1.

Introduction

Optical parametric oscillators (OPOs) convert a pump frequency ${\omega }_p$ into signal ${\omega }_s$ and idler ${\omega }_i$ frequencies, satisfying the energy conservation law (with the second-order nonlinearity, ${\omega }_p={\omega }_i+{\omega }_s$; with the third-order nonlinearity, $2{\omega }_p={\omega }_i+{\omega }_s$). These indispensable devices have been widely used in creating tunable and coherent light for the application of spectroscopy.¹ In addition, OPOs have attracted considerable interest in other fields such as the generation of squeezed light,^2,3 correlated photons,^4–6 and quantum information including quantum random number generation and Ising machines.⁷ In traditional systems, OPOs usually require noncentrosymmetric crystals (second-order nonlinearity) embedded in an external resonator, which is resonant with the pump wavelength as well as the wavelength of generated signal and idler states. Such generated signal and idler states can be further tuned by controlling the phase matching condition via changing the temperature or angle of the nonlinear crystal or tuning the pump wavelength.⁸ However, such traditional OPOs usually suffer from a high power threshold,⁸ since anisotropic crystals require stringent birefringence phase matching requirements and usually exhibit limited high-order nonlinearity.⁹ Moreover, crystals in centrosymmetric space groups such as all-inorganic cesium lead halide perovskites (${\mathrm{CsPbBr}}_3$) need to break inversion-symmetry by anion substitution or other specific complex processes.^10–12 Despite the recent progresses achieved in various bulk whispering gallery mode-based OPOs,^13–16 the threshold powers are still relatively large, particularly the chip-scale planar OPOs,^8,17–19 which hinder the road toward integrated nonlinear photonic devices.

Alternatively, exciton–polaritons are hybrid quasi-particles resulting from the strong coupling between photons and excitons, inheriting a high nonlinearity from their excitonic component. The nonlinearity of such a polariton system is orders of magnitude stronger than that of traditional nonlinear optical systems, which opens a new way for nonlinear polaritonic devices.^20–22 Thanks to S-shaped polariton dispersion, the idler at a high $\mathit{k}$ (wavevector) state and the signal at the ground state can be obtained when two polaritons are resonantly pumped at the inflection point, obeying the conservation law of both energy and momentum.^23–25 In addition to this nondegenerate polariton oscillator geometry, in a system with multiple branches, two polaritons at the lowest energy of one polariton branch can scatter to momentum-degenerate states^26–28 or energy-degenerate states^29–32 at adjacent polariton branches. The large third-order polaritonic nonlinearity promotes the realization of polariton oscillators at lower threshold, which has been demonstrated in a variety of semiconductor microcavities.^23–32 Compared with the conventional OPOs, the polaritonic configuration is more versatile and suitable for the realization of quantum correlation and parametric down-conversion toward miniaturized, integrated devices.^22,28–30 So far, polariton oscillators in GaAs or CdTe-based quantum wells demand cryogenic temperatures due to the small exciton binding energy, whereas polariton oscillators have not been realized in organic microcavities due to the low nonlinearity of Frenkel excitons.

Halide perovskites with a wide structural diversity, tunable bandgap, and remarkable optical properties, have rapidly emerged as excellent semiconductors for photonic technologies ranging from light-emitting diodes^33,34 and lasers^35,36 to photodetectors.³⁷ More recently, for engineering their applications in next-generation photonic devices, the nonlinear properties of perovskite attract tremendous interest. The versatile architecture of halide perovskites along with their scalable synthesis allows for structural and electronic engineering for nonlinear optical functionalities including OPOs, ultra-fast laser modulators,^11,38 and THz generators/detectors.^39,40 Due to the large exciton binding energy, perovskite microcavities can sustain robust exciton polaritons and polariton lasing with lower threshold at room temperature.^41–44 Moreover, the strong nonlinear polariton–polariton interaction has been demonstrated in both 2D hybrid perovskites and 3D all-inorganic perovskites.^32,45 Combining these advantages, halide perovskites provide a promising platform for nonlinear polaritonic devices with low thresholds. Although energy-degenerate parametric scattering has been reported in 3D all-inorganic perovskites, the fixed wavelength of the signal and idler is not adjustable. This limits some applications, specifically down conversion, as well as the possibility of reaching the quantum correlated regime, due to the presence of degenerate uncorrelated scattering processes.⁴⁶

Here, we demonstrate nondegenerate polariton parametric oscillators with low thresholds in all-inorganic ${\mathrm{CsPbBr}}_3$ microcavities at room temperature. This is achieved by taking advantage of the large third-order nonlinearity and S-shaped polariton dispersion of our on-chip perovskite microcavities.

2.

Methods

3.

Configuration of the Perovskite Polariton Parametric Oscillator

In our experiment, the ${\mathrm{CsPbBr}}_3$ single-crystal film grown by CVD (Sec. 2)^47,48 exhibits a flat surface with strong green fluorescence, as shown in Fig. 1(a) (see also Fig. S1 in the Supplementary Material). The geometry of the polariton parametric oscillator is schematically displayed in Fig. 1(b), where the signal and idler can be generated along the $k_x$ axis in far-field emission after the ${\mathrm{CsPbBr}}_3$ microcavity is resonantly excited with a critical (magic) angle along $k_x$. The ${\mathrm{CsPbBr}}_3$ microcavity itself consists of a ${\mathrm{CsPbBr}}_3$ single-crystal film with a thickness of 280 nm (Fig. S2 in the Supplementary Material), sandwiched between two DBRs deposited by electron beam evaporation (Sec. 2). Figure 1(c) presents the angle-resolved photoluminescence spectrum of the microcavity in horizontal ($H$) polarization under nonresonant CW laser (457 nm) excitation. Using a coupled oscillator model to fit the polariton dispersion obtained in the measurement, we extract a bare exciton energy of 2.407 eV, cavity-exciton detuning $\mathrm{\Delta }=-82\mathrm{meV}$, Rabi splitting of 120 meV, and refractive index of 2.860. If this system is excited by a resonant pump laser matching with the polariton dispersion at $k_p$, the polariton pairs could scatter and oscillate to the signal state and the high $k$ state (idler), respectively. The intensity of the polariton dispersion shown in Fig. 1(c) is weaker at higher $k$ states. We attribute this to the small photonic fraction of these states as well as their effective losses caused by additional energy relaxation processes. We can also see that the polariton blueshift is larger for higher $k$. This can be attributed to $k$-dependence of the excitonic fraction, where the exciton fraction of the pump state at $k_p$ is twice as large as that of the signal state at $k_s$. Such nonuniform renormalization of the dispersion has also been discussed theoretically.⁴⁹

Fig. 1

Schematic diagram and mechanism of polariton parametric oscillator in the perovskite microcavity. (a) Microscopy image and fluorescence microscopy image of the ${\mathrm{CsPbBr}}_3$ perovskite single crystal. (b) Experimental geometry of the ${\mathrm{CsPbBr}}_3$ perovskite microcavity, in which a thick ${\mathrm{CsPbBr}}_3$ perovskite is sandwiched by two DBRs. (c) Angle-resolved photoluminescence spectrum of ${\mathrm{CsPbBr}}_3$ microcavity along $H$ polarization under CW excitations. The dashed black line displays the theoretical fitting dispersion of the LP dispersion; the solid black lines show the dispersions of uncoupled ${\mathrm{CsPbBr}}_3$ perovskite exciton ($X$) and cavity photon mode ($C$); the detuning $\mathrm{\Delta }$ is indicated in this figure. (d) Hopfield coefficients illustrating the exciton ($X_{\mathrm{LP}}$) and photon ($C_{\mathrm{LP}}$) fraction of the LP dispersion along $x$ polarization; the blue vertical line denotes the signal state polariton ($k_s$); the green vertical line represents the pump state polariton ($k_p$).

4.

Observation and Characterizations of Polariton Oscillation

The system is further resonantly excited by a pulsed nanosecond laser at 533 nm to reach the nonlinear regime in the transmission configuration, and the resonant excitation is spectrally tuned to match the high $\mathit{k}$ state ($k_x=6.8\mu {\mathrm{m}}^{-1}$) in the polariton dispersion with a negative detuning of $\mathrm{\Delta }=-82\mathrm{meV}$. At the pump power of $0.5P_{\mathrm{th}}$, where $P_{\mathrm{th}}$ is the power threshold for parametric oscillation, the polariton energy dispersion along $k_x$ is observed without a clear signal state in Fig. 2(a), in accordance with the dispersions displayed in Fig. 1(c). Similarly, the $k_x$-$k_y$ far-field emission [Fig. 2(b)] shows the strong pump state along $k_x$. With increasing pump power, polariton scattering becomes more efficient and triggers polariton parametric oscillation, where we observe strong emission from the ground state as the signal state. As shown in Figure 2(c), at the pump power of $3P_{\mathrm{th}}$, the signal state appears at the ground state of the dispersion, whereas the idler state at $k_x=13.6\mu {\mathrm{m}}^{-1}$ was not observed (partly since the wavevector of the idler was beyond the collected range). Accordingly, the $k_x-k_y$ far-field emission exhibits a signal state at $k_x=0\mu {\mathrm{m}}^{-1}$, $k_y=0\mu {\mathrm{m}}^{-1}$ and a pump state at $k_x=6.8\mu {\mathrm{m}}^{-1}$, $k_y=0\mu {\mathrm{m}}^{-1}$. Considering the polariton–polariton nonlinear pump term, the theoretical calculations [Figs. 2(e)–2(h)] are in good agreement with experiments [Figs. 2(a)–2(d)], respectively.

Fig. 2

Observation and characterizations of polariton oscillation at room temperature. Experimental far-field emission of (a) energy–$k_x$ and (b) $k_x$-$k_y$ at the pump power of $0.5P_{\mathrm{th}}$. Experimental far-field emission of (c) energy–$k_x$ and (d) $k_x$-$k_y$ at the pump power of $3P_{\mathrm{th}}$. Theoretically calculated far-field emission of (e) energy–$k_x$ and (f) $k_x$-$k_y$ at the pump power of $0.5P_{\mathrm{th}}$. Theoretically calculated far-field emission of (g) energy–$k_x$ and (h) $k_x$-$k_y$ at the pump power of $3P_{\mathrm{th}}$. (i) Signal-state $k_s$ emission intensity as a function of pump $k_p$ fluence in a log–log scale, demonstrating a super-linear increase by three orders of magnitude near threshold. (j) Signal-state $k_s$ emission linewidth as a function of pump $k_p$ fluence along with a sharp narrowing linewidth from 12 to 2 meV at the threshold. (k) Signal-state $k_s$ emission peak energy with a continuous blueshift trend.

To characterize the occurrence of polariton parametric oscillation quantitatively, we extract the emission intensity, linewidth, and peak energy of the signal state from the power-dependent angle-resolved emission spectra. A super-linear increase of emission intensity by three orders of magnitude is observed near the threshold $P_{\mathrm{th}}=0.8\mu \mathrm{W}$ [Fig. 2(i)], as well as a sharp linewidth narrowing from 12 to 2 meV [Fig. 2(j)]. Importantly, with increasing pump power, the peak energy of the signal state exhibits a continuous blueshift [Fig. 2(k)], arising from polariton–polariton interaction in the system.

5.

Characterizations of Polariton Oscillator versus Pump States

To further prove the occurrence of polariton parametric oscillation, we have conducted measurements by changing the incident pump state along the polariton dispersion for three different cavity-exciton detunings. Specifically, the wavelength (energy) of the excitation can be changed by the nanosecond pulsed laser in steps of one nanometer precision, while the incident pump angle (momentum) is continuously tuned at each wavelength of the excitation to obtain the maximum intensity with the lowest threshold and in resonance with the LP dispersion. As shown in Figs. 3(a)–3(c), the pump states are resonantly excited, while a slight blueshift is observed between pump states and polariton dispersion at higher $\mathit{k}$, resulting from the higher exciton fraction. The parametric oscillation thresholds as a function of pump states in Figs. 3(a)–3(c) are plotted in Figs. 3(d)–3(f), respectively. A strong reduction of threshold is observed at the critical resonant angle, where phase matching conditions best match the shape of the LP dispersions. Above the resonant critical angle, the threshold increases with the increase of the pump angle. When the resonant pump angle is smaller than the resonant critical angle, the oscillator threshold increases with the decrease of pump angle and is absent approaching normal incidence. Such evidence strongly suggests that the signal is dominantly contributed from parametric oscillation rather than energy relaxation. Furthermore, the critical angle changes with the detuning: $k_x=5.7\mu {\mathrm{m}}^{-1}$ for detuning $\mathrm{\Delta }=-50\mathrm{meV}$ with $P_{\mathrm{th}}=0.3\mu \mathrm{W}$ [Figs. 3(a) and 3(d)], $k_x=6.8\mu {\mathrm{m}}^{-1}$ for detuning $\mathrm{\Delta }=-82\mathrm{meV}$ with $P_{\mathrm{th}}=0.8\mu \mathrm{W}$ [Figs. 3(b) and 3(e)], and $k_x=7.6\mu {\mathrm{m}}^{-1}$ for detuning $\mathrm{\Delta }=-100\mathrm{meV}$ with $P_{\mathrm{th}}=2.5\mu \mathrm{W}$ [Figs. 3(c) and 3(f)], following the principle of larger critical angle for more negative detuning due to the conservation of energy and momentum. In addition, the lowest threshold at critical angle is lower at a less negative detuning as a result of a higher exciton fraction leading to a stronger polariton–polariton interaction, which further implies the appearance of polariton parametric oscillation.

Fig. 3

Characterizations of polariton oscillator versus pump states for three samples with different detunings $\mathrm{\Delta }=-50$, $-82$, $-100\mathrm{meV}$, respectively. (a)–(c) The pump state is tuned with energy and angle to resonantly excite the LP dispersion for detunings (a) $\mathrm{\Delta }=-50\mathrm{meV}$, (b) $\mathrm{\Delta }=-82\mathrm{meV}$, and (c) $\mathrm{\Delta }=-100\mathrm{meV}$. (d)–(f) The energy conversion threshold as a function of pump state angle for detunings (d) $\mathrm{\Delta }=-50\mathrm{meV}$, (e) $\mathrm{\Delta }=-82\mathrm{meV}$, and (f) $\mathrm{\Delta }=-100\mathrm{meV}$. The lowest energy conversion threshold peaks at (d) $P_{\mathrm{th}}=0.3\mu \mathrm{W}$, (e) $P_{\mathrm{th}}=0.8\mu \mathrm{W}$, and (f) $P_{\mathrm{th}}=2.5\mu \mathrm{W}$, respectively. The black circles denote the occurrence of OPO, whereas the red circles represent cases where the OPO was not present.

6.

Polarization Dependence of the Polariton Parametric Oscillator

We further investigate the polarization dependence of the signal in our perovskite microcavity.^26,50 Under CW laser (457 nm) excitation, due to the intrinsic anisotropy of the perovskite crystal,⁵¹ the LP dispersion shows a linearly polarized splitting at $k=0$, $E_{sV}=2.296\mathrm{eV}$ along $V$ polarization, and $E_{sH}=2.287\mathrm{eV}$ along $H$ polarization in Fig. 4(a). The sample is oriented with the crystal boundary exhibited in Fig. S1 in the Supplementary Material, so the linear polarization direction coincides with the crystal axes. For characterizing the polarization dependence of the signal in the perovskite polariton oscillator, the polarization of the signal is explored under a linearly polarized pump and circularly polarized pump, respectively. Figure 4(b) displays the high $H$ linearly polarized pump after the DBR microcavity. Under this $H$ polarized pump at critical point [$E_p=2.326\mathrm{eV}$ (533 nm), $k_x=6.8\mu {\mathrm{m}}^{-1}$], the polar plot of the signal is detected and fitted by Malus’s law, showing high $H$ linear polarization as well [Fig. 4(c)]. Furthermore, the system is excited by a left circular pump [Fig. 4(d)] near the critical angle [$E_p=2.326\mathrm{eV}$ (533 nm), $k_x=6.8\mu {\mathrm{m}}^{-1}$], where the pump in $k$ space is wide enough to cover the $H$ polarized polariton mode and $V$ polarized polariton mode simultaneously. The $H$ linearly polarized signal at $E_{sH}=2.287\mathrm{eV}$ or $V$ linearly polarized signal at $E_{sV}=2.296\mathrm{eV}$ [Fig. 4(e)] with respective blueshifts is observed, rather than inheriting the circular polarization of the pump, corresponding with the states noted in Fig. 4(a). The pump angle is the critical (magic) angle for the $H$ polariton mode, while slightly larger than that for $V$ polariton mode, thus the intensity of the $H$ polarized signal is found to be about two times stronger than that of the $V$ polarized signal in Fig. 4(e). These linearly polarized signal dependences correspond with the strong linear anisotropy in the perovskite system that could split the polarization of excitation into linearly polarized components.

Fig. 4

Polarization dependence of the polariton parametric oscillator. (a) Angle-resolved photoluminescence spectrum of ${\mathrm{CsPbBr}}_3$ microcavity along $V$ polarization and $H$ polarization under CW excitation. (b) Polar plot of the $H$ polarized pump excited at $E_p=2.326\mathrm{eV}$ (533 nm), centered $k_x=6.8\mu {\mathrm{m}}^{-1}$ (black circle dots), and fitting function (black solid line) $f\propto {\cos }^2\theta$. (c) Under excitation of (b), polar plot of the measured polarization emission of the signal state at $E_{sH}=2.287\mathrm{eV}$, $k_x=0\mu {\mathrm{m}}^{-1}$ (red circle dots) and fitting function (red solid line) $f\propto {\cos }^2\theta$. (d) Polar plot of the left circularly polarized pump excited at $E_p=2.326\mathrm{eV}$ (533 nm), centered $k_x=6.8\mu {\mathrm{m}}^{-1}$ (black circle dots), as well as a fitting constant function (continuous line). (e) Under excitation of (d), polar plot of the measured polarization emission of the signal state at $E_{sH}=2.287\mathrm{eV}$, $k_x=0\mu {\mathrm{m}}^{-1}$ (red circle dots), and fitting function (red solid line) $f\propto {\cos }^2\theta$; at $E_{sV}=2.296\mathrm{eV}$, $k_x=0\mu {\mathrm{m}}^{-1}$ (blue circle dots), and fitting function (blue solid line) $f\propto {\cos }^2(\theta +90\mathrm{deg})$.

7.

Conclusions and Discussions

By implementing resonant excitation at a critical (magic) angle, we experimentally and theoretically report the nondegenerate polariton parametric oscillator in perovskite exciton–polaritons at room temperature. The result corresponds to spontaneous parametric down conversion over a range of angles. Meanwhile, the signal state is split into two nondegenerate orthogonal linear polarizations due to the strong anisotropy of perovskite. Our work reveals an alternative avenue for lower threshold nonlinear polaritonic devices.