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. 2025 Feb 21;19(8):8152–8161. doi: 10.1021/acsnano.4c16649

Polariton-Mediated Ultrafast Nonlinear Energy Transfer in a van der Waals Superlattice

Tzu-Yu Peng †,‡, Jason Lynch §, Jing-Wei Yang ‡, Yen-Yu Wang ‡, Xing-Hao Lee ‡, Ben R Conran ∥, Clifford McAleese ∥, Deep Jariwala §,*, Yu-Jung Lu †,‡,*
PMCID: PMC11887482  PMID: 39981960

Abstract

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Exciton-polariton dynamics in 2D materials have garnered substantial attention across diverse scientific domains for fundamental research with potential applications in optoelectronics. However, practical implementation has been hindered by the challenge of maintaining stable and long-range polariton propagation. Here, we present an innovative material platform featuring extensive monolayer WS2/Al2O3 superlattices (a square with a length of >0.5 cm) coupled to a waveguide mode designed to host exciton-polaritons with operation at room temperature. Time-resolved transient absorption spectra show picosecond nonlinear energy transfer phenomena between upper and lower polariton states, clarifying the dynamic behavior within this quantum realm. In addition, we observed population inversion behavior between the two polariton states that facilitate potential avenues for creating polariton-based ultrafast modulators and switches. This research not only advances our fundamental understanding of polariton dynamics but also promotes the development of innovative technologies that harness these fascinating quantum phenomena.

Keywords: van der Waals superlattices, exciton-polariton dynamics, angle-dependent transient absorption spectroscopy, light-matter interactions, nonlinear energy transfer

Introduction

Exciton-polaritons emerge from the strong coupling of excitons and photons and form a hybrid quantum state possessing extraordinary properties, including ultrafast response times1−3 and the capability for Bose–Einstein condensation,4−7 superfluidity,8,9 and quantum vortices.10,11 In practical applications, polaritons can spontaneously emit coherent light during condensation, which facilitates the development of low-threshold lasers that can be operated at room temperature.6,12,13 Additionally, due to their propagative characteristics, polaritons are suitable candidates for accessing topological insulator materials.14,15 Moreover, the distinctive nonlinear effects16−19 associated with polaritons provide a novel platform for advancing integrated photonics and all-optical transistors.1−3 Among the excitonic materials, monolayer transition metal dichalcogenides (TMDCs) exhibit unique properties, such as a direct bandgap and strong spin–orbit coupling; thus, they promise to aid in the understanding of fundamental physics and exploring novel applications.20−25 Owing to their high exciton binding energy,26 exciton-polaritons based on TMDCs can remain stable at room temperature. Various types of cavity coupling involving TMDCs have been extensively reported.27−30 However, the inherent exciton oscillator strength of monolayer TMDCs has been a constraint in achieving stronger coupling systems. The use of van der Waals (vdW) heterostructures, which are composed of stacked unit cells of wafer-scale monolayer TMDCs and oxide insulators, helps to overcome this limitation while preserving their direct bandgap characteristics.17,31,32 Additionally, these superlattices are capable of sustaining a waveguide mode, eliminating the need for extra nanostructuring in the gain medium and facilitating the formation of strongly coupled exciton-polaritons at the wafer scale.

Although exciton-polaritons have been observed in various materials and different types of resonant cavities, the dynamics of exciton-polaritons in TMDCs is less known. Understanding these dynamics is crucial because it not only provides fundamental insights into the behavior of quasiparticles at the nanoscale but also has immense potential for the development of revolutionary optoelectronic and quantum technologies. Here, we construct a van der Waals (vdW) superlattice using monolayer WS2 and Al2O3 as single unit cells. The formation of exciton-polaritons was confirmed by Rabi splitting in the angle-dependent reflection spectra. We then examined the dynamics of exciton-polaritons in this superlattice using angle-resolved pump–probe transient absorption spectroscopy (TAS). Conducting TAS across a broad visible spectrum, specifically from 450 to 700 nm, enables the detection of hot carrier dynamics and the various recombination pathways of carriers.33−35 By adjusting the incident angle of the probe beam, we can investigate the exciton-polariton dynamics across varying light–matter interaction strengths. These results are compared with the dynamics of the uncoupled exciton in the monolayer WS2. Notably, unlike previous reports that observed the quenching of Rabi splitting at high excitation powers, our findings showed a unique Rabi splitting behavior due to nonlinear energy transfer in a nonequilibrium state under high pumping power. When integrated into van der Waals superlattices, these quasiparticles engage with layered two-dimensional materials in a highly controllable manner. This enables the precise adjustment of their properties. This unparalleled control over exciton-polaritons facilitates numerous exciting opportunities, particularly in the advancement of sophisticated photonic and quantum devices. In addition, the observed nonlinearities are fast on the subpicosecond scale, providing future opportunities for developing polariton-based ultrafast modulators and switches.

Results and Discussion

In this study, all-optical measurements were carried out at room temperature. The superlattice was constructed through the artificial layering of the Al2O3 and WS2 monolayers. Large-area WS2 monolayers grown on sapphire substrates via metal–organic chemical vapor deposition (MOCVD) technology from Aixtron Ltd. were transferred via a wet process. An Al2O3 thin layer was deposited through atomic layer deposition (ALD). Additional details on sample growth are provided in the Methods section. To investigate the formation of exciton-polaritons through the coupling of excitons from WS2 with waveguide mode-induced cavity photons, a gold substrate was used as a bottom mirror with a 37-nm alumina layer on top to form the waveguide mode (Figure 1a). The superlattice is composed of five layers of WS2, and each WS2 monolayer is separated by a 3-nm Al2O3 insulating spacer, which confines the exciton wave function to individual WS2 monolayers and preserves their direct bandgap. Our previous studies on monolayer TMDC/hBN and monolayer TMDC heterostructures have demonstrated that a 3-nm layer of hBN is sufficient to electrically isolate excitons within a single TMDC monolayer.31 Given that the bandgap of Al2O3 is larger than that of hBN, we can conclude that Al2O3 is also sufficient for electronically isolating the WS2 monolayers. Since all layers experience the same dielectric screening across the superlattice, the exciton peak will not shift due to dielectric screening. The measured Raman spectra indicate that the superlattice retains the material properties of the monolayers (Figure S1). A continuous-wave laser with an excitation wavelength of 405 nm was used to perform photoluminescence (PL) measurements and the PL spectra from the WS2 monolayer and WS2/Al2O3 superlattice (Figure S2). The PL spectra were decomposed by multipeak Lorentzian fitting. Thus, individual excitonic components (e.g., neutral excitons, trions, dark excitons, biexcitons, defect-bound excitons, and localized excitons) can be identified by analyzing the power-dependent PL emission from the WS2 monolayer and the WS2/Al2O3 superlattice. Although the fitting results show that the neutral exciton emissions of the monolayer and the superlattice are both at 611 nm, the PL spectrum of the superlattice indicates that the emission is dominated by a biexciton (641 nm), and this result is different from the emission from the monolayer; this difference can be attributed to the light trapping ability of the superlattice.31 In addition, adjusting the thickness of the bottom alumina layer can modulate the waveguide mode that is strongly coupled to the WS2 excitons; this enables exciton-polariton formation in the superlattices when light is coupled into the superlattices at a large incident angle. It is worth noting that gray excitons may exist in our angle-dependent experiments. However, gray excitons reported in the literature are typically observed under low temperatures or high magnetic fields, which break their degeneracy.36−38

Figure 1.

Figure 1

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Exciton-polariton formation in large-area vdW superlattices coupled to TE waveguide modes. (a) Schematic of the ultrafast pump–probe exciton-polariton excitation and detection in a WS2/Al2O3 superlattice coupled with a waveguide mode, accompanied by an image showcasing the large-area WS2 superlattice on Al2O3/Au substrate. (b) Simplified energy-level diagram depicting the hybridization of the cavity mode and the excitonic transition of WS2, forming upper (UP) and lower (LP) exciton-polariton states with an energy separation known as the Rabi splitting. (c) Measured reflectance spectra displayed on a color graph for different incidence angles of transverse electric (TE) polarized light. Dashed lines indicate the peaks of the UP and LP exciton-polariton states. (d) Calculated reflection spectra plotted against the thickness of the bottom alumina layer. The peak of A exciton and TE0 modes are marked by dashed lines. Utilizing the Jaynes–Cummings model, the Rabi splitting (Inline graphicRabi) is calculated to be 158 meV. (e,f) Factions for the components of the UP and LP states from the exciton coupled to the cavity photon are adjustable by altering the thickness of the bottom alumina layer.

A schematic energy-level diagram shows that two new hybrid states are formed under strong coupling between excitons and cavity photons; the energy of the new eigenstates of the system is called the upper (UP) and lower (LP) polaritons (Figure 1b). As the incident angle increases, the light–matter coupling strength in the superlattice gradually intensifies, leading to Rabi splitting behavior under transverse electric (TE)-polarized illumination at incident angles greater than 65°, as confirmed by steady-state reflectance spectra (Figures 1c, S3, andS4). This Rabi splitting matches well with the simulations in which the reflectance spectra dependence on the thickness of the bottom alumina layer at an incident angle of 80° using the transfer matrix method (TMM) was calculated (Figure S5). Figure 1d shows the characteristic anticrossing behavior that defines the strong coupling regime. By varying the thickness of the bottom Al2O3, we confirmed the presence of strong coupling, as made evident by the anticrossing behavior. Notably, the system transitions into the strong coupling regime when the bottom Al2O3 thickness is approximately 37 nm. This interaction leads to the formation of exciton-polaritons, characterized by a Rabi splitting of 158 meV. Compared to the reported strong coupling systems based on monolayer WS2 (Table S1), the WS2 superlattice preserves the advantages of monolayers while achieving a larger Rabi splitting.

Here, we utilized a coupled oscillator model based on the Jaynes–Cummings Hamiltonian to simulate polariton dispersion (Section S4). However, by considering that the vdW superlattice is composed of N monolayers of WS2, we can extend the Jaynes–Cummings model to the Tavis–Cummings model.39−41 The results of the calculations confirm the potential existence of N–1 dark states, in addition to the bright UP and LP states in the superlattice. While these dark states do not directly influence the steady-state spectra, they play an essential role in the relaxation dynamics of polaritons.19,41 Additionally, we calculated that the exciton and cavity photon fractions for both UP and LP could be adjusted by changing the thickness of the bottom alumina layer, known as the Hopfield coefficient42 (Figure 1e,f). The results illustrate that in this exciton-polariton system, the contributions of the exciton and photon are nearly equal when the bottom Al2O3 thickness is approximately 37 nm. The Hopfield coefficients indicated that UP was more photon-like when the thickness of the bottom alumina layer was less than 37 nm. As the exciton–cavity photon detuning changed with increasing thickness of the bottom alumina layer, the UP gradually became a more exciton-like quasiparticle, while the LP became more photon-like.

We utilized angle-dependent pump–probe TAS with femtosecond temporal resolution to investigate the behavior of exciton-polaritons. This was achieved using a Ti:sapphire laser system to generate a 400-nm pump beam with a pulse duration of 100 fs and a repetition rate of 1 kHz; the probe was a white light continuum spanning 450–700 nm (see Methods section). The angle between the pump and probe beams was set to a fixed value of 20°. To excite waveguide modes in our design structures with an external laser beam, momentum matching must be achieved. Thus, we conducted pump–probe TAS in reflection mode at large probing angles to study exciton-polaritons with a fixed pump fluence (40 μJ cm–2). Figure 2a displays the transient differential reflection (ΔmOD) spectra of the WS2 monolayer and superlattice probing with both TE- and transverse magnetic (TM)-polarized beams at a large angle of 80° relative to the surface normal. The measured negative signal indicated ground-state bleaching (GSB), a consequence of carriers being excited to a higher state by the pump beam, reducing the number of carriers in the ground state.43 The pump–probe TAS results of the WS2 monolayer showed that GSB at 608 nm (A exciton) and 518 nm (B exciton) aligned with excitonic features in the steady-state reflection spectra (Figure S6). When the superlattices were coupled with the waveguide mode while probing at a large angle, new GSB signals were observed with the same energy as the polaritonic features in the steady-state measurements.

Figure 2.

Figure 2

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Unveiling the ultrafast exciton-polariton dynamics by using angle-dependent transient absorption spectroscopy (TAS). (a) TAS of the WS2 monolayer and WS2/Al2O3 superlattices on top of Al2O3/Au substrates under TE- and TM-polarized probe beams at an incident angle of 80°. The top diagram illustrates beam paths for the reflective type of pump and probe configuration. (b) TAS of the WS2 monolayer at a probe delay of 0.5 ps, with various TE-polarized probe angles from 60° to 80°. The dotted line represents the photoinduced bleaching signals of the A and B excitons. (c) TAS of the WS2/Al2O3 superlattices at a probe delay of 0.5 ps, with TE-polarized probe angles varying from 60° to 80°. Dashed lines mark the UP (blue) and LP (red) peaks, emerging when probe angles exceed 70°.

Due to the limited oscillator strength of the exciton in monolayer WS2, polaritons could not be generated under either TE- or TM-polarized probe beams, even at large angles. However, stacking the monolayers into a superlattice enhanced the light–matter coupling strength by Inline graphic(44,45) (where N represents the number of layers), reaching the strong coupling condition, as evidenced by the emergence of UP and LP in the steady-state reflectance spectra (Figure 1c). Notably, polaritons were not observed under the TM-polarized probe beam because the superlattice thickness was insufficient to support the TM mode. The calculation results using the TMM revealed that to achieve strong coupling in the TM mode, a bottom alumina layer with a thickness of 133 nm is required (Figure S7). Furthermore, for TAS with a TM-polarized probe beam, the signal of photoinduced bleaching in the superlattice appeared at 623 nm, which was redshifted from that of the monolayer A exciton (608 nm). This shift was attributed to the contribution of trions and biexcitons to the photoluminescence in the stacked superlattice, as confirmed through the decomposed PL spectra (Figure S2).

To further understand the transformation of excitons into exciton-polaritons, we analyzed the angle dependence of the pump–probe TAS in both the WS2 monolayer and the superlattice. Figure 2b,c shows the angle-dependent pump–probe TAS results for the monolayer and superlattice, respectively, measured at a probe delay of 0.5 ps and a fixed pump fluence of 40 μJ cm–2. Compared to that of the monolayer, the superlattice exhibits a strong dependence on the probe angle because the waveguide mode volume decreases with the probe angle, which alters the light–matter coupling strength. As the probe angle increases from 60° to 80°, excitons gradually form exciton polaritons; this results in a gradual redshift of the GSB in the spectrum and is identified as LP. Notably, the photoinduced bleaching signal of UP appears at approximately 70°, a value significantly higher than that observed in steady-state experiments. This discrepancy is attributed to the low pump fluence of 40 μJ cm–2, which is insufficient for resolving the UP at probe angles less than 70°.

Figure 3a shows the TAS color maps for both the WS2 monolayer (top) and superlattice (bottom) under an 80° TE-polarized probe plotted against the probe delay time and wavelength. In the case of the monolayer WS2, we identified three negative absorption changes; these were indicative of the photoinduced bleaching of the A (608 nm), B (518 nm), and C (460 nm) excitons. In addition, the positive absorption signal was caused by photoinduced line width broadening and photoinduced bandgap renormalization.46−49 The positive absorption signal at wavelengths longer than that of the A exciton was due to the excited photocarriers facilitating the formation of trions, biexcitons, and trapped carriers.50−52 Similar photoinduced bleaching signals could also be observed in the superlattice, but the positions and intensities of these signals were significantly different from those in monolayer samples; this primarily occurred because the exciton–photon coupling in the waveguide mode formed UP (568 nm) and LP (629 nm). We compared the lifetimes of the uncoupled A exciton in the monolayer and the signals of the LP in the superlattice extracted from Figure 3a at probe angles of 80°, as shown in Figures 3b and S8. For direct comparison, the lifetime measurement under a probe angle of 60° can be found in Figure S9. After the instrument response was corrected via Gaussian deconvolution, each kinetic trace was fitted with a three-exponential decay model. The detailed fitting formula and parameters can be found in Sections S8–S10. Based on the carrier dynamics of TMDCs,48,53,54 each decay component could be assigned to exciton–exciton/polariton–polariton scattering, exciton–phonon/polariton–phonon scattering, and radiative recombination from the fastest to slowest decay components (τ1–τ3). All carrier scattering times are indeed very fast, with the intermediate lifetime on the order of tens of picoseconds.48,53 To study the contribution of Auger scattering in the stacked superlattice, we examined the changes in the dynamic trace under varying excitation powers, as shown in Figure S10. The results show that the lifetime does not significantly decrease with increasing power, differing from the reported behavior of Auger annihilation at higher power.55,56 Therefore, we exclude Auger scattering from our analysis. By an increase in the coupling strength, the fast decay time τ1 of the LP decreases from an exciton lifetime of 0.85 ps (monolayer) down to 0.68 ps (superlattice), as shown in Figure 3b. Since the variations in probe angles affect the strength of exciton–photon coupling, the Rabi splitting can be calculated from the steady-state spectra, as shown in Figure 1c. Figure 3c reveals the relation between the coupling strength and the decay time (τ1, τ2) in the vdW superlattice. The fitted data revealed that the lifetime of the GSB signal from the superlattice decreased with increasing probe angle, consistent with stronger exciton–photon coupling.57Figure 3d shows a comparison of the fastest decay component (τ1) of A exciton (LP) between the WS2 monolayer and superlattice at various probing angles. Under a probe angle of 60°, the signal lifetime of the WS2 monolayer (uncoupled A exciton) was shorter than that of the superlattice. However, as the probe angle increased, momentum matching could excite the waveguide modes to form exciton-polaritons. This ultimately led to a shorter signal lifetime in the superlattice (LP) than in the WS2 monolayer (uncoupled A exciton) under a large probe angle of 80°. In this analysis, we did not constrain any specific parameters during the fitting process. The current error bars represent the fitting errors.

Figure 3.

Figure 3

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Ultrafast exciton-polariton dynamics in large-area vdW superlattices. (a) The color plot of the time-resolved TAS for the WS2 monolayer and WS2/Al2O3 superlattice under a TE-polarized probe beam at an angle of 80°. (b) Comparison of the time-resolved TAS of A exciton in the WS2 monolayer (blue line) and LP in the vdW superlattice (red line) under a TE-polarized probe beam at an angle of 80°. By increasing the probe angle to 80°, a waveguide mode can be supported in the superlattice. This results in a reduction of the fast decay time (τ1) of the lower polariton (LP), decreasing from the exciton lifetime of 0.85 to 0.68 ps. (c) The decay time of LP in the vdW superlattice as a function of the Rabi splitting. Black (red) dots represent the fitted decay time τ1 (τ2), while the shaded areas mark probe angles at which Rabi splitting is absent. (d) Fast decay time τ1 and (e) slow decay time τ2 of the peak of A exciton in the monolayer and the peak of LP in the vdW superlattice as a function of the incident angle of the probe beam.

Similarly, Figure 3e shows a comparison of the intermediate decay component (τ2) between the signal lifetime of the WS2 monolayer (uncoupled A exciton) and that of the superlattice. As mentioned earlier, the intermediate lifetime is influenced mainly by the scattering between carriers and phonons. In the superlattice, the intermediate lifetime of LP (uncoupled A exciton) is shorter than the signal lifetime of the monolayer (uncoupled A exciton) due to the participation of more phonons in the collision relaxation process. Considering the effect of the phonon bottleneck, the number of phonons that can participate in the process is fixed.58 Therefore, even as the probe angle is increased to form the waveguide mode, the involvement of additional phonons remains limited, resulting in a relatively constant intermediate decay component.

In the angle-dependent experiments, although the UP signal was detectable, its weak intensity made it highly susceptible to interference from the blue shift of photoinduced absorption on both sides, making it difficult to analyze the UP signal. To address this issue, we increased the pump power densities. The TAS color maps at various pump power densities, ranging from 70 to 240 μJ cm–2, are shown in Figure S11a. As indicated by the color maps, when the excitation power density exceeds 70 μJ cm–2, the UP signal gradually becomes more pronounced. Figure S11b shows the dependence of the photoinduced bleaching signal on pump power, indicating that power levels exceeding 240 μJ cm–2 have entered the nonlinear regime, where nonlinear effects become pronounced. To further explore the carrier dynamics of the UP and LP states under weak and strong power excitation, we analyzed the TAS data at pump power densities of 70 μJ cm–2 (linear regime) and 240 μJ cm–2 (nonlinear regime), as shown in Figure 4a,d. Under low-power excitation (70 μJ cm–2), we fitted the lifetimes of the UP and LP states, as presented in Figure S11c and the detailed parameters are summarized in Table S4. The results indicate that the majority of the decay contributions for both UP and LP arise from the shortest lifetime component (τ1), with UP exhibiting a shorter lifetime (0.40 ps) compared with LP (0.57 ps). At this time scale, the decay of UP and LP is predominantly driven by carrier–carrier scattering. The difference in their lifetimes directly reflects the density of states involved during the relaxation process. As illustrated in the mechanism diagrams of Figure 4b,c, and consistent with predictions from the Tavis–Cummings model for superlattices, most excitons occupy dark (incoherent) states. These dark states, which have a relatively high density of states situated between UP and LP, therefore create a much faster decay pathway for the UP.

Figure 4.

Figure 4

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Working mechanism of nonlinear energy transfer between UP and LP in large-area vdW superlattices. (a) Temporal evolution of the photoexcited carrier dynamics of the exciton-polariton in the WS2 superlattice at a low pump power density of 70 μJ cm–2. (b) The distribution of UP and LP states under weak pumping power for probe delays under 2 ps and (c) probe delays exceeding 2 ps. (d) Temporal evolution of the photoexcited carrier dynamics of the exciton-polariton in the WS2 superlattice at a high pump power density of 240 μJ cm–2. A significant population inversion behavior was observed. (e) The distribution of UP and LP states under high pumping power for probe delays under 2 ps and (f) probe delays exceeding 2 ps.

Under strong power excitation (240 μJ cm–2), as shown in Figure 4d, the UP signal intensifies while the LP signal diminishes with increasing probe delay time, revealing an unusual population inversion behavior, as depicted in Figure 4e,f. This behavior is indicative of an atypical energy transfer process. Initially, within subpicosecond time scales, carriers in the UP state rapidly relax due to the high density of states. Under strong power excitation, the UP signal begins to increase at a short time scale due to carriers generated from polariton–polariton annihilation (PPA) through the LP state, filling the dark states. These dark states then couple back to the cavity mode, refilling the UP state and completing an unusual energy transfer process. Additionally, as shown in Figure S11d, the UP lifetime exhibits a rapid decay phase, followed by carrier refilling (∼2 ps), and finally transitions to a subsequent decay phase.

To further investigate the energy-transfer dynamics between UP and LP states, we conducted excitation-power-dependent experiments at fixed probe delay times on a picosecond scale. Figure 5a shows the evolution of the power-dependent pump–probe TAS of the WS2 superlattice at probe delay times of 0.5, 1, 2, 5, and 10 ps. As the probe delay time increases, the LP signal gradually decays. The UP signal also decays at a long probe delay time (10 ps) but at a slower decay rate than the LP signal; this presumably occurs because the LP is more susceptible to light-induced spectral broadening. We extracted the bleaching signal of the UP (568 nm) and LP (629 nm) from Figure 5a and plotted them against photoexcited carrier densities in Figure 5b,c, corresponding to delay times at 0.5 ps and 2 ps, respectively. We prepared two superlattice samples for ultrafast exciton-polariton dynamics measurements. Although the lifetime values exhibit slight variations between the samples, the overall trends and physical behaviors remain consistent (Figure S12). Further detailed information on the power-dependent pump–probe TAS with various probe delays can be found in Figure S13. To understand the power-dependent energy transfer dynamics in the system, we further estimated the photoexcited carrier densities under different pump powers (Section S13). At a probe delay time of 0.5 ps, the intensities of the LP and UP reach the same population at a photoexcited carrier density of 2.4 × 1014 cm–2 (530 μJ cm–2) as shown in Figure 5b. Interestingly, the intensities of the LP and UP reach an equal population at photoexcited carrier densities of 6.4 × 1013 cm–2 (140 μJ cm–2) under probe delay times at 2 ps as shown in Figure 5c. When the probe delay time is increased to 2 ps, the populations of the two quasiparticles are inverted when the carrier density is higher than 6.4 × 1013 cm–2, and this critical density can be observed at longer probe delay times (2 to 10 ps). In contrast, there is no inversion phenomenon for probe delays under 2 ps. This inconsistency indicates that in this nonequilibrium system, a nontrivial energy transfer between UP and LP can be observed. Nevertheless, once the probe delay time exceeds 2 ps, the population of UP and LP stabilizes and becomes more consistent with the pump power, indicating that the ratio of UP and LP can be modulated by controlling the pump power. Additionally, Figure 5d shows the population ratio between the UP and LP states at different excitation densities. It can be observed that at 2 ps, the population ratio is approximately 0.08 when controlling the photoexcited carrier density of 5.1 × 1012 cm–2, whereas at an excitation density of 2.2 × 1014 cm–2, the population ratio reaches 2.06 when controlling the photoexcited carrier density of 2.2 × 1014 cm–2. This suggests the potential for over 25-fold all-optical modulation between the UP and LP states in the vdW superlattice.

Figure 5.

Figure 5

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Ultrafast energy-transfer dynamics of polariton states in large-area vdW superlattices. (a) Temporal evolution of the power-dependent pump–probe TAS from the vdW superlattice under strong coupling, measured at set probe delays of 0.5, 1, 2, 5, and 10 ps. (b,c) Photoinduced bleaching signals of UP and LP as a function of the photoexcited carrier densities at probe delay times of 0.5 and 2 ps. (d) The ratio between UP and LP states is influenced by probe delays and photoexcited carrier densities. The system reaches equilibrium after an optimal delay time of 2 ps, and a population inversion behavior can be observed with photoexcited carrier concentration higher than 6.4 × 1013 cm–2. The most significant modulation effect can be reached at a probe delay of 5 ps.

Conclusion

In summary, angle-resolved pump–probe TAS is used to investigate exciton-polariton dynamics in a vdW superlattice comprising alternating WS2 and alumina layers on an Al2O3/Au substrate under strong coupling. The exciton-polariton coupling strength in the WS2 superlattice can vary as a function of the incident angle of the TE probe beam. With large angle probing, the excitons in WS2 are effectively coupled to the waveguide mode to form a sufficient density of polaritons to overcome the phonon bottleneck effect at low injection, resulting in lifetimes 5 times shorter for LP than for uncoupled A exciton. Interestingly, the nonlinear energy-transfer dynamics of the two polariton states show that equilibrium occurs at an optimal probe delay time of 2 ps, and we observed a population inversion behavior between the UP and LP states. In particular, 25-fold all-optical modulation was achieved by varying the photoexcited carrier densities. These results indicate that self-hybridized polaritons can strongly interact with each other in the nonlinear excitation regime, leading to unique energy transfer, which has implications for a wide range of nonlinear, ultrafast optical devices in the visible frequency range. Our results provide a clearer understanding of the fundamental dynamics of exciton-polaritons, highlighting the need for additional research into the nonlinear energy transfer between the LP and UP states.

Methods

Sample Fabrication

Uniform and wafer-scale monolayer WS2 was synthesized on c-plane sapphire substrates using MOCVD technology provided by Aixtron Ltd., employing a Close Coupled Showerhead MOCVD reactor. This process utilized tungsten hexacarbonyl and ditertiarybutylsulfide as precursors. The deposition of an Al2O3 layer was achieved through Atomic Layer Deposition (ALD), using equipment from Cambridge Nanotech (USA). In each cycle, a metal–organic precursor, trimethylaluminum (TMA), was reacted with water vapor. The creation of Au/Ti (100/10 nm) films was conducted via physical vapor deposition, specifically using the e-beam evaporation technique, with an apparatus manufactured by K.J. Lesker.

For the transfer of MOCVD-grown WS2 monolayers from their original sapphire substrates to create superlattice or exciton samples, a wet chemical transfer method was employed. This involved coating approximately 200 nm of poly(methyl methacrylate) (PMMA) 950k A4 onto a WS2 sample (1 cm2), which was then left to dry overnight in air. The PMMA-coated samples were submerged in deionized (DI) water heated to 85 °C for 1 h, during which air bubbles indicated the initiation of delamination. Subsequently, the samples were gently immersed at a 45° angle into a 3-M potassium hydroxide (KOH) solution, also at 85 °C. This caused the WS2 and PMMA layers to detach from the substrate and float on the solution’s surface. The floating PMMA-supported WS2 layer was then transferred onto a clean glass slide to fresh DI water; this step was repeated multiple times to eliminate any residual contaminants from the delamination process. The final transfer of the floating PMMA-supported WS2 was onto the new substrate. After drying for 6 h, the sample was placed on a hot plate at 70 °C for two h to enhance adhesion to the substrate. Finally, to remove the PMMA, the sample was immersed in acetone at 45 °C for 1 h.

Optical Characterization

The steady-state reflection spectra, dependent on the angle, were captured using a commercial spectroscopic ellipsometer (VASE, J.A. Woollam Co.). Time-resolved TAS was conducted with a FemtoFrame II spectrometer from IB Photonics. For excitation, a Ti:sapphire femtosecond laser (Spectra-Physics, Tsunami) was employed, amplified by a chirped pulse amplification system (Spitfire, Spectra-Physics) to boost the pulse repetition rate from 80 MHz to 1 kHz. This laser was divided into two beams using a 1:9 beamsplitter. The stronger path generated a 400 nm pump source via an optical parametric amplifier (OPA, TOPAS-C, Light Conversion), which was then focused onto the sample surface. The weaker beam was converted to a white light pulse covering 450–700 nm using a sapphire crystal, serving as the polarized probe beam. The pump and probe beams had focal spot sizes of approximately ∼7 × 10–4 and ∼1.6 × 10–4 cm2, respectively. A rotatable sample holder was used for angle-related measurements. These optical measurements were all performed under ambient conditions, maintaining a humidity range between 40% and 50%.

Theoretical Modeling

We developed MATLAB code to execute calculations using the Transfer Matrix Method (TMM) and the Jaynes–Cummings model. For simulating the reflectance of the superlattice structure, a 2 × 2 TMM was employed. In the 2 × 2 Jaynes–Cummings Hamiltonian, the undisturbed energies of the waveguide mode and exciton are represented as diagonal terms. The Rabi energy, valued at 158 meV, defines the interaction strength between the exciton and cavity photon states and is incorporated as the off-diagonal terms in the Hamiltonian.

Acknowledgments

The authors would like to thank Hsing-Yu Kuo for useful discussions. We acknowledge financial support from the National Science and Technology Council, Taiwan (Grant No. NSTC-110-2124-M-001-008-MY3, NSTC-113-2112-M-001-014, NSTC-113-2622-8-002-015-SB), and Academia Sinica of Taiwan (AS-TP-113-M02, AS-GCS-114-M06, AS-iMATE-114-41). D. J. and J. L. acknowledge primary support for this work from the Asian Office of Aerospace Research and Development (AOARD) of the Air Force Office of Scientific Research (AFOSR) FA2386-21-1-4063.

Data Availability Statement

The data from this study are available from the corresponding author upon reasonable request.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsnano.4c16649.

  • Additional experimental details on the optical characterizations of WS2 superlattice and monolayer. It also offers an overview of strong light-matter coupling using WS2, calculation of the carrier density, calculated waveguide modes in the superlattice, and detailed information on the ultrafast carrier dynamics in both the monolayer and superlattice (PDF)

Author Contributions

⊥ T.-Y.P. and J.L. contributed equally to this work. Y.-J.L. led the project, proposed the idea, and designed all experimental investigations, and data analysis. T.-Y.P. performed experiments and data analysis. J.L. fabricated the samples and data analysis. J.-W.Y. proposed the theoretical model and performed calculations. B.C. and C.M. provided the MOCVD monolayer WS2 samples. Y.-Y.W. and X.-H.L. helped with the optical measurements. All authors discussed and revised the final manuscript. T.-Y.P., J. L., and Y.-J.L. wrote the first version of the manuscript. D.J. and Y.-J.L. revised the manuscript, and all authors discussed the results and commented on the manuscript.

The authors declare no competing financial interest.

Supplementary Material

nn4c16649_si_001.pdf (2MB, pdf)

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Associated Data

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Supplementary Materials

nn4c16649_si_001.pdf (2MB, pdf)

Data Availability Statement

The data from this study are available from the corresponding author upon reasonable request.

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