The quantum control of ultrafast excited state dynamics remains an unachieved goal within the chemical physics community. In this study, we assess how strongly coupling to cavity photons affects the excited state dynamics of strongly coupled zinc (II) tetraphenyl porphyrin (ZnTPP) and copper (II) tetraphenyl porphyrin (CuTPP) molecules. By varying the concentration of each chromophore within different Fabry–Pérot (FP) structures, we control the collective vacuum Rabi splitting between the energies of cavity polariton states formed through the strong coupling of molecular electrons and cavity photons. Using ultrafast transient reflectivity and transmission measurements probing optical transitions of individual ZnTPP and CuTPP molecules, we find that the polaritonic states localize into uncoupled excited states of these chromophores through different mechanisms. For ZnTPP, we build a simple kinetic model including a direct channel of relaxation between the polaritonic states. We find that our models necessitate a small contribution from this interpolaritonic relaxation channel to explain both our steady-state and transient optical spectroscopic measurements adequately. In contrast, we propose that strong cavity coupling slows the internal conversion between electronic states of CuTPP not directly interacting with the photons of FP structures. These results suggest that researchers must consider the vibrational structure and excited state properties of the strongly coupled chromophores when attempting to use polariton formation as a tool to control the dynamics of molecules central to photo-sensitizing and light harvesting applications.

The manipulation of excited state molecular dynamics via fully quantum mechanical means remains one of the central goals of the chemical physics community. To achieve this, lofty goal researchers have begun to assess the ability of resonator photons to control the photophysics and photochemistry of cavity-confined molecules.1–24 In particular, by embedding photo-activated molecules in a nano- or micro-scale electromagnetic resonator, one can take advantage of the quantum nature of photonic fluctuations to form strongly coupled states of light and molecular electrons known as cavity polaritons. Over the course of the last few years, theorists have predicted that cavity polariton formation amends several molecular properties, including photochemical rates5,8,9,16,25 and excited state photophysical processes, such as singlet fission.13 

In contrast to these theoretical predictions, studies examining the experimental dynamics of molecular polaritons conclude that the presence of a large density of dark states (DSs) corresponding to molecules uncoupled from cavity photons impedes the precise manipulation of excited state molecular processes central to quantum mechanically controlled optoelectronic technologies.19,24,26 In particular, the authors of these studies proposed that when one excites the higher energy of the two polariton states, the upper polariton (UP), localization into the reservoir of dark states (DSs) out-competes non-radiative relaxation into the lower polariton (LP) and complicates how polariton formation can be used to amend molecular dynamics crucial to applications such as lasers, light emitting diodes, and photo-catalytic platforms. Despite these claims, it remains unclear if the dynamics uncovered in these studies stem from the choice of optical transitions to probe.

Given their large linear and nonlinear interactions with light, many researchers examine polariton dynamics by measuring changes in the transmission or reflection of a probe pulse resonant with one or both of the polaritonic transitions.24,27 While straightforward in principle, the collective nature and many-body interactions necessary to form stable polaritons complicate the interpretation of these dynamical spectroscopic signals. Specifically, recent studies report that non-zero ΔT/T or ΔR/R signatures appear at the polariton energies for pump–probe time delays exceeding the known lifetimes of molecular excited states.24,27 Researchers propose that these features result from a variety of sources ranging from the reduction of the vacuum Rabi splitting energy due to the depletion of the molecular ground state and excited state absorption (ESA) into the manifold of multi-polaritonic states.

The choice of probe energy in assessing the ultrafast dynamics of cavity polaritons can be cast clearly by considering samples in which zinc (II) tetraphenyl porphyrin (ZnTPP) molecules couple strongly to photonic fluctuations in micro-scale Fabry–Pérot cavity structures. Early studies by Lidzey and co-workers indicated that the lower polariton (LP) state relaxed into the states of localized ZnTPP molecules at a rate of 0.33 ps−1 and did not depend dramatically on the Hopfield coefficients characterizing the photonic and molecular contributions to the LP state.28 In stark contrast, we showed previously that the ultrafast relaxation from the UP to the localized states of ZnTPP can occur as fast as 2.25 ps−1 when we probed the dynamics experimentally through the lens of excited state absorption processes imprinted onto the localized ZnTPP molecules.23 Furthermore, we found that this localization rate depended sensitively on the concentration of ZnTPP we embed within the resonator structure. These differences indicate that local molecular probes can play an important role in assessing how polariton formation affects ultrafast relaxation dynamics of molecular moieties. While we showed experimentally that the conversion of polaritons into localized molecules could occur more rapidly than thought previously, in that study, we did not fundamentally assess the dynamical mechanism of polaritonic control. Moreover, we did not extend our studies to other metalloporphyrin moieties to uncover trends in cavity-amended dynamics.

In this study, we systematically analyze both steady-state and time-resolved spectroscopic measurements to understand how polariton formation affects non-radiative relaxation in ZnTPP and copper (II) tetraphenyl porphyrin (CuTPP). Like other metalloporphyrins, ZnTPP and CuTPP both possess two prominent absorptive transitions in the visible region: a transition between the S0 and S2, or B, states denoted the Soret transition near 400 nm and a transition between the S0 and S1, or Q, states near 530 nm. While both transitions stem from a degenerate set of HOMO states, configuration interactions split these states’ energies and cause the observation of distinct peaks in the absorption spectra of ZnTPP and CuTPP.29 Given its significantly larger oscillator strength, we use the Soret transition of each molecule to form cavity polaritons, like several previous studies.18,23,28,30

Using ZnTPP and CuTPP to study polariton dynamics benefits from earlier work on the ultrafast dynamics of each molecule in the solution phase. Zewail and co-workers show when one pumped the Soret transition of ZnTPP, the photoexcited electronic population internally converts with a rate of 0.67 ps−1 to the molecule’s Q state.31 In addition, these researchers found that the B state of ZnTPP absorbs probe pulses possessing central energies between 2.14 and 1.77 eV, which allows one to characterize the internal conversion process directly through conventional pump–probe measurements. Furthermore, while they could not measure the dynamics of light emission from the B state excited initially with their pump pulse, they did find that the B state emits fluorescence. This light emission competes with the internal conversion process and affects the overall efficiency of the non-radiative relaxation in ZnTPP.

Several studies report that the ultrafast spectroscopic excited state dynamics of CuTPP differ significantly from those of ZnTPP.32–35 Most recently, Jeong et al. showed that the initially excited B state of CuTPP decays to the molecule’s Q state within the 100 fs temporal resolution of their time-resolved spectroscopic apparatus. Following this initial decay, these authors showed that the Q state relaxes into the manifold of triplet states at a rate of ∼4 ps−1 in benzene. We found similar results in toluene. The ultrafast formation of the triplet states in CuTPP stems from the open shell configuration of the central Cu atom, which confers a total doublet multiplicity onto the molecular electronic states possessing both singlet and triplet spin configurations. While the fundamental processes governing the ultrafast dynamics of CuTPP differ from those that dominate similar dynamics in ZnTPP, several authors showed that the triplet absorption between 2.64 and 2.48 eV allows one to track the formation of triplet states directly following photo-excitation.32–35 

We leverage the existing knowledge of the ultrafast excited state dynamics of ZnTPP and CuTPP to study how cavity polariton formation affects non-radiative relaxation processes. In particular, we use the established spectral signatures of specific excited electronic states characteristic to localized molecules within cavity structures to assess the rates at which polaritons formed from each respective chromophore localize. We also vary the concentration of each respective chromophore in different Fabry–Pérot cavity structures to understand how the change in the collective coupling of photons and molecules affects polariton relaxation rates.

To achieve our goal, we develop quantitative models of the transmission spectra of cavity polaritons formed from each molecule and use the coherence of the photonic contribution to the polariton states as an additional restraint on relaxation rates of the polariton states imprinted on the properties of peaks corresponding to each polariton peak. For the case of ZnTPP, we use these upper limits on the relaxation rates in a kinetic model to motivate a physical picture in which the vibronic couplings present in ZnTPP play a critical role in how polariton formation can control ultrafast excited state relaxation. We find that the lifetime of the UP state reduces significantly as we increase the concentration of chromophores within the Fabry–Pérot resonators. Based on currently predominant theories of polariton relaxation, we use a harmonic model of polaritonic potential energy surfaces (PESs) to propose that vibronic resonances enhance a direct, interpolaritonic nonradiative relaxation path that can populate the LP substantially before the UP decays to the DS manifold. Furthermore, vibrationally mediated relaxation from the dark states to the LP increases with the collective vacuum Rabi splitting energy, ΩR, and drives an overall increased rate of localization into cavity-embedded ZnTPP molecules. By comparing to models in which we neglect this interpolaritonic relaxation, we find that a quantitatively accurate prediction of the ultrafast localization rates necessitates that we include these direct channels.

In the case of CuTPP, we find that the fastest dynamical signals we measure in cavity polariton samples differ significantly from those we measure in the solution phase. We find that the transient absorption (TA) signal stemming from triplet excited state absorption (ESA) at 2.64 eV decays with an initial rate that does not depend on the intracavity chromophore concentration systematically but is significantly slower than the rise of the triplet ESA in solution. By comparing to the steady-state photoluminescence spectra of nano-fabricated control samples, we propose that the ultrafast TA dynamics of CuTPP cavity polaritons stem from a novel ESA signal that decays as strongly coupled molecules localize into their individual excited states. We propose further experimental measurements to determine the fundamental mechanism explaining these findings. Our results indicate the important role local molecular probes can play in elucidating the ultrafast non-radiative dynamics central to the applicability of molecular cavity polaritons in optoelectronic and photochemical technologies.

Microscale Fabry–Pérot resonators were fabricated by first depositing 13 alternating layers of Si3N4 and SiO2 under UHV conditions on a cleaned, optical grade fused silica substrate. Using a transfer matrix model, we designed the layers to possess equal thicknesses of ∼60 nm. Ex situ ellipsometry measurements following the deposition of the first Si3N4 layer showed a film thickness of 59.55 nm, which we presume was reproduced within 1 nm for the subsequent layers in the structure. We then formed films of polymethyl methacrylate (PMMA) from anisole-toluene solutions containing different concentrations of ZnTPP and CuTPP. To form active resonator layers capable of sustaining cavity polaritons, we spun 470 μl of the polymer/chromophore solutions on the DBR (distributed Bragg reflector) structure at 5500 rpm for ZnTPP and 6000 rpm for CuTPP. We capped the cavity structures with Al layers whose thicknesses varied from 12 to 20 nm depending on the performance of the deposition system. A transfer matrix model indicates that we form polaritons due to excitations of the TM mode of the DBR structure detuned from the Soret resonances of ZnTPP and CuTPP by −235 and −286 meV, respectively, at normal incidence using these fabrication parameters. Angularly resolved transmission measurements confirmed the formation of cavity polaritons for all the samples we fabricated, as shown below.

Steady-state transmission measurements were carried out using a fiber-coupled deuterium lamp, free space optics to collimate the lamp output and focus the resulting beam onto the cavity samples, and a fiber-coupled spectrometer (OceanOptics OceanFX). Steady-state transmission spectra were taken at several incident angles to observe the dispersive and anti-crossing behavior of the cavity polariton transmission peaks. In addition to the cavity polariton samples, we fabricated DBR structures without converting them into complete cavity samples to reduce significant portions of the background on the polariton transmission spectra due to the highly dispersive DBR reflectivity. After subtracting the DBR background, we collected cavity polariton transmission spectra using light polarized in the plane of the optical table to ensure excitation of the TM mode of the DBR structure. We also used this system to measure the steady-state absorption spectra of ZnTPP and CuTPP in polymer precursor solutions and characterized the energies and widths of the peaks corresponding to the Soret transition in each molecule, as discussed in Sec. III. Steady-state photoluminescence measurements on CuTPP polaritons and control samples were made with a Horiba XPLoRA PLUS micro-spectrometer. We collected light emission spectra following excitation at 2.33 eV in a back-scattering geometry using a 10× microscope objective.

Ultrafast transient absorption measurements were carried out using the 1.55 eV output of a regenerative amplified seed pulse from a titanium-doped sapphire oscillator (Spectra-Physics Solstice Ace). We frequency-doubled a portion of the amplified output to form 3.1 eV pump pulses. We used another portion of the fundamental output for our probe pulse. After steering the two beams to the sample, we overlapped them in space and collected the transmitted or reflected portions of the probe beam. We then steered those portions of the probe beam to a Si photodiode to which we affixed a 30 meV wide bandpass filter chosen based on excited state absorption features pertinent to cavity polariton localization in samples formed from each respective metalloporphyrin. For ultrafast transient transmission measurements on ZnTPP polariton samples, we used the band of white light continuum around 1.97 eV formed in a 3 mm thick sapphire plate to probe internal conversion from the B state manifold involved in polariton formation to the Q states of localized molecules. Additionally, we used the output of an optical parametric amplifier to form <50 fs pulses at 2.64 eV to probe the formation of triplet states in localized CuTPP molecules following polariton pumping. To ensure transient measurements under resonant conditions between the molecular resonances and vacuum electromagnetic field of the cavity mode, we angled the Fabry–Pérot structure nearly 50° relative to the pump incidence direction. We construct the transient absorption signals by measuring both transient transmission and reflectivity using the equation ΔA = −ΔT − ΔR. We extract the relaxation rates following pump excitation by deconvolving a Gaussian response function from the TA data whose shape matches that of the rise of the measured signal. We find that these response functions change between ∼225 and ∼100 fs for transient measurements on ZnTPP and CuTPP, respectively, which are consistent with the difference in the mechanism through which we form probe pulses in each measurement.

To establish a fundamental physical understanding of changes to the dynamics of ZnTPP polaritons as a function of ΩR, we used the numerical diagonalization of harmonic potential energy surfaces (PESs) of polariton states to compute their vibrational sub-states based on the methods of Mukamel and co-workers, which we used previously to understand the resonance Raman spectra of molecular polaritons theoretically.8,18,36,37 This approach allowed us to compute the vibrational sub-structure of each respective polariton state, their overlaps, and the matrix elements of different molecular operators, as defined below. We assigned the modes along which each chromophore re-organizes using density functional theory (DFT) calculations with B3LYP exchange and correlation functionals38–40 and the 6-31g(d,p) basis set as implemented in the Gaussian09 package.41 

Figure 1 compares the UV–vis absorption spectra of ZnTPP and CuTPP in the region around the Soret resonance of each respective molecule to the transmission spectrum of a model cavity structure we computed using transfer matrix theory with the parameters detailed in the Sec. II. Figure 1 shows the established blueshift of the CuTPP Soret resonance relative to its counterpart in ZnTPP. Close inspection of the absorption spectra shows that the excited state photophysics of each molecule differs despite the resemblance of the structure of their respective macrocycles. In particular, we can discern the presence of a clear vibronic overtone in the absorption spectrum of ZnTPP we assign to a nearly 1190 cm−1 totally symmetric vibration found from DFT calculations and shown in the top right panel of Fig. 1. In contrast, we model the absorption spectrum of CuTPP using a 394 cm−1 vibrational mode shown in the bottom right panel of Fig. 1 whose low frequency causes the appearance of a shoulder on the blue-edge of the molecule’s Soret resonance. This difference suggests that the reorganization of the B state in each molecule differs due to the difference in the electronic configuration of each respective central metal cation, which is also consistent with the difference in the B state lifetimes established experimentally in previous studies.31,34,35

FIG. 1.

Left panel: comparison of the measured and modeled absorbance spectra of zinc (II) tetraphenyl porphyrin (ZnTPP) and copper (II) tetraphenyl porphyrin (CuTPP) to the transmission spectrum of a cavity mode calculated using our experimental fabrication parameters in a custom transfer matrix model. We set the incident angle to 52° to approximate resonant molecule-cavity coupling for the CuTPP chromophore, as indicated by the overlap of those spectra. Model absorption spectra are calculated using harmonic potential energy surfaces displaced along reorganization modes identified by the vibronic overtones present in experimental spectra. Top right panel: spatial representation of the eigenvector of a 1190 cm−1 totally symmetric vibration of ZnTPP that we assign as the mode along which the B state of this molecule re-organizes based on the linear absorption spectrum shown in the left panel. Bottom right panel: spatial representation of the eigenvector of a 394 cm−1 totally symmetric vibration of CuTPP that we assign as the mode along which the B state of this molecule re-organizes based on the linear absorption spectrum shown in the left panel.

FIG. 1.

Left panel: comparison of the measured and modeled absorbance spectra of zinc (II) tetraphenyl porphyrin (ZnTPP) and copper (II) tetraphenyl porphyrin (CuTPP) to the transmission spectrum of a cavity mode calculated using our experimental fabrication parameters in a custom transfer matrix model. We set the incident angle to 52° to approximate resonant molecule-cavity coupling for the CuTPP chromophore, as indicated by the overlap of those spectra. Model absorption spectra are calculated using harmonic potential energy surfaces displaced along reorganization modes identified by the vibronic overtones present in experimental spectra. Top right panel: spatial representation of the eigenvector of a 1190 cm−1 totally symmetric vibration of ZnTPP that we assign as the mode along which the B state of this molecule re-organizes based on the linear absorption spectrum shown in the left panel. Bottom right panel: spatial representation of the eigenvector of a 394 cm−1 totally symmetric vibration of CuTPP that we assign as the mode along which the B state of this molecule re-organizes based on the linear absorption spectrum shown in the left panel.

Close modal

We model the cavity transmission spectrum for an incidence angle of 52° to simulate resonant photon–molecule interactions, given the detuning of our resonator structures from the molecular resonances, as detailed above. We find that the width of the cavity resonance nearly matches that of each respective molecular resonance. We tabulate the energies and widths of each peak of Fig. 1 in Table I.

TABLE I.

Quantitative comparison between the steady-state energy and width of Soret resonances in the absorption spectra of solution phase ZnTPP and CuTPP molecules and the energy and width of the transmission spectrum of a model cavity mode consistent with our experimental fabrication parameters.

Sampleℏω (eV)Γ (ps−1)
ZnTPP 2.923 ± 0.001 9.7 ± 0.3 
CuTPP 2.984 ± 0.001 13.7 ± 0.1 
Cavity 2.900 ± 0.07 11.8 ± 0.1 
Sampleℏω (eV)Γ (ps−1)
ZnTPP 2.923 ± 0.001 9.7 ± 0.3 
CuTPP 2.984 ± 0.001 13.7 ± 0.1 
Cavity 2.900 ± 0.07 11.8 ± 0.1 

The comparison in Fig. 1 confirms a fundamental difference in the collective nature of the electronic states of molecules and the photons in the cavity mode. In particular, we need to model the molecular absorption peaks using Gaussian line shapes whose width, Γinhom, stems from the inhomogeneous broadening caused by differences in the local microscopic environments surrounding each excited molecule and we cannot assess the lifetime of the B state of either molecule from the width of the Soret peak directly. In contrast, the coherent nature of photons within the cavity mode means we can extract photonic lifetimes directly from the homogeneous width of the Lorentzian peak, Γph, in the model transmission spectrum.

The panels of Fig. 2 compare the dispersion of the UP and LP states as a function of in-plane cavity photon momentum for three samples containing different concentrations of ZnTPP and three samples containing different concentrations of CuTPP. We model these dispersion curves using the equations42,43

ELPθ=Ephθ+Eex212EphθEex2+4V2,
(1a)
EUPθ=Ephθ+Eex2+12EphθEex2+4V2,
(1b)

where Ephθ=Ecutoff1sin2θneff1/2 is the dispersive energy of the cavity photon as a function of the angle the incident field makes with the surface normal of the resonator structure, θ; Eex is the energy of the excitonic Soret resonance, which we established from the models in Fig. 1; and V is the strength of the interaction between cavity photons and molecular excitons. Since we load the cavity structures with chromophores, we also allow for the adjustment of the intracavity index of refraction from that of neat PMMA, which we call neff.43 We use the relation ΩR = 2 V to estimate the collective vacuum Rabi splitting for each polariton sample.42 

FIG. 2.

Top row of panels: comparison between the measured (open circles) and modeled (solid line) dispersion of the upper polariton (UP, red) and lower polariton (LP, blue) states formed from the strong coupling of cavity photons to the Soret transition of ZnTPP molecules for 0.498 (left), 0.996 (middle), and 1.991 mM (right) polymer precursor solutions. Bottom row of panels: comparison between the measured (open circles) and modeled (solid line) dispersion of the upper polariton (UP, red) and lower polariton (LP, blue) states formed from the strong coupling of cavity photons to the Soret transition of CuTPP molecules for 0.499 (left), 0.998 (middle), and 1.996 mM (right) polymer precursor solutions. The dispersion of the exciton Soret resonances and cavity photon energies are shown as black solid and dashed lines, respectively, in each panel.

FIG. 2.

Top row of panels: comparison between the measured (open circles) and modeled (solid line) dispersion of the upper polariton (UP, red) and lower polariton (LP, blue) states formed from the strong coupling of cavity photons to the Soret transition of ZnTPP molecules for 0.498 (left), 0.996 (middle), and 1.991 mM (right) polymer precursor solutions. Bottom row of panels: comparison between the measured (open circles) and modeled (solid line) dispersion of the upper polariton (UP, red) and lower polariton (LP, blue) states formed from the strong coupling of cavity photons to the Soret transition of CuTPP molecules for 0.499 (left), 0.998 (middle), and 1.996 mM (right) polymer precursor solutions. The dispersion of the exciton Soret resonances and cavity photon energies are shown as black solid and dashed lines, respectively, in each panel.

Close modal

The dispersion curves of the cavity polariton transmission spectra for all our samples formed from polymer precursor solutions of ZnTPP and CuTPP demonstrate our successful formation of polaritons using both chromophores at all intracavity concentrations. These spectra show that the polariton states formed using CuTPP lie at higher energies than their counterparts formed from ZnTPP, which conforms with the relative blueshift of the Soret resonance of CuTPP when compared to ZnTPP we found in steady-state absorption spectra shown in Fig. 1. We detail the model parameters used to explain the experimental dispersion curves in Table II.

TABLE II.

Quantitative comparison between the collective vacuum Rabi splitting energies, cavity photon energy cutoff, and effective index of refraction found from models of the polariton dispersion curves shown in the panels of Fig. 2.

ChromophoreConc. (mM)ℏωR (meV)Ecutoff (eV)neff
ZnTPP 0.498 77 2.68 1.84 
0.996 108 2.66 1.84 
1.991 160 2.63 1.84 
CuTPP 0.499 85 2.65 1.82 
0.988 117 2.66 1.82 
1.966 164 2.68 1.82 
ChromophoreConc. (mM)ℏωR (meV)Ecutoff (eV)neff
ZnTPP 0.498 77 2.68 1.84 
0.996 108 2.66 1.84 
1.991 160 2.63 1.84 
CuTPP 0.499 85 2.65 1.82 
0.988 117 2.66 1.82 
1.966 164 2.68 1.82 

Unlike the case of cavity polariton formation using the progression of vibronic transitions common to acene molecules, such as tetracene20,24 and rubrene,44 we do not observe the formation of a middle polariton state when strongly coupling ZnTPP to cavity photons despite the presence of a vibronic overtone in this molecule’s absorption spectrum. We attribute this difference in the polariton spectra of these respective samples to quantitative differences in the relative intensities of the vibronic overtones in these molecules. For example, while the 0–1 vibronic transition of tetracene is over 50% as intense as the 0–0 transition of this molecule in solution,45 we find that the 0–1 vibronic overtone of the Soret resonance in ZnTPP is 7% as intense as the transition at the vibrational origin. This significant difference in the oscillator strengths of the vibronic transitions of ZnTPP implies that one cannot form polaritons from 0 to 1 transition at the chromophore concentrations we use in our samples.

Given the collective nature of the coupling between the cavity photons and metalloporphyrin chromophores, we expect ΩRNg, where g is the strength of the light–matter coupling and N is the number of chromophores coupled to the cavity photons.7Figure 3 confirms this expectation by showing that the values of the collective vacuum Rabi splitting energies we find from our models using Eq. (1) obey the square root dependence on the concentration of each chromophore we form in polymer precursor solutions prior to cavity fabrication.

FIG. 3.

Comparison of the concentration dependent values of ΩR found from the dispersion of cavity polariton states formed from ZnTPP (red circles) and CuTPP (blue x’s) to N models (dashed lines) confirming the collective nature of the strong coupling.

FIG. 3.

Comparison of the concentration dependent values of ΩR found from the dispersion of cavity polariton states formed from ZnTPP (red circles) and CuTPP (blue x’s) to N models (dashed lines) confirming the collective nature of the strong coupling.

Close modal

Figure 4 shows the peaks of ZnTPP and CuTPP cavity polaritons as a function of intracavity chromophore concentration at angles that maintain the cavity-molecule resonance extracted from steady-state transmission spectra shown in Fig. S1 of the supplementary material. One can discern the appearance of two distinct peaks in each of the transmission spectra shown in Fig. 4. However, the shapes of these peaks change as a function of the concentration of chromophores we embed in each respective cavity structure. In particular, we find the peaks corresponding to the UP states become increasingly asymmetric for polariton samples formed from the highest concentrations of both ZnTPP and CuTPP we consider.

FIG. 4.

Comparison between the cavity polariton transmission spectra of samples formed from ZnTPP (left column of panels) to those formed from CuTPP (right column of panels) for the following chromophore concentrations in precursor polymer solutions: ∼0.5 (top panels), ∼1 (middle panels), and ∼2 mM (bottom panels). We extract spectra following the fitting routine detailed in the supplementary material.

FIG. 4.

Comparison between the cavity polariton transmission spectra of samples formed from ZnTPP (left column of panels) to those formed from CuTPP (right column of panels) for the following chromophore concentrations in precursor polymer solutions: ∼0.5 (top panels), ∼1 (middle panels), and ∼2 mM (bottom panels). We extract spectra following the fitting routine detailed in the supplementary material.

Close modal

To assess how the polariton states change in response to different concentrations of each molecule, we fit the peaks measured in the transmission spectra to Lorentzian shapes using two separate model functions. For the LP state, we used a conventional Lorentzian shape possessing a constant width, Γ. In contrast, we fit the UP peaks using a Lorentzian possessing a phenomenologically asymmetric shape,46 which we write as

Iω=I0ωωUP2+ΓUPω2,
(2)

where ΓUPω = 2ΓUP/1+expa(ωωUP) captures the asymmetry of the line shape through the value of a for a constant ΓUP. Similar features appear in the absorption spectra of cavity polaritons formed from III–V semiconductor quantum wells and were shown to stem from the dispersive nature of exciton–exciton scattering in those systems caused by the finite effective mass of the exciton’s constituent charges.47 In the case of our samples, we believe that the asymmetric line shapes stem from the dispersive density of states into which the UP decays non-radiatively following excitation. Given that we observe the most prominent asymmetries for the largest chromophore concentrations, we believe that the overlap of the UP state with the 0–1 vibronic transition of each molecule causes a portion of the asymmetry. However, the introduction of additional relaxation channels at higher chromophore concentrations can also cause similar effects and affect the UP transmission line shape,48 as discussed below.

While we seek to use the polariton peak shapes to assess the lifetimes of the hybrid light–matter states, previous studies consider the effect of strong light-molecule coupling on the shapes of spectra emitted by cavity polaritons following localization into the reservoir of dark exciton states. In particular, Mony et al. used the independence of the light emission lifetime of cavity polariton samples formed from perylene derivatives to propose most radiative relaxation stems from those cavity-embedded molecules decoupled from the cavity’s photons.49 However, many other studies stemming from fundamental treatments of the cavity photon–molecule interaction, like those we cite above, show that the transmission, reflection, and absorption spectra of cavity polaritons retain information on the coherent nature of the polariton states, which includes their lifetimes.

Table III compares the parameters we extract from fitting the peaks in Fig. 4 to the shapes we detail above. One can ascertain several features of the dynamics of polaritons formed from each molecule directly from this comparison. First, cavity polaritons formed from CuTPP possess systematically broader peaks we assign to the LP state. This trend mirrors our observation that the peak corresponding to the Soret resonance of solvated CuTPP molecules is nearly 50% wider than that of ZnTPP as reported in Table I. We discuss the connection between these quantities in more detail below. Second, we find that the width of the UP state becomes significantly larger as we increase the concentration of either molecule within the cavities. This increase in peak width with increased concentration occurs simultaneously with our need to increase the asymmetry of the UP peak, as indicated by the value of the asymmetry parameter, a.

TABLE III.

Quantitative comparison between the energies and widths of cavity polaritons formed from the stated concentrations of ZnTPP and CuTPP in cavity structures prepared using the procedures detailed in Sec. II.

ChromophoreConc. (mM)ℏωLP (eV)ΓLP (ps−1)Asym. factorℏωUP (eV)ΓUP (ps−1)
ZnTPP 0.498 2.871 ± 0.001 8.61 ± 0.4 2.977 ± 0.001 11.7 ± 0.3 
0.996 2.856 ± 0.001 9.12 ± 0.1 29.64 2.915 ± 0.002 68.4 ± 4.6 
1.991 2.825 ± 0.001 8.80 ± 0.1 29.11 2.872 ± 0.015 328 ± 63 
CuTPP 0.499 2.918 ± 0.001 11.7 ± 0.3 0.015 3.027 18.5 
0.988 2.898 ± 0.001 19.9 ± 0.4 20.38 2.911 ± 0.016 160 ± 63 
1.966 2.877 ± 0.001 10.3 ± 0.1 24.82 2.895 ± 0.006 631 ± 114 
ChromophoreConc. (mM)ℏωLP (eV)ΓLP (ps−1)Asym. factorℏωUP (eV)ΓUP (ps−1)
ZnTPP 0.498 2.871 ± 0.001 8.61 ± 0.4 2.977 ± 0.001 11.7 ± 0.3 
0.996 2.856 ± 0.001 9.12 ± 0.1 29.64 2.915 ± 0.002 68.4 ± 4.6 
1.991 2.825 ± 0.001 8.80 ± 0.1 29.11 2.872 ± 0.015 328 ± 63 
CuTPP 0.499 2.918 ± 0.001 11.7 ± 0.3 0.015 3.027 18.5 
0.988 2.898 ± 0.001 19.9 ± 0.4 20.38 2.911 ± 0.016 160 ± 63 
1.966 2.877 ± 0.001 10.3 ± 0.1 24.82 2.895 ± 0.006 631 ± 114 

While we find that the phenomenological model of the UP peak helps establish estimated trends in the lifetime of this state as a function of ΩR values, we also find that this model predicts UP state energies different from the values we find from simply identifying the peak position by hand, as done in most studies. While there exists no fundamental understanding of this discrepancy currently, we point out that fundamental theoretical treatments of vibrational anharmonicity do predict that asymmetric peak shapes in vibrational spectra coincide with shifts in the apparent peak positions.50–53 In the case of vibrational spectra, these coupled features of the peak characteristics stem from the presence of a dispersive density of states into which vibrational excitations can decay. This analogy to vibrational spectra may suggest the presence of a dispersive density of states into which the UP can decay when the energy of this state becomes pushed to higher and higher values through stronger and stronger coupling between cavity photons and intracavity molecular chromophores. However, we do not investigate this facet of the polariton dynamics explicitly in the current study.

The changes in peak shapes in steady-state polariton transmission spectra indicate that the relaxation dynamics of metalloporphyrin cavity polaritons depend sensitively on the value of Ω. To investigate this possibility, we undertook ultrafast transient spectroscopic studies of the ZnTPP and CuTPP cavity polariton samples whose steady-state spectra are shown in Figs. 2 and 4.

Figure 5 shows the comparison between the ultrafast transient absorption signals we measure at 1.97 eV for the three ZnTPP samples and at 2.64 eV for the three CuTPP samples whose steady-state transmission spectra are shown in Fig. 4 after extracting the Gaussian rise to the signal. Figure S2 of the supplementary material shows the raw TA signals of each cavity polariton sample. We use a multi-exponential model to extract the relaxation dynamics of each sample. In addition, we use an exponentially decaying sinusoidal function to extract the decay dynamics of each ZnTPP cavity polariton sample. The sinusoid stems from our excitation of coherent acoustic phonons in the Al thin film mirror whose evolution modulates both the transmission and absorption of the probe pulse. The first two decay rates we find from this analysis are shown in Table IV as functions of chromophore concentration in the polymer precursor solutions. Figure S3 of the supplementary material shows the comparison between the experimental and fitted kinetic traces of CuTPP cavity polaritons, while similar comparisons for the ZnTPP cavity polaritons can be found in our earlier study.23 

FIG. 5.

Comparison of the ultrafast transient absorption of cavity polariton samples formed from precursor polymer solutions containing ∼0.5 (blue), ∼1 (green), and ∼2 mM (red) of ZnTPP (top panel) and CuTPP (bottom panel) following 3.1 eV excitation. We probe ZnTPP and CuTPP cavity polariton samples at 1.97 ± 0.015 eV and 2.64 ± 0.015 eV, respectively.

FIG. 5.

Comparison of the ultrafast transient absorption of cavity polariton samples formed from precursor polymer solutions containing ∼0.5 (blue), ∼1 (green), and ∼2 mM (red) of ZnTPP (top panel) and CuTPP (bottom panel) following 3.1 eV excitation. We probe ZnTPP and CuTPP cavity polariton samples at 1.97 ± 0.015 eV and 2.64 ± 0.015 eV, respectively.

Close modal
TABLE IV.

Quantitative comparison between the decay rates of cavity polariton signals following a 3.1 eV pump pulse probed at 1.970 ± 0.015 eV for samples formed from ZnTPP and at 2.64 ± 0.015 eV for samples formed from CuTPP. We report these values for three different chromophore concentrations in precursor solutions made before cavity fabrication.

ChromophoreConc. (mM)k1 (ps−1)k2 (ps−1)
ZnTPP 0.498 0.87 ± 0.07 0.052 ± 0.003 
0.996 1.28 ± 0.07 0.051 ± 0.004 
1.991 2.25 ± 0.10 0.063 ± 0.004 
CuTPP 0.499 1.32 ± 0.05 0.032 ± 0.006 
0.988 1.22 ± 0.05 0.014 ± 0.003 
1.966 1.43 ± 0.06 0.015 ± 0.003 
ChromophoreConc. (mM)k1 (ps−1)k2 (ps−1)
ZnTPP 0.498 0.87 ± 0.07 0.052 ± 0.003 
0.996 1.28 ± 0.07 0.051 ± 0.004 
1.991 2.25 ± 0.10 0.063 ± 0.004 
CuTPP 0.499 1.32 ± 0.05 0.032 ± 0.006 
0.988 1.22 ± 0.05 0.014 ± 0.003 
1.966 1.43 ± 0.06 0.015 ± 0.003 

The comparison in Fig. 5 shows that the rate of the initial decay process in our ZnTPP samples increases as we increase the concentration of this molecular species in our polariton samples, as we have reported previously. This increase in the initial decay rate coincides with the increased width of the peak we assign to the UP state in that steady-state transmission measurements shown in Fig. 4. In addition, we find that the overall behavior of the transient absorption signal of the ZnTPP cavity polaritons resembles that of solvated molecules reported by Zewail and our group previously. In contrast, our analysis indicates that the ultrafast localization dynamics of cavity polaritons formed from CuTPP do not change systematically as we change the concentration of this chromophore in our cavity structures.

For all three CuTPP cavity polariton samples, we consider in this study we find an initial decay rate on the order of 1.3 ps−1. Furthermore, we find that the overall behavior of the transient absorption signal of the CuTPP polaritons does not resemble that of solvated molecules reported previously. While the relaxation of solvated molecules into the triplet states of CuTPP manifests itself as an ∼4.3 ps−1 rise in the TA signal at 2.64 eV, we find that the TA signal for all the cavity polariton samples appears as an initial spike followed by a decay. The difference in the appearance of the TA signal from the CuTPP polaritons relative to solvated samples can be attributed to the significant increase in nonlinear interactions between the pump and probe pulses we anticipate to occur when these beams interact with the cavity polaritons.54 However, this difference in the behavior of the TA signals complicates the assignment of the states participating in polariton relaxation and necessitates further spectroscopic investigation to better understand from which mechanism the difference stems, as discussed below.

Steady-state and ultrafast dynamical spectroscopic measurements suggest that cavity polaritons formed from ZnTPP differ fundamentally from those formed from CuTPP despite the fact that each organometallic molecule possesses the exact same organic ligand. To unravel how differences in the excited-state properties of each respective molecule imprint themselves on the dynamics of the cavity polaritons they form, we discuss the connections of the absorptive properties of ensembles of each molecular chromophore to the polariton spectra and possible mechanisms leading to polariton localization in each chromophore in Subsections IV AIV C. We conclude the study by comparing these mechanisms and suggesting future studies to better elaborate the relationship between molecular and polariton dynamical properties.

The steady-state transmission spectra of Fig. 4 indicate that the cavity polaritons formed from ZnTPP and CuTPP differ on a fundamental level. As mentioned above and shown by several authors,55–57 strong coupling between the molecule and cavity photons imparts the photonic coherence onto the polariton states. However, the connection between molecular and photonic broadening mechanisms to the widths of peaks in the steady-state spectra of polaritonic samples depends on the strength of the light–matter coupling. In the limit that ΩR ≫Γinhom and ωph = ωex, Houdré et al. showed that the width of both polariton peaks should be the geometric mean of the homogeneous widths of both the cavity photon and exciton peaks, i.e., Γpol = Γph+Γhom/2. In contrast, when ΩR ≈ Γinhom, the same authors demonstrated that the polariton peaks possess a width of Γpol = Γph+Γinhom/2. Using the values for Γph and Γinhom reported in Table I and the fact that our polaritons form in the limit that ΩR ≈ Γinhom, we expect that the peaks in the steady-state polariton spectra of ZnTPP and CuTPP should possess widths of 10.8 ± 0.3 and 12.7 ± 0.1 ps−1, respectively. By comparing these values to those we report for the peak widths we find experimentally in Table III, we find that the model of Houdré et al. can qualitatively predict the widths of the LP peaks at all concentrations of ZnTPP but cannot account for the significant broadening of the UP peaks for either chromophore we measure as we increase their concentrations in the polariton samples. We note that while Houdré et al. developed their treatment to explain the steady-state spectra of cavity polaritons formed from III–V semiconductor quantum wells, the equations stated above only necessitate the presence of an intracavity layer whose optical properties can be treated by a Lorentzian model, which can phenomenologically account for the dielectric properties of an ensemble of chromophores embedded with polymer layers, such as those we use to form our own cavity polariton samples.

The deviations between standard theories of polariton steady-state spectra and our measured results may result from changes in the ultrafast relaxation dynamics of metalloporphyrin cavity polaritons as we increase ΩR. Since strong light–matter coupling imparts the photonic coherence onto the polariton states, we expect that one can infer the polariton lifetime, τpol, directly from the width of the polariton peaks.57 In the absence of new relaxation channels caused by polariton formation, we propose that τpol will be 1/Γpol = 2/Γph+Γinhom, as described above. However, when additional relaxation channels become active through polariton formation, the decay of the polariton states can increase beyond this simple superposition of weighted rates stemming from photonic and excitonic losses.

For example, in their early work on cavity polaritons formed from resonator-confined III–V semiconductor quantum wells, Tassone et al. found that polariton formation created new channels through which the UP state could relax into the LP state directly through phonon scattering events.48 These workers predicted that the presence of resonant coupling between the polariton states not only increased the UP to LP relaxation rate by almost a factor of 10 but also led to significant asymmetries between the relaxation rates of the UP and LP states. This asymmetry results from the fact that very few states lie below the LP state into which it can relax. These predictions indicate that polariton formation can drive new types of relaxation processes that will affect polariton state lifetimes and should manifest themselves in the widths of polariton transmission peaks directly.

While Ref. 41 considers cavity polaritons formed from the excitons of nano-fabricated quantum wells of inorganic semi-conductors, we believe that these interpolaritonic relaxation channels should be even more important in the dynamics of cavity polaritons formed from molecular chromophores since the localized molecular vibrations play no role in the conservation of polariton momentum. This lack of a role in momentum conservation implies that the selection rules for vibrational transitions will be less strict in cavity polaritons formed from an isotropic sample of uncoupled molecules than inorganic systems whose electronic excitations possess well-defined momentum in these materials’ Brillouin zones. This presumption conforms with more recent results from two-dimensional electronic spectroscopic studies of the dynamics of cavity polariton samples formed from aggregates of a cyanine dye, which show that UP population relaxes to the LP state via an interpolaritonic relaxation channel with the same efficiency as localization into the DS.58 

Under these conditions, we expect that the total polaritonic decay rate becomes ΓLP,UP = |Xph|2Γph + |Xex|2Γinhom + Γpol, where Γpol represents the relaxation rate stemming from processes such as phonon-mediated interpolaritonic scattering considered by Tassone et al. By determining Γph and Γinhom from model calculations and steady-state absorption measurements in the solution phase, one can then subtract these values from the total width of the Lorentzian peak in the polariton transmission spectrum to estimate Γpol. This approach provides a means to constrain unknown rates in the complex relaxation dynamics of strongly coupled molecules and better understand the overall dynamics of metalloporphyrin cavity polaritons, which we use below.

To help determine the mechanism by which the rate of polaritons that relax into the localized states of cavity-embedded ZnTPP molecules changes as a function of ΩR, we modeled the dynamics of the state populations most likely to contribute to the results we found experimentally. Figure 6 shows the excited states involved and defines the different rates of relaxation between them. Using these definitions, we find that the populations obey the following rate equations:

dNQdt=ΓICLPNLP+ΓICDSNDS,
(3a)
dNLPdt=GLP(t)+ΓLPDSNDS+ΓUPUPNUPΓICLP+αΓphLPNLP,
(3b)
dNDSdt=GDS(t)+ΓDSNUPΓICDS+ΓLPDSNDS,
(3c)
dNUPdt=GUP(t)ΓDS+ΓLPUP+αΓphUPNUP,
(3d)

where the factors Gi(t) correspond to the photoexcitation of the i-th state of the model by a 100 fs-wide Gaussian pulse weighted by the probability that different states will absorb the pump pulse. In this model, we neglect the radiative and non-radiative decay rates of the Q state since the time constant corresponding to these rates is at least 102 longer than the temporal window we consider experimentally in Fig. 5. The term α represents the square of the Hopfield coefficient characterizing the photonic contribution to each polaritonic state,59 |Xph|2, which we set to 0.5, given the undertaking of the ultrafast measurements at resonant cavity-molecule conditions.

FIG. 6.

Schematic representation of the states and relaxation rates pertinent to model the dynamics of ZnTPP cavity polaritons shown in Fig. 5. GS is the global ground state, UP is the upper polariton, LP is the lower polariton, DS are the B states of localized ZnTPP molecules uncoupled from cavity photons, Q is the S1 state of localized ZnTPP molecules within the cavity structure, ΓphUP is the photonic loss from the UP state, ΓphLP is the photonic loss from the LP state, ΓLPUP is the relaxation rate from UP to LP, ΓDS is the relaxation rate from UP to DS, ΓLPDS is the relaxation rate from DS to LP, ΓICDS is the internal conversion rate from DS to Q, and ΓICLP is the internal conversion rate from LP to Q.

FIG. 6.

Schematic representation of the states and relaxation rates pertinent to model the dynamics of ZnTPP cavity polaritons shown in Fig. 5. GS is the global ground state, UP is the upper polariton, LP is the lower polariton, DS are the B states of localized ZnTPP molecules uncoupled from cavity photons, Q is the S1 state of localized ZnTPP molecules within the cavity structure, ΓphUP is the photonic loss from the UP state, ΓphLP is the photonic loss from the LP state, ΓLPUP is the relaxation rate from UP to LP, ΓDS is the relaxation rate from UP to DS, ΓLPDS is the relaxation rate from DS to LP, ΓICDS is the internal conversion rate from DS to Q, and ΓICLP is the internal conversion rate from LP to Q.

Close modal

Previous studies use similar simple rate equations to model the dynamics of polaritonic systems and determine how population flows from the UP states into their lower lying counterparts.26,60,61 In particular, we use the approach of Tassone et al. and explicitly consider a possible role for the direct relaxation between the UP and LP states,48 as described above. Since we know that the total decay rate of the UP state imprints itself on the width of the corresponding peak in the steady-state transmission spectrum, we justify our consideration of a direct interpolaritonic decay channel by noting that the width of the UP peak in Fig. 4 increases significantly and becomes very asymmetric as we increase the concentration of cavity-embedded ZnTPP molecules. However, we also expect changes in the polariton decay rates due to the localization rates ΓDS and ΓLPDS, which could increase due to changes in vibronic resonance controlled by modulating ΩR.

In addition, we use our proposed relations between the polariton decay rates and those of the cavity photons and molecular excitons to estimate ΓICLP. Specifically, we equate ΓLP = |Xph|2Γph + |Xex|2Γinhom = |Xph|2Γph+ΓICLP, which allows us to estimate ΓICLP = ΓLP −|Xph|2Γph using the values of ΓLP we measure experimentally and Γph we find from our transfer matrix model calculations.

While we can accurately estimate the values of ΓICDS, ΓphUP, ΓphLP, and ΓICLP in Eqs. (3a)(3b) from Table III, we must motivate the values of the remaining rate constants from calculations that depend on the value of ΩR we estimate from the spectra in Fig. 4. Specifically, we computed the potential energy surfaces (PESs) of the UP and LP along a 1330 cm−1 vibrational mode. While our previous analysis suggests that the B state of ZnTPP reorganizes along a vibrational mode near 1190 cm−1, which is shown as an inset in Fig. 1, Raman spectroscopy studies undertaken in resonance with the Soret transitions of other metalloporphyrins find substantial activity of totally symmetric ring stretching modes in the region between 1300 and 1550 cm−1.62,63 These studies indicate that the B states of these molecules also reorganize along such modes. Furthermore, our DFT calculations predict that the most intense Raman active vibration of ZnTPP corresponds to a totally symmetric ring distortion mode whose harmonic frequency is at 1400 cm−1.18 After multiplying by established anharmonic factors, we find that this harmonic frequency shifts to nearly 1330 cm−1. By varying ΩR in the computation of the polaritonic PESs, we find that specific values of the vacuum Rabi splitting energy drive resonances between vibrational sub-levels on different polaritonic PESs. In particular, by changing ΩR from 75 to 110 to 160 meV, we reduce the energy gap between the ν = 0 sub-level of the UP state and the ν′ = 1 sub-level of the LP state when we consider PESs along the 1330 cm−1 mode, as shown in the panels of Fig. 7. Previously, we proposed similar resonances because of the interference in the Raman scattering excitation spectra of molecular cavity polaritons.18 

FIG. 7.

Comparison between the harmonic potential energy surfaces of the upper (blue) and lower (red) polariton states along a 1330 cm−1 reorganization mode for vacuum Rabi splitting energy values of 75 (left panel), 110 (middle panel), and 160 meV (right panel). The ν = 0 and ν = 1 vibrational states on each PES are shown as solid and dashed lines, respectively.

FIG. 7.

Comparison between the harmonic potential energy surfaces of the upper (blue) and lower (red) polariton states along a 1330 cm−1 reorganization mode for vacuum Rabi splitting energy values of 75 (left panel), 110 (middle panel), and 160 meV (right panel). The ν = 0 and ν = 1 vibrational states on each PES are shown as solid and dashed lines, respectively.

Close modal

Given the dependence of the transition probability on the energy gap between the states involved in the transition, we use a simple time-dependent perturbation calculation to conservatively estimate how much the probability of making a non-radiative transition from the UP to LP, PUPLP, changes as a function of polariton vibronic resonance conditions we depict in the panels of Fig. 7. Given the finite lifetime of the UP due to the decay to the DS and free space photons, we expect PUPLP ∝ |cLP|2, where

cLP=ı0tdtVUPν,LPνeıωLPνωUPνteΓUPt,
(4)

the interaction matrix is

VUPν,LPν=2JUP,LPdqχUPν*qqχLPνq
(5)

for an interpolaritonic coupling JUP,LP caused by the kinetic energy of the molecule’s nuclei as defined by Bixon and Jortner,64 and ΓUP is the sum of the rates of population loss from the UP caused by photonic decay and localization into the dark states, which we assume is ∼11.2 ps−1 based on the width we find in the polariton transmission spectra and detail in Table III for the 0.498 mM ZnTPP polariton sample. We presume that the UP → LP relaxation process adds a factor of 0.5 ps−1 to the overall decay rate to produce the 11.7 ps−1 rate we report in Table III. Furthermore, we presume that the normal coordinate q corresponds to the 1330 cm−1 vibrational mode along which we calculate the polaritonic PESs. More elaborate theoretical descriptions of the coupling between the polaritonic states may better estimate the value of these interactions13 but are beyond our capabilities currently.

Figure 8 shows how PUPLP depends on the value of the Rabi splitting energy separating the manifold of states in each respective polaritonic state. In Fig. 8, we show the values of ΩR used to form the PESs in Fig. 7 as color-coded vertical lines. Inspecting Fig. 8, we find two important facets of the calculated transition probability. First, we find relatively large transition probabilities for small values of ΩR. At these small vacuum Rabi splitting energies, the two polariton states remain in close energetic proximity and can more easily couple to one another, as expected from previous theoretical treatments of the non-radiative polaritonic relaxation rate.65 In addition, one anticipates a lower density of dark states for these values of ΩR, which would reduce the magnitude of ΓDS in these molecule-cavity systems. As a second point of importance shown in Fig. 8, we highlight the increase in PUPLP as ΩR approaches the energy of the vibrational mode along which the polaritons reorganize. We find that the probability at these vacuum Rabi splitting energies nearly doubles relative to the small values of ΩR. This finding can also help explain the substantial broadening of the peak corresponding to the UP state in the transmission spectra of Fig. 4 for the largest concentration of ZnTPP we consider. In the presence of an increasing interpolaritonic relaxation rate, the width of the transmission peak should also increase due to the lifetime broadening caused by the introduction of an additional channel through which the UP state can decay. We use these qualitative trends in the transition probability to estimate the dependence of the interpolaritonic rate ΓLPUP on the intracavity ZnTPP concentration.

FIG. 8.

The dependence of the probability of making a non-radiative transition between the upper and lower polaritons due to the interactions caused by the nuclear momentum on the vacuum Rabi splitting energy, ΩR, between the polaritonic potential energy surfaces. Blue, green, and red vertical lines correspond to the values of ΩR used to assess the PES in Fig. 7 and qualitatively resemble the values observed experimentally.

FIG. 8.

The dependence of the probability of making a non-radiative transition between the upper and lower polaritons due to the interactions caused by the nuclear momentum on the vacuum Rabi splitting energy, ΩR, between the polaritonic potential energy surfaces. Blue, green, and red vertical lines correspond to the values of ΩR used to assess the PES in Fig. 7 and qualitatively resemble the values observed experimentally.

Close modal

While we observe a vibronic overtone in the absorption spectrum of ZnTPP we assign to the structural re-organization of this molecule’s B state along the normal coordinate corresponding to a totally symmetric vibration at 1190 cm−1, there is no fundamental reason that this vibration should dominate the non-radiative relaxation of the UP state in strongly coupled photon-ZnTPP samples. As shown by Eq. (5), we expect those vibrational modes most able to couple the UP and LP via the constant JUP,LP to dominate the non-radiative relaxation, which will correspond to the vibrations possessing the largest Raman intensity. The results of Somaschi et al. support this physical picture.60 In their study, these authors found that resonance conditions between the DS reservoir and vibronically excited sub-levels of the LP state induce large rates of incoherent pumping of the polariton state following resonant excitation of bare excitons. However, one only observes these enhanced pumping rates when the detuning of the cavity photon energy from that of the molecular exciton transition matched the frequency of intense peaks in the vibrational Raman spectrum of the molecule of interest.

To further motivate the manner in which we expect the quantitative values of non-radiative decay rates to vary with changes to the collective vacuum Rabi splitting energy, we consider the intensity of Raman-active vibrations found from our DFT calculations whose energies lie close to either ΩR and ΩR/2 for each ZnTPP cavity polariton sample, which we compare in Table V. These comparisons reveal two important implications for understanding the ultrafast dynamics of ZnTPP cavity polaritons. First, since the 1330 cm−1 (165 meV) vibration possesses such a dramatically larger Raman intensity than the vibrations maintaining interpolaritonic resonances in lower concentration polariton samples, we expect that the 1330 cm−1 mode will dominate the interpolaritonic relaxation of the UP state in all the samples, as we discussed above.

TABLE V.

Comparison between the values of ΩR found from models of the dispersion of ZnTPP cavity polaritons to the energies and intensities of local molecular vibrations found from DFT calculations.

ChromophoreConc. (mM)ΩR (meV)ων(1) (meV)I(1) (a. u.)ων(1/2) (meV)I(1/2) (a. u.)
 0.498 77 79 10.14 40 2.1 
ZnTPP 0.996 108 107 51.6 56 0.4 
 1.991 160 165 1371 81 71.7 
ChromophoreConc. (mM)ΩR (meV)ων(1) (meV)I(1) (a. u.)ων(1/2) (meV)I(1/2) (a. u.)
 0.498 77 79 10.14 40 2.1 
ZnTPP 0.996 108 107 51.6 56 0.4 
 1.991 160 165 1371 81 71.7 

Second, not only do we expect vibrational resonances to enhance a coupling between the UP and LP states as we increase the value of ΩR near 160 meV, but we also anticipate enhancement of the relaxation rates ΓDS and ΓLPDS. This anticipation stems from the fact that we drive a resonance between the UP state and DS reservoir and a resonance between the DS reservoir and the LP state along a Raman-active vibration possessing a scaled energy of 81 meV whose intensity is an order of magnitude larger than those of the vibrations that maintain similar resonances for ΩR values of 77 and 108 meV. The large increase in the Raman activity of the vibration capable of mediating resonant relaxation channels between the relevant states of increasingly strongly coupled ZnTPP cavity polariton samples indicates that those relaxation processes should also become progressively more probable as we increase ΩR.

We propose to understand the role of interpolaritonic conversion in the localization of strongly cavity-coupled ZnTPP molecules into their Q states by modeling the dynamics of the excited state populations shown in Fig. 5 using solutions to Eq. (3) with rates estimated from the following equations:

ΓUP=αΓphUP+αΓZnTPP+ΓDS+ΓLPUP,
(6a)
ΓLP=αΓphUP+αΓZnTPP+kICLP,
(6b)

where we set α = 0.5. We find the rate ΓICLP by quantifying the rate ΓphLP from Table I and ΓICDS from the experimental solution phase transient absorption signal of ZnTPP and subtracted these rates from the overall width of the LP peak in each steady-state spectrum of the ZnTPP cavity polaritons shown in the left panels of Fig. 4. Furthermore, we estimate the rates ΓDS and ΓLPUP by subtracting the rate ΓphUP in Table I and ΓICDS established by modeling the resonator structure and measuring the solution phase transient absorption signal of ZnTPP, respectively, and subtracting these rates from the overall width of the UP peaks. Moreover, we estimated the rate ΓLPDS from previous experimental studies of ultrafast polariton dynamics.26 Based on the values we report in Table V for vibrations mostly likely to participate in the non-radiative relaxation of ZnTPP cavity polaritons, we propose that the rates ΓLPUP, ΓDS, and ΓLPDS will increase by factors of 2 and 10 as we increase ΩR from 77 to 110 and 160 meV, respectively. While one cannot use these values to quantitatively reproduce ΓUP for the two more concentrated samples reported in Table III, they provide a conservative estimate to enable our probing how the probability of these dynamical processes impacts the overall localization rate. To estimate a total conversion rate, we invert the time at which the Q state population reaches 1 − exp(−1) of the initial population excited into the UP state, NUP(0). We report the values of each rate used in the model defined by Eq. (3) in Table VI. We mark those values we found from our experiments with an asterisk in Table VI.

TABLE VI.

Relaxation rates of pertinent decay channels in a ZnTPP cavity polariton at Rabi splitting energies of 77, 108, and 160 meV. All model parameters found from experimental measurements are denoted with an asterisk.

Conc. (mM)0.4980.9961.991
rate (ps−1)
ΓLPUP 0.5 
ΓDS 5.3* 10 50 
ΓphUP 11.8* 11.8* 11.8* 
ΓICDS 0.67* 0.67* 0.67* 
ΓLPDS 0.1 0.2 
ΓICLP 2.71* 3.22* 2.90* 
ΓphLP 11.8* 11.8* 11.8* 
Conc. (mM)0.4980.9961.991
rate (ps−1)
ΓLPUP 0.5 
ΓDS 5.3* 10 50 
ΓphUP 11.8* 11.8* 11.8* 
ΓICDS 0.67* 0.67* 0.67* 
ΓLPDS 0.1 0.2 
ΓICLP 2.71* 3.22* 2.90* 
ΓphLP 11.8* 11.8* 11.8* 

The panels of Fig. 9 show the results of the model simulations using the parameters detailed in Table VI. We use NUP(0) values of 1, 4, and 9 for the dynamical simulations of the ΩR values of 77, 108, and 160 meV, respectively. Using these models, we find that as we increase the ZnTPP concentration, we observe a corresponding increase in the localization rate of the Q state population. Quantitatively, we find that ΓIC increases from 0.78 to 0.89 to 2.39 ps−1 as we increase [ZnTPP] from 0.5 to 1 to 2 mM, respectively. These values agree qualitatively with the experimental results reported in Table IV. Deviations between the results of our model dynamics and the experimental kinetic traces shown in the top panel of Fig. 5 stem from the coherent interaction between the pump and probe pulses, which make it impossible to resolve the polariton dynamics at the shortest pump–probe times.

We also carried out model simulations in which we neglected the interpolaritonic relaxation channel for comparison to our experimental results, as shown in the right panel of Fig. 9. In these cases, we left all the other model parameters unchanged. For those cases, we find that the total conversion rates change from 0.74 to 0.85 to 1.92 ps−1 as we increase [ZnTPP] from 0.498 to 0.996 to 1.991 mM, respectively. While the values of these localization rates are slightly smaller than those we find from simulations in which we explicitly consider non-zero values of ΓLPUP, we find that we can reproduce the qualitative trend of ΓIC we observe experimentally in both sets of calculations. The inclusion of non-zero values of ΓLPUP causes the localization rate to increase by 10% to 20% for each simulation, which indicates that the vibrational resonances between the polaritons and dark state excitons play an important role in the relaxation dynamics of ZnTPP cavity polaritons.

FIG. 9.

Left panel: ultrafast dynamics of the electronic population in the Q states of cavity-embedded ZnTPP molecules for interpolaritonic relaxation rates of kLPUP = 0.5, 1.0, and 5 ps−1 modeled to occur for polariton samples formed from 0.5 (blue), 1 (green), and 2 mM (red) ZnTPP precursor solutions using the decay rate values detailed in Table IV. Right panel: same ultrafast dynamics we model when kLPUP = 0 ps−1 for polariton samples formed from 0.5 (blue), 1 (green), and 2 mM (red) ZnTPP precursor solutions.

FIG. 9.

Left panel: ultrafast dynamics of the electronic population in the Q states of cavity-embedded ZnTPP molecules for interpolaritonic relaxation rates of kLPUP = 0.5, 1.0, and 5 ps−1 modeled to occur for polariton samples formed from 0.5 (blue), 1 (green), and 2 mM (red) ZnTPP precursor solutions using the decay rate values detailed in Table IV. Right panel: same ultrafast dynamics we model when kLPUP = 0 ps−1 for polariton samples formed from 0.5 (blue), 1 (green), and 2 mM (red) ZnTPP precursor solutions.

Close modal

In addition to the changes in the dynamics of ZnTPP cavity parameters that we expect to observe as a function of ΩR stemming from the physical arguments we made above, we expect that vibrationally mediated relaxation channels should depend sensitively on the relative detuning between the cavity photon and Soret transition of ZnTPP molecules, which can be controlled using the dispersion of the energy differences between the polariton states and between the polariton and dark states, as shown in the panels of Fig. 2. In the case that vibrationally mediated relaxation depends on resonance conditions, such as those shown in Fig. 7, we expect to observe an increase in the width of the UP state peak in the transmission spectrum of the ZnTPP cavity polariton sample for those incident angles of a probe light beam, θinc, that force the dispersive energy differences to match those of the 1330 cm−1 (165 meV) and 653 cm−1 (81 meV) vibrations. Figure 10 shows this behavior for the ZnTPP cavity polariton sample we formed from the 1.991 mM polymer precursor solution. We find UP widths nearly equal to the ZnTPP inhomogeneous width, Γinhom, for θinc values below 50° due to this state being dominated by the excitonic content at low angles, but then we observe a significant increase in ΓUP as we increase θinc toward those values at which the cavity photon energy matches that of the molecule’s Soret transition. Further increasing θinc causes a decrease in ΓUP and results in a peak-like shape to the overall dispersion of the UP decay rate. Given that neither the cavity photon lifetime nor the inhomogeneous broadening of the exciton energies depends so sensitively on the value of θinc, we propose that the peak in the dispersion of ΓUP stems from changes in the values of the non-radiative relaxation rate as we change the energy difference between the LP and UP states with θinc, which would conform with the qualitative features of the dependence of PUPLP on ΩR shown in Fig. 8 and the relative changes in ΓDS and ΓLPDS detailed in Table VI.

FIG. 10.

Dispersion of the UP peak width, ΓUP, as a function of the incident angles of a probe light beam, θinc, found using the phenomenological model described by Eq. (2).

FIG. 10.

Dispersion of the UP peak width, ΓUP, as a function of the incident angles of a probe light beam, θinc, found using the phenomenological model described by Eq. (2).

Close modal

While a kinetic model suggests that increased collective coupling between ZnTPP and cavity photons enables increased non-radiative relaxation capable of increasing the existing path of polariton localization onto individual molecules, the ultrafast TA results from our CuTPP cavity polariton samples suggest that polariton formation fundamentally changes existing relaxation pathways. In particular, we find that the initial decay imprinted onto our TA signals measured from three separate CuTPP polariton samples does not change substantially or systematically as we change the concentration of this chromophore within the cavity structures. We find internal conversion rates near 1.3 ps−1 for all the samples. These decay rates are nearly half of that we find for CuTPP photo-excited at 400 nm when we solvate this chromophore in toluene. However, the appearance of the TA signal does change systematically relative to measurements done on solution-phase samples. This difference creates ambiguity in assigning those states participating in the ultrafast localization dynamics of polaritons formed from CuTPP.

To ameliorate this uncertainty, we measured the steady-state photoluminescence spectra of cavity polariton samples formed from CuTPP and control samples in which we maintain the same spin processing parameters and Al capping layer but do not deposit a DBR structure on the fused silica substrate. A comparison of the PL spectra emitted by these samples should provide clear insights into only those excited-state processes affected by polariton formation while holding constant any effects that stem from loading chromophores into a solid polymer matrix under UHV conditions.

Figure 11 shows that the PL spectra from these samples possess two prominent features when we make the measurements at 80 K. First, we find a relatively smaller peak centered near 1.9 eV, which we assign as the fluorescence emitted by the 2Q state of CuTPP. Second, we find a significantly more intense feature near 1.6 eV, which we assign as the formal fluorescence and phosphorescence from the 2T1 and 4T1 states of localized CuTPP molecules, respectively, which have been characterized thoroughly in previous studies.66 Analysis of these spectra shows that the integrated intensity of the fluorescence signal doubles when we embed the CuTPP-doped polymer layer in the cavity and form polaritons relative to the non-cavity sample. The low temperature at which we undertake these measurements suggests that the difference in the fluorescence signal does not stem from processes such as thermally activated delayed fluorescence (TADF), which would need to overcome a 30 meV difference in energy manifest in the spacing between the features shown in Fig. 11. Recent studies indicate that TADF can be enhanced by polariton formation.20 

FIG. 11.

Comparison between the steady-state photoluminescence spectrum of CuTPP molecules strongly coupled to the photons of a Fabry–Pérot cavity formed from an ∼2 mM precursor solution (blue) to the same spectrum of CuTPP embedded in a metal-capped film formed in the absence of a cavity structure (red). Inset: close comparison between the fluorescence emitted by the Q states of CuTPP in each sample showing the factor of 2 increase in this signal we observe in the presence of strong cavity coupling.

FIG. 11.

Comparison between the steady-state photoluminescence spectrum of CuTPP molecules strongly coupled to the photons of a Fabry–Pérot cavity formed from an ∼2 mM precursor solution (blue) to the same spectrum of CuTPP embedded in a metal-capped film formed in the absence of a cavity structure (red). Inset: close comparison between the fluorescence emitted by the Q states of CuTPP in each sample showing the factor of 2 increase in this signal we observe in the presence of strong cavity coupling.

Close modal

While some previous studies have used comparisons of the optical power stored in resonators used to form cavity polaritons to the power incident on non-cavity samples to better quantify changes in the overall efficiency of the light-mediated process,67 we do not believe that such a treatment is necessary in the case of examining the PL efficiency of our CuTPP cavity polariton samples. In particular, we excite both our polariton and control samples at an energy significantly below that of the cavity photon mode. Furthermore, the ∼140 nm intracavity polymer layers drive the formation of resonators incapable of sustaining standing modes at energies below 2.5 eV. The large gap between this energy and those of the excitation or emission sources implies that such photonic structures do not store energy from the incident laser or the radiating molecules.

Based on the fact that a factor of 2 increase in the fluorescence emitted by the Q state of CuTPP molecules strongly coupled to cavity photons coincides with our observations of an initial transient signal whose decay rate is nearly half of that we find for solution phase molecules, we propose that cavity polariton formation causes an increase in the lifetime of the 2Q state in CuTPP. While the 2Q state does not directly couple to the cavity photons due to the fact that its resonant transition from the molecule’s ground state lies nearly 0.6 eV below that of the Soret resonance, the complex interplay between nuclear and electronic structures in this chromophore could enable a novel mechanism to control the excited state dynamics of states not strongly coupled to the cavity photons.

Distortions to the PES of the CuTPP 2B excited state driven by polariton formation could explain at least two facets of our steady-state PL and TA measurements. First, changes to the position at which the molecular excited states achieve a minimum energy could reduce the ability of the central Cu atom to exchange its unshared d electron with the surrounding porphyrin macrocycle. Since the 2T1 and 4T1 states of CuTPP split due to this exchange interaction, any changes to its value will manifest as shifts in the phosphorescence spectra of this chromophore. As seen in Fig. 9, the phosphorescence of the cavity-coupled CuTPP sample appears at a lower energy than its non-cavity counterpart, which indicates a smaller energy splitting between the 2T1 and 4T1 states. Second, distortions to the excited state PESs of CuTPP would change the Franck–Condon factors central to the oscillator strengths of absorptive transitions of CuTPP excited states. The appearance of a prompt absorptive feature in the TA measurements may indicate the presence of newly allowed excited state absorption transitions whose decay indicates relaxation of the polariton states into the 2Q states of localized CuTPP molecules. The ability of polariton formation to affect excited state absorption processes has been proposed to affect the time-resolved spectroscopic signatures of vibrational polaritons,68 but there has been little experimental investigation on similar effects in molecular exciton cavity polaritons. We will need further work to decipher the mechanism explaining the differences in the TA signals of solvated and strongly cavity-coupled CuTPP molecules.

Establishing the role of polariton formation in amending the dynamics of molecular excited states not directly coupled to cavity photons necessitates further experimental investigation. In particular, since we propose that distortions to those PESs involved in excited state reorganization drive the changes in excited state photophysics we observe, coherent vibrational spectroscopic techniques could be well suited to assess our proposals. In these approaches, one excites a coherent wavepacket using impulsive stimulated Raman processes and spectrally resolves the transmission or reflection of a probe pulse whose energy matches that of the polaritonic transitions.69–72 One can then use known models to determine if the position at which the PES reaches it minimum energy changes as a function of polariton formation and properties of the cavity mode, such as resonant detuning and photon lifetime. We intend to undertake such measurements in future studies.

In this study, we examine ultrafast polariton localization into the excited states of cavity embedded metalloporphyrin molecules. Using a simple kinetic model, we find that we can reproduce the change in the rate of polariton localization into the Q states of strongly cavity-coupled ZnTPP molecules as a function of collective vacuum Rabi splitting energy found from experimental ultrafast pump–probe measurements. To achieve this qualitative agreement, we find that we need to introduce a direct channel of interpolaritonic relaxation neglected in the previous models of ultrafast polariton dynamics in J-aggregate systems. We justify this proposal using simple perturbation methods with vibrational energy states determined from models of polaritonic potential energy surfaces. These models suggest that vibronic resonances between the polariton states could enhance both interpolaritonic relaxation dynamics and the ultrafast relaxation into the band of states stemming from molecular chromophores decoupled from cavity photons. One could test this proposal by maintaining the same ΩR values across several polariton samples in which isotopically different ZnTPP species strongly couple to the cavity photons. The differences in the isotopic substitution of different molecules would affect the energies of the vibrations along which the polaritons reorganize and cause changes to the resonance conditions necessary to induce ultrafast interpolaritonic relaxation prior to internal conversion to the Q state.

In addition, we find that the structure of the ultrafast transient absorption signal we measure in resonance with the trip-doublet excited state absorption feature of CuTPP molecules changes qualitatively under strong light–matter conditions relative to the signals reported in solution-phase samples. By comparing the steady-state light emission spectra of CuTPP polariton and thin film control samples, we found that the rate of internal conversion between the 2Q and manifold of trip-doublet states in CuTPP changes when an ensemble of this molecular species strongly couples to cavity photons. However, the changes to this non-radiative relaxation rate do not correlate with the value of Ω or the concentration of CuTPP we add to each cavity sample. These results indicate that the complexity of the molecular electronic structure enables a mechanism through which cavity polariton formation affects the dynamics of molecular orbitals not coupled to the cavity photons directly. Overall, the results of this study indicate that local molecular probes provide novel insights into the ultrafast dynamics of strongly coupled molecule–photon systems and allow researchers to more completely assess how polariton formation enables future photochemical and optoelectronic technologies.

See the supplementary material for comparisons between measured and modeled steady-state ZnTPP and CuTPP cavity polariton spectra, presentation of unprocessed ZnTPP and CuTPP cavity polariton ultrafast transient absorption traces, and comparisons between the measured and modeled transient absorption kinetic traces of CuTPP.

The authors acknowledge useful comments from Professor Vinod Menon and financial support from the Air Force Office of Scientific Research through its Young Investigator Program under Award No. FA9550-19-1-023 and Wayne State University. The authors also thank the donors of the American Chemical Society Petroleum Research Fund for support (or partial support) of this research through Award No. 60003-DNI6. The Fabry–Pérot cavity structures were fabricated in the Lurie Nanofabrication Facility at the University of Michigan, Ann Arbor.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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