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Abstract
Random lasing is an intriguing phenomenon occurring in disordered structures with optical gain in which light scattering provides the necessary feedback for lasing action. Unlike conventional lasers, random lasing systems emit in all directions due to light scattering. While this property can be desired in some cases, directional emission remains required for most applications. In a vertical microcavity containing the hybrid perovskite CH3NH3PbBr3, we report here the coupling of the emission of a random laser with a cavity polaritonic resonance, resulting in a directional random lasing, whose emission angles can be tuned by varying the cavity detuning and reach values as large as 15.8° and 22.4°.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In a random laser, cavity feedback is replaced by multiple scattering [1–5]. For example, in the case of coherent feedback random lasing, light is scattered in closed loops and forms random cavities [5,6]. The lasing emission is then characterized by narrow peaks, similar to the conventional lasers, originating from the random cavity modes. In contrast with conventional lasers, random lasers emit in all directions [7]. Different methods have been proposed and/or demonstrated for controlling the random lasing directionality, such as pump shaping [8], coupling the random lasing medium to a Bragg grating [9], to an optical fiber [10], to a photonic crystal microcavity [11,12] or to a planar microcavity [13–17]. All these techniques are based on the coupling of the random laser emission with a more directional resonance mechanism. Typically, the random lasing occurs in two dimensions, and the third dimension is used to sandwich the random laser inside a directional output coupling system. However, there exists another system in which the emission direction is governed by the coupling between a light cavity mode and an excitonic resonance, namely the cavity exciton-polariton resonance [18–20]. In this case, the strong coupling between light and matter leads to modes, which are superposition states of light and matter. This results in the existence of two cavity polaritonic branches for which the emission direction is correlated with the energy of the quasi-particle. One could thus imagine coupling a 2D random laser with a cavity polaritonic resonance in order to control the emission direction of the random laser.
To implement such an approach, one needs to find a material in which both random lasing and strong coupling between excitons and cavity modes have been obtained. This is the case of organic-inorganic hybrid perovskites. Lasing with perovskites has been demonstrated with several different resonators in the past such as nanowires [21], nanoplatelets [22], distributed feedback cavities (DFB) [23], photonic crystals [24], and microcavities [25]. Additionally, an interesting feature of perovskites is the continuous tunability of the emission wavelength through the entire visible spectrum via halide substitution [26]. Moreover, in the present context, the advantage of these materials is that random lasing can also be observed without an external resonator, i.e. directly from polycrystalline and nanocrystals thin films. This has indeed been demonstrated in iodine-based perovskites [27–31], chloride-based perovskites [32], and bromide-based perovskites [32–40]. Besides, strong coupling between a microcavity mode and an exciton has been observed both in 2D and 3D hybrid perovskites [41–44].
In this article, we investigate random lasing action with coherent feedback in a polycrystalline thin film of the perovskite $CH_3NH_3PbBr_3$ capped with PMMA. This 2D random laser is embedded in a microcavity in which strong coupling between the cavity mode and the perovskite exciton is obtained, and we demonstrate that coupling the emission of this 2D random laser with the cavity polaritonic resonance permits to control the direction of emission of the random laser.
2. Results and discussion
Two samples, sketched in Fig. 1(a), have been studied in this work. The first sample is a 100 nm-thick thin film of the perovskite $CH_3NH_3PbBr_3$, called hereafter MAPB, deposited on a quartz substrate by spin coating. A layer of around 350 nm of PMMA (Poly(methyl) methacrylate) has been later deposited by spin coating on the MAPB layer. The second sample is a 3$\lambda /2$ MAPB-based microcavity, with $\lambda =535$ nm the MAPB emission wavelength. This microcavity is composed by a commercial Bragg mirror (Layertec, corp) on which have been deposited the layers of MAPB ($\sim$ 100 nm) and PMMA ($\sim$ 350 nm) by spin coating and a layer of 30 nm of silver by evaporation. More details on the samples are given in Supplement 1, section 1. Figure 1(b) shows the absorption and photoluminescence spectra of a control thin film of MAPB. The absorption spectrum is composed by an excitonic resonance at around 2.35 eV and a band absorption continuum at higher energies. The PL is Stokes-shifted at an energy of 2.32 eV with a Full Width at Half Maximum (FWHM) of 96 meV. Figure 1(c) presents an AFM scan of a control layer of MAPB: it reveals a polycrystalline film with a roughness of about 15 nm composed by grains of 500 nm to 1 $\mu$m size. Photoluminescence (PL) spectroscopy and angle-resolved photoluminescence (ARPL) as a function of the pump power have been performed on both samples. More details on the optical set-ups and experimental methods are given in Supplement 1, section 2.
Fig. 1. (a) Sketches of the two samples (b) Photoluminescence (PL) and absorption spectra of the MAPB thin film. (c) AFM image of the MAPB thin film.
Due to the roughness of the MAPB layer, random lasing action is observed from the MAPB/PMMA sample. Such random lasing from perovskite polycrystalline thin films have already been demonstrated in the literature in MAPB thin layers [39,40]. The PL spectroscopy results demonstrating the random lasing are shown in Supplement 1, section 3. Figures 2(a) and 2(b) show the ARPL pseudo-colour maps below (at 0.4 $P_{th}$) and above (at 1.3 $P_{th}$) the random lasing threshold obtained on a position of the MAPB/PMMA sample. More data on this position are given in Supplement 1, section 4. The ARPL map below the excitation threshold shows an angle-independent emission centred at 2.3 eV with an FWHM of 100 meV. Above the threshold, two random laser peaks can be clearly observed as two horizontal red lines at 2.275 eV and 2.283 eV while the broadband PL signal similar to the one below the threshold appears in dark blue. Such as the PL emission below the threshold, the random laser peaks emit in all directions from the sample surface as expected for a random lasing action in thin films [7]. Indeed, the gain occurs within the plane of the MAPB film and the lasing emission is scattered out of the plane, resulting in an angle-independent emission from the surface of the MAPB/PMMA sample.
Fig. 2. Angle-resolved photoluminescence (ARPL) pseudo-colour maps (in linear scale), (a) under (0.4 $P_{th}$) and (b) above (1.3 $P_{th}$) the random lasing threshold of the thin film of MAPB on quartz substrate capped with PMMA. The resolutions of the ARPL maps are respectively 1.7 meV for the energy axis and 0.7$^\circ$ for the angle axis.
Considering the ease with which the strong coupling regime is observed in MAPB [44–46], the question of the photonic or polaritonic nature of the lasing can be reasonably raised here as it was raised by Niyuki et al. from a resonance-controlled ZnO random laser [47]. Especially, the blueshift of the MAPB/PMMA lasing peaks as a function of the pump power (of around 1-2 meV between 1.1 and 1.8 $P_{th}$, see Supplement 1, section 5) could be in favour of a polaritonic lasing. However, the blueshift could just be explained by thermal effects as MAPB shows blueshift with temperature increase (of around 24 meV between 300K and 370K) [48]. Nevertheless, distinguishing between the photonic and polaritonic nature of the random lasing is hard and not within our reach in this paper. Indeed, the only way to demonstrate without ambiguity the existence of the polaritons is to measure the mode dispersion from the random lasing emission and it is impossible in practice here due to the multiple light scattering.
Let us now focus on the 3$\lambda$/2 MAPB-based microcavity. In our previous study [44], the strong coupling between the perovskite exciton and the microcavity photonic mode has been demonstrated on the same microcavity and cavity polaritons have been observed experimentally (the theory of the cavity polaritons is given in Supplement 1, section 6). In particular, we have shown that, due to the overall lateral roughness of the MAPB and PMMA layers, the cavity detuning, $\delta =E_0-E_X$, with $E_0$ the cavity mode energy at normal incidence and $E_X$ the exciton energy, can be tuned by probing different lateral positions. Only the lower cavity polariton dispersion could be observed in the ARPL maps of our previous study [44]. We will then only consider the lower cavity polariton whose eigenvalue $\mu _{LP}(\theta )$ is given by Eq. (1):
Figures 3 shows the ARPL pseudo-colour maps below ((a) to (c)) and above ((d) to (f)) the lasing threshold of three different positions on the microcavity. Additional data are shown for each of these positions in Supplement 1, section 7. The dispersions corresponding to the three positions below the threshold in Fig. 3(a), (b) and (c) are fitted with the lower cavity polariton dispersion, with the detuning, $\delta$, as the only free parameter and the other parameters fixed at the values found in our previous study [44]. The fitting method is presented in Supplement 1, section 8. The detunings obtained for the three different positions are $\delta$=-107 meV, -75 meV, and -34 meV, respectively. A good agreement is met between the lower cavity polariton dispersions and the dispersions of the ARPL maps confirming the strong coupling regime in this microcavity.
Fig. 3. Angle-resolved photoluminescence (ARPL) pseudo-colour maps (in linear scale) of three different positions on the MAPB-based microcavity. The resolutions of the ARPL maps are respectively 1.7 meV for the energy axis and 0.7$^\circ$ for the angle axis. The first row ((a) to (c)) corresponds to the ARPL maps below the lasing threshold and the second row ((d) to (f)) above the lasing threshold. The lower and upper cavity polaritons dispersions (black lines), cavity mode dispersions (dashed red line) and the exciton energy (green dashed line) are plotted on top of all the ARPL maps. The dispersions are derived from Supplement 1, Eq. (S3), with $n_{eff}$=1.75, $E_X$=2.355 eV, $\gamma _{ph}$ =25 meV, $\gamma _{X}$=90 meV and $V$= 48 meV. The detunings of the three positions are $\delta$=-107 meV, -75 meV and -34 meV, respectively. The figures in the third row ((g) to (i)) are the numerical lower cavity polaritons dispersions plotted with the lower cavity polariton linewidths (gray shaded area) using the same parameters mentioned above. The centers of the lower cavity polariton dispersions are plotted as black solid lines. The green dashed lines correspond to a laser emission energy at 2.28 eV, the blue solid lines correspond to the intersections between the laser emission energy and the lower cavity polariton dispersions, the red dashed line indicates the expected angle of emission.
In the three ARPL maps above the threshold in Figs. 3(d), 3(e), and 3(f), laser peaks appear in red while the lower cavity polariton emissions, similar to the ones below the threshold, appear in cyan and dark blue. To better distinguish the lasing peaks, vertical and horizontal slices of the ARPL maps are respectively taken at given angles and energies (Supplement 1, section 9). The lasing peaks energies, angles and divergences are obtained from the slices. For the first position corresponding to the largest detuning in Fig. 3(d), two very close laser peaks appear in dark red at 2.282 eV and 2.286 eV at the angles of $\pm$ $\sim$ 22.4$^\circ$ with a divergence of 12.5$^\circ$. For the second position (Fig. 3(e)), one laser peak in red emerges at 2.28 eV at angles around $\pm$ $\sim$ 15.8$^\circ$ with a divergence of $\sim$ 12.3$^\circ$. For these two cases, the angles at which the lasing peaks lie correspond to the intersection between the lower cavity polariton dispersion and the energy of lasing emission. For the third position (Fig. 3(f)), two very close lasing peaks emerge at 2.282 eV and 2.286 eV in dark red. However, unlike the first two positions, the emission occurs at 0$^\circ$ with a divergence around 29.7$^\circ$. Moreover, the positions of the laser peaks lie under the theoretical lower cavity polariton dispersion.
Figure 4(a) shows the photoluminescence spectra as a function of the pump power varying from 0.9 $P_{th}$ to 1.35 $P_{th}$ of another position on the microcavity. The photoluminescence spectrum below the threshold is coupled to the microcavity mode, which leads to a spectrum shifted to 2.272 eV with an FWHM of 53 meV. When the pump power exceeds the threshold, laser peaks appear on top of the broadband PL with a dominant peak at 2.273 eV with an FWHM of around 3 meV. Such as for the PL spectroscopy of the MAPB/PMMA sample (Supplement 1, section 3), when the pump power further increases, other peaks occur at different energies, and the overall lasing spectrum is broadened as the modes begin to overlap. The log-log integrated PL as a function of the pumping power, shown in Fig. 4(b), exhibits a threshold of 140 $\mu$W (a discussion on the effect of the cavity on the lasing threshold is given in Supplement 1, section 10).
Fig. 4. PL spectroscopy of the lasing action from the $3\lambda /2$ microcavity. The resolution is here of 0.38 meV for the energy axis. (a) PL spectra of one position on the MAPB-based microcavity at different pumping powers. (b) Log-log PL intensity spectrum as a function of the pumping power. (c) Four PL spectra above the lasing threshold of (a) are plotted with a vertical offset for better readability. Five lasing modes are indicated by blue triangles and the blue dotted lines are guides for the eye. (d) Study of the free spectral range in energy, $FSR_E=E_{m+1}-E_{m}$ with $m$ an integer, of the lasing spectra in (c) to obtain the characteristic size of the MAPB pseudo-cavities. The difference in energy between the $m^{th}$ modes and the $1^{st}$ mode is plotted against the modes numbers and is fitted with a linear function. The pseudo-cavity characteristic length of 144 $\mu$m is retrieved from $L=hc/(n s)$, where $n=2.3$ is the MAPB refractive index (at 2.28 eV from ellipsometry measurements [49]), $c$ is the light velocity, and $s$ is the slope of the linear function.
The lasing from the microcavity cannot originate from a photonic laser such as a VCSEL (Vertical-Cavity Surface-Emitting Laser). In such a case, the lasing would have occurred at zero angle, and the emission should have been monomodal between 2.2 and 2.3 eV as the microcavity length is three times half the MAPB emission wavelength (3$\lambda$/2). However, several modes have been observed in Fig. 4 and also from another position of the microcavity (Supplement 1, section 11).
We note that the lasing peaks seen in Figs. 3 and 4 occur at the same range of energy, between 2.26 eV and 2.29 eV, than the MAPB/PMMA sample (Supplement 1, section 3). Indeed, for a random lasing action, the gain medium properties define the energy region of the lasing emission. In our case, the lasing modes occur in the region of highest net gain of MAPB, i.e. where the ASE (Amplified Spontaneous Emission) takes place in MAPB thin films [50]. The study in Fig. 4(d) of the free spectral range in energy, $FSR_E = E_{m+1}-E_m$ with $m$ an integer, of the lasing spectra in Fig. 4(c) gives a characteristic pseudo-cavity length (i.e. the length of the closed loops formed by the multiple scattering) of around 144 $\mu$m (see more details in the Fig. 4 caption). A value of the same order of magnitude (of around 215 $\mu$m) has been found from the other microcavity position presented in Supplement 1, section 11. We note that the pseudo-cavity length is much higher than the microcavity vertical size and is similar to the value of 100 $\mu$m found for the MAPB/PMMA sample (Supplement 1, section 3). These arguments are in favor of a random lasing within the MAPB layer of the microcavity, filtered directionally by the lower cavity polariton resonance. In this hypothesis, light amplification occurs within the plane of MAPB and is scattered out of the plane, but due to the strong coupling regime, only some sets of energy/wavevectors are allowed, which results in the directional control of the random lasing emission.
One could wonder if the microcavity lasing is related to the condensation of the cavity polaritons. A blueshift could be the signature of polariton-polariton interactions but unfortunately, the presence of a blueshift does not allow to conclude as it can also be related to the shift of the band gap with temperature in halide perovskites. Indeed, a slight blueshift of the lasing modes of about 1 meV between 1 Pth and 1.2 Pth, can be observed in Fig. 4(c) with the pumping power increasing, but as already discussed previously for the MAPB/PMMA sample, can be due to the perovskite thermal effects. On the other hand, the energies of the lasing peaks are always at the same energies for all the detunings (in Figs. 3 and 4), between 2.26 and 2.29 eV, even when the polariton dispersion is at higher energies as in the case of the lowest detuning in Fig. 3(f). This last argument is not compatible with polaritonic lasing.
To further investigate the coupling of the random lasing with the lower cavity polariton resonance, the expected lasing angle and divergence as a function of the detuning is determined with a numerical approach illustrated by the Figs. 3(g), 3(h), and 3(i), using Eq. (1) and the parameters found from the fit of the dispersions. The energy of the random lasing emission is considered here to be 2.28 eV. The lower cavity polariton dispersions are plotted for a given detuning $\delta$ by taking into account the lower cavity polariton linewidths, $\gamma _{LP}^{\delta }(\theta )$, and are represented by the gray shaded areas. The center of the dispersions, $E_{LP}^{\delta }(\theta )$, are plotted as black solid lines. The intersections between the lasing emission energies (green dashed lines) and the cavity polariton dispersions (gray shaded areas), give then the expected lasing angles (red dashed line) and divergences (solid blue line).
For large negative detunings, lower than -74 meV, the intersection between the lasing emission energy and the cavity polariton dispersion gives rise to two distinct lobes of lasing emission. The two lobes at negative and positive angles are symmetric with respect to the normal direction. The ARPL maps obtained from the first two positions on the microcavity in Figs. 3(d) and 3(e) as well as their theoretical dispersions (Figs. 3(g) and 3(h)) clearly demonstrate the cavity polaritonic filtering. When the detunings are above -74 meV, the intersection between the lasing emission energy and the lower cavity polariton dispersion generates only one lasing lobe centered at 0$^\circ$ with a large divergence. This is due to the two lobes merging into one due to their increased widths. This is the case of the emission of the third position probed on the microcavity in Figs. 3(f) and 3(i). When the detuning is further increased, the numerical divergence decreases as the FWHM (Full Width at Half Maximum) in angle of the lower polariton dispersion at the lasing energy of 2.28 eV decreases with the detuning increasing (more details in Supplement 1, section 12). Figures 5(a) and 5(b) illustrate the numerical method at the detunings $\delta$=-75 and -73 meV and show the transition between the two cases of directional coupling.
Fig. 5. (a) and (b) transition between the two cases of coupling, below and above $\delta =-74$ meV. The lower cavity polariton dispersions are plotted as black solid lines with their linewidths (gray shaded areas). The green dashed lines correspond to a laser emission energy at 2.28 eV, the blue solid lines correspond to the intersections between the laser emission energy and the lower cavity polariton dispersions, the red dashed line indicates the expected angle of emission. (c) and (d) comparison of the experimental and the numerically expected emission angles (c) and divergences (d). The red and blue solid lines correspond to the numerical results of respectively the lasing emission angle and divergence. The black crosses correspond to the experimental results. The purple stars correspond to the case of the detuning $\delta =-75$ meV illustrated in (a) and the green stars to the detuning $\delta =-73$ meV in (b).
Figure 5(c) shows the numerical results for the expected emission angle (red line) and Fig. 5(d) the divergence (blue line) both along with the experimental results (black crosses). We first point out that the experimental divergence obtained in the one-lobe configuration is larger than the one obtained in the simulation (see the black cross on the right in Fig. 5(d)), which suggests that the quality of the filtering is reduced when occurring via the tail of the polariton dispersion curve. Nevertheless, the numerical simulation has the merit to qualitatively explain the experimental results presented in Fig. 3 for both the large negative detunings (Figs. 3(d) and 3(e)) and also for the low negative detuning in Fig. 3(f) for which the random lasing appears at energies lower than the polariton dispersion curve. More importantly, a good agreement arises between the experimental and numerical lasing angles and divergences for the detunings in the two-lobe configuration ($\delta$<-74 meV), the most interesting type of filtering presented in this article. Indeed, the two-lobe configuration permits to tune the emission angle with the detuning while presenting low divergences. Therefore, the good agreement between the experimental and numerical results validates the directional filtering of the lasing emission by the lower cavity polariton resonance in the two-lobe configuration.
3. Conclusion
In conclusion, we have shown that the directionality of the random lasing in a $CH_3NH_3PbBr_3$ polycrystalline thin layer can be controlled by the lower cavity polariton resonance of a 3$\lambda$/2 microcavity in the strong coupling regime. In particular, we highlight here that we have obtained a directional random lasing assisted by the cavity polaritons at angles as large as 22.4$^\circ$ with divergence angles of around 15$^\circ$ and that the angle of emission can be controlled in such a system by changing the detuning, that is to say the thickness of the microcavity. To decrease the emission divergence, one has to decrease the lower cavity polariton linewidth by improving the microcavity quality factor (Supplement 1, section 12). Contrary to a VCSEL operating in the weak coupling regime, the polariton could offer a unique configuration to tune the emission angle dynamically, by using the blueshift of the polaritonic dispersion due to the polariton-polariton or exciton-polariton interactions. This could be achieved by increasing the pumping power. A much better scheme is to implement a second laser, as an optical gate, which injects a local excitonic reservoir, thus induces a blueshift via interaction between the excitonic reservoir with the polaritons pumped by the first laser, as similarly reported in [51] for GaAs-based polaritons. Additionally, directing random laser emission through a photonic structure acting as an external knob is expected to open bright perspectives in the area of hybrid perovskites optoelectronics. Beyond vertical Fabry-Perot cavities, emission could be filtered by photonic crystals or dispersion-engineered metasurfaces, bringing additional degrees of freedom, together with a high compactness [52]. Used as external wavelength and direction filters rather than laser cavities, such nanophotonic structures can be technologically tolerant, and compatible with electrical injection.
Funding
Direction Générale de l’Armement; Agence Nationale de la Recherche (ANR-17-CE24-0020, ANR-18-CE24-0016).
Acknowledgments
We would like to thank Le Si Dang and Joël Leymarie for the fruitful discussions. This work is supported by Agence Nationale de la Recherche (ANR) within the projects POPEYE (ANR-17-CE24-0020) and EMIPERO (ANR-18-CE24-0016). The work of Paul Bouteyre is supported by the Direction Générale de l$^\prime$Armement (DGA). Jean-Sébastien Lauret and Hai Son Nguyen are junior members of the Institut Universitaire de France.
Disclosures
The authors declare no conflicts of interest.
See Supplement 1 for supporting content.
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