Abstract
BoseEinstein condensates of excitonpolaritons in inorganic semiconductor microcavities are known to possess strong interparticle interactions attributed to their excitonic component. The interactions play a crucial role in the nonlinear dynamics of such systems and can be witnessed as the energy blueshifts of polariton states. However, the localised nature of Frenkel excitons in strongly coupled organic microcavities precludes interparticle Coulomb exchangeinteractions that change mechanisms of the nonlinearity and blueshifts accordingly. In this report, we unravel the origins of blueshifts in organic polariton condensates. We examine the possible contributions: intracavity optical Kerreffect, gaininduced frequencypulling, polariton interactions and effects related to saturation of optical transitions for weakly and stronglycoupled molecules. We conclude that blueshifts in organic polariton condensates arise from the interplay of the saturation effects and intermolecular energy migration. Our model predicts the commonly observed steplike increase of both the emission energy and degree of linear polarization at the polariton condensation threshold.
Introduction
Electronic excitations in organic semiconductors can be described in terms of Frenkel excitons in which strongly bound electron–hole pairs are localized on a single molecule. Frenkel excitons typically have a binding energy of the order of 0.5–1 eV that allows them to survive at ambient temperatures. Following the first observation of strong coupling in organic microcavities^{1}, the rapid development of organic polaritonics has culminated in the observation of polariton condensates at room temperature. Emission wavelengths spanning the visible spectrum have been demonstrated through the selection of appropriate molecular materials^{2,3,4,5,6,7,8}. Furthermore, polariton condensation in organic microcavities has led to the demonstration of polariton transistors operating at ambient conditions having a recordhigh optical gain (~10 dB μm^{−1})^{9}. The coherent nature of organic polariton condensates also results in superfluid propagation^{10}, suggesting further applications in polariton circuits.
Despite the rapid progress of organic polaritonics and their potential for applications, the mechanisms underlying polariton nonlinearities remain poorly understood. In organic semiconductors, the localization of Frenkel excitons on a single molecule dramatically weakens Coulomb exchange interactions and interparticle scattering. The blueshift of a polariton mode is considered a key manifestation of polariton interactions in inorganic microcavities^{11,12}. However, in organic polariton systems, the origin of a steplike energy shift observed at condensation thresholds remains unclear, despite its omnipresence across a diverse range of organic materials^{3,4,5,6,7,8,9}.
In this article, we explore the origin of blueshifts in organic polariton condensates. We examine the relative contribution of a number of processes, including intracavity optical Kerreffect, gaininduced frequency pulling, polariton–exciton and polariton–polariton scattering, as well as the quenching of the Rabi splitting and renormalization of the cavity mode energy both induced by the saturation of molecular optical transitions due to states filling at higher excitation densities (Pauli blocking). Through a quantitative analysis, we conclude that the blueshifts in organic polariton condensates and the steplike energy increase, observed at threshold^{3,4,5,6,7,8,9}, result from an interplay between stimulated relaxation to the polariton ground state and intermolecular energy transfer. The latter process results in a depolarization of the emission with respect to the polarization of the excitation beam. Our interpretation is qualitatively and quantitatively corroborated by a concomitant steplike increase of the degree of linear polarization of the emission at condensation threshold^{3,4,5,8}.
Results
Strong coupling
The organic microcavities studied here, consisted of a ~λ/2 spincast thin film of BODIPYG1 dye uniformly dispersed in a polystyrene matrix (see Supplementary Note 1) that was positioned between two distributed Bragg reflectors (DBRs) consisting of 8 and 10 pairs of SiO_{2}/Nb_{2}O_{5} placed on the top and bottom of the structure, respectively. For more information about sample fabrication, see Methods. We have found that the spincasting process used to deposit the organic film results in a gradual increase of film thickness towards the edges of the substrate (bottom mirror). We use this nonuniformity to access a broad range of exciton–photon detuning (δ).
We measure angleresolved reflectivity of a typical microcavity, as shown in Fig. 1a. Here both upper and lower polariton branches can be observed as local minima in the broad DBR reflectivity stopband that are split around the BODIPYG1 peak absorption wavelength at 507 nm. For further experimental details, see Methods. We plot the energy of these modes as a function of angle, creating a dispersion plot as shown in Fig. 1b (red squares). These data are superimposed over a falsecolor plot of polariton photoluminescence intensity obtained under nonresonant excitation at 400 nm in the linear excitation regime. We fit the upper and lower polariton branches in Fig. 1b using a two coupledoscillator model^{13,14}, and obtain a vacuum Rabi splitting (\(\hbar {\mathrm{\Omega }}_0\)) of ~116 meV and an exciton–photon detuning of −160 meV (further details are given in Supplementary Note 2).
Blueshifts in polariton condensates
Recent studies have shown that a number of the BODIPY family of molecular dyes undergo polariton condensation/lasing following nonresonant optical excitation^{6,7}. To demonstrate condensation using BODIPYG1, we record the dispersion of polariton photoluminescence emission as a function of excitation density using single excitation pulses in a transmission configuration (see Methods). The excitation laser used provides 2 ps pulses at 400 nm having a horizontal polarization. Figure 2a shows the timeintegrated polariton photoluminescence distributed across the lower polariton branch below condensation threshold. Figure 2b shows microcavity emission abovethreshold, where it can be seen that polariton photoluminescence collapses to the bottom of the lower polariton branch. In Fig. 2c we plot the photoluminescence intensity and the fullwidth at halfmaximum of the emission linewidth (right axis, in red) integrated over ±1° (±0.2 μm^{−1}) around normal incidence versus excitation density. The corresponding energy shift and the degree of linear polarization of the emission spectrum are also shown in Fig. 2d, e, respectively. At an excitation density of ~6 mJ cm^{−2} (120 μJ cm^{−2} of absorbed pump fluence), we observe a rapid increase of the photoluminescence intensity, a concomitant linewidth narrowing from 1.6 to 0.25 nm and a steplike increase of the degree of linear polarization and a steplike blueshift of the emission spectrum. Such blueshifts of the polariton emission wavelength occurring around a lasing threshold are commonly considered a hallmark of polariton condensation. In inorganic semiconductor microcavities, such energy shifts originate from the repulsive interparticle Coulomb exchange interactions between Wannier–Mott excitons^{15}. However, such interactions are in principle precluded in polaritons created using molecular semiconductors as a result of the highly localized nature of Frenkel excitons^{16,17}.
To explore the mechanism behind such blueshifts, we examine the contribution of various nonlinear optical phenomena, omnipresent both in the strong and weakcoupling regimes, namely the intracavity optical Kerr effect, the gaininduced frequency pulling, and interparticle interactions.
Optical Kerr effect
A steplike increase in the intensity of the electric field inside the cavity at condensation threshold (determined at the lower polariton mode wavelength) could potentially shift the resonance through a change in the nonlinear refractive index of the intracavity material by means of the conventional Kerr effect. To examine the contribution of the Efield induced difference in the refractive index, we measure the optical nonlinearities of the bare intracavity medium using both a closed and openaperture Zscan technique^{18} (for details, see Supplementary Note 3 and Methods). Figure 3a shows an openaperture Zscan transmission recorded at two pulse energies, probing the imaginary part of the nonlinear susceptibility. We find that at the lower incident pulse energy of 9.5 nJ, we do not observe any nonlinear change of the absorption. We note that at the foci, the 9.5 nJ excitation pulse induces an electricfield intensity of 17 GW cm^{−2}; a value that is approximately an order of magnitude higher than the electricfield intensity at the antinode within the microcavity at 1.4 P_{th} (~2 GW cm^{−2}) (calculation is shown in Supplementary Note 4). At the considerable higher intensity of 779 GW cm^{−2} at the foci of the beam, we observe an optical nonlinearity in the form of reverse saturable absorption.
The closedaperture Zscan measurements presented in Fig. 3b provides a measure of the real part of the nonlinear optical susceptibility. Here, we do not detect any change in the nonlinear refractive index when pumping at the lower incident pulse energy. However, at the higher incident intensity of 779 GW cm^{−2}, we find that the material exhibits a weak selffocusing effect from which we determine a positive nonlinear refractive index (n_{2}) of ~1.89 × 10^{−14} cm^{2} W^{−1} (calculation is shown in Supplementary Note 4). We note that even if such high electromagnetic fields could be generated within a microcavity, the positive value of n_{2} that we determine would induce a redshift. We conclude, therefore, that the optically induced change of the intracavity nonlinear refractive index is not responsible for the blueshift observed at the condensation threshold.
Gaininduced frequency pulling
We now consider whether the gaininduced frequency pulling could be responsible for the blueshift at the condensation threshold. This mechanism is expected to be particularly important in negatively detuned microcavities in which the polariton mode has a large photonic fraction. We characterize the spectral distribution of the optical gain by recording amplified spontaneous emission (ASE) from a control (noncavity) film of BODIPYG1 dye molecules dispersed in a polystyrene matrix (see Supplementary Note 1 and Methods). A typical ASE spectrum is plotted in Fig. 4a [red line], where it can be seen that the emission (corresponding to the peak of optical gain) is peaked around 2.272 eV (545.8 nm).
We explore the extent to which gaininduced frequency pulling affects the condensate’s blueshift by tuning the frequency of the lower polariton branch across the optical gain spectrum. Such tunability in the lower polariton branch wavelength is possible through the variation in the thickness of the intracavity film across the sample. This effect allows us to explore polariton condensation over a broad range of exciton–photon detuning conditions. Figure 4b shows the measured energy shift for ~400 singleshot measurements of polariton condensation at a wide range of different polariton ground state energies. For each measurement, the energy shift is defined by comparing the energy of the emission below and above the threshold. Here, we avoid averaging over the intensity fluctuations of the laser by utilizing a singleshot dispersion imaging technique. In Fig. 4a, we superimpose the measured blueshift using the Sturge binning rule with the amplified spontaneous emission spectrum (for details see Supplementary Note 2). It is apparent that at condensation threshold, the recorded energy shifts are always positive, and thus we conclude that the blueshift is not induced by gain frequency pulling. Indeed, if the gaininduced frequency pulling considerably contributes to polariton energy shifts, one would expect a negative sign of the shift observed for the left side of the ASE peak instead. However, we systematically observe polariton blueshifts regardless of the side of the gain peak.
Polariton interactions
We now investigate the possible contribution of polariton–exciton and pairpolariton scattering in determining the observed blueshift at the condensation threshold. In semiconductor microcavities containing Wannier–Mott excitons, the experimentally observed energy shifts (ΔE) are attributed to a combination of pairpolariton (g_{p−p} N_{p}) and polariton–exciton (g_{p−x} N_{x}) interaction terms. This is summarized by the following equation^{12,19}:
where the pairpolariton scattering interaction constant can be related to the exciton–exciton scattering constant (g_{x−x}) using \(g_{\mathrm{{p  p}}} = g_{\mathrm{{p  x}}} \cdot \left X \right^2 = g_{\mathrm{{x  x}}} \cdot \left X \right^4\), where X is the amplitude of the exciton fraction that is mixed into a polariton state, and N_{p} and N_{X} are the polariton and exciton reservoir densities, respectively. Since the occupancy of polaritons at the condensation threshold does not depend on the exciton fraction, the measured dependence of the energy shift versus the square of the amplitude of the exciton fraction (X^{2}) should reveal whether pairpolariton or polariton–exciton interactions dominate the blueshift.
To determine the dependence of the measured blueshift shown in Fig. 4b versus the exciton fraction, we need first to describe the dependence of the experimentally measured emission frequency of the polariton state on its exciton fraction. The latter depends on the exciton–photon detuning (δ) and vacuum Rabi splitting through \( {X_{k_\parallel = 0}} ^2 = \frac{1}{2}( {1 + \frac{\delta }{{\sqrt {\delta ^2 + \left( {\hbar {\mathrm{\Omega }}_0} \right)^2} }}} )\). To avoid any excitation densitydependent energy shifts of the lower polariton branch, we perform white light, angleresolved reflectivity measurements across the available detuning range. We fit the linear polariton dispersions by varying the vacuum Rabi splitting and the exciton–photon detuning, while keeping the exciton energy and the effective refractive index of the intracavity layer constant (see Supplementary Note 2). Figure 4c, d plot the fitted values of vacuum Rabi splitting and exciton–photon detuning vs the energy of the polariton state. This analysis indicates that the vacuum Rabi splitting is virtually invariant across the whole sample area and has an average value of (116 ± 1.5) meV, with the exciton–photon detuning spanning the range 120 meV, δ ϵ [−240, −120] meV. From this, we plot the dependence of \( {X_{k_\parallel = 0}} ^2\) on the energy of the polariton state, as shown in Fig. 4e.
Using this approach, we can also determine the dependence of the measured energy shift, ΔE, on \( {X_{k_\parallel = 0}} ^2\), shown in Fig. 5. This indicates that the energy shift of the polaritons on condensation has a sublinear dependence on \( {X_{k_\parallel = 0}} ^2\); a result that firmly precludes pairpolariton scattering as the underlying mechanism for the observed blueshift and suggests that polariton–exciton scattering is also unlikely; here the former process would result in a quadratic dependence on \( {X_{k_\parallel = 0}} ^2\) and the latter on a linear dependence (see Eq. (1)).
In the absence of pairpolariton interactions and for a constant exciton fraction/detuning (as expressed by Eq. (1)), we expect that polariton–exciton interactions should lead to a linear energy shift with increasing excitation and thus exciton density. At the condensation threshold, stimulated relaxation from the exciton reservoir to the polariton ground state would lead to clamping of the exciton density and, therefore, of the energy shift. However, to date, all noncrystalline semiconductor microcavities undergo a nearly steplike increase of polariton blueshift at condensation threshold^{3,4,5,6,7,8,9}, as shown in Fig. 2d, subject to the accuracy of the measured excitation density. Thus, the steplike dependence precludes polariton–exciton interactions as the driving mechanism for the observed blueshifts; a conclusion that is also corroborated by the sublinear dependence of the energy shift on \( {X_{k_\parallel = 0}} ^2\). Such a conclusion is also consistent with the high degree of localization of Frenkel excitons on a single molecule, as such exciton localization is expected to dramatically weaken Coulomb exchange interactions and suppress interparticle scattering.
Saturation of molecular optical transitions
In the following, we propose and experimentally verify that the observed blueshifts are due to quenching of the Rabi splitting and a nonlinear change of the cavity refractive index n_{eff}. Both mechanisms are a consequence of the same nonlinear process, namely saturation of molecular optical transitions. Owing to the Pauliblocking principle, excited (i.e., occupied) states cannot be filled twice, thus effectively reducing the oscillator strength of Frenkel excitons. Therefore, occupied states do not contribute to optical absorption at the exciton resonance that in turn reduces the Rabi splitting^{4,20} through the relation
(for a microscopic theory of Rabi quenching see Supplementary Note 5). Here, Eq. (2) describes the quenching of the vacuum Rabi splitting, \(\hbar {\mathrm{\Omega }}_0\), as a function of the total number of excitations, namely the sum of excitons and polaritons n_{x} + n_{p}, where n_{0} is the total number of molecules contributing to strong coupling. Since the optical pump results in a saturation of the molecular optical transitions that contribute to strong coupling, we expect a partial quenching of the Rabi splitting; an effect that results in a measurable blueshift of the lower polariton mode with increasing excitation density. We note here that only a small fraction of molecules in the intracavity layer are strongly coupled to the cavity mode (\(f_{\mathrm{c}} = \frac{{n_0}}{{n_{\mathrm{{tot}}}}}\) is the fraction of coupled molecules), as was suggested by Agranovich et al.^{21}. Therefore, a renormalization of the lightmatter interaction constant originates exclusively from strongly coupled molecules, while the remaining weakly coupled molecules do not contribute to the blueshift through the Rabi quenching mechanism. However, nonresonant pumping leads to a uniform excitation of molecules across the intracavity volume and equally populates both strongly and weakly coupled molecules. Thus, the large amount of weakly coupled molecules dispersed in the cavity can contribute to the blueshift via the renormalization of the cavity mode energy that occurs from the decrease of the intracavity effective refractive index, n_{eff}: a consequence of the quenching of the oscillator strength for the molecules' optical transition. Analogously, the effect of the carrier densitydependent nonlinear refractive index change on the polariton dispersion was recently shown in inorganic ZnO microcavities^{22}. In weakly coupled microcavities, mode energy shifts induced by refractive index changes of the intracavity material have been used as a probe for the measurement of optical nonlinearities^{23}.
The change in refraction under quenching of the oscillator strength is inherent to the causality principle, the Kramers–Kronig relation, that couples the real and imaginary parts of the complex dielectric function^{24}. The relation predicts a decrease of the refractive index above the induced absorption resonance and an increase below the resonance, resulting in an anomalous dispersion that usually appears within the width of an optical transition. We address the problem of refractive index change by general Kramers–Kronig analysis:
where PV stands for integration over the Cauchy principal value, and k(ω) is an extinction coefficient, being an imaginary part of the refractive index.
In order to calculate the real part of the complex refractive index using Eq. (3), one needs to know the k(ω′), which is related to the absorption spectrum. We use the absorption spectrum of the bare film to extract k(ω); for details, see Supplementary Note 6. As the absorption spectrum can be perfectly decomposed by a couple of Gaussian distributions centered at 2.446 and 2.548 eV for the excitonic energy and its vibronic replica, respectively, it is quite convenient to calculate Eq. (3) through the known Hilbert transformation of Gaussians in the form of the weighted sum over the Dawson functions:
where the imaginary part is taken in the form of the sum over the Gaussian distributions \(k\left( \omega \right) = \mathop {\sum }\nolimits_i \,A_i{\mathrm{e}}^{\frac{{  (\omega  \omega _{o,i})^2}}{{2\sigma _i^2}}},\) accordingly, and \(F\left[ {\frac{{(\omega  \omega _{o,i})}}{{\sigma _i\sqrt 2 }}} \right]\) is the Dawson function (integral) with an argument \(\frac{{(\omega  \omega _{o,i})}}{{\sigma _i\sqrt 2 }}\).
Equation (4) describes the anomalous dispersion that naturally appears on the average effective cavity refractive index n_{eff} = 1.81 as the consequence of the molecular optical transitions, see Supplementary Note 2. Therefore, with decreasing the imaginary part, one can observe a reduction in the real part of the refractive index over the lower energy sideband. Figure 6a shows the imaginary and real parts of the complex refractive index as a function of energy. Note that Δn is positive on the highenergy side of the exciton resonance and negative on the lowenergy side.
The change in refractive index is evident over a range of energies on either side of the resonance that induces a correspondent energy shift of the cavity mode E_{c} by a value of ΔE_{c}. For small changes of \(\Delta n \ll n_{\mathrm{{eff}}}\), one can approximate the energy shift with
where n_{eff} = 1.81 is the effective cavity refractive index.
Equation (5) describes the blueshift of the lower polariton dispersion due to the change that occurs in the cavity refractive index from the saturation of weakly coupled molecular optical transitions. The net effect of both the quenching of the vacuum Rabi splitting and cavity mode renormalization on the blueshift ΔE_{LPB} is given by
where E_{x}, E_{c} are the energies of the bare exciton and cavity modes respectively, and \(E_{\mathrm{{LPB}}}^0\) is the unperturbed energy of the ground polariton state in the limit of small excitation numbers (linear regime), \(\hbar {\mathrm{\Omega }}\) and Δn are the densitydependent Rabi splitting and the change of cavity refractive index, respectively.
In the case of a small saturation parameter ξ, namely \(\xi = \frac{{(n_{\mathrm{x}} + n_{\mathrm{p}})}}{{n_0}} \cong \frac{{n_{\mathrm{x}}}}{{n_0}} \ll 1\), we can significantly simplify the above equation for the polariton blueshift. First, we describe the change in refractive index Δn by means of parameter ξ as follows:
We replace the weighted sum over the Dawson functions from Eq. (4) to a single Dawson function with argument \(d = \frac{{\left\lceil \delta \right\rceil \cdot 2\sqrt {\mathrm{{ln}}2} }}{{\mathrm{{FWHM}}}}\), where δ = E_{c} − E_{x} is the detuning and the fullwidth at halfmaximum (FWHM) of the main absorption peak which is attributed to the \(S_{0,0} \to S_{1,0}\) singlet optical transition. The scaling parameter α in Eq. (7) corresponds to the oscillator strength of the optical transition as it is proportional to the absorption maximum (Abs_{max}), \(\alpha = \frac{{\mathrm{{Abs}}_{\mathrm{{max}}} \cdot \lambda _{\mathrm{{max}}}}}{L}\), where L is the cavity thickness. Thus, we can now reformulate Eq. (6) for the total polariton blueshift in a more convenient way within the approximation of a small saturation parameter ξ:
where \(s = \frac{{\hbar {\mathrm{\Omega }}_0}}{{\delta }}\) is a dimensionless parameter of strong coupling; we exploit the reasonable assumption of f_{c} ≪ 1.
Both terms in Eq. (8) reflect the influence of the same physical process of saturation of the optical transition on the polariton energy, but rely on different subsets of molecules. The first term corresponds to the quenching of the vacuum Rabi splitting in strongly coupled molecules. The second term corresponds to the renormalization of the cavity mode energy due to the change of the intracavity effective refractive index from the excitation of weakly coupled molecules. Surprisingly, we find that the renormalization of the cavity mode energy dominates over the quenching of the Rabi splitting in the total polariton blueshift as \(\rho = \frac{{\Delta E_{\mathrm{{LPB}}}^{\mathrm{c}}}}{{\Delta E_{\mathrm{{LPB}}}^\Omega }} = \frac{{(E_{\mathrm{x}}  \left \delta \right) \cdot F[d] \cdot \alpha \cdot (\sqrt {1 + s^2} + 1)}}{{5n_{\mathrm{{eff}}} \cdot s \cdot \hbar {\mathrm{\Omega }}_0}} \,{> }\, 1\) for the whole range of exciton–photon detuning accessible in this study. Clearly, the ratio is invariant over the saturation parameter ξ, and it depends on \(\hbar {\mathrm{\Omega }}_0\), δ, the absorption of the optical transition, α, its linewidth FWHM and cavity thickness L. Figure 6b shows the ρ ratio versus the detuning. To the best of our knowledge, the significance of the renormalization of the cavity mode energy to the total energy shift of organic polariton condensates has not been considered to date. Although Eq. (8) ultimately describes the magnitude of blueshifts in strongly coupled organic microcavities, neither of the involved mechanisms nor their superposition can explain the ubiquitous steplike increase of the blueshift at condensation threshold, P_{th}, but instead predicts a continuous increase of the blueshift with an increasing number of excitations in the system, characterized by parameter ξ.
Intermolecular energy transfer
To explain the pump power dependence of polariton blueshifts, we construct a model that distinguishes between molecules that have a nonzero projection of their optical dipole moment aligned parallel \((N_0^\parallel )\) and perpendicular \((N_0^ \bot )\) to the linear polarization of the excitation laser. We assume that upon nonresonant optical excitation, only parallelaligned molecules are initially occupied. These molecules constitute an exciton reservoir \((N_{\mathrm{x}}^\parallel )\) whose population is then depleted through: (i) energetic relaxation to the ground polariton state having the same optical alignment \((N_{\mathrm{p}}^\parallel )\), (ii) intermolecular energy transfer to perpendicularaligned molecules as well as to other uncoupled molecules having some outofplane projection of the dipole moment \(N_0^ \times\) and (iii) decay via other nonradiative channels (γ_{NR}). We propose that intermolecular energy transfer from exciton reservoir \(N_{\mathrm{x}}^\parallel\) populates exciton reservoirs \(N_{\mathrm{x}}^ \bot\) and \(N_{\mathrm{x}}^ \times\), whose populations are in turn depleted through the same energy relaxation channels with the \(N_{\mathrm{x}}^ \bot\) reservoir creating polaritons having an optical alignment that is perpendicular to the excitation laser \((N_{\mathrm{p}}^ \bot )\). Figure 7 shows a schematic of the involved molecular transitions and relaxation paths of excited states considered within our model.
In densely packed organic films, intermolecular energy transfer is an efficient process that results in the ultrafast depolarization of fluorescence^{25,26}. When such films are embedded in a strongly coupled microcavity, intermolecular energy transfer below condensation thresholds is evidenced by a nearzero degree of linear polarization, as shown in Fig. 2e. With increasing excitation density and upon condensation threshold, energy relaxation to the ground polariton state becomes stimulated, resulting in subpicosecond relaxation times, i.e., stimulated relaxation becomes faster than intermolecular energy transfer. Thereby, polariton condensation occurs with optical alignment parallel to the excitation laser^{3,4,5,8}. The interplay between stimulated relaxation to the ground polariton state and intermolecular energy transfer can qualitatively describe the steplike increase of the degree of linear polarization at the condensation threshold, experimentally observed here in Fig. 2e. The quenching of intermolecular energy transfer upon condensation threshold, effectively increases the occupation of \(N_0^\parallel\)molecules, which in turn quenches the corresponding Rabi splitting, \(\hbar {\mathrm{\Omega }}^\parallel = \hbar {\mathrm{\Omega }}_0^\parallel \sqrt {1  \frac{{2(N_{\mathrm{x}}^\parallel + N_{\mathrm{p}}^\parallel )}}{{N_0^\parallel }}}\), and blueshifts the ground polariton state accordingly, by \(\Delta E_{\mathrm{{LPB}}}^{\mathrm{\Omega }} = 1/2\cdot (E_{\mathrm{x}} + E_{\mathrm{c}}  \sqrt {(E_{\mathrm{c}}  E_{\mathrm{x}})^2 + (\hbar {\mathrm{\Omega }}^\parallel )^2} )  E_{{\mathrm{LPB}}}^0\), where E_{x} and E_{c} are the energies of the bare exciton and cavity modes respectively, and \(E_{\mathrm{{LPB}}}^0\) is the energy of ground polariton state in the limit of small excitation numbers (linear regime). Analogously, the blueshift accompanied with renormalization of the cavity mode energy can be described by the densitydependent function \(\Delta E_{\mathrm{{LPB}}}^{\mathrm{c}} = 1/2\cdot \left\{ {E_{\mathrm{x}}\, + \, E_{\mathrm{c}}( {1  \frac{{\Delta n}}{{n_{\mathrm{{eff}}}}}} )\,  \,\sqrt {( {E_{\mathrm{c}}( {1  \frac{{\Delta n}}{{n_{\mathrm{{eff}}}}}} )  E_{\mathrm{x}}} )^2 + (\hbar {\mathrm{\Omega }}_0^\parallel )^2} } \right\}\,  \, E_{{\mathrm{LPB}}}^0\), where Δn is defined by Eq. (7). In the case of small saturation, namely \(\frac{{\left( {N_{\mathrm{x}}^\parallel + N_{\mathrm{p}}^\parallel } \right)}}{{N_0^\parallel }} \ll 1\), the net polariton blueshift ΔE_{LPB} is just a linear superposition of both contributions: \(\Delta E_{\mathrm{{LPB}}}^{\mathrm{\Omega }} + \Delta E_{\mathrm{{LPB}}}^{\mathrm{c}}\) that is described by Eq. (8). The competition between stimulated relaxation to the ground polariton state and intermolecular energy transfer qualitatively predicts the saturation of molecular optical transitions that are optically aligned with the excitation laser, and the concomitant steplike energy shift at condensation threshold, as shown in Fig. 2d.
To quantitatively describe the experimental dependence of the polariton emission intensity, energy shift, and degree of linear polarization with increasing excitation density, shown in Fig. 2c–e, we formulate the above model in terms of coupled rate equation (for more information see Supplementary Note 7):
where \(P^{\parallel , \bot }\left( t \right)\) is the term corresponding pulsed optical excitation, in the case of linearly polarized pump \(P^ \bot \left( t \right) = 0\), \(\gamma _{\mathrm{{NR}}} = 2.5 \times 10^8\,{\mathrm{s}}^{  1}\) is the nonradiative decay rate of the exciton reservoirs, γ_{p} = 10^{13} s^{−1} is the polariton decay rate, \(\gamma _{\mathrm{{xx}}} = 3.33 \times 10^{10}\,{\mathrm{s}}^{  1}\) are decay rates of intermolecular energy transfer between \(N_{\mathrm{x}}^\parallel\), \(N_{\mathrm{x}}^ \bot\) and \(N_{\mathrm{x}}^ \times\), \(\gamma _{\mathrm{{xp}}} = 1.75 \times 10^5\,{\mathrm{s}}^{  1}\) is the relaxation rate from exciton reservoirs (\(N_x^\parallel\), \(N_{\mathrm{x}}^ \bot\)) towards the ground polariton states (\(N_p^\parallel\), \(N_{\mathrm{p}}^ \bot\)), respectively. In the energy relaxation from the exciton reservoir to the ground polariton state, we have included a stimulation term \(N_{\mathrm{x}}^{\parallel , \bot }\left( t \right)\{ N_{\mathrm{p}}^{\parallel , \bot }\left( t \right) + 1\} \gamma _{\mathrm{{xp}}}\). The solid lines in Fig. 2c–e show the result of the numerical simulations, where we find good quantitative agreement with the experimental observations by using two variable parameters, namely the exciton to polariton relaxation rate (γ_{xp}) and the fraction of strongly coupled molecules (f_{c}). We note that by switching off intermolecular energy transfer (γ_{xx} = 0), we obtain a linear dependence of the energy shift with increasing excitation density that saturates above condensation threshold, see Supplementary Note 7.
Discussion
We further extend our analysis to another strongly coupled organic microcavity with less than half the BODIPYG1 concentration, ~4%. With decreasing dye concentration, we observe a reduction of the vacuum Rabi splitting from 116 meV, for the 10% sample, to 72 meV for the 4% sample, see Supplementary Note 8. For the 4% sample, we observe ~27% lower absorbed pump power at the condensation threshold of the same exciton fraction presumably due to the inverse dependence of the film’s quantum yield on dye concentration. We thus obtain that at the condensation threshold, the saturation of the molecular optical transitions is twice stronger for the 4% sample, and therefore we expect a stronger blueshift. Figure 8a shows the experimentally measured blueshift versus threshold pump power both for the 10% (red) and the 4% (blue) samples at detuning conditions that correspond to equal exciton fractions \(\left {X_{k_\parallel = 0}} \right^2 \cong 0.05\), where indeed we observe a stronger blueshift for the 4% sample. The solid lines in Fig. 8a correspond to numerical simulations containing a densitydependent energy shift due to Rabi quenching and the renormalization of the cavity mode energy. Since the 4% sample exhibits smaller exciton–photon detuning (by means of its modulus δ), we observe a stronger impact of the cavity mode energy renormalization term on the overall polariton shift (see Supplementary Note 8). The higher blueshift in the 4% sample is consistent across the whole accessible range of exciton fractions in the two samples. Figure 8b demonstrates blueshifts as a function of exciton fraction \(\left {X_{k_\parallel = 0}} \right^2\) plotted for the 4% (blue) and 10% (red) samples, respectively. We fit the data using Eq. (8), wherein the saturation parameter ξ is the only variable and considering nearly constant condensation threshold across the whole range of available detuning values, in agreement with our experimental observations (see Supplementary Note 9). According to the bestfit results, at the condensation threshold, we saturate the optical transitions for ξ_{10%} = 0.03 and ξ_{4%} = 0.06 for 10% and 4% samples respectively which is in excellent agreement with experimental assessment above \(\xi _{4\% }/\xi _{10\% } \cong 2\). In the particular case of \(\left {X_{k_\parallel = 0}} \right^2 \cong 0.05\), we obtain similar contributions from the Rabi quenching for both samples (see Supplementary Note 10), while the renormalization of the cavity mode energy in both cases produces a stronger polariton blueshift. The larger polariton blueshifts for the “diluted” system elucidates the importance of uncoupled molecules in the observed energy shifts in organic microcavities. Under nonresonant optical pumping, uncoupled molecules contribute to energy shifts via the change of the intracavity refractive index through the saturation of their optical transition leading to a nonmonotonous dependence on the exciton fraction, see Supplementary Note 10.
Unlike inorganic semiconductor microcavities that bear Wannier–Mott excitons, interparticle Coulomb exchange interactions are virtually absent in organic microcavities due to the localized nature of Frenkel excitons in molecular semiconductors. In the absence of Coulomb interactions, we have explained the origin of blueshifts in organic semiconductor microcavities and the steplike energy shift at the condensation threshold via the interplay of vacuum Rabi splitting, renormalization of cavity mode energy, and intermolecular energy transfer. The ultrafast energy migration mechanism is omnipresent in densely packed organic films and underlies the rapid depolarization of the emission upon optical excitations. We have shown that the steplike blueshift occurs at the condensation threshold when stimulated relaxation of optically aligned excitons to the ground polariton state exceeds the rate of intermolecular energy transfer. The interplay of intermolecular energy transfer and stimulated exciton relaxation predicts a steplike increase of the degree of linear polarization related to the steplike blueshift at the condensation threshold that is also observed experimentally. We constructed a simple model of the transient dynamics of optically aligned excitons and polaritons that reproduces qualitatively and quantitatively the ubiquitous steplike blueshift at the condensation threshold in noncrystalline organic microcavities. We also derived an analytic expression that allows for the evaluation of the relative contribution of the saturation of molecular optical transitions to the experimentally observed polariton blueshifts through Rabi quenching and cavity mode energy renormalization. Since polariton condensation is not a prerequisite for cavity mode energy renormalization, the experimental observation of blueshifts at the onset of nonlinear emission in organic microcavities does not provide a sufficient condition in distinguishing between polariton condensation and lasing in the weakcoupling regime.
Methods
BODIPYG1 neat film preparation
Polystyrene (PS) with an average molecular weight of (M_{w}) ≈ 192,000 was dissolved in toluene at 35 mg mL^{−1} following heating at 70 °C and stirring for 30 min. BODIPYG1 (1,3,5,7tetramethyl8phenyl4,4difluoroboradiazaindacene) was then dispersed into the PS/toluene inert matrix solution at 10% concentration by mass. The PS/BODIPYG1 blend was spincast onto quartzcoated glass substrates to create neat thin films for absorption, photoluminescence, ASE, and nonlinear Zscan measurements. The rotation speed was tuned between 4300 and 7900 RPM with the substrates being held on the rotating plate by a vacuum chuck and spun for 50 s before they dried.
Microcavity fabrication
The studied microcavities utilized double DBR mirrors with the bottom DBR having 10 pairs of alternate layers of SiO_{2}/Nb_{2}O_{5} and the top DBR having 8 pairs. The dielectric materials were deposited with an ionassisted electron beam (Nb_{2}O_{5}) and reactive sublimation (SiO_{2}). The deposition of dielectric materials initiated at a chamber pressure of 8 × 10^{−6} mbar with a deposition rate of 2 Å s^{−1} for Nb_{2}O_{5} and 10 Å s^{−1} for SiO_{2}. The bottom mirror was deposited on a quartzcoated glass substrate. A layer of PS/BODIPYG1 was then spincast on top of the bottom DBR. The thickness of the organic active layer was controlled via the rotation speed of the spin coater to achieve λ/2 microcavities. The rotation speed was tuned between 4300 and 7900 RPM with the substrates being held on the rotating plate by a vacuum chuck and spun for 50 s before they dried. A thickness gradient, occurring from the spincasting process, permitted different photonexciton detuning values. For the deposition of the top DBR, the ion gun was kept turnedoff for the first few layers of Nb_{2}O_{5}/SiO_{2} to avoid any damage on the organic active layer.
Linear spectroscopy
Absorption (Abs) of the bare BODIPYG1 thin film was measured using a Fluoromax 4 fluorometer (Horiba) equipped with an Xelamp. Photoluminescence (PL) of the film was measured using an Andor Shamrock CCD spectrometer following 473 nm laser diode optical excitation. For absorption and photoluminescence spectra, see Supplementary Fig. 1.
A fibercoupled halogen–deuterium white light source (Ocean Optics DH2000) was used for the angular reflectivity measurements. Two motorized optical rails connected to two concentric rotation mounts allowed the illumination of the sample at different angles and the collection of the reflected white light accordingly. An attached fiber bundle at the end of the collection optical rail was used to direct light into an Andor Shamrock chargecoupled device (CCD) spectrometer. The polariton modes were fitted with Lorentzian curves in order to extract the energy of the LPB and UPB at different angles.
Singlepulse dispersion imaging
We investigated polariton condensate emission using 2 ps single pulses optical excitation from a Ti:Sapphire laser (Coherent LibraHE), which was frequencydoubled through a barium borate crystal providing a wavelength of 400 nm. The pump beam was focused onto a sample by Nikon Plan Fluor 4X microscope objective in 12 µm pump spot size at FWHM. Photoluminescence was collected in transmission configuration using Mitutoyo Plan Apo 20X microscope objective with a numerical aperture of 0.42. To block the residual light from the excitation beam, a Semrock LP02442RU longpass filter was used in the collection path. Filtered photoluminescence from a microcavity was coupled into a 750 mm focal length spectrometer (Princeton Instruments SP2750) equipped with an electronmultiplying CCD camera (Princeton Instruments ProEMHS 1024 × 1024). In all, 1200 grooves mm^{−1} grating and 20 µm entrance slit were used to achieve a spectral resolution of 30 pm.
ASE measurements
ASE measurements were performed using a 355 nm pulsed laser with 350 ps pulse width and 1 kHz repetition rate. A 25 mm cylindrical lens was used to focus the beam on the sample creating a stripe excitation profile (1470 μm × 80 μm). ASE emission from the neat 172 nm thin film was detected from the edge of the film, in a direction perpendicular to that of the propagation of the incident pump beam. An Andor Shamrock CCD spectrometer was used to record ASE spectra. The power threshold for ASE was defined at P_{th} = 6 mW. For ASE spectra, see Supplementary Fig. 2.
Zscan measurements
We studied two thin films of BODIPYG1 in polystyrene host matrix and polystyrene film itself, both 600 nm thickness. Measurements were carried out using an optical parametric amplifier (Coherent OPerA SOLO) pumped by the highenergy Ti:sapphire regenerative amplifier system (Coherent LibraHE) with the central wavelength emission at 545 nm coinciding with the photon energy of the particular polariton condensate realization. Pulse duration and repetition rate were 140 fs and 10 Hz, respectively. The beam was tightly focused by 100 mm focal length lens resulting in 16 µm spot radius. Data acquisition was performed using Si photodetectors (ThorlabsDet10/M) connected with an oscilloscope (Keysight DSOX3054T). For a sketch of the Zscan experimental setup, see Supplementary Fig. 3.
Data availability
The data that support the findings of this study are available in University of Southampton Institutional Repository with the identifier https://doi.org/10.5258/SOTON/D1159.
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Acknowledgements
We thank Professor Nikolay Gippius for helpful discussions. A.Z. and A.B. acknowledge financial support from the Russian Scientific Foundation (RSF) grant No. 187200227. O.K. and I.S. acknowledge support from the Government of the Russian Federation (projects 14.Y26.31.0015 and 3.2614.2017/4.6) and ITMO Fellowship Program. We also acknowledge partial funding from the UK EPSRC via Programme Grant “Hybrid Polaritonics” EP/M025330/1.
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Contributions
D.L. designed the organic microcavity structures and supervised sample fabrication within the project; K.G. fabricated the neat PS/BODIPYG1 films and organic microcavities, performed linear measurements of absorbance and emission the neat films as well as angledependent reflectivity and emission spectra of microcavities, and conducted ASE measurements; L.G. and Z.S. synthesized BODIPYG1 dye. T.Y. and D.S. made analysis of angledependent reflectivity and extracted parameters of strong lightmatter interaction, designed polarizationresolved singlepulse dispersion imaging setup, conducted the pump power measurements, and analyzed the data; T.Y. conducted detuning dependent measurements and performed statistical analysis of blueshifts; A.B. contributed with automation the experiments, conducted Zscan measurements, analyzed the data and together with A.Z. determined role of optical Kerr effect; O.K. and I.S. developed microscopic model of vacuum Rabiquenching; A.Z. contributed with the results interpretation and data analysis, developed model for blueshifts and polarization properties of the condensate, carried out the numerical simulations; P.L. supervised the research; T.Y., A.Z., and P.L. wrote the paper with input from all authors. T.Y., D.S., and A.Z. contributed equally to this work.
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Yagafarov, T., Sannikov, D., Zasedatelev, A. et al. Mechanisms of blueshifts in organic polariton condensates. Commun Phys 3, 18 (2020). https://doi.org/10.1038/s4200501902786
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