energy from the donor reservoir to the acceptor one through the lower polaritonic state. Thus, the lower polaritonic state in our experimental setup serves as an intermediate state for energy transfer between the donor and acceptor, and is responsible for the redistribution of the donor and acceptor contributions to the emission (Fig. 6b-c). Overall, in the resonant cavity the fraction of the emission due to the acceptor molecules with respect to the donor ones is enhanced by a factor of 6 compared to the bare donor/acceptor multilayer. By contrast, in the off-resonant cavity the redistribution between donor and acceptor is weakened because of the reduced efficiency of (i) the radiative pumping from the donor excitonic reservoir to the LP state (arrow 1 in Fig. 6f) due to a decrease of the overlap between the LP dispersion and MC emission band and, (ii) the non-radiative relaxation of lower polaritons to the acceptor excitonic reservoir (arrow 3 in Fig. 6f) since the efficiency of this channel is proportional to the acceptor fraction in the LP, which is largely decreased. Indeed, for the off-resonant case, the LP consists mostly of the photonic part (see the calculated Hopfield coefficient of the LP in Fig. S34).
In conclusion, we have demonstrated the possibility of controlling the polariton formation between two different molecules via external optical gating in a donor-acceptor system. This is achieved by    The solution is kept in a sonicator for two hours to dissolve completely the organic materials.
The second solution is made by embedding the BRK molecules in a PVA matrix. Materials

Characterization of BRK and MC first-order cavities
The  Fig. S8a-b. Analogously to the procedure described above for BRK, we approximate the dielectric permittivity of PMMA-MC as a superposition of two Voigt profiles, with a constant background permittivity due to the PMMA host matrix taken from Ref. [2]. Then, we fit angle-resolved spectra using the TMM and, through a best fit procedure, we retrieve the optimal parameters that allow us to get the refractive index of the PMMA-MC (Fig. S8c-d).    Figures S9, S10, S11.
In order to get coupling strengths corresponding to the experiment we perform one fitting procedure for all the exposure times , where we vary and trying to minimize the difference between ( , ) and the spectral position of the polaritonic states taken from experimental angle-resolved transmission spectra. It should be noted that for every exposure time we take different coupling strength for the donor (since we expected an increase of the number of MC molecules) and kept fixed the coupling strength between acceptor molecules and cavity mode. The dependence of ( ) is reported in the Fig. S12.          PL spectra of the cavity as a function of the initial UV and subsequent green light exposure times measured at 0°. Excitation wavelength for the emission measurements: 532 nm. Each spectrum is normalized to its maximum intensity value. The spectra are vertically shifted for better clarity.

The model for the cavity emission
We assume that the cavity emission signal can be regarded as emission of each molecular species modulated by an effective filtering induced by the cavity. Thus, we use the following expression:  It can be seen that for both molecular species, the maps are similar to the total cavity transmission. The main deviations are in the short-wavelength region, which is off-resonant from the emission of the molecular species. We also note that the scale of BRK and SP/MC filter functions are similar, so that the cavity transmission is a good approximation for the emission filter for both molecular species. We also note that the difference in absolute scale between the filter functions and cavity transmission does not play any role, since for the analysis we use normalized weight coefficients.

Rate equations model
In order to validate the approach that we use to describe emission dynamics for our system, we also implement a rate equations model for the lower polariton branch (LPB) 3 . Since the photochemical reaction has a rate comparatively small to the polariton dynamics we can a use steady state condition for the population of the LPB: where is the lower polariton branch population,| | 2 (i=A, D, ph) is the LPB Hopfield (S4) coefficient for acceptor, donor and cavity photon respectively, and is the overlap between LPB and emission spectra of the bare molecules. In this equation, the first two terms describe the processes of vibrational scattering from donor and acceptor excitonic reservoirs, the third term denotes the radiative pumping, the fourth one stands for radiative decay through the photonic component of lower polariton, and the last two terms describe relaxation to excitonic reservoirs.
We assume that for our system radiative pumping dominates over vibrational scattering, since the LPB significantly overlaps with the emission spectra of both molecular species. Also, due to very fast cavity decay (cavity photon lifetime is less than 10 fs), we disregard the last two terms in the equation, assuming that their contribution to the LPB population is negligible compared to the radiative mechanism, in full accordance with previous studies [3][4][5] .
Since the emission intensity ∝ | ℎ | 2 , we can write: This equation is fully equivalent to the approach we use for analysis of the emission properties of the hybrid system. The comparison of the two approaches with experimental data are reported in Fig. S20. In order to calculate the radiative pumping contribution for the rate equation approach we retrieve the LPB from the cavity transmission spectra. Since for high angles this peak is barely visible, we compute the graphs only for angles smaller than 30°. It could be noticed that the approach we used for the emission dynamics analysis is able to reproduce the same behavior as experimental data and gives qualitatively the same results as the rate equations method, which, in turn, proves the validity of aforementioned assumptions.        As can be seen from Fig. S29, the emission spectra of the multilayer outside the cavity can be very well described as linear superposition of the spectra of separate molecular species. The temporal dynamics of the normalized weight coefficients = + and = + is presented in Fig. 6b of the main text.

Model sensitivity to experimental parameter variations
The intensity of the effective excitation can vary during the experiments. This variation may be related to the excitation laser or to variations in the excitation efficiency within the cavity. The latter is affected by various factors such as changes in refractive index due to UV exposure and modifications in the cavity transparency resulting from shifts in polaritonic states.
The changes of effective pumping can significantly affect the overall emission from the sample, which in turn leads to variations in the weight coefficients and used for the emission analysis. However, both and should be proportional to the excitation intensity , as the absorbance of molecules and, in turn, the emission intensity both depend linearly on . The subsequent normalization of the weight coefficients that we perform has the result that = + and = + do not depend on the excitation intensity. Normalizing the weight coefficients also allows for a fair comparison of results obtained inside and outside the cavity, provided that the thickness ratio of the active layers remains constant.
It is also important to note that emission of the multilayer structure, both inside and outside the cavity, is affected by the emission pattern of the SP/MC layer in PMMA. This pattern is significantly modified throughout the UV exposure due, on one side, to the increase of MC concentration and, on the other side, to the concomitant photo-bleaching effects related to photo-oxidation and other fatigue or aggregation mechanisms impacting on the merocyanine molecules [6][7][8][9] , as evidenced by the emission spectra / ( ; ) (Fig. S22a). However, this does not affect the weight coefficients since these effects are already accounted for in Eq. 1 of the main text and in Eq. S7 of SI, which consider the quantity / ( ; ).

Dependence of energy transfer on cavity detuning
To investigate the underlying nature of the observed results, we performed analogous experiments with the cavity intentionally off-resonant to the molecular species. To achieve this, we realized a cavity with BRK and SP/MC layer thicknesses 240 nm and 225 nm, respectively.
It is worth noting that in the resonant cavity the thicknesses are 180 nm and 150 nm. Hence the choice of layer thickness values ensures that the ratio between them remained approximately constant for a meaningful comparison. The distribution of the electric field inside the offresonant cavity is show in Figure S30. In Figure S31, we present the transmission of the off-resonant cavity sample at 0-180 s UV exposure times. Additionally, in the Figure S32 we display the angle-resolved emission spectra of the same cavity sample.   To fit the experimental emission data, we employed the procedure described in the main text.
The results of the simulations are presented in the bottom row of Figure S33. The fitting results accurately reproduce the experimental emission maps. The corresponding weight coefficients for these simulations are shown in Figure 6e of the main manuscript. Furthermore ( Figure 6d of the main manuscript), using a similar procedure, we determined the weight coefficients corresponding to BRK and SP/MC molecules for the emission from the multilayer outside the cavity (with film thicknesses corresponding to the off-resonant cavity experiment).
The weight coefficients obtained with the off-resonant cavity thicknesses exhibit a similar qualitative behavior over time for both the outside-cavity and inside-cavity cases. Moreover, for the outside-cavity scenario, the contributions of BRK and MC to the emission show similar values to those obtained in the resonant case, which can be attributed to the approximately constant ratio between the thicknesses of the active layers in both experiments.