Introduction

A cavity polariton is a quasiparticle formed by the strong coupling between a photon and an exciton in an optically active microcavity1,2. As this bosonic quasiparticle possesses a small effective mass inherited from the photonic nature and a nonlinearity derived from the excitonic nature, the ensemble of cavity polariton particles reaches a threshold density for the Bose-Einstein condensation at a relatively high temperature. This phenomenon is known as polariton condensation (or polariton lasing)3,4. Furthermore, the room-temperature (RT) polariton condensation has also been revealed in several material systems, including widegap inorganic semiconductors5,6, organic semiconductors7,8,9,10, transition-metal dichalcogenides11,12, and lead–halide perovskites13,14,15. To utilize the RT polaritons for future quantum technologies, a methodology for forming a qubit state that can be readily created and manipulated should be established16,17. The polarization degree of freedom is a promising candidate as a means of forming the polaritonic qubit states, analogous with the photonic quantum computing systems18. In fact, anisotropic optical features of polariton modes have been widely discussed in organic semiconductors19,20,21,22 and perovskites23,24. The Spin Meissner effect, which arises in the presence of an external magnetic field, has also been explored as a mechanism for manipulating the circular polarization state of the polariton condensed phase25,26,27. However, a coupling of linearly polarized polariton condensed states has not been realized yet in RT polariton systems. It is a challenging issue to develop a strategy in which an energy resonance and non-zero interaction between the two orthogonally polarized states are simultaneously obtained.

In this study, we demonstrate a polarization superposition of RT polariton condensed states. In an all-inorganic perovskite microcavity, we achieve an energy resonance at the Γ point of the two orthogonally polarized modes by exploiting the blue shift of a polariton condensed state. The orthorhombic crystal structure of the perovskite active layer and/or a slight off-axis orientation of the perovskite crystal axis from the microcavity normal enable interaction between the two polarized modes. Systematic photoluminescence (PL) results show that by a non-resonant optical pulse pumping, a polarization-hybridized condensed mode can be initialized to one of the polarization directions. As a result of the polarization hybridization of polariton condensed states, furthermore, we observed a polarization-switching phenomenon in the polariton lasing operation. A detailed analysis of emission using the Stokes parameters demonstrates that the polariton condensation state can be described as a superposition of polarization. These observations demonstrate a great promise of polariton condensed states as an RT qubit technology.

Results and discussion

Room temperature polariton in CsPbBr3 microcavity

In order to create polarization-coupled polariton condensed states, we employ an all-inorganic lead-halide perovskite, CsPbBr3, as the anisotropic active medium in a microcavity. This compound has been demonstrated to show a high PL quantum yield and a large exciton binding energy, leading to an RT stability of exciton. Previous studies have experimentally demonstrated the RT polariton condensation in CsPbBr3 microcavities13,14,15. A possibility of condensation in the polaritonic Bardeen-Cooper-Schrieffer phase has been proposed for CsPbBr3 microcavity at high excitation densities23,28.

Meanwhile, anisotropic polaritonic features also gather attention [see Fig. 1a]. Polarization anisotropy of CsPbBr3 crystal, which shows the orthorhombic structure, breaks a rotation symmetry of the microcavity system, inducing a ‘X–Y’ polarization splitting in lower polariton branches (LPBs) at the Γ point [see Fig. 1b]23,24. The LPB splits also into transverse-electric (TE) and transverse-magnetic (TM) modes at large wavevector regions because of quasi-optical spin-orbit-coupling [see Fig. 1b]23,29,30. These dispersion characteristics lead to polarization-dependent polariton lasing phenomena: Spencer et al. have reported that the split LPB modes show an independent polariton lasing at the energy position of each polarization mode23. Li et al. have reported in a study of liquid crystal-filled CsPbBr3 microcavity that circularly polarized polariton lasing occurs from LPB modes split in in-plane wavenumber direction by optical Rashba–Dresselhaus coupling30. However, a coupling between linearly polarized condensed states has not been reported. For this purpose, we need to meet two requirements: (i) a fine-tuning of X-Y energy resonance and (ii) a non-zero interaction between the X- and Y-polarized states. The X–Y energy resonance must be arranged for the LPB modes having the same number of antinodes, and the spatial distribution of wavefunctions along the vertical direction should be the same for the two polarizations. In CsPbBr3 microcavity, however, a fine-tuning of the X- and Y-polarized modes with the same antinode number is impossible because they are originally detuned due to the X–Y splitting. To overcome this problem, we exploit the blue shift of the polariton condensed state that emerges at the above-threshold density.

Fig. 1: CsPbBr3 microcavity with X–Y splitting.
figure 1

a A schematic of a CsPbBr3 crystal and electromagnetic waves with orthogonal polarizations. b A schematic of dispersion curves with X–Y splitting and TE-TM splitting in LPB and UPB modes. c A schematic showing the configuration of angular-dependent PL measurement. d Colormaps of X-polarized [panels (i–iv)] and Y-polarized [panels (v–viii)] angle-resolved PL. Pumping fluences \(P\) are (i, v) 245, (ii, vi) 449, (iii, vii) 1260, and (iv, viii) 8170 µJ/cm2. e \(P\)-dependence of PL signal intensity at the Γ point. Red and blue circles plot the data at X- and Y-polarizations, respectively.

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Coupling of polariton condensed modes

We show angle-resolved PL results for a CsPbBr3 microcavity fabricated with a solution-based crystallization method28,31,32,33,34. Figures S1–S3 in the Supplementary Information depict the fabrication procedure, microscopic images of fabricated crystals, and optical properties of the microcavity, respectively. The quality factor is evaluated from transmission measurement to be ~180. A schematic diagram of the Fourier-space imaging setup is shown in Fig. S4 in the Supplementary Information. One can find details of the experimental methods in the Method section. In the angle-resolved PL measurements, X- and Y-polarizations correspond to TE and TM polarizations, respectively [see Fig. 1c]. Figure 1d shows colormaps of linearly polarized angle-resolved PL results obtained under the various pumping fluence \(P\). The full dataset is shown in Fig. S5 in the Supplementary Information. At \(P\) as low as ~245 µJ/cm2, we find that the LPB modes at both polarizations are in the strong coupling regime and show a parabolic dependence on the in-plane wavevector \({k}_{y}\) around zero [see panels (i) and (v) of Fig. 1d]. Rabi splitting energies are evaluated from the fitting analyses using a coupled oscillator model to be 62 meV and 45 meV for the X-polarized and Y-polarized LPB modes, respectively (see Supplementary Text S1 and Fig. S6 in the Supplementary Information). The X–Y splitting energy at \({k}_{y}\) ~ 0 is ~6.1 meV at the lowest \(P\) in this measurement. The mode number for both the X- and Y-polarized modes is three, which is expected from the group index (~2.4) and the crystal thickness (~440 nm). In this measurement, the quality factor Q was found to be not very large (Q ~ 200), which may be due to unexpected losses in the cavity and can be improved in future studies.

In the X-polarization, the parabolic LPB mode disappears at \(P\) ~ 449 µJ/cm2, and instead, a highly directional PL signal appears at ~2.316 eV [see panel (ii) of Fig. 1d]. Furthermore, the emission intensity that reflects the polariton density shows a threshold behavior [see Fig. 1e], indicating the RT condensation of polariton particles. With increasing \(P\), the energy of the condensed state shows a blue shift [see panel (iii) of Fig. 1d] caused by polariton–polariton interaction. It should be noted that the energy of the blue-shifted condensed state is ~2.330 eV, which already exceeds the energy of Y-polarized LPB mode at \({k}_{y}\) ~ 0 [~2.322 eV, see panel (v) of Fig. 1d].

A further increase in \(P\) (>~6150 µJ/cm2) leads to the second threshold behavior for the Y-polarized LPB mode [see panel (viii) of Fig. 1d]. Interestingly, we find a drastic switching in the PL signal intensities between the two polarized states at the second threshold, where the Y-condensed state appears and the X-condensed state almost disappears [see panel (iv) of Fig. 1d], i.e. polarization switching. To the best of our knowledge, this phenomenon is observed for the first time in this study and is clearly different from a previous observation showing independent polariton lasing from orthogonally polarized LPB modes23.

To track detailed footprints of the X- and Y-polarized states, we exhibit \(P\)-dependent PL spectra at \({k}_{x}={k}_{y}\) ~ 0 [see Fig. 2a]. We divide the experimental results into three pumping fluence ranges; namely, the first range is below the first threshold (\(P\) < ~340 µJ/cm2), the second range is between the first threshold and the second threshold, and the third one is above the second threshold (\(P\) > ~5330 µJ/cm2). In the range below the first threshold, the X–Y split two LPB modes are independently observed. This is seen as two polarization degree (PD) signals with opposite signs, as shown in panels (i)–(iii) of Fig. 2b. Here, the PD is defined as

$${PD}=\frac{{I}_{X}-{I}_{Y}}{{I}_{X}+{I}_{Y}},$$
(1)

where \({I}_{X}\) and \({I}_{Y}\) are PL intensities at the X- and Y-polarizations, respectively, and is identical to the Stokes parameter \({S}_{1}\) described later. The X-polarized signal shows an onset of condensation at \(P\) just before the threshold.

Fig. 2: Polarization coupling of polariton condensed state in CsPbBr3 microcavity.
figure 2

a \(P\)-dependent PL spectra at the Γ point. Red and blue curves show X- and Y-polarization, respectively. Orange and blue shaded region show the second and third ranges of \(P\), which describe in the main text. No shaded region indicates the first range of \(P\). b Colormaps of polarization degrees for polariton signals recorded at various \(P\). c Peak energies of PL signals as functions of \(P\). Colors of each plot shows the polarization degree of the signals. Dashed lines exhibit functions derived from a fitting analysis using Eqs. (2) and (3). d \({|{\alpha }_{X}|}^{2}\) and \({|{\alpha }_{Y}|}^{2}\) for polarization coupled LPB mode calculated from the fitting results. This result exhibits one of the results for the lower mode. For the higher mode, curves for \({|{\alpha }_{X}|}^{2}\) and \({\left|{\alpha }_{Y}\right|}^{2}\) are simply exchanged.

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In the second range, a PL signal showing the polariton condensation is observed at ~2.320 eV in the X polarization [see panel (iv) of Fig. 2b]. In addition to the conventional blue shift with the increased \(P\), we find that the condensed mode is not perfectly polarized to the X direction but exhibits a small Y-polarized component. This fact is clearly found in normalized PL colormaps shown in Fig. S7 in the Supplementary information. More importantly, the blue-shifted condensed state exhibits an “energy hopping” from ~2.32 to ~2.33 eV at \(P\) ~ 1260 µJ/cm2 [see panels (v) and (vi) in Fig. 2b]. These results suggest the emergence of X–Y polarization coupling in the polariton condensed states. The coupling is made possible by the energetic resonance between the blue-shifted X-polarized condensed state and the Y-polarized LPB mode. It is worth noting that the coupling can be established even though the Y-polarized mode may still be incoherent. Meanwhile, non-zero interaction between the two modes is achieved by the orthorhombic crystal structure of CsPbBr3, which will be discussed later in detail, leading to the polarization hybridization of polariton condensed state. Note that our results do not show independent condensations of the X- and Y-polarized LPB modes because the energy of the two orthogonally polarized PL are the same within this pumping fluence range.

In the third pumping fluence range (\(P\) > ~6150 µJ/cm2), the X-polarized condensed state shifts to ~2.34 eV and is completely separated from the energy of the Y-polarized state [see panels (xi and xii) of Fig. 2b]. Meanwhile, the polarization of the condensed state at ~2.33 eV switches to Y-polarization, leading to polarization switching.

We employ a simple model to formulate our results. The coupling between the X- and Y-polarized states is described well by a coupling model with a phenomenological Hamiltonian of

$$\left[\begin{array}{cc}{E}_{X} & V\\ V & {E}_{Y}\end{array}\right]\left[\begin{array}{c}{\alpha }_{X}\\ {\alpha }_{Y}\end{array}\right]={E}_{c}\left[\begin{array}{c}{\alpha }_{X}\\ {\alpha }_{Y}\end{array}\right].$$
(2)

Here, \({E}_{X}\) and \({E}_{Y}\) are energies of uncoupled X- and Y-polarized states, and \({E}_{c}\) is the eigenenergy of X–Y coupled state. We assume that the interaction term \(V\) is constant against the polariton density. \({|{\alpha }_{X}|}^{2}\) and \({|{\alpha }_{Y}|}^{2}\) show the fractions of X- and Y-polarized states, respectively. In Gross-Pitaevskii equation, the blue shift of \({E}_{X}\) or \({E}_{Y}\) (\(\Delta E\)) is described to be proportional to the density of polariton particles, \({N}_{{{{{\rm{pol}}}}}}\)1,35,36,37. On the other hand, previous reports have shown that the experimentally observed \(\Delta E\) follows a logarithmic function on \(P\)38,39. We employ the latter case and express \(\Delta E\) as a logarithmic function on \(P\).

$$\Delta E\left(P/{P}_{{th}}\right)=C\log \left(P/{P}_{{th}}-1\right)$$
(3)

Here, \(C\) is a constant and \(P/{P}_{{th}}\) is the pumping fluence normalized by that at the threshold.

Figure 2c compares the experimental result and the theoretical model shown above, revealing that the model can express the experimental result well. \(V\) is estimated to be ~2.6 meV. In Fig. 2d, we find that the two polarized states are hybridized well when \({|{\alpha }_{X}|}^{2}\) and \({|{\alpha }_{Y}|}^{2}\) are in a range of 0.2–0.8, which approximately corresponds to the second range on \(P\). Interestingly, the condensed mode in this range is successfully “initialized” to the X polarization by the non-resonant pulse pumping. When \({\left|{\alpha }_{X}\right|}^{2}\) and \({\left|{\alpha }_{Y}\right|}^{2}\) are outside this range, the hybridization becomes small, and thus the independent polariton condensation appear in the third range of \(P\).

It should be noted that the doublet of cross-polarized components is not clearly observed in the second range on \(P\). While we have not identified the cause of this phenomenon within the scope of this study, one potential contributing factor may be that our experiments rely on emission signals to determine the energy levels of modes, which is proportional to the population of excited particles (i.e., polariton particles). Consequently, states with short lifetimes are challenging to observe, similar to the general difficulty in observing emission from upper polariton branches. The relaxation dynamics, based on polariton lifetimes at each energy level, warrant detailed investigation and present an intriguing avenue for future research. Nevertheless, from the viewpoint of application as a quantum technology, this is an interesting finding indicating that the polariton condensed states formed by the optical pumping are initialized to one of the polarization states.

Here, we discuss the origins of interaction between the X- and Y-polarizations. As shown in a recent paper40, the mode coupling equation at an energetic resonant condition between the orthogonally polarized cavity photon modes with the same number of antinodes is expressed as

$$E\left[\begin{array}{c}{\alpha }_{X}\\ {\alpha }_{Y}\end{array}\right]=\left\{\left[\begin{array}{cc}{E}_{X} & 0\\ 0 & {E}_{Y}\end{array}\right]+\frac{{\left({{\hslash }}c\right)}^{2}}{{\varepsilon }_{{zz}}}\left[\begin{array}{cc}{\varepsilon }_{{xx}}{k}_{x}^{2}+{\widetilde{\varepsilon }}_{{zz}}{k}_{y}^{2} & \left({\varepsilon }_{{yy}}-{\varepsilon }_{{zz}}\right){k}_{y}{k}_{x}\\ \left({\varepsilon }_{{xx}}-{\widetilde{\varepsilon }}_{{zz}}\right){k}_{y}{k}_{x} & {\varepsilon }_{{zz}}{k}_{x}^{2}+{\varepsilon }_{{yy}}{k}_{y}^{2}\end{array}\right]\right\}\left[\begin{array}{c}{\alpha }_{X}\\ {\alpha }_{Y}\end{array}\right].$$
(4)

Here \({\varepsilon }_{{ij}}\) denotes the dielectric tensor inside the cavity, and \({\widetilde{\varepsilon }}_{{zz}}={\varepsilon }_{{zz}}+{\varepsilon }_{{xz}}{\varepsilon }_{{zx}}/{\varepsilon }_{{zz}}\). Note that Eq. (4) is equivalent to Eq. (2), and we focus on the non-diagonal terms here. For CsPbBr3 showing the orthorhombic crystal structure at RT, we thus obtain \({\varepsilon }_{{xx}}\ne {\varepsilon }_{{yy}}\ne {\varepsilon }_{{zz}}\) under the assumption that one of the crystal axes is along the normal direction of the microcavity surface. Furthermore, as the wavefunction of polariton condensed state is localized in the real space and shows a spread in the wavenumber space, we take into account not only the origin of wavenumber space but also the vicinity of it. We should note two things, that are (i) the function of \({k}_{y}{k}_{x}\) is not always an odd function but behaves as an even function when the coordinates are rotated by 45° around the energy axis (see Fig. S8 in the Supplementary Information) and (ii) in general, the wavefunction of polariton condensate state is not symmetrically spread in the radial direction24. As a consequence, we should consider that \({k}_{y}{k}_{x}\) is not perfectly zero, and thus the off-diagonal terms, \(({\varepsilon }_{{xx}}-{\widetilde{\varepsilon }}_{{zz}}){k}_{y}{k}_{x}\) and \(({\varepsilon }_{{yy}}-{\varepsilon }_{{zz}}){k}_{y}{k}_{x}\), are found to be non-zero in a CsPbBr3 microcavity, showing that the polarization coupling is possible. Note that the off-diagonal terms become zero in the case of highly symmetric crystal (i.e. \({\varepsilon }_{{xx}}={\varepsilon }_{{yy}}={\varepsilon }_{{zz}}\)) or in the case of too strong anisotropy (too large detuning between the X- and Y- modes). From these aspects, it is noteworthy that the CsPbBr3 microcavity can fulfill these two requirements simultaneously owing to the ‘very small’ anisotropy. We know that the non-zero off-diagonal terms discussed here might be small values, but in a cavity with high quality factor, the overall hybridization degree is significantly enhanced in an optical cavity.

In addition to the non-zero off-diagonal terms discussed above, we might consider the deviation of the CsPbBr3 crystal axis from the normal direction to the microcavity as another unexpected reason for the X–Y polarization coupling. As shown in Fig. S9 in the Supplemental Information, we occasionally observe LPB modes with the X–Y splitting showing non-clean polarization features. As such, the misalignment leads to the nonzero off-diagonal terms, and crystal growth techniques, in which the crystal orientation can be strictly controlled, are highly required.

Evaluation of polarization states

Finally, we validate the polarization state of the coupled polariton condensed states. We show the angle-resolved PL results for the complete polarization components, encompassing the horizontal/vertical (i.e., \({I}_{X}/{I}_{Y}\)), diagonal/anti-diagonal (\({I}_{D}/{I}_{A}\)), and right-circular/left-circular (\({I}_{R}/{I}_{L}\)) polarizations in the vicinity of the first threshold (Fig. S10 in the Supplementary Information). This measurement was performed for a shifted position within the same crystal, resulting in a slightly elevated energy level of the LPB states compared to the results mentioned above. Below the threshold, there is no significant difference in the polarization components of PL intensities. Stokes parameters, denoted as \({S}_{1}=({I}_{X}-{I}_{Y})/({I}_{X}+{I}_{Y})\), \({S}_{2}=({I}_{D}-{I}_{A})/({I}_{D}+{I}_{A})\), and \({S}_{3}=({I}_{R}-{I}_{L})/({I}_{R}+{I}_{L})\), approximate zero values, indicating that the polarization state below the threshold resides in a ‘mixed state’. Around the threshold, as shown in Fig. 3a, \({I}_{X}\) markedly increases to 0.5 or higher due to the onset of polariton condensation, resulting in a positive value for \({S}_{1}\) [see Fig. 3c]. Importantly, \({I}_{A}\) also increases concurrently with \({I}_{X}\), whereas \({I}_{D}\) remains relatively weak. In Fig. 3d, the parameter \({S}_{0}(=\scriptstyle\sqrt{{S}_{1}^{2}+{S}_{2}^{2}+{S}_{3}^{2}})\), which characterizes the degree of polarization, substantially rises to 0.8 above or at the threshold fluence. This high degree of polarization persists up to at least ~1.6 \({P}_{{th}}\), demonstrating that the polariton condensed state approaches a ‘pure polarization state’ undergoing the polarization superposition. On the other hand, \({S}_{3}\) remains close to zero, even beyond the threshold. This observation is consistent with the X–Y coupling described by Eq. (4), which exhibits mixing with off-diagonal terms of real numbers, resulting in the conversion to the diagonal and/or anti-diagonal polarization modes. Nevertheless, it is noteworthy that \({S}_{2}\) undergoes significant variations, including a change in sign [see Fig. 3b, c], suggesting the potential for quantum manipulation of the polarization state in the polariton condensed state. Further refinement of pumping fluence and exploration of synergies with the Rashba-Dresselhaus coupling effect is expected to facilitate comprehensive manipulation of the polarization state on the Poincaré sphere.

Fig. 3: Polarization states of polariton condensed states in CsPbBr3 microcavity.
figure 3

a, b Colourmaps of angle-resolved PL spectra observed at pumping fluences of ~\({P}_{{th}}\) (a) and ~1.28\({P}_{{th}}\) (b). PL intensities at horizontal, vertical, diagonal, anti-diagonal, right-circular, and left-circular polarizations are shown in panels (i)–(vi), respectively. The intensities are normalized in each pumping fluence. c Pumping fluence dependencies of Stokes parameters, \({S}_{1}\), \({S}_{2}\), and \({S}_{3}\). d Pumping fluence dependencies of Stokes parameter \({S}_{0}\).

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Conclusions

We demonstrated a polarization superposition of RT polariton condensed states. CsPbBr3 crystal, which has proven to be an excellent medium for the RT polariton condensation, exhibits an anisotropic feature suitable for achieving the polarization superposition. Specifically, the orthorhombic crystal structure of CsPbBr3 can simultaneously address the two requirements: small but non-zero X–Y splitting and non-zero off-diagonal interaction terms. By exploiting the blue shift of the polariton condensed state, we tuned energies of two orthogonally polarized modes, leading to the polarization superposition of the RT polariton condensed state.

The results shown here imply a great promise of polariton as RT quantum technologies. The polarization superposition is considerable progress toward the RT polariton qubit and quantum simulator. As a future work, it is intriguing to challenge the demonstrations of interactions between the polariton qubits and operations as a quantum logic gate. These challenges would open new perspectives on quantum applications of polaritons.

Methods

Microcavity fabrication

Distributed Bragg reflectors (DBRs) used in this study were multilayers of SiO2 and TiO2 on BK7 glass plates (area: 10 × 10 mm2 and thickness 0.5 mm). The rf-magnetron sputtering method was employed for the deposition of nine pairs of SiO2 and TiO2 layers. In this study, we used two types of DBRs. One of them had a reflection band (>98%) of ~450–550 nm and was used as the top mirror. The other had a reflection band of ~500–600 nm and was used as the bottom mirror.

To prepare precursor solutions of CsPbBr3 perovskite, cesium bromide (CsBr) and lead(II) bromide (PbBr2) were purchased from TCI. Dimethyl sulfoxide (DMSO) was purchased from Nacalai Tesque. We dissolve CsBr and PbBr2 in DMSO in a molar ratio of 1:1 at a concentration of 0.5 M, stirred at 700 rpm with a screw tube and a stirring bar for ~1 h at 50 °C.

CsPbBr3 microcavities were fabricated by a solution-processed crystallization method, as shown in Fig. S1 in the Supplementary Information. First, the two DBR mirrors mentioned above were washed with ultrasonic cleaning in ethanol and acetone for 10 min each and with UV ozone for 15 min. We cast the 10 μl of supersaturated precursor solution on a bottom DBR mirror. After that, the sample was capped with a top DBR mirror and then pinched with a double clip (19 mm). The crystal was grown at room temperature for one day. Next, we injected 1 μl of precursor solution into the gap of DBR mirrors using a micropipette from the three sides of the sample. The crystal was then grown further for one day at room temperature. This procedure was repeated for 4–5 times without intervals. Finally, we injected a pure solvent into the gap and dissolved all crystals once. The sample was left in atmospheric condition for 3–4 days at 50 °C to re-grow a large-sized crystal again. After the growth, we removed the DMSO solvent using ethanol. Three days later, we removed the double clip. The thickness of the crystal depended on the strength of the clipping and the amount of solution at the casting stage and was typically in a range of 300–700 nm.

Characterizations

All optical measurements were performed in atmospheric conditions (~23 °C and ~40 %RH). We used a pulse laser (FTSS355-Q4, CryLas) for sample excitation. The emission spectra were measured with a CCD spectrometer (Kymera 328i & Newton DU971PBV, Oxford ANDOR). The emission counts were recorded with a time-integration of 1 s and an accumulation of 10 times. In angle-resolved PL measurements, we used a Fourier space imaging setup (see Fig. S4 in the Supplementary Information) using an objective with NA ~ 0.5 (UPLFLN 20X, Olympus). The angle limits of angle-resolved measurement are estimated from a relationship of \({\theta }_{\max }={\sin }^{-1}\left({{{{{\rm{NA}}}}}}\right)\) to be 30°. Polarization measurements were performed by using a Glan–Thompson prism as the polarizer and a quartz quarter-wave plate. Spectral resolution of the measurement system was up to ~0.4 nm.