# Peer-Review Record

# Turbulent Intermittency in a Random Fiber Laser

*Reviewer 1:*Anonymous

*Reviewer 2:*Anonymous

*Reviewer 3:*Anonymous

**Round 1**

*Reviewer 1 Report*

The work is interessant and the paper is well written. I agree for publication in the present form.

*Author Response*

Referee 1: The work is interesting and the paper is well written. I agree for publication in the present form.

Answer: We thank the referee for the very positive evaluation, including the general remarks on manuscript structure, English quality, validity of method, results and conclusions.

*Reviewer 2 Report*

Report for article atoms-447265

Title: Turbulent Intermittency in a Random Fiber Laser

Authors: Antônio M. S. Macêdo *, Ivan R. Roa González, Ernesto P. Raposo,

Leonardo de S. Menezes, Anderson S. L. Gomes

The manuscript represents continuation of the previous research [9,…] of the authors. Here, the authors experimentally observe and further investigate some phenomena in RFL. I think that the manuscript will be interesting for potential readers. I would like to recommend publications of this paper in Atoms. But it is necessary to make some corrections and improvement of the paper.

Some requests:

-I have the most complaints about the presentation of the results.

-The Abstract is poorly written. It should be expanded with sentences about

Context:

Aims: …

Methods: …

Results: “We obtain an estimate of …”

Conclusions: “These results can help to model ...”

-Section Introduction should be numbered as first i.e. 0. Introduction =>1. Introduction (also 1. Results= 2. Results, etc.)

-Introduction should be extended because it now looks like the Abstract.

-After the first paragraph in the Introduction, the authors should give the aim of this work, as e.g. 'The aim of this work is to....' or similar, i.e. what is the reason to write this paper?

Fig 3: The tick labels are barely visible. Especially in Fig3 b). Please enlarge.

Respectfully

*Author Response*

Referee 2: The manuscript represents continuation of the previous research [9,…] of the authors. Here, the authors experimentally observe and further investigate some phenomena in RFL.

Answer: That is correct. We thank the referee for having carefully analyzed our work.

Referee 2: I think that the manuscript will be interesting for potential readers. I would like to recommend publications of this paper in Atoms. But it is necessary to make some corrections and improvement of the paper.

Answer: We are happy that the referee considers our work potentially interesting for readers and to read he/she supports the publication of the manuscript after we perform some corrections. In what follows, we comment on each point raised by him/her.

Referee 2: The Abstract is poorly written. It should be expanded with sentences about: Context, Aims, Methods, Results: “We obtain an estimate of …”, Conclusions: “These results can help to model ...”

Answer: We accept this criticism and in the revised manuscript we have entirely rewritten the abstract in order to accommodate the referee’s observations. In particular, we have made an effort to improve the abstract considerably so to make it more accessible to a broad readership.

Referee 2: Section Introduction should be numbered as first i.e. 0. Introduction =>1. Introduction (also 1. Results= 2. Results, etc.)

Answer: We have renumbered the manuscript’s sections accordingly.

Referee 2: Introduction should be extended because it now looks like the Abstract.

Answer: We have extended the introduction in order to accommodate the referee’s observation, with a wider overview of RFL and their applications and new research trends. We have also made clearer in the introduction the novelties brought about in this contribution, mainly the study of the evolution of the intermittency effect with the increasing of the time separation between output spectra and the interpretation of the number of relevant scales of the photonic hierarchy in terms of a discrete hierarchical model.

Referee 2: After the first paragraph in the Introduction, the authors should give the aim of this work, as e.g. ‘The aim of this work is to....’ or similar, i.e. what is the reason to write this paper?

Answer: We thank the referee for this suggestion. In the revised manuscript, we have made clearer in the introduction what is the aim of this work and the new results it brings about. We subdivided this information into two parts. In the last sentence of the first paragraph of the introduction, we now inform that “In this work, we show that intermittency gradually disappears as larger time separations between spectra are considered, yielding in this case a non-turbulent state with Gaussian distribution of intensity increments for large time scales.” Right next, in the second paragraph of the introduction, we now turn to the theoretical novelty of this manuscript: “…by means of a discrete version of the hierarchical model we provide a general direct interpretation for the number of relevant scales in the photonic hierarchy as the order of the transitions induced by the non-linearities in the medium.”

Referee 2: Fig 3: The tick labels are barely visible. Especially in Fig3 b). Please enlarge.

Answer: We have produced a new figure 3 for making the tick labels more visible.

We hope with this we have satisfactorily commented on referee’s 2 observations. For sure it contributed for improving the quality of our work.

*Reviewer 3 Report*

The manuscript “Turbulent Intermittency in a Random Fiber Laser” by Antônio M.S. Macêdo et al. shows experimental observation of turbulent intermittency in a disordered erbium-doped RFL. The experimental findings are supported by a hierarchical stochastic model.

This topic is interesting for publication. However, I am not sure if this topic fits the scope of Atoms. Maybe another MDPI journal would be better suited, e.g. Photonics.

The manuscript has a large overlap with other papers from the authors. Eg. Ref. 9, 10 and 12. The introduction should also give that information and clearly point out why turbulent intermittency is the next important step. And what is the novelty compared to Ref. 9, 10 and 12. The introduction should also give a wider overview of RFL and their applications and new research trends.

Section 1.1, 1.2. and 1.2.1 are very similar to the above mentioned papers (figures and formulas). In that papers the description is more compact than in this manuscript. Why is it here so excessive?

The comparison of experimental results with simulations shows very good agreement. In the Discussion and Conclusions is missing which new implications for further studies are given by that. And open question raised in the Introduction (why is that important, novel and interesting) should be answered and an outlook for further research should be given.

Minor comments:

- Affiliations are not filled out correctly. Did some authors contribute equally to this work?

- It should be 1. Introduction, not 0.

- Figure 1 has very large axis labels etc and layout looks differently to all other plots.

- Author Contributions is not filled out correctly.

*Author Response*

Referee 3: Comments and suggestion for the authors: The manuscript “Turbulent Intermittency in a Random Fiber Laser” by Antônio M.S. Macêdo *et al.* shows experimental observation of turbulent intermittency in a disordered erbium-doped RFL. The experimental findings are supported by a hierarchical stochastic model. This topic is interesting for publication.

Answer: We thank the referee for careful analysis of our manuscript and for recognizing that our theoretical model containing hierarchical stochastic ingredients explains well the experimental data and is interesting for publication.

Referee 3: However, I am not sure if this topic fits the scope of Atoms. Maybe another MDPI journal would be better suited, e.g. Photonics.

Answer: Atoms created a special issue (“Cooperative Effects in Light Scattering by Atomic Clouds”) dedicated to the Coscali V Conference – Workshop on Collective Scattering of Light and the authors of contributions accepted in the conference (our case) were invited to submit manuscripts to the special issue. For details, we kindly ask the referee to access https://romain.df.ufscar.br/coscali2018/journal.html

Referee 3: The manuscript has a large overlap with other papers from the authors. Eg. Ref. 9, 10 and 12. The introduction should also give that information and clearly point out why turbulent intermittency is the next important step. And what is the novelty compared to Ref. 9, 10 and 12. The introduction should also give a wider overview of RFL and their applications and new research trends.

Answer: We thank the referee for this observation. We have now considerably rewritten the abstract and introduction in order to make clearer to the interested reader the principal motivations of our work and the main (both experimental and theoretical) novelties regarding our previous contributions. For instance, in the last sentence of the first paragraph of the introduction, we now inform that “In this work, we show that intermittency gradually disappears as larger time separations between spectra are considered, yielding in this case a non-turbulent state with Gaussian distribution of intensity increments for large time scales.” Indeed, in the present work we analyze experimentally and theoretically not only the intensity increments between nearest neighbor output spectra, i.e., spectra separated by one time unit t = 1 (corresponding to the integration time to acquire one spectrum), a study already taken into account in the former ref. 9 (present ref. 5 in the revised manuscript). Actually, in order to analyze the evolution of the photonic intermittency effect from the turbulent state, with heavy-tailed non-Gaussian distribution of intensity increments for small t, to a non-turbulent regime, with Gaussian distribution of increments for large t, we had also to provide two new analysis concerning the time separations t = 2 and t = 5000, which are not included in any of our previous works. Only by doing this, it was possible to see the fading of the intermittency effect with the increasing of t. Moreover, concerning the theoretical advance put forward in the present contribution, in the second paragraph of the introduction we write: “…by means of a discrete version of the hierarchical model we provide a general direct interpretation for the number of relevant scales in the photonic hierarchy as the order of the transitions induced by the non-linearities in the medium.” This important piece of information was lacking in the previous articles and corresponds to a relevant advance to better understand the emergence of multiscale photonic turbulence in RFL systems.

Referee 3: Section 1.1, 1.2. and 1.2.1 are very similar to the above mentioned papers (figures and formulas). In that papers the description is more compact than in this manuscript. Why is it here so excessive?

Answer: The description we show in the present manuscript is in fact more extended than in our previous publications. This has two main reasons: first, to safely reason our argumentation on the existence of intermittency this was necessary; second, in the other works manuscript space was needed to discuss other aspects related to the central points we were studying in each of them. Nevertheless, we believe that the new amendments mainly in the introduction (see above) now contribute to justify the necessity of a more comprehensive review of some previous results in order to facilitate the understanding of the improvements and new results brought about in the present contribution.

Referee 3: The comparison of experimental results with simulations shows very good agreement. In the Discussion and Conclusions is missing which new implications for further studies are given by that. And open question raised in the Introduction (why is that important, novel and interesting) should be answered and an outlook for further research should be given.

Answer: We thank the referee for the suggestions. In the section Discussion and Conclusions of the revised manuscript we have addressed the questions raised in the introduction and perspectives for further research have been presented.

Referee 3: Affiliations are not filled out correctly. Did some authors contribute equally to this work?

Answer: This has been fixed in the revised version of the manuscript.

Referee 3: It should be 1. Introduction, not 0.

Answer: We have renumbered the manuscript’s sections accordingly.

Referee 3: Figure 1 has very large axis labels etc and layout looks differently to all other plots.

Answer: This has been fixed in the revised version of the manuscript.

Referee 3: Author Contributions is not filled out correctly.

Answer: This has been fixed in the revised version of the manuscript.

We hope we have satisfactorily addressed the referee’s comments, which we think helped improving the quality of our manuscript.

**Round 2**

*Reviewer 3 Report*

The authors improved the manuscript according the reviewers suggestions.

I recommend the manuscript for publication in Atoms.