All-optical switching based on interacting exciton polaritons in self-assembled perovskite microwires

All-optical switching is demonstrated on the basis of interacting exciton polaritons in self-assembled perovskite microwires.

Abstract

Ultrafast all-optical switches and integrated circuits call for giant optical nonlinearity to minimize energy consumption and footprint. Exciton polaritons underpin intrinsic strong nonlinear interactions and high-speed propagation in solids, thus affording an intriguing platform for all-optical devices. However, semiconductors sustaining stable exciton polaritons at room temperature usually exhibit restricted nonlinearity and/or propagation properties. Delocalized and strongly interacting Wannier-Mott excitons in metal halide perovskites highlight their advantages in integrated nonlinear optical devices. Here, we report all-optical switching by using propagating and strongly interacting exciton-polariton fluids in self-assembled CsPbBr₃ microwires. Strong polariton-polariton interactions and extended polariton fluids with a propagation length of around 25 μm have been reached. All-optical switching on/off of polariton propagation can be realized in picosecond time scale by locally blue-shifting the dispersion with interacting polaritons. The all-optical switching, together with the scalable self-assembly method, highlights promising applications of solution-processed perovskites toward integrated photonics operating in strong coupling regime.

INTRODUCTION

Metal halide perovskites, solution-processable semiconductors with high defect tolerance, long photocarrier lifetime, and high quantum efficiency (1, 2), hold exceptional promises for optoelectronic and photonic devices, such as solar cells (3), light-emitting diodes (4), photodetectors (5), and lasers (6–8). In contrast to these devices operating in linear optics regime, all-optical switching, a fundamental element that uses photons as information carriers and nonlinear optical properties (9–11), offers an unprecedented opportunity in constructing ultrafast, energy-efficient integrated circuits and networks for computation and communication applications, which remains largely unexplored in perovskites. The essential challenge is that tiny optical nonlinearity in materials imposes general trade-offs between speed, energy, footprint, and dissipation. To circumvent this challenge, strong coupling can be realized by confining optical field with a cavity (12–14), in which the light-matter energy exchange rate surpasses the decay or decoherence rates of each constituents, thus affording considerable nonlinearity stemming from the matter part.

Exciton polaritons, bosonic quasiparticles formed by strong coupling of electronic excitations and photons in semiconductor microcavities, integrate extremely low effective mass and high-speed propagation inherited from the photonic component with strong nonlinearity offered by the exciton fraction (15, 16), leading to emerging optical device implementations (17–22). On the basis of III-V semiconductor quantum wells, high-quality factors (more than 10⁴) (23, 24) and strong nonlinear interactions (25, 26) permit long-range coherent propagation and ease of manipulation of polariton fluids for realizing all-optical switches and transistors (17–22), albeit at cryogenic temperature because of the small exciton binding energy of materials. For pursuing integrated polaritonic devices operating at room temperature (27–34), stringent and simultaneous requirements of large exciton binding energy, strong coupling, and delocalized propagating polaritons are imposed on a semiconductor. Metal halide perovskites are promising materials for polariton devices because of the discovered strong coupling (27, 35–37), polariton condensation (27, 28, 34), and long-range exciton diffusion. In particular, solution processibility of perovskites signals the potential for shaping the energy landscape of polaritons by deterministic, scalable assembly of micro-/nanostructures in solution process (38), which is more efficient and has lower cost than III-V semiconductor devices fabricated by molecular beam epitaxy and lithography.

Here, we realize all-optical switching by leveraging interacting exciton polaritons in solution-processed self-assembled CsPbBr₃ perovskite microwires at room temperature. These single-crystalline microwires can sustain strong coupling and exciton-polariton condensation with a threshold of 3.2 μJ cm⁻². Taking advantages of strong nonlinear polariton-polariton interactions and a propagation length of up to around 25 μm, ultrafast all-optical switching with a picosecond response time is demonstrated by injecting interacting polaritons to manipulate energy landscape. Our results open up opportunities for practical device implementations of exciton polaritons through a feasible and scalable approach.

RESULTS

Operation principle and fabrication of polariton switching

The polariton switches were constructed by embedding self-assembled perovskite microwires between distributed Bragg reflectors (DBRs) (Fig. 1A). These devices are designed and fabricated on the basis of three considerations. First of all, high quality and single crystallinity of perovskites suppress scattering and localization induced by defects and imperfections, while one-dimensional (1D) microwires guarantee directional propagation of polariton fluids with reduced scattering channels (39). Second, delocalized Wannier-Mott excitons in all-inorganic perovskites with considerable binding energy (ca. 40 meV for CsPbBr₃) and Bohr radius (ca. 3.5 nm for CsPbBr₃) not only sustain stable and propagating polaritons at room temperature (40) but also permit strong nonlinearity for manipulation of polariton fluids. Third, the self-assembly in solution process provides a platform to scalable integration of polaritonic devices.

Fig. 1. All-optical switching based on exciton polaritons in self-assembled perovskite wires.

(A) Schematic of all-optical switching by using interacting exciton polaritons in self-assembled CsPbBr₃ wires. Single-crystalline CsPbBr₃ wire arrays are directly assembled onto a DBR substrate followed by deposition of top DBR to construct a Fabry-Pérot cavity. Polariton fluids propagating along the wires are resonantly excited by a source beam at a high in-plane momentum. To control the on/off of the polariton propagation, a block beam at zero momentum with tunable delay is introduced to create an energy barrier by nonlinear polariton-polariton interactions. This all-optical switching can operate at room temperature. (B) Schematic of capillary bridge–mediated self-assembly of single-crystalline CsPbBr₃ microwires with pure crystallographic orientation. The crystallographic axes along the length, width, and height directions of microwires are labeled with white arrows. (C) Representative SEM image of perovskite wire arrays. Scale bar, 10 μm. (D) High-resolution x-ray diffraction of wires. Inset is a rocking curve with a full width at half maximum (FWHM) of 0.018°. (E) GIWAXS pattern of wire arrays. Discrete diffraction spots can be assigned to (101)-oriented orthorhombic CsPbBr₃, illustrating the pure crystallographic orientation and single crystallinity of these microwires.

The all-optical switching in our case is rooted in propagating quantum fluids of light and strong nonlinear interactions of exciton polaritons in self-assembled microwire arrays (Fig. 1A). The propagation length of polaritons in microcavities is directly correlated to the quality of the structure. For organic materials operating at room temperature, propagating microcavity polaritons out of the excitation region have yet to be demonstrated, because of structural defects and imperfections (41). Therefore, single-crystalline semiconductors with suppressed defect density are crucial for the construction of polaritonic devices. Another obstacle for room temperature polaritonic devices lies in relatively small polariton-polariton interaction strength. Strong nonlinearity in III-V quantum wells has bolstered intriguing phenomena, such as optical bistability and parametric scattering (15), and plays a pivotal role in device applications toward transistors (19, 33), spin switches (17), tunneling diodes (20), and interferometers (21). Strong nonlinearity is found in CsPbBr₃ microwires at room temperature in this study, which permits manipulation of the polariton potential landscape with accumulated polariton populations. In our experiments, directional propagating polariton fluids are injected by resonant excitation of the lower polariton branch at a high momentum with an obliquely incident laser beam. To manipulate the propagating polariton fluids, we introduce a second resonant beam with a zero in-plane momentum for blue-shifting the polariton band by exploiting the nonlinear interactions between these injected localized polaritons. The locally blue-shifted polariton band gives rise to an energy barrier for blocking the propagation of polariton fluids. Through controlling the time delay between the two beams, an ultrafast on/off switching of polariton propagation is realized.

Practical device implementations impose additional requirements of scalable and efficient device fabrication. In contrast to III-V counterparts, semiconductors sustaining robust exciton polaritons at room temperature are still constrained by the lack of a versatile platform for microcavity construction. For instance, spin-coated organic thin films have been demonstrated for Bose-Einstein condensation and transistor application (29, 33) but suffer from relatively low-quality factor and limited versatility for engineering of potential landscape. On the other hand, perovskite semiconductors exhibit the advantages of straightforward spin-coated preparation. Nonetheless, this method often leads to a polycrystalline thin film due to rapid crystallization, which may not be a considerable problem for photovoltaic and light-emitting devices; however, such film quality introduces serious scattering losses for exciton polariton formation and propagation. Thus far, polariton condensation was only realized on dry-transferred single-crystalline epitaxial film, which has limited area and efficiency (27, 28). Therefore, future polaritonic devices demand a versatile platform for large-scale assembly of high-quality microstructures with suppressed defects, long-range order, and controllable dimensions for sustaining long-range polariton propagation, which is pivotal in the on-chip integration applications toward polaritonic logic circuits.

Motivated by scalable fabrication of polaritonic devices, we have developed a solution-processing method by harnessing capillary bridges and self-assembled surfactant monolayers at liquid-air interface for guiding the nucleation and growth of CsPbBr₃ (see Materials and Methods, text S1, and figs. S1 and S2 for details). Self-assembled cesium octoate affords a negatively charged air-liquid interface, which concentrates Pb²⁺ ions for preferential nucleation and directional growth of perovskites. This mechanism underpins growth of oriented CsPbBr₃ with a high optical quality, which is difficult to be attained by spontaneous crystallization in capillary bridges (42, 43). As illustrated in Fig. 1B, single-crystalline CsPbBr₃ microwires with pure crystallographic orientation can be deterministically fabricated onto the target DBR substrate by using a silicon template to steer the self-assembly process. The scanning electron microscopy (SEM) image illustrates large-scale microwire arrays with perfect alignment, smooth surface, and a homogeneous width of ~4.0 μm (Fig. 1C). Smooth surface is characterized by a root mean square roughness of 0.8 nm in atomic force microscopy topography (fig. S3), which signals their high optical quality. High-resolution x-ray diffraction (Fig. 1D), together with grazing-incidence wide-angle x-ray scattering (GIWAXS) (Fig. 1E), shows that these microwires are (101)-oriented CsPbBr₃ along the out-of-plane direction. Combining with selective-area electron diffraction, the single crystallinity and pure crystallographic orientation are demonstrated for these microwires with (101) planes parallel to the substrate and (010) planes stacking along the microwire length direction (Fig. 1B and fig. S4). The crystallinity of microwires is also validated with a narrow linewidth of 0.018° in the rocking curve (Fig. 1D, inset), which is comparable with bulk single crystals and higher than epitaxial thin films (44, 45). The single crystallinity with suppressed defects of these microwires lays the foundation for realizing extended polariton condensate fluids and all-optical circuits, which is in notable contrast with the spin-coated thin films with random orientation (fig. S5).

Strong coupling and polariton lasing

In 1D microcavities, strong coupling and optical confinement manifest as (i) nonparabolic exciton-polariton branches with flattened dispersion at high momenta, (ii) continuous multiple polariton branches along the microwire length direction and discrete confined modes along the width direction, and (iii) extended condensates at high momenta due to the repulsive polariton-reservoir and polariton-polariton interactions as the pump fluence exceeds a threshold. Experimentally, we exploited angle-resolved photoluminescence (PL) spectroscopy to characterize these features in microwire cavity arrays with a homogeneous width of 4.0 μm (see Materials and Methods). The exciton-polariton dispersion in transverse electric polarization presents two lower nonparabolic polariton sub-bands (Fig. 2A), which can be fitted by a coupled oscillator model considering the strong coupling of multiple quantized cavity modes with the exciton mode. A fitted Rabi splitting of 127 meV is extracted with the exciton resonance E_X at 2.407 eV (fig. S6) and two parabolic cavity modes. When the entrance slit of the spectrometer is orthogonal to the microwire direction, a series of discrete quantized polariton modes is observed (Fig. 2B). Exciton-polariton condensation is further investigated under the nonresonant femtosecond pulsed-laser excitation. The dispersion above a finite threshold displays polariton condensates located at high momenta (Fig. 2C), indicating nonzero polariton velocity along the microwire. The nonlocal polariton condensates outside the pump region are also validated by a real-space image captured above the threshold (fig. S7). Last, the exciton-polariton condensation in these self-assembled microwires is also confirmed by the evolution of emission intensity and linewidth with pump fluences (Fig. 2D). Above a threshold of 3.2 μJ cm⁻², the abrupt rise of integrated emission intensity and narrowing of linewidth explicitly evidence the exciton-polariton lasing emissions. To unequivocally demonstrate the polariton lasing in strong coupling regime, angle-resolved PL is performed at higher pump fluences. Two thresholds can be observed with the rise of pump fluences. The first threshold represents the onset of polariton condensation, and the second threshold can be attributed to Mott transition for the formation of electron-hole plasma, yielding photon lasing in weak coupling region at higher pump fluences (see text S2 and fig. S8 for details). This two-threshold behavior explicitly demonstrates polariton lasing in perovskite microwire cavity.

Fig. 2. Strong coupling and exciton-polariton condensation in self-assembled perovskite wires.

(A) Dispersion of exciton polaritons shown by angle-resolved photoluminescence with the microwire length direction parallel to the entrance slit of the spectrometer. Upper (UP1 and UP2) and lower (LP1 and LP2) polariton bands illustrated by white solid lines are fitted with a Rabi splitting of 127 meV, while the exciton state (X) with an energy of 2.047 eV and cavity photon modes (C1 and C2) are displayed by dashed lines. (B) Discrete confined polariton states measured with the microwire length direction perpendicular to the entrance slit of the spectrometer. (C) Exciton-polariton lasing and extended polariton condensate at high momentum illustrated by dispersion above threshold (P = 1.97 P_th). (D) Emission intensity and FWHM as a function of pump fluence, indicating a lasing threshold (P_th) of 3.2 μJ cm⁻². a.u., arbitrary units.

Nonlinearity and propagation

Rigorous evaluation of polariton-polariton interaction strength requires a careful evaluation of the impact of exciton reservoirs. A pulsed beam with a linewidth of ca. 24 meV is tuned in resonance with the lower polariton band, thus avoiding the participation of polariton-reservoir interactions. Figure 3A displays a set of reflectance spectra as a function of pump fluence. The dips over reflected laser spectra originate from the absorption by the polariton modes. At a low pump fluence, the polariton band is located at 2.299 eV, which experiences a continuous blueshift to 2.304 eV with the increase of pump fluence. To extract the polariton-polariton interaction coefficients, the polariton populations at different pump fluences are estimated as the absorbed photons in the microcavity, which is a conservative method used in previous reports, thus resulting in a lower-bound value (32, 37). The blueshift of the polariton band ∆E_EP increases as a linear function of polariton density N_EP, which gives rise to polariton-polariton interaction constant g_EP as g_EP = ∆E_EP/N_EP. Polariton bands taken from microwires with different cavity lengths and detunings present a linear dependence of blueshift on the polariton density (Fig. 3B and fig. S9). Polariton-polariton interaction constants of 0.155 ± 0.011, 0.122 ± 0.008, 0.083 ± 0.004, and 0.075 ± 0.003 μeV μm² are extracted from different detuned polariton bands with energies of 2.299, 2.275, 2.248, and 2.218 eV, respectively. By a quadratic fitting of polariton-polariton interaction constants with exciton fractions, the exciton-exciton interaction constant is determined as 4.1 ± 0.6 μeV μm², which is comparable with those in GaAs quantum wells at cryogenic temperature (26) and in 2D hybrid perovskites at room temperature (37). The 2D exciton-exciton interaction constant can be converted into the 3D model by considering the cavity length along the z direction. With a calibrated cavity length of 350 nm (fig. S10), the 3D exciton-exciton interaction constant is calculated as 1.4 ± 0.2 μeV μm³.

Fig. 3. Nonlinearity and propagation of polaritons.

(A) Normalized reflectance spectra as a function of pump fluence of an exciton polariton mode under resonant excitation. (B) Blueshift as a function of calculated polariton density for exciton polariton bands with different detunings. The error bars represent the SD introduced by calibration of polariton density and fitting of polariton energy. Solid lines represent linear fitting of polariton density and blueshift. The energy of lower polariton bands at k_x = 0 are labeled. (C) Optical image (top) and spatially resolved PL intensity (bottom) are shown in a logarithmic scale. (D) Integrated PL intensity as a function of propagation distance, which is fitted by a single exponential decay function (solid line). The propagation length is 23.8 μm for decay of polariton population to 1/e of its initial value.

Long-range propagation of polaritons in a microcavity has laid the foundation for the integrable polaritonic devices. To evaluate the propagation length of polaritons in perovskite microwire cavity, we pump polaritons with a defined group velocity with a beam in resonance with the lower polariton band at k_x of 4.3 μm⁻¹. The resonant excitation configuration injects polariton fluids at a controllable momentum in the linear region. According to the polariton dispersion (fig. S11), the group velocity V_g is 18.3 μm ps⁻¹, calculated by V_g = (1/ℏ)(dE_LP/dk_x), where E_LP is the energy of lower polariton band. Figure 3C shows a real-space image of propagating polaritons along a segment of a microwire in length of 80 μm. The polariton propagation over 80 μm of length can be observed. By integrating the polariton populations as a function of length, the propagation of polaritons can be fitted by a single exponential decay function with a propagation constant of 23.8 ± 0.6 μm, which represents the length for the decay of polariton intensity to 1/e of its initial value. This value is comparable to those of Bloch surface wave polaritons in transition-metal dichalcogenides and organic materials with extremely large group velocities (32, 46). Combining the group velocity (18.3 μm ps⁻¹) and propagation length (23.8 μm), a microcavity polariton lifetime of 1.3 ps is calculated, which highlights the importance for the self-assembly fabrication of microwires with suppressed defects. The polaritons in perovskite microwire cavity exhibit a propagation loss coefficient α of 0.18 dB μm⁻¹, defined by α = (1/l)10 log (I_out/I_in), where I_in is the initial intensity and I_out is the intensity at propagation length of l. Compared to the propagating polariton condensates in transferred perovskite wires (28), the long-range homogeneity of self-assembled microwire arrays underpins a uniform energy landscape for the polariton propagation and device integration.

All-optical switching based on interacting polaritons

On the basis of the interacting polaritons in microcavity with relatively long-range propagation, we sought to develop all-optical switching by introducing two pulsed beams at different in-plane momenta onto a perovskite microcavity with a transmission configuration (Fig. 4A). A momentum space image of two beams (Fig. 4B) illustrates that k_x are 4.4 and 0 μm⁻¹ for source and block beams, respectively. The source beam injects polariton fluids, which propagate along the microwire. The transverse confinement inside the 1D structure avoids any lateral spatial spreading of the propagating polaritons. In contrast, the block beam with a zero k_x injects polaritons accumulated within the excitation region. An energy-resolved spatial image indicates polariton fluids with a single mode propagating along the microwire (Fig. 4C). To manipulate the energy landscape for stopping the polariton fluids, the block beam is spatially shifted away from the source beam with a distance of ca. 20 μm (Fig. 4D).

Fig. 4. All-optical switching based on interacting exciton polaritons.

(A) Optical setup for realizing all-optical switching. DL, delay line; OL1 and OL2, objectives; BS1, BS2, and BS3, beam splitters; L1, L2, L3, and L4, lenses; M1, M2, and M3, mirrors. (B) Far-field image (top) illustrates a source beam at k_x = 4.4 μm⁻¹ and a block beam localized at k_x = 0, while the k_y is at zero for both two beams. The dispersion of polariton bands at k_y = 0 (bottom) highlights the resonant energy of two beams. (C) Real-space energy-resolved PL intensity of the microwires without the block beam. (D) Real-space image illustrates the position of the block beam. (E to G) PL spectra as a function of distance along the microwire at the delay time (∆t) of (E) −1.74 ps, (F) 0 ps, and (G) 1.92 ps, between the source and block beams. The positive time delay represents that the source beam arrives on the microwire before the block beam. The polariton propagation is switched off at ∆t = 0 ps and turned on within 2.0 ps. The zero distance is defined as the position of block beam, which divides propagating polariton fluids into the upstream region with positive distance and the downstream region with negative distance. (C to G) All images are plotted in a linear scale. (H) Integrated PL intensity as a function of distance, indicating a sharp decrease of polariton density as the polariton fluids pass through the block beam at ∆t = 0 ps. (I) PL intensity as a function of delay time integrated from upstream and downstream regions of the block beam. Polariton fluids can be switched on/off within 2.0 ps, which is determined by polariton lifetime in microcavity.

Under this experimental configuration, all-optical switching is evaluated by tuning the delay time between two beams. At delay time (∆t) far from zero, polariton fluids propagating along the microwire can be observed (Fig. 4, E and G). With the synchronization of two beams, the propagating polariton fluids experience a drastic decrease in intensity after encountering the block beam spot (Fig. 4F). The traces integrated along the microwire length direction illustrate the polariton populations as a function of distance at delay time of −1.74, 0, and 1.92 ps (Fig. 4H). A noticeable decrease in polariton populations occurs after passing through the block beam spot at ∆t = 0, while the upstream region of block beam spot shows negligible variation in polariton intensity during the change of delay. These results demonstrate the successful block of polariton propagation with the introduction of interacting polaritons. The constant intensity in the upstream region is also related to the experimental configuration, in which the low k block beam, together with the accumulated and backscattered polaritons from the source beam, is filtered out. It is instructive to perform further characterizations to correlate the propagation switching with the polariton-polariton interactions. Another microwire with a more positively detuned polariton mode is used to perform the switching experiments (fig. S12). The polariton propagation is switched off with the gradual synchronization of source and block beams. At some intermediate delay time (∆t = −0.46 and 0.7 ps), polariton propagation is stopped with a blue-shifted tail, thus indicating that the accumulated polaritons in the block beam spot elevate the polariton energy to create an energy barrier. Time overlaps between two beams affect the polariton density in the block beam region when the propagating polaritons reach it, thus introducing a barrier by shifting the polariton dispersion. The barrier height can also be manipulated by the power of the block beam at the time delay of zero (fig. S13). For block beams with a low fluence, blueshift is difficult to discern. Under a moderate fluence, the blueshift of polariton mode occurs when the propagating polaritons encounter the block beam, while the polariton propagation is preserved because of a blueshift within the polariton linewidth. On the contrary, the polariton propagation can be fully switched off by a larger energy barrier. This polariton switching is also supported by the theoretical model with the introduction of polariton-polariton interaction (see Materials and Methods). The theoretical results indicate that the polariton intensity experiences notable attenuation after passing through the block beam region and polariton propagation can be switched on/off within 2 ps (fig. S14), which are in good agreement with the experimental observations. These results explicitly demonstrate that polariton switching stems from the energy barrier introduced by interacting polaritons.

To estimate the response speed and on-off ratio of this switch, we tune the delay time ranging from −2 to 2 ps. The response time of polariton switching is determined as 1.3 ps for decay and 1.6 ps for rise by integrating the polariton population in the downstream region of the block beam, while the polariton populations in the upstream region show no pronounced dependence on the delay time (Fig. 4I). The response speed is correlated to polariton lifetime in microcavity. Although higher response speeds have been realized in organic microcavities (33) and plasmonic waveguides (11), the relatively low-quality factor of these systems causes serious losses during the propagation of optical signals. The on/off intensity ratio of our switch can reach 10, corresponding to an extinction ratio of 10 dB. These results demonstrate that an ultrafast all-optical switching with terahertz operation speed can be achieved at room temperature by shaping the energy landscape of propagating polaritons with strong nonlinearity in self-assembled semiconductor microcavities.

DISCUSSION

In conclusion, an ultrafast all-optical switching is demonstrated by exploiting interacting exciton polaritons in self-assembled perovskite microwire microcavities at room temperature. Combining strong polariton-polariton interactions in perovskites with low-loss polariton fluids in a microwire cavity, switching on/off of polariton propagation is demonstrated in a picosecond time scale. Given the revealed strong nonlinear interactions in inorganic perovskites that directly leads to the device implementation of ultrafast polaritonic switching, together with the scalable self-assembly method, our work presents a versatile and efficient platform for deterministic integration of polaritonic devices with emerging applications, such as all-optical logic gates, on-chip coherent sources, and photonic information processing. Combination of polaritonic devices with integrated photonic platform is important for practical applications because of the restricted propagation length of polariton fluids and the complicated injection and detection configuration. We envision that the perovskite polariton waveguides developed by the self-assembly technique are possible to integrate with photonic chip by using diffraction gratings for in- and out-coupling of light (47), thus leading to the synergy of strong nonlinearity in polaritonic devices and long-range propagation in photonic systems.

MATERIALS AND METHODS

Self-assembly of CsPbBr₃ microwire arrays and microcavity fabrication

Silicon templates with micropillars were used to control the assembly of CsPbBr₃. The templates were fabricated by photolithography and development followed by reactive ion etching using photoresist as etching masks. The CsPbBr₃ solution (0.02 M) was prepared by directly dissolving stoichiometric CsBr and PbBr₂ in dimethyl sulfoxide. Two mole percent of cesium octanoate was added into the CsPbBr₃ solution to control the nucleation and growth of microwires. The assembly system was constructed by combining a bottom DBR substrate (20.5 pairs of SiO₂/Ta₂O₅ on silica), a micropillar template, and 5.0 μl of perovskite solution. The assembly process was carried out in a vacuum oven at 60°C for 7 hours to evaporate the solvents, yielding CsPbBr₃ microwire arrays on the bottom DBR substrate (see text S1 for details). Then, 10.5 pairs of SiO₂/Ta₂O₅ were deposited onto perovskites by electron beam evaporation to generate perovskite wires in a microcavity.

Angle-resolved PL measurements and fitting

Exciton-polariton dispersion was measured by angle-resolved PL spectroscopy with a Fourier imaging configuration. Microwires in the cavity were nonresonantly excited by a continuous-wave 455-nm laser. PL signal was captured by a 100× microscope objective with a numerical aperture (NA) of 0.85 and was detected by a spectrometer (HORIBA, iHR550) with a 600 g mm⁻¹ grating and a liquid nitrogen–cooled charge-coupled device. Exciton-polariton condensation was pumped at 400 nm by using a Ti:sapphire femtosecond laser (Spectra-Physics) to generate pluses with a 1-kHz repetition rate and with a duration of 100 fs.

The exciton-polariton dispersion was fitted with a 1D microcavity model. In this context, the wave vectors k_z and k_y in microwire height and width directions are quantized, while the photonic modes along the length direction (k_x) are continuous. The quantized wave vectors can be expressed as k_z = π/L_z and k_y = (j + 1) π/L_y, where L_z and L_y are effective cavity lengths along the height and width directions, respectively; j = 0, 1, 2…, is a positive integer. The multiple cavity modes along the x direction can be expressed as (48)

$$E_{\mathrm{c}}( j,k_x)=\frac{\mathrm{\hslash }}{c}\sqrt{k_x^2+k_y^2+k_z^2}$$ (1)

$$=E_0\sqrt{1+{\left[\frac{(j+1)\mathrm{\pi }}{L_y}\right]}^2\frac{1}{k_z^2}+\frac{k_x^2}{k_z^2}}$$

where E₀ = ℏck_z/n_c, n_c is the effective refractive index. These confined cavity modes can be strongly coupled with exciton modes independently, which can be described by a coupled oscillator model (16)

$$E_{\text{UP},\text{LP}}(j,k_x)=\frac{1}{2}\{E_{\mathrm{X}}+E_{\mathrm{c}}( j,k_x)\pm \sqrt{4g_0^2+{[(E_{\mathrm{X}}-E_{\mathrm{c}}( j,k_x))]}^2}\}$$ (2)

where E_X = 2.407 eV is the energy of exciton mode of CsPbBr₃ and 2g₀ is the Rabi splitting.

Determination of polariton-polariton interaction strength

Polaritons were injected by using a normal incident pulsed beam with a 1-kHz repetition rate and 100-fs duration. The laser beam was focused onto a microwire by a 50× objective (NA = 0.42). The polariton populations were determined by estimating the absorbed photons in microcavity. Polariton bands with different detunings were achieved by selecting microwires with various cavity lengths. To evaluate the exciton-exciton interaction strength, the exciton fraction is given by the Hopfield coefficient |X|²

$${\mid X\mid }^2=\frac{1}{2}(1+\frac{∆E}{\sqrt{∆E^2+4g_0^2}})$$ (3)

where the cavity detuning ∆E = E_c − E_X. The exciton-exciton interaction constant can be calculated by fitting the polariton-polariton interaction constants g_xp as a quadratic function of exciton fractions

$$g_{\text{xx}}=\frac{g_{\text{xp}}}{{\mid X\mid }^4}$$ (4)

All-optical switching measurements

Perovskite microcavities with transmission configuration were prepared by electron beam evaporation of 8.5 pairs of SiO₂/Ta₂O₅ onto a sapphire substrate followed by self-assembly of perovskite microwires and deposition of top DBRs (8.5 pairs of SiO₂/Ta2O₅). A pump beam with a 1-kHz repetition rate, 100-fs duration time, and a tunable wavelength was generated by using an optical parametric amplifier (TOPAS, Spectra-Physics) and split by a 50:50 beam splitter. One of the beams (source beam) was time-delayed by a delay line and obliquely hit onto the sample through a 50× objective (NA = 0.42) on the top side of microcavity to produce propagating polariton fluids. The other beam (block beam) at normal incidence was focused onto the microcavity from the bottom side by using a 50× objective (NA = 0.65) and spatially shifted away from the source beam. The zero delay time is determined by the highest visibility of the interference pattern formed by two beams. The positive delay represents that the source beam first arrived on the microwire. The polariton PL emissions were collected by the objective on the bottom side. To detect the propagation of polaritons excited by the source beam, the block beam at k_// of zero was filtered out in momentum space by an optical iris followed by sending the filtered signal to a spectrometer (HORIBA, iHR550).

Theoretical calculations

To model the polariton switching, the wave function for polaritons, ψ(x, t), and density of an exciton reservoir, n(x, t), are described by the following equation (for simplicity, a 1D model is considered)

$$\begin{array}{c}i\mathrm{\hslash }\frac{\mathrm{\partial }\mathrm{\psi }(x,t)}{\mathrm{\partial }t}=(-\frac{{\mathrm{\hslash }}^2{\nabla }^2}{2m}+\mathrm{\alpha }{\mid \mathrm{\psi }(x,t)\mid }^2-\frac{i\mathrm{\Gamma }}{2}-i\mathrm{\beta }{\mid \mathrm{\psi }(x,t)\mid }^2)\\ \mathrm{\psi }(x,t)+F(x,t)+P(x,t)\end{array}$$ (5)

where m is the polariton effective mass, α is the polariton-polariton interaction, Γ is the polariton dissipation rate, and β represents nonlinear loss processes. The nonlinear loss processes are typically accounted for when exciting polariton condensates under nonresonant excitation (49); however, it is, in principle, still present under resonant excitation. In particular, experiments in GaAs materials have shown that it is possible for exciton-polaritons to undergo scattering to dark exciton (50) or reservoir states (51).

To model the experiments, two coherent excitation laser pulses, corresponding to the source beam, F (x, t) and the block beam, P (x, t) are introduced

$$F=F_0{e}^{i{k}_{\mathrm{p}}x}{e}^{-i\mathrm{\omega }t}{e}^{-\frac{{(x-x_0)}^2}{\mathrm{d}{x}^2}}{e}^{-\frac{{(t-t_0)}^2}{\mathrm{d}{t}^2}}$$ (6)

$$P=P_0{e}^{-i\mathrm{\omega }t}{e}^{-\frac{{(x-x_1)}^2}{\mathrm{d}{x}^2}}{e}^{-\frac{{(t-t_1)}^2}{\mathrm{d}{t}^2}}$$ (7)

where F₀ and P₀ are the pulse amplitudes; k_p is the in-plane wave vector of the source beam; x₀ and x₁ denote the spatial position of the source and block beams, respectively; and t₀ and t₁ represent the pulse arrival times. The angular frequency ω, pulse width dx, and pulse duration dt are taken the same for both pulses.

The k_p of 4.4 μm⁻¹ as well as parameters defining positions and widths of beams were directly taken from experiments. The Γ of 0.2535 meV was consistent with the experimentally measured polariton lifetime of 1.3 ps. The polariton-polariton interaction strength α in 1D model was taken as 0.01875 μeV μm, which is a conservative estimate given the range of reported values (26). The parameter β of 0.002 ps⁻¹ μm was taken as a fitting parameter. A Gaussian filter was applied in k space as

$$G=(1-e^{\frac{-{(k_x-k_0)}^2}{\mathrm{d}{k}^2}})(1-e^{\frac{-{(k_x+k_{\mathrm{p}})}^2}{\mathrm{d}{k}^2}})$$ (8)

The first bracket on the right-hand side of the equation was applied to filter out the source beam at k₀ = 0, while the second bracket was used to filter out the reflected polariton at −k_p = −4.4 μm⁻¹.

Supplementary Materials

This PDF file includes:

Texts S1 and S2

Figs. S1 to S14

References