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Abstract
An optical resonator is utilized to enhance interactions between photons and solid-state emitters. In particular, when the coupling strength between the exciton within the material is faster than the dissipation rate, the eigenstates of the system are mixed light-matter quasiparticles referred to as exciton-polaritons. In this work, we demonstrate an open, planar cavity platform for investigating a strong coupling regime. The open cavity approach supports ease of integration of diverse material systems and in situ tunability of the photonic resonance. We characterize the strong coupling regime in systems ranging from thin 2D semiconductors, perovskites, and II-VI semiconductor quantum wells.
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1. Introduction
Planar optical resonators can be used to obtain a strong localization of the electric field [1,2]. A typical microcavity design that resembles a Fabry-Pérot resonator consists of two distributed Bragg reflectors. The microcavity can be a monolithic structure or can be assembled from two or more independent parts [3–5]. In another, open cavity approach, it can be assembled from two independent mirrors with controllable distance between them [6]. The open cavities can use different types of mirrors: dielectric [7], semiconductor [8], or metallic [9]. The advantage of the open-cavity scheme is the possibility of tuning the resonant frequency of the photonic modes of the cavity by control over the distance between the mirrors. The open cavity also allows for the ease of integration of various materials within the cavity. Of special interest are material systems in which photons through a dipole transition can excite excitons. Especially, the cavity can operate in a strong coupling regime, in which the interaction strength between the photonic field and excitons is faster than the dissipation rate, and the eigenstates of the cavity can be described by means of mixed light-matter quasiparticles known as exciton-polaritons. Polaritons inherit properties of both their constituents such as low effective mass from the photonic part and possibility of interactions that arise from the excitonic component. Due to the latter, polaritons exhibit strong non-linear behavior that leads to polariton condensation [10] with emerging applications in classical and quantum computing [11]. In recent years, in addition to the classical solid-state semiconductors [12], there has been an emerging interest in various organic-based materials [13–19].
Various different material systems have been investigated towards polaritonic applications in open cavities. A strong coupling regime has been reported in thin layers of transition metal dichalcogenides, both at cryogenic [20] and at room temperature [9], organic materials [21–25], or GaAs-based semiconductor quantum wells (QWs) [8] or quantum dots [26].
Polariton condensation has been observed in open cavities with the semiconductor QWs [27,28]. Open cavities are also suitable for operation in a quantum regime [29], with recent demonstration of antibunching at a single polariton level [30,31].
In this work, we demonstrate the realization of a strong coupling regime in open cavities based on three different material systems, all schematically depicted in Fig. 1. In all the approaches, the cavity is constructed from two independent DBRs, with the distance between them controlled by a piezoelectric element. The general construction of the microcavities is described in Section 2. Section 3 concentrates on the cavity made of 2 dielectric DBRs incorporating monolayer of WS$_{2}$ [Fig. 1(a)]. In section 4 the active material is exchanged for a spin-coated organic-inorganic PEPI perovskite with the same cavity design [Fig. 1(b)]. In section 5 the investigated cavity consists of a dielectric DBR and a (Cd,Zn,Mg)Te DBR with CdTe:Mn quantum wells [Fig. 1(c)]. Here, we present operation of the cavity at cryogenic temperature, demonstrate strong coupling with both heavy- and light-hole exciton in CdTe:Mn quantum wells, and show polariton lasing.
Fig. 1. Different realizations of microcavities tunable by a piezoelectric chip. (a) Cavity incorporating WS2 monolayer. (b) Cavity incorporating 2D perovskite. (c) Cavity formed by dielectric DBR and semiconductor half-cavity with semimagnetic (Cd,Mn)Te quantum wells. (d) Schematic image of the holder with the assembled microcavity. (e) Photo of the holder with assembled microcavity.
2. Assembly of the microcavity
A schematic image of the holder used for assembling of the microcavities is presented in Fig. 1(d) with a photo of the final realization in Fig. 1(e). The holder was made of brass and fits into a cold-finger cryostat to allow measurements at cryogenic temperatures, if required. From the top side a round aperture with diameter of 4 mm allows for the optical access with a microscope objective. The top mirror of the cavity, with dimensions slightly exceeding the aperture, is glued directly to the holder. To allow for optical measurements, the top mirror has to be grown on a transparent substrate, such as glass or fused silica.
As the top mirror is stationary, the tunability of the microcavity is provided with the second, bottom mirror. Macroscopic adjustment is realized by rotating a screw that pushes a piston. This scheme was predominantly used during the assembly of the microcavity and setting the initial cavity width. The precise control over the width of the cavity is provided by a piezoelectric chip mounted on top of the piston. Applying an external electric bias to the electrodes of the piezoelectric element, expands it in the $z$ direction, which provides tunability of the separation distance between the two mirrors that form the cavity.
All the results described in this work were performed using macroscopic-sized mirrors with dimensions of around 7$\times$7 mm incorporating different active materials, as described below.
It is important to note that in our realization no precise alignment of the mirrors forming the cavity is required. The parallelism of the mirrors is a direct result of the large contact area between both DBRs. Simultaneously, the rigidity of the holder allows to bring two surfaces close enough for observation of the strong coupling regime in various material systems.
3. Transition metal dichalcogenides monolayers
Transition metal dichalcogenides (TMDC) such as MoS$_{2}$, MoSe$_{2}$, WSe$_{2}$ or WS$_{2}$ are layered van der Waals crystals. In their monolayer form they exhibit a direct bandgap with their optical response dominated by robust excitonic transitions [32]. The high exciton binding energy and exciton oscillator strength in these materials resulted in significant interest in light-matter interactions in microcavity systems [33,34]. Strong coupling of TMDC excitons was observed in multiple different microcavity configurations: solid dielectric cavities [35–40]; tunable planar-concave cavities [20,41,42]; tunable planar cavities [9]; Tamm plasmon polaritons [43–45]; exfoliated DBR microcavities [3]; plasmonic nano-cavities [46] or photonic crystals [47,48]. Although most of the monolayer flakes are mechanically exfoliated, it is possible to grow large-area layers using various techniques [49,50] and incorporate them into optical cavities [51]. Recent progress in fabrication allowed the construction of optical parametric amplifier [52] and observation of bosonic condensation of TMDC-polaritons [53,54].
In this work, we investigate WS$_{2}$ monolayer flakes in dielectric cavities at room temperature.
WS$_{2}$ monolayers exhibit spectrally narrow excitonic emission and absorption at room temperature. Fig. 2(a) shows reflectance contrast spectrum of WS$_{2}$ monolayer flake deposited on top of dielectric DBR made of 8 pairs of SiO$_{2}$ and TiO$_{2}$. WS$_{2}$ monolayer is deposited on 120 nm thick flake hBN to isolate and provide an atomically flat substrate, which results in narrowing of the excitonic transition [55]. The spectra consist of a single peak at 2.01 eV corresponding to the absorption of a neutral exciton in a monolayer WS$_{2}$.
Fig. 2. Room temperature strong coupling in WS2 monolayer. (a) Reflectance contrast spectrum of the WS2 monolayer deposited on top of dielectric DBR. (b) Reflectance at normal incidence from the cavity incorporating the WS2 monolayer at varying voltage applied to the piezoelectric chip revealing lower (LP) and upper (UP) polariton branches. (c) Photoluminescence at normal angle from the cavity incorporating a WS2 monolayer at varying voltage applied to piezoelectric chip. (d) Angle-resolved photoluminescence spectra collected at 60 V applied to the piezoelectric stage. (e,f) Angle-resolved reflectance spectra detected in the TE (e) and TM (f) linear polarizations. (g) Simulated angle-resolved reflectance spectra for TE and TM polarizations. (h) Experimental and simulated TE-TM splitting for the upper (UP) and lower (LP) polariton branch.
The measured reflectance spectra can be simulated using the transfer matrix method in which the exciton transition in the WS$_{2}$ monolayer is introduced as a 0.65 nm thick [56] layer with dielectric function with excitonic contribution given by the Lorentz model [57]:
Fitting the simulated reflectance contrast, presented by the red line in Fig. 2(a), leads to good agreement with the experimental results for fitting parameters: $E_{\rm Ex}=2.011$ eV, $f_{\rm osc}= 2.66$ (eV)$^2$, $\gamma = 21.4$ meV.
A full cavity was formed with another dielectric DBR made of 6 SiO$_{2}$/TiO$_{2}$ pairs from the detection side. Fig. 2(b) presents reflectance spectra at normal incidence for the varying voltage applied to the piezoelectric chip that decreases the spacing between the mirrors. As cavity resonance crosses the exciton energy in WS$_{2}$ monolayer, a clear anticrossing behavior between lower (LP) and upper polariton (UP) branches can be observed. Anticrossing behavior can also be observed in photoluminescence. Fig. 2(c) presents emission spectra at normal angle when the flake within the cavity is nonresonantly excited with a laser beam at 405 nm (3.06 eV). The emission intensity is stronger for the lower polariton branch, but the upper polariton branch exhibiting anticrossing behavior is clearly visible when the cavity is tuned with the external voltage closer to the excitonic transition in WS$_{2}$ (corresponding to around 80 V), or at high emission angles in angle-resolved spectra Fig. 2(d) obtained by imaging the Fourier plane of the microscope objective collecting the emitted light.
The upper polariton branch is more clearly visible in angle-resolved reflectance spectra. Fig. 2(e–f) presents spectra collected under the same conditions but polarization-resolved in transverse electric (TE) and transverse magnetic TM polarizations. Following the coupled oscillator model, both spectra were fitted with exciton-polariton dispersion relations (white lines) with coupling strengths of 22.4 meV and resulting energies of the bare exciton ($E_{\rm X}$) and the cavity photon ($E_{\rm Ph}$) marked in dashed gray lines.
Angle-resolved reflectance spectra can be simulated using the transfer matrix method using the dielectric function of the WS$_{2}$ flake obtained by fitting the reflectance contrast spectra [Fig. 2(a)]. The calculations performed for the thickness of the air gap between the mirrors that form the cavity, presented in Fig. 2(g) show a perfect agreement with the experimental results in Fig. 2(e–f).
Comparing the results obtained for TE-TM polarizations of incident light shows significant splitting, especially for the upper polariton branch, with a higher cavity mode contribution. Fig. 2(h) presents TE-TM splitting of both polariton branches in experiment and transfer matrix simulations. The observed values are significantly higher than for typical monolithic semiconductor microcavities [58–60]. As discussed in Ref. [27] splitting is higher in open cavities with high refractive index difference interfaces of the air gap, and here are additionally pronounced by the asymmetric DBR design and additional thick hBN flake.
4. Perovskites
Another material system which can be integrated into an open cavity is perovskites. In particular, two-dimensional (2D) organic-inorganic perovskites exhibit desirable optoelectronic properties, such as high exciton binding energy at room temperature and can be easily tuned in energy by changing the organic or inorganic ions or thickness of the layer. It makes them an ideal system for the investigation of strong light-matter coupling phenomena in cavities, and they open a new path towards polaritonic devices working at room temperature.
There are multiple methods for the preparation and incorporation of perovskites into planar cavities [61]. Perovskite nanoplatelets can be CVD-grown on top of a DBR and the full cavity structure can be completed with the deposition of an additional PMMA spacer and growth of the top DBR [62]. Other methods include exfoliation and transfer of a chemically grown perovskite crystal [63] or crystallization from a solution directly within a cavity [64]. In this work, we used the spin-coating method [65,66] to obtain thin polycrystalline perovskite layers.
In our research, we used a 2D-layered perovskite-type semiconductor, (C$_6$H$_5$C$_2$H$_4$NH$_3$)$_2$PbI$_4$ (hereinafter referred to as: PEPI). The perovskite precursor solution was prepared in a glovebox under an argon atmosphere by mixing PEAI with lead iodide (PbI$_{2}$) in a stoichiometric 2:1 molar ratio and dissolving the mixture in N,N-dimethylformamide (DMF) (mass percent: 10${\% }$). The solution was stirred for 2 hours at 50 $^\circ$C. The solution of PEAI and PbI$_{2}$ was spin-coated in air on a dielectric mirror made up of six SiO$_{2}$/TiO$_{2}$ (with SiO$_{2}$ top layer) pairs, with maximum reflectance occurring at 520 nm. After solvent evaporation on the hot plate for 1 minute at 100 $^\circ$C, a 60-nm-thick 2D-layered, homogeneous polycrystalline PEPI perovskite was obtained. The surface of the dielectric mirror was cleaned and activated in plasma before crystallization from precursor solution using spin-coating technique. The photoluminescence and absorption spectra of a bare material can be found in Ref. [66].
The full cavity structure was obtained by approaching with the second DBR. As previously, the distance between the two dielectric mirrors (one with polycrystalline 2D perovskite and the other without) was controlled through a piezo element. It allows, at the same time, for the realization of high finesse open microcavities with tunable photonic mode and to avoid deterioration of perovskite crystals caused by the growth of the upper mirror.
Angle-resolved photoluminescence and reflectivity experiments at room temperature (shown in Fig. 3) revealed strong coupling between the excitons in the perovskite and the cavity mode. The energy of the observed lower polariton branch in both the photoluminescence [Fig. 3(a–d)] and reflectivity [Fig. 3(f–i)] spectra changed depending on the applied voltage. The revealed high-angle bending of the mode indicating a strong coupling between the exciton from the perovskite and the photon confined in the cavity. The upper polariton mode was not observed due to the high absorption of the perovskite just above the exciton energy. The exciton-photon coupling strength was approximately 100 meV. Figure 3(e) shows energy-resolved photoluminescence spectra measured at 0 angle ($k=0$) with increasing piezo voltage (0–150 V), while Fig. 3(j) shows similar tuning of the lower polariton depending on the piezo voltage in the cross-sections of the reflection spectra.
Fig. 3. Room temperature strong coupling in polycrystalline PEPI perovskite. (a–d) Angle-resolved photoluminescence (PL) spectra for increasing voltage applied to the piezoelectric electrodes and the corresponding (f–i) reflectivity (R) spectra. Cross-sections at $k=0$ in energy-resolved (e) PL and (j) R versus applied voltage.
5. II-VI quantum wells
Another realization of exciton-polaritons in tunable microcavity was based on II-VI semiconductors is schematically shown in Fig. 1(c). The structure consists of dielectric SiO$_{2}$/TiO$_{2}$ DBR and semiconductor half cavity. MBE-grown semiconductor half-cavity consists of a DBR made of (Cd,Zn,Mg)Te with different cation ratios to create layers of different refractive index. The DBR is finished with (Cd,Zn,Mg)Te layer incorporating CdTe:Mn quantum wells (QWs).
In contrast to WS$_{2}$ and PEPI perovskite, low exciton binding energy in CdTe QWs requires operation at cryogenic temperatures. For observation of strong coupling phenomena, cavity structure was formed inside a cold finger cryostat and cooled to 4.5 K. To tune the cavity length semiconducting half cavity was mounted directly on piezoelectric chip. The sample was observed from the side of dielectric DBR with 4 SiO$_{2}$/TiO$_{2}$ layer pairs grown on a transparent glass substrate.
Fig. 4 presents angle-resolved reflectance spectra obtained for increasing voltage applied to the piezoelectric chip. Decreasing cavity length results in increasing cavity mode energy ($E_{\rm Ph}$, gray dashed line), which crosses both heavy hole ($E_{\rm hh}$, dashed green line) and light hole ($E_{\rm lh}$, dashed purple line) resonances in (Cd,Mn)Te QWs. The coupling between these resonances is visible on the spectra as the formation of three polariton branches, which can be described by the 3$\times$3 coupled oscillator model [67,68]:
Fig. 4. Strong coupling in dielectric-semiconductor open cavity. (a–d) Angle-resolved reflectance spectra for increasing voltage applied to the piezoelectric stage. Measured at 4.5 K.
Results of fitting of eigenvalues of Eq. (2) to reflectance spectra are shown as white solid lines in Fig. 4. From the fitting we obtained the energies of bare excitonic resonances as $E_{\rm hh} = 1.610$ eV and $E_{\rm hh} = 1.626$ eV with corresponding coupling strengths of $\Omega _{\rm hh} = 9.8$ meV and $\Omega _{\rm lh} = 7.9$ meV.
To observe polariton condensation we used a similar setup using dielectric DBR with 6 SiO$_{2}$/TiO$_{2}$ layer pairs and semiconductor half cavity with 23 DBR pairs and 6 CdTe:Mn QWs.
Fig. 5(a–d) presents angle resolved photoluminescence spectra in the spectral range of lower polariton for increasing excitation powers. The cavity was pumped non-resonantly with a ps pulsed Ti:Sapphire laser at a photon energy of 1.7463 eV. At low excitation power [Fig. 5(a)] emission comes from lower polariton branch. With increasing excitation power [Fig. 5(b)] we observe an increase of the polariton energy that results from the increasing repulsive polariton-polariton interactions at high densities. For even higher excitation powers [Fig. 5(c–d)] just above polariton condensation threshold emission linewidth abruptly decreases while emission energy still increases. The full dependence on the excitation power is summarized in Fig. 5(e) presenting emission intensity, linewidth and energy for the cross section at normal emission angle. With increasing excitation laser intensity typical polariton condensation behavior can be observed: nonlinear emission intensity increases with simultaneous spectral narrowing and emission energy increases [69].
Fig. 5. Polariton lasing in open cavity. (a–d) Angle-resolved photoluminescence spectra for increasing nonresonant pulse energy: (a) 0.07 pJ ($0.6$ $\mathrm{\mu}$J cm$^{-2}$), (b) 1.6 pJ ($12.7$ $\mathrm{\mu}$J cm$^{-2}$), (c) 3.1 pJ ($25$ $\mathrm{\mu}$J cm$^{-2}$) and (d) 4.2 pJ ($33$ $\mathrm{\mu}$J cm$^{-2}$). Measured with approx. 3 ps laser pulses. (e) Emission intensity, spectral linewidth, and energy shift for increasing excitation power. Temperature 4.5 K.
6. Summary
To summarize, in this work, we presented a general scheme for construction of open, tunable microcavities allowing for observation of the strong coupling regime. We present the operation of our platform using different material systems: WS$_{2}$ monolayers, spin-coated PEPI perovskites and CdTe QWs. In all configurations, we observed a strong coupling regime between the photonic cavity mode and excitons in a given material. We demonstrate the operation of the cavity under both ambient and cryogenic conditions. Due to the high exciton binding energies in WS$_{2}$ and PEPI perovskite, the realization of a strong coupling regime was possible at room temperature. In the cavity based on II-VI semiconductor QWs, while the cavity was operated at cryogenic temperature, we observed polariton lasing when the structure was excited with a pulsed laser.
Funding
H2020 Future and Emerging Technologies (No. 964770, TopoLight); Narodowe Centrum Nauki (2018/31/N/ST3/03046, 2019/35/B/ST3/04147, 2020/37/B/ST3/01657).
Disclosures
The authors declare no conflicts of interest.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
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