Review Reports - Generation and Manipulation of Airy Breathing Solitons in an Inhomogeneous Medium with Periodic Potential

Round 1

Reviewer 1 Report

Comments for author File: Comments.pdf

Author Response

List of Responses

Dear Editors/Reviewers:

Thank you for your letter and for the reviewers’ comments concerning our manuscript entitled “Generation and manipulation of Airy breathing solitons in an inhomogeneous medium with periodic potential”. Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made correction which we hope meet with approval. Revised portion are marked in red in the paper. The main corrections in the paper and the responds to the reviewer’s comments are as flowing:

Reviewer #1:

Some related references about the Airy beams。

Response: References have been added as follows:

Peng X, Peng Y L, Li D D, et al. Propagation properties of spatiotemporal chirped Airy Gaussian vortex wave packets in a quadratic index medium[J]. Optics Express, 2017, 25(12),13527-13538.
Chen C D, Peng X, Chen B, et al. Propagation of an Airy–Gaussian vortex beam in linear and nonlinear media[J]. Journal of Optics, 2016, 18: 055505.
Deng F, Deng D M. Nonparaxial propagation of an Airy-Gaussian beam in uniaxial crystal orthogonal to the optical axis[J]. Optics Communications, 2016, 380: 280-286.
Zhu W, Guan J, Deng F, et al. The propagation properties of the first-order and the second-order Airy vortex beams through strongly nonlocal nonlinear medium[J]. Opt. Commun.,2016, 380: 434-441.
Zhang J B, Zhou K Z, Liang J H, et al. Nonparaxial propagation of the chirped Airy vortex beams in uniaxial crystal orthogonal to the optical axis[J]. Optics Express 2018, 26(2): 1290-304.
Peng Y L, Peng X, Chen B, et al. Interaction of Airy–Gaussian beams in Kerr media[J]. Optics Communications, 2016, 359:116-122.

In equations (5)-(7), what is the relation between u(x,y) and u?

Response: This is my own negligence. They should be all u(x,y). I carefully checked all the formulas and made corresponding modifications. For example, formulas 5,6 and 7 have been modified.

In the line 106 of page 4 after Equation (15), “From Equation (16),” should be checked carefully.

Response: We have carefully checked all the contents and made corresponding modifications.

In the line 114 of page 4, “that the period decreases with P₀ and ω₀.” where “P₀ and ω₀ ” should give the physics.

Response: We carefully checked lines 114 and we think that the modulation intensity is P and the modulation frequency is ω. P and ω have been defined previously. Corresponding modifications have been made in the article.

In the line 391 of page 12 as references 25, “Opt exp,” should be “Opt Express”.

Response: Corresponding modifications have been made in the article.

We tried our best to improve the manuscript and made some changes in the manuscript. These changes will not influence the content and framework of the paper. And here we did not list the changes but marked in red in revised paper.

We appreciate for Editors/Reviewers warm work earnestly, and hope that the correction will meet with approval.

Once again, thank you very much for your comments and suggestions.

Author Response File: Author Response.docx

Reviewer 2 Report

Manuscript ID: photonics-2170152

Review of the manuscript “Generation and manipulation of Airy breathing solitons in an inhomogeneous medium with periodic potential” by C. Gao et al. submitted for consideration to Photonics.

In this manuscript, the authors have studied the propagation of Airy beams inside an inhomogeneous medium with the periodic potential. Making use of the underlying equation the breathing solitons are numerically described when two kind of incident beams are launched into the medium; i.e. a single Airy beam and two Airy beams with opposite spatial positions. The simulation results have shown the influence of the characteristic parameters (like; modulation intensity, modulation frequency, chirp and position) on how the incident beam propagates inside the medium.

I believe the manuscript is original, has a merit for publication and is of interested the readers in the field of nonlinear optics. However, I will bring out some points to be clarified as part of the changes for the manuscript.

1- The authors must discuss which kind of medium has a periodic potential like Eq. 3. Give an example.

2- The parameter \eta presented in Eq. 3 was not defined.

3- Why did the authors assume that the two parts of Eq. 5 are equal to zero?

4- I believe there are typo errors in Eq. 5 and Eq. 6. Please check them.

5- In Eq. 8, the arguments of the function should be corrected. By the way, the parameter “a” must be defined.

6- What is the quantity “T” in the argument of the function introduced in Eq. 19?

7- The sentence “The numerical simulation results of the effect of the modulation intensity P on the breathing period of Airy space solitons in an inhomogeneous medium with periodic potential are basically consistent with the theoretical analysis of Equation (11).” are mentioned several times with a small change. Please rephrase them.

For example, this sentence is mentioned twice in lines 194-198.

8- Please rephrase the sentence mentioned in the lines 56-58.

9- Lines 241-245: For clarity, I recommend the authors to exhibit the statement on the corresponding figure (by using arrow).

Finally, there are many vague sentences and English language errors in the manuscript. It must be written in clear English. Before you resubmit your manuscript here or elsewhere, I advise a very careful and thorough edit to ensure the text is easily understood by readers.

Author Response

List of Responses

Dear Editors/Reviewers:

Reviewer #2:

1.The authors must discuss which kind of medium has a periodic potential like Eq. 3. Give an example.

Response: We introduce the medium generated by the periodic potential in lines 86,87. Revised portion as follows：

Due to the periodic structure of the lattice, the periodic potential model is widely used in the study of various crystal materials and devices.

2.The parameter \eta presented in Eq. 3 was not defined.

Response: We define η in line 88.

Revised portion as follows：η is the anisotropy factor.

3.Why did the authors assume that the two parts of Eq. 5 are equal to zero?

Response: This is a method of solving Gross-Pitaevskii equation by separating variables. Separation of variables method is introduced in reference 19. It is based on the assumption that the two parts of the equation are equal to 0, but the periodic potential we use is different. 19. Liu C F, Zhu A J. Matter-wave exact periodic solutions in optical lattices with periodic potential[J]. AIP Conference Proceedings, 2013, 1558:1947-1950.

4.I believe there are typo errors in Eq. 5 and Eq. 6. Please check them.

Response: We carefully checked Eq. 5 and Eq. 6 and made corresponding modifications.

5.In Eq. 8, the arguments of the function should be corrected. By the way, the parameter “a” must be defined.

Response: We carefully checked Eq. 8 and made corresponding modifications.

Revised portion as follows: Where a is an arbitrary constant from −1 to 1.

6.What is the quantity “T” in the argument of the function introduced in Eq. 19?

Response: We carefully checked Eq. 19 and we think the independent variable should be the spatial transverse coordinate x. Corresponding modifications have been made in the article.

7.The sentence “The numerical simulation results of the effect of the modulation intensity P on the breathing period of Airy space solitons in an inhomogeneous medium with periodic potential are basically consistent with the theoretical analysis of Equation (11).” are mentioned several times with a small change. Please rephrase them.

Response: Corresponding modifications have been made in the article.

8.Please rephrase the sentence mentioned in the lines 56-58.

Response: Corresponding modifications have been made in the article.

9.Lines 241-245: For clarity, I recommend the authors to exhibit the statement on the corresponding figure (by using arrow).

Response: Corresponding modifications have been made in the article.

We appreciate for Editors/Reviewers warm work earnestly, and hope that the correction will meet with approval.

Once again, thank you very much for your comments and suggestions.

Author Response File: Author Response.docx

Reviewer 3 Report

The manuscript by Gao et al. reports the propagation of Airy beams and the interaction of two Airy beams in an inhomogeneous medium with periodic potential, changing different parameters.

I found the manuscript reading heavy, with a lot of repetition of the same concept. In addition, the abstract needs to be improved and synthesized, and the grammatical errors in the entire manuscript need to be corrected.

Moreover, the manuscript lacks an explanation of the simulation method implemented. Please add a paragraph.

Line 34: diffractive should be replaced with non-diffractive.

Line 80-83: This seems a general statement. So please insert references to support it.

In section 2, why are you reporting a 2D+1 theoretical model? If you then study the 1+1D case? This is misleading to the reader, so it would be better to put it in an appendix and perhaps add a paragraph in the conclusion section about the future implications in 2D+1.

line 106: 16 must be replaced with 15

line 112: What does "breathing law is similar" means? This must be improved. Doing further simulations, can you show a graph of \lambda vs. \omega and \lambda vs. P showing the scaling relations \lambda ~ 1/ \omega^2 and \lambda ~ 1/P^2?

Line 166: Please avoid terms such as "photorespiration"

Line 210: Center of Mass instead of gravity.

Line 235: There is an error in explaining how the Airy beam deflects.

Figure 4: The caption is incorrect.

Author Response

List of Responses

Dear Editors/Reviewers:

Reviewer #3:

1.diffractive should be replaced with non-diffractive.

Response: Corresponding modifications have been made in the article.

2.Line 80-83: This seems a general statement. So please insert references to support it.

Response: References have been added.

3.In section 2, why are you reporting a 2D+1 theoretical model? If you then study the 1+1D case? This is misleading to the reader, so it would be better to put it in an appendix and perhaps add a paragraph in the conclusion section about the future implications in 2D+1.

Response: The electric field distribution is equivalent in the x and y directions from Eqs.(1)-(4), thus the propagation properties of Airy beams is similarity in the x and y directions. To reduce the computational complexity, we only consider (1+1)-D GPE in numerical simulation.

This paragraph has been added to the article.

4.line 106: 16 must be replaced with 15

Response: Corresponding modifications have been made in the article.

5.line 112: What does "breathing law is similar" means? This must be improved. Doing further simulations, can you show a graph of \lambda vs. \omega and \lambda vs. P showing the scaling relations \lambda ~ 1/ \omega^2 and \lambda ~ 1/P^2?

Response: In this paper, although the exact solution of Airy beam in the periodic potential Gross-Pitaevskii is not solved, the soliton solution of the equation shows the propagation law of the beam. When different beams are transmitted in the periodic potential, their basic laws are basically the same. The soliton solutions solved in this paper are basically consistent with the numerical simulation results.

In addition, the graphs λ vs. ω and λ vs. P are statistical graphs for graphs 1 and 2. If so, we also need to draw statistical figures for Figure 3 and Figure 4. This article has 12 pages and 7 pictures, it is better not to increase the length of the article.

5.Please avoid terms such as "photorespiration"

Response: Corresponding modifications have been made in the article.

7.Line 210: Center of Mass instead of gravity.

Response: Corresponding modifications have been made in the article.

8.Line 235: There is an error in explaining how the Airy beam deflects.

Response: Corresponding modifications have been made in the article.

9.Figure 4: The caption is incorrect.

Response: Corresponding modifications have been made in the article.

Revised portion as follows：Figure 4. When a₀=0.3 P=3 and ω=0.03，the spatial propagation characteristics of Airy beams with four different initial transverse position: (a) x₀=-4, (b) x₀=-2, (c) x₀=4 and (d) x₀=2；(e) the center position evolution of Airy beams; (f) the maximum intensity evolution of the Airy beams: x₀=-4 (black line), x₀=-2 (red line), x₀=4 (green line) and x₀=2 (blue line).

We appreciate for Editors/Reviewers warm work earnestly, and hope that the correction will meet with approval.

Once again, thank you very much for your comments and suggestions.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The revised version of this manuscript can be accepted for publication.

Author Response

Dear Reviewer:

Thank you for your comments concerning our manuscript entitled “Generation and manipulation of Airy breathing solitons in an inhomogeneous medium with periodic potential”. Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches.

Reviewer #1:

1.The revised version of this manuscript can be accepted for publication.

Response: We appreciate for reviewer warm work earnestly, and hope that my paper can be published in this journal.

Once again, thank you very much for your comments and suggestions.

Reviewer 2 Report

I would like to thank authors for their responses. All my comments have been addressed properly, therefore, I recommend acceptance.

Author Response

Dear Reviewer:

Reviewer #1:

I would like to thank authors for their responses. All my comments have been addressed properly, therefore, I recommend acceptance.

Response: We appreciate for reviewer warm work earnestly, and hope that my paper can be published in this journal.

Once again, thank you very much for your comments and suggestions.

Reviewer 3 Report

The authors' answers are unsatisfactory and lack scientifically based clarifications. In addition, the paper does not present anything new compared to previous work. The changes made concern only typos and language errors. In my opinion, the article does not reach the levels of innovation and scientific soundness to approve its publication.

Author Response

List of Responses

Please see the attachment.

Author Response File: Author Response.docx