Lead halide perovskite vortex microlasers

Lead halide perovskite microlasers have been very promising for versatile optoelectronic applications. However, most perovskite microlasers are linearly polarized with uniform wavefront. The structured laser beams carrying orbital angular momentum have rarely been studied and the applications of perovskites in next-generation optical communications are thus hindered. Herein, we experimentally demonstrate the perovskite vortex microlasers with highly directional outputs and well−controlled topological charges. High quality gratings have been experimentally fabricated in perovskite film and the subsequent vertical cavity surface emitting lasers (VCSELs) with divergent angles of 3o are achieved. With the control of Archimedean spiral gratings, the wavefront of the perovskite VCSELs has been switched to be helical with topological charges of q = −4 to 4. This research is able to expand the potential applications of perovskite microlasers in hybrid integrated photonic networks, as well as optical computing.

The manuscript by Q. Song et al presents an approach with experimental demonstration to perovskite vortex microlasers by introducing a nanograting into a perovskite film. By fabricating different Archimedean spiral gratings, the perovskite vortex microlasers could emit optical vortices with different topological charges. The output vortex mode is related to the specific grating, but cannot be manipulated dynamically. The technique and its supporting experimental results reported in the manuscript are convincing and sophisticated, could be of interest to the optics community.
I do not think, however, that this work is significant and novel enough to meet the criterion of Nature C ommunications. This is mainly due to the fact that it only provides a trivial improvement (i. e. changing the structures from nanowires to gratings) compared to the reported perovskite lasers (e. g. Gu Z, et al. Advanced Optical Materials, 4(3), 2015;Zhang Q, et al. Nano Letters, 14(10), 2014;Ref [43], etc.), without any real conceptual or practical advantages. For journal like Nature C ommunications, it pursues profound works which could impact the general science research community with fundamental mechanism novelty or striking application potentials, and these aspects are hardly seen in this case. Therefore, I believe that this manuscript could be more appropriate for publication in a specialized journal in optical materials or photonics areas.
Besides, there are several typos in the References, the authors may need to check their manuscript more carefully.
Reviewer #2 (Remarks to the Author): NC OMMS-20-15607 The manuscript from W. Sun et al. describes a perovskite based microlaser scheme allowing the generation of highly directional vortex beams. The large refractive index of lead halide perovskites, combined with a large optical gain, enables the fabrication of microlasers where the feedback element (grating) is also the active material. Using five different microstructures the authors trigger lasing in radially polarized modes with orbital angular momentum (OAM) charges |q|=0,…,4. Due to the change of the handedness under mirror symmetry, the emission from the top and bottom of the structures presents opposite OAM. As the rotational symmetry of the structure is explicitly broken in spiral grating structures, the emission OAM is imposed at the fabrication step.
The main claim of the article, namely the generation of vortex beams with |q|>1 in a perovskitebased microstructure, is well documented by the experimental evidence presented in the manuscript. I particularly appreciated the rich supplementary materials detailing, among others, an improved etching technique. Although this nice work constitutes the first demonstration of perovskite-based microlasers emitting higher order vortex beams, potentially compatible with photonic integrated circuits, a similar scheme was implemented in ref. 10 using organic materials. In my opinion, it thus constitutes a relevant technological but not conceptual advance for the field.
However, a more quantitative analysis of the microlaser emission properties would extend the scope of the paper and its relevance for the community. This would provide a stronger argument to recommend publication. I append some remarks and questions for the authors below: 1) In all the measured far-field emission patterns in the main text there is no scale: although a calibration is presented in the supplementary materials (Fig. S11), a scale is necessary to compare the far-field and self-interference images in Fig. 2,4,5. At what power density where the images in Fig. 2 and 4 taken? The authors should also add colour gradient indicators allowing the reader to deduce the relative intensity of the different features in the image. For instance: which is the degree of radial polarization of the beam in Fig. 2 and 4? Are the intensities of all the spatial patterns normalized? In Fig. 2a, 5b and 5c I have the impression that the intensity is saturated.
2) The measured full-width at half maximum of the emission peak above threshold (1.5nm) does not appear to be limited by the resolution of the spectrometer, nor by the expected cavity mode linewidth (0.5 nm), nor by the Fourier-limited envelope of the 100fs pulsed excitation (5.3 nm @ 400nm). C an the authors explain what is limiting the spectral width of the microlaser emission peak?
3) In the interferograms presented in Fig. 5 the phase singularities (pitchfork bifurcations) scatter across all the far-field. I would expect them to concentrate about the optical axis of the two beams producing the interferogram. When comparing Fig. S9 and S10, it seems that the lens used to image the objective back-focal plane in Fig. S9 has been removed for the interferometric measurements. If this is the case, which is the reason for such choice? This might also explain the sparseness of the pitchfork bifurcations in the interferograms. C an the authors provide the phasemaps associated to the fringe patterns to help the reader visualize the optical vortices? 4) What is limiting the purity of the lasing mode radial polarization? What is the degree of linear polarization of the emission as a function of the angle of the polarizer axis? 5) (Possibly related to points 2 and 4) In all emission spectra above threshold [ Fig. 1e, Fig. 3b and Fig. S13a-S15a] the lasing peak presents a shoulder on the longer wavelengths side. Do the authors have an explanation for this feature? I wonder if it is possible that the bullseye grating does not present a perfect rotational symmetry, yielding two preferential polarization axes and lifting the degeneracy between the transverse modes. Then, the laser emission would present a double peaked spectrum and an elliptically polarized spatial pattern. If this is the case, the authors should remove the claim of single-mode operation. 6) In the conclusion, the authors indicate the possibility to extend this method to larger topological charges. Isn't it there any constraint related to the number of arms in the spiral grating and the smallest feature which etched? Up to which OAM value they expect their scheme to be realistically extended?
Minor remarks: 7) Is the emission peak energy constant as a function of the input power density? Does the laser keep to be single mode above the saturation threshold? 8) C omparing the spectra and IP curves in Fig.2-(e,f) or Fig.3-(b,c) I have the impression that the intensities reported in the IP plots correspond to either the peak intensity at the lasing mode wavelength (λ0~545 nm), or to the integrated intensity in a few nm bandwidth about λ0 . If this is the case, the IP curves should be corrected with the integrated intensity over all the spectrum. Anyway, the label of the y axis in the IP curve plots should be changed to "Integrated intensity". 9) Line 143: which thickness difference are the authors referring to? I believed the thickness of the perovskite layer was roughly constant among the different devices as stated in line 61. The work "Lead halide perovskite vortex microlasers" submitted to Nature C ommunication reports on the experimental demonstration of the perovskite vortex microlasers in the form of halide perovskite gratings. The experimental results are supported by numerical modeling. The work is well-organized, very timely, and important for the field of perovskite-based photonics. Thus, I believe it deserves to be published after addressing some technical comments: 1) Fig.3c: I am not sure that "power density" is the correct name for the value corresponding to pulse energy per cm^2, because "power" deals with temporal characteristics of the laser pulse, which is not the case here. Usually, it is called "fluence". 2) Fig.3b: the authors show spectra with single-mode lasing below a fluence of 40 uJ/cm2. However, it would be useful to show the spectra at fluences higher than 40 uJ/cm2. Is there any dramatic change to the multimode regime of lasing?
3) It is important to give the fluence values for Figs. 3d, 4, and 5 as well as give corresponding PL spectra. Indeed, there should be information on the ratio between spontaneous PL background and intensity of lasing mode. 4) The etching procedure of the perovskites might affect the PL quantum yield. Thus, it is important to show any comparison of PL properties before and after the etching. 5) I encourage to explicitly show the image with pumping beam distribution on the gratings to understand how many periods are involved in the process. 6) The authors wrote "the material refractive indices are measured by ellipsometer". However, I did not find the corresponding plot with these values. 7) The text quality should be improved. I found a number of typos like "to each other. and two emission". 8) In Ref.
[4] the authors also observed vortex beam generation from nanopatterned perovskite. C an they compare the current results with their previous work to show the advantages and differences more clearly?
First of all, we would like to thank the reviewer for the very careful review and the recognition of our observations. We have carefully read the reviewer's report and replied in details below. impact the general science research community with fundamental mechanism novelty or striking application potentials, and these aspects are hardly seen in this case. Therefore, I believe that this manuscript could be more appropriate for publication in a specialized journal in optical materials or photonics areas.

Comment
Our response: We thank the reviewer for the recognition of our results. We are sorry that we haven't clearly stated our main contributions in our previous version. We have to note here that this research is not a simple and trivial improvement from the previous researches. All of the previously reported perovskite lasers are linearly polarized and have Gaussian shaped laser beams. Such kind of microlasers can be on-chip integrated and of course have important applications. However, they are limited in high density mode division multiplexing. In contrast, the vortex beams with orbital angular momentum (OAM) are highly desirable in such applications. In principle, vortex beams with different topological charge q are orthogonal and can therefore be multiplexed. As a result, the vortex lasers have very promising potential to expand the capacity of optical communications and have been intensively studied.
Very recently, the on-chip integrated vortex microlasers have attracted considerable research attention. For such application, the solution processed lead halide perovskites are very promising. This material is easy to achieve and compatible with the current photonic chips.
Meanwhile, it has exceptional gain coefficient and higher refractive index than Si 3 N 4 . These 2 characteristics make lead halide perovskites to possibly tackle the long-standing problem of on-chip integrated coherent light sources. Therefore, the combination of vortex microlasers and lead halide perovskites are highly desirable and essential.
In this research, we experimentally demonstrate the perovskite vortex microlasers with highly directional outputs and well-controlled topological charges. We have fabricated high quality perovskite gratings in perovskite film with a precise control of the grating size and etching depth. Consequently, vertical cavity surface emitting lasers (VCSELs) with divergent angles of 3 o have been successfully achieved. By simply controlling the Archimedean spiral, the wavefront of the perovskite VCSELs can be switched to be helical with topological charges of q = ±1, ±2, ±3, and ±4, respectively. By further increasing the arm number, we have also In the revised manuscript, we have added the corresponding information in Para-1, Page-1, Para-1, Page-2, Para-2, Page-2, and Para-2, Page-10.
"However, most perovskite microlasers are linearly polarized with uniform wavefront. The structured laser beams carrying orbital angular momentum have rarely been studied and the applications of perovskites in next-generation optical communications are thus hindered." "Recently, vortex beams with different topological charge q are found to be mutually orthogonal and can therefore be multiplexed. [5-7] As a result, the generation of on-chip integrated OAM microlasers has been recognized as an effective approach to address the exponentially growing demand for worldwide network capacity. Our response: We thank the reviewer for the very careful review. Following the reviewer's suggestion, we have carefully checked the references and removed several typos.
We thank the reviewer for the very careful review and valuable suggestions. We particularly appreciate the comments on the linewidth, the polarization purity, and the shoulder in the laser spectra. These comments let us realize that the sample quality is not perfect. Based on the reviewer's suggestions, we have improved our nanofabrication technique and made the following main revisions.
1. New samples have been fabricated and measured. With these new samples, single-mode operation has been achieved and the laser linewidth is improved to ~ 0.4 nm. The purity of polarization is also subsequently improved. All the corresponding figures in main text and SI are updated.
2. The topological charge number has been increased from 4 to 32. This is a significant step for the on-chip integrated vortex microlaser.

Numerical calculation and theoretical analysis have also been added.
In the revised manuscript, all the comments have been addressed accordingly and the quality of our research is significantly improved. The details can be seen below.

Comment-1:
In all the measured far-field emission patterns in the main text there is no scale: although a calibration is presented in the supplementary materials (Fig. S11), a scale is necessary to compare the far-field and self-interference images in Fig. 2 3. The degree of polarization has also been added in the figure.

Comment-2:
The measured full-width at half maximum of the emission peak above threshold (1.5nm) does not appear to be limited by the resolution of the spectrometer, nor by the expected cavity mode linewidth (0.5 nm), nor by the Fourier-limited envelope of the 100fs pulsed excitation (5.3 nm @ 400nm). Can the authors explain what is limiting the spectral width of the microlaser emission peak?
Our response: We thank the reviewer for this valuable comment. In our VCSEL, the Q factor of VCSEL should be mainly determined by the imperfect rotational symmetry and the radiation loss. The Q factor related the radiation loss is calculated shown in Fig. 1b in the main text. The corresponding linewidth is about 0.43 nm. In this sense, it is straightforward to know that the main loss comes from the imperfect rotational symmetry. This is also consistent with another important comment raised by the reviewer that a shoulder appears at higher pumping fluence.

7
To check this assumption, we have refabricated the samples by compensating the fabrication deformation in GDS file. The corresponding laser spectra are shown in Fig. R4 below. The single mode laser is well kept from laser threshold to gain saturation. No shoulder can be observed even the pump fluence is above saturation point. As a result, we know that the rotational symmetry has been significantly improved. Simultaneously, the laser linewidth at the transparent threshold has also been measured. It is reduced to ~ 0.4 nm, consistent with the numerical simulation very well. The slight difference should come from the resolution of spectrometer (0.1 nm) and the influence of material gain. Then we can confirm that the main loss in our previous version comes from the imperfect rotational symmetry.
In the revised manuscript, we have replaced the Fig. 1(e)  Our response: We thank the reviewer for this valuable comment. We have checked the 8 optical setup and Fig. S9 and S10. There are some mistakes in the plots and they have been fixed in the revised manuscript.
The reviewer is absolutely right that the bifurcation of pitchfork comes from the optical setup.
It is caused by the wedged beam splitter in previous setup. The wedged beam splitter introduces additional phase shifts and induces the bifurcation. In the revised manuscript, we have fixed the optical setup and re-measured the self-interference patterns. As depicted in Fig.   R5 below, the bifurcation of pitchfork has been completely removed and the self-interference pattern is much better now. In additional to the self-interference patterns, the phase profiles of the emissions from Archimedean spirals have also been calculated. All the results are shown in Fig. R6 below.
With the increase of arm number of Archimedean spirals, it is clear to see that the number of phase singularity increases from 0 to 4, consistent with the self-interference pattern as well. In the revised manuscript, we have added the above experimental results and numerical calculations in Fig. 4 and Fig. 5 in the main text. The corresponding experimental descript has also been added in Para-1, Page-8 and Para-1, Page-10 in the main text.
"The corresponding numerical calculation shows a phase singularity at the center of the beam (see Fig. 4(d)). The phase shift along a circle surrounding the singularity is 2π. As a result, vortex microlasers with reversed topological charge q= ±1 are obtained in two directions." "These results, associated with the numerically calculated phase profiles in Fig. 5(d), confirm that the topological number of OAM increases from 2 to 4 with the increase of arm number." 9 Comment-4: What is limiting the purity of the lasing mode radial polarization? What is the degree of linear polarization of the emission as a function of the angle of the polarizer axis?
Our response: We thank the reviewer for this valuable comment. We agree with the reviewer that our previous results are somehow strange. The polarization degree is not perfect. When the radially polarized donut beams pass through a linear polarizer, they look more like modulated rings instead of two lobes. This effect is also caused by the imperfect rotational symmetry of the nanograting. By compensating the imperfection, the new linearly polarized lobes are measured and shown in Fig. R7. The intensity distributions behind the linear polarizer are now very close to the theoretical predictions. We have also checked the degree of the linear polarization as a function of the angle of polarizer axis. In the new samples, we find that the linear polarization almost parallel to the polarizer axis with a deviation less than 5 o . In the revised manuscript, we have replaced Fig. 2(b) with the new data. 1e, Fig. 3b and Fig. S13a-S15a] the lasing peak presents a shoulder on the longer wavelengths side. Do the authors have an explanation for this feature? I wonder if it is possible that the bullseye grating does not present a perfect rotational symmetry, yielding two preferential polarization axes and lifting the degeneracy between the transverse modes. Then, the laser emission would present a double peaked spectrum and an elliptically polarized spatial pattern.
If this is the case, the authors should remove the claim of single-mode operation.
Our response: We really appreciate the reviewer's very careful review and valuable suggestion. Following the reviewer's suggestion, we have checked our sample carefully. We indeed found the imperfect rotational symmetry in the samples that were caused by the 10 nanofabrication deviations. Then we compensated the deviations in GDS files and re-fabricated all the samples. The results are shown in Figure R8-R12 below. After removing the imperfection, all the samples show very nice single mode operation from laser threshold to gain saturation. No shoulders can be observed even at the highest pump fluence. The reviewer is absolutely right that the imperfect rotational symmetry also relates to comment 2 and comment 4. By removing the imperfection, the polarization two lobes become very clear and the linewidth is reduced to ~ 0.4 nm.
In the revised manuscript, we have replaced all the laser spectra and the LI curves in the main text and in the supplementary information. According to our current experimental results, we keep the claim of single mode operation in our paper.

12
In the revised manuscript, we have replaced all the emission spectra in the main text and in the supplementary information. The corresponding single mode operation information has been emphasized in Para-1, Page-5 and Para-1, Page-7 in the main text.
"The single mode operation is well preserved from the laser threshold to the gain saturation." "Note that the Archimedean spiral grating also supports the single mode operation. The ration between the laser peak and the photoluminescence is more than 10 dB at the largest pump fluence (see Fig. S21 in the supplementary information)." Archimedean spirals with small arm numbers, the perovskite microlasers also keep the single mode operation (column-II) and the donut beam profiles (column-IV). The beams also change from donut to two lobes after passing through a linear polarizer (see Figure R13). The self-interference patterns of the laser beams have also been studied and shown in Figure R14,

Comment
where 8, 16, and 32 pairs of inverted forks can be clearly seen. Therefore, we can confirm that our scheme can at least support the vortex beam with topological charge of 32. The experimental results also show the limitations of our scheme. The column-IV of Figure   R12 shows the back focal plane beam profiles of the perovskite lasers. With the increase of arm number, we can see that the divergent angle keeps increasing. For the case of l = 32, the divergent angle is almost 25 degree, which is too large for a lot of practical applications. This will be one limitation of our scheme. Another limitation comes from the nanofabrication. As depicted in column-I of Figure R12, the Archimedean spiral remains perfect with arm number of l = 8. However, for the case of l = 16 and 32, there are obvious defect are formed at the center. This will also affect the device performances such as laser threshold and beam uniformity etc. Such defect will be more dramatic at larger arm numbers. Based on these results, we would like to set the limitation below topological charge of q = 32. We should note here that the topological charge of q = 32 is already a record for the on-chip integrated vortex microlasers and should be useful for many practical applications.  Does the laser keep to be single mode above the saturation threshold?
Our response: We thank the reviewer for these two valuable comments. In our previous samples, the imperfect rotational symmetry increased the laser linewidths and introduced the shoulders. In our new samples, by removing the imperfection in rotational symmetry, as shown in all the above figures, the single mode operation is maintained even at the saturation threshold and higher pump fluence. The emission peak energy is constant as a function of the input power density. Taking the sample with q=0 as an example, we fixed the pump fluence and measured the output intensity as a function of laser shots. As shown in Figure R15, the laser intensity is only slightly reduced after they sample was pumped with 3.6×10 6 laser shots, clearly demonstrating the stability of our microlasers. The corresponding discussion has been added in Para-1, Page-6 in the main text and the related results are shown in Section 6 in Supplementary Information.
"The perovskite VCSELs also have very nice stability. No obvious reduction has been observed after 3.6×10 6 continuous pump with a fluence of 37 µJ/cm 2 (see Fig. S20 in the supplementary information)."

Comment-8:
Comparing the spectra and IP curves in Fig.2-(e,f) or Fig.3-(b,c) I have the impression that the intensities reported in the IP plots correspond to either the peak intensity at the lasing mode wavelength (λ0~545 nm), or to the integrated intensity in a few nm bandwidth about λ0 . If this is the case, the IP curves should be corrected with the integrated intensity over all the spectrum. Anyway, the label of the y axis in the IP curve plots should be changed to "Integrated intensity".
Our response: We thank the reviewer for the careful review. The reviewer is correct that the IP curves are the integrated intensity of the spectra. The difference in value is caused by the integration time during the experiment. Following the reviewer's suggestion, we have replaced the label of y axis in the IP curve to "Integrated intensity (a.u.)".

Comment-9:
Line 143: which thickness difference are the authors referring to? I believed the thickness of the perovskite layer was roughly constant among the different devices as stated in line 61.
Our response: We thank the reviewer for the very careful review. The reviewer is absolutely right that the thickness of perovskite layer was controlled at 300 nm during the experiment.
However, the real experiments cannot be this accurate. There is always around ±10 nm variation in thickness. As a result, the lattice needs to change slightly to fit the same lasing Our response: We thank the reviewer for the very careful review. We are sorry that the 20% power in this sentence is very confusing. This is a meter number of the system and has been replaced to the exact power in Methods of the revised manuscript. "The 13 nm ITO coated substrate was hydrophilic treated with oxygen in a plasma cleaner (Diener Electronic, Femto

Reply to Reviewer #3：
We thank the reviewer for the careful review and valuable suggestions. Based on the reviewer's comments, we have carefully revised our manuscript and all the comments have been addressed accordingly. The details of revision can be seen below.
Comment-1: Fig.3c: I am not sure that "power density" is the correct name for the value corresponding to pulse energy per cm^2, because "power" deals with temporal characteristics of the laser pulse, which is not the case here. Usually, it is called "fluence".
Our response: We thank the reviewer for the very careful review. The reviewer is correct that the power density is not accurate. The word "power" is a typo of "pump" and has been changed to the conventional expression of "Pump fluence (µJ/cm2)" in Fig. 1, Fig. 3 and the supplementary materials. Fig.3b: the authors show spectra with single-mode lasing below a fluence of 40 µJ/cm 2 . However, it would be useful to show the spectra at fluences higher than 40 µJ/cm2. Is there any dramatic change to the multimode regime of lasing?

Comment-2:
Our response: We appreciate the valuable comment of the reviewer. We agree with the reviewer that lots of the single mode microlasers change to multimode laser at higher pumping fluence in previous experiments. We have carefully checked our samples. We find that the shoulder at high pump fluence comes from the symmetry defect of the sample structure. Based on the reviewer's comment, we have improved our nanofabrication process and solved this problem. With these new samples, the single mode laser operation is well maintained from the laser threshold to gain saturation (see Fig. R17 below). In the revised manuscript, we have replaced the experimental results of perovskite VCSELs and the corresponding discussion in Para-1, Page-5 and Para-1, Page-7 in the main text.
"The single mode operation is well preserved from the laser threshold to the gain saturation." "Note that the Archimedean spiral grating also supports the single mode operation. The ration between the laser peak and the photoluminescence is more than 10 dB at the largest pump fluence (see Fig. S21 in the supplementary information)."

Comment-3:
It is important to give the fluence values for Figs. 3d, 4, and 5 as well as give corresponding PL spectra. Indeed, there should be information on the ratio between spontaneous PL background and intensity of lasing mode.
Our response: We thank the reviewer for this very careful review and valuable suggestions.
Following the reviewer's suggestion, we have added the pump fluence in Figs. 3d, 4, and 5.
We have also added the ratio between PL and intensity of lasing mode in the main text. As shown in Fig. R18, the intensity difference is more than 10 dB. In the revised manuscript, we have also added the ratio between the lasing mode and photoluminescence in Para-1, Page-7 of the main text. "Note that the Archimedean spiral grating also supports the single mode operation. The ration between the laser peak and the photoluminescence is more than 10 dB at the largest pump fluence (see Fig. S21 in the supplementary information)." The corresponding experimental results have been added in Section-6 of the supplementary information.

Comment-4:
The etching procedure of the perovskites might affect the PL quantum yield.
Thus, it is important to show any comparison of PL properties before and after the etching.
plays an essential role in the manuscript, the comparison of photoluminescence before and after the etching is very important and necessary. Following the reviewer's suggestion, we have compared the photoluminescence spectra from a grating and a film with the same pump fluence. The results are summarized in Fig. R19. It is easy to see that the central peak positions of two spectra are very close. The intensity of photoluminescence from the grating is about 1477. Considering the air region in the grating (~ 0.225), the scaled intensity should be around 1477/0.775=1905, which is close to the measured value from the film (1935). The slight difference should be induced by the intensity variation of the pump laser. Therefore, we can confirm that the etching process won't degrade the photoluminescence of lead halide perovskites. This is an important basis for this research. Our response: We thank the reviewer for this valuable suggestion. Following the reviewer's suggestion, we have studied the pump profile on the grating. As depicted in Fig. R20, the 21 beam size is about 10 µm, which is smaller than the grating size and locates at the center of the grating. Considering the lattice size of the grating, the pump beam roughly covers 36 periods of the grating.

Figure R20:
The pump profile on the grating. The beam size is about 10 µm, which is smaller than the grating size.
In the revised manuscript, the above information has added the pump beam distribution

Comment-7:
The text quality should be improved. I found a number of typos like "to each other. and two emission". By further increasing the arm number, the topological charge can even be increased to 32.
In the revised manuscript, we have added the corresponding discussion in Para-2, Page-10 of the main text. "It is important to note that the difference between Archimedean VCSELs essential for high density mode division multiplexing." In the revised manuscript, the authors present new data and have fabricated new samples to support their claims. I believe that the overall quality of the experimental results is significantly improved. Furthermore, the authors have characterized the robustness and stability of the device along with the emission polarization properties. Although it is still true that a similar scheme was implemented in ref. 10 using organic materials, in the revised manuscript the authors explicitly demonstrate the scalability of their approach by fabricating three additional devices presenting a single-mode emission carrying an |OAM|=(8,16,32). This paves the way to high density mode division multiplexing with perovskite-based microlasers. Given the overall quality of the experimental results in the revised manuscript, the detailed analysis of the material and microlaser properties and the experimental demonstration of the scalability of the platform, I believe the manuscript has become rich enough to interest the broad readership of Nature C ommunications. I support its publication.
Below I append some questions and minor remarks for the authors: C ould the authors clarify how do they extract these phase maps? In the case the phase maps were directly extracted from the interferograms via a Fourier filtering technique, i.e. they are just a refinement of the experimental data, I would suggest to avoid using "numerically calculated" as it might be misleading. In any case, a sentence explaining how the phase maps have been obtained is necessary.
2) Both In the response to reviewer 1 and 2 (comment 6) the authors write: "The topological charge of 32 is the current record value for on-chip integrated vortex microlasers". Although I agree that the present demonstration of lasing with |OAM|=1,.. Sincerely, Nicola C arlon Zambon