From Saddle-Shaped to Dual-Peak Radiation: Synergistic Control of Laser Parameters for Collimation Leap and Quadratic Power Scaling in Nonlinear Thomson Scattering

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript titled "From Saddle-Shaped to Dual-Peak Radiation: Synergistic Control of Laser Parameters for Collimation Leap and Quadratic Power Scaling in Nonlinear Thomson Scattering" presents an interesting numerical study on the coupling between laser intensity and beam waist radius in nonlinear Thomson scattering (NTS). However, significant issues in presentation and clarity severely hinder the manuscript’s suitability for publication in its current form.

Positive Aspects:

• The manuscript investigates an important nonlinear regime in NTS that could have implications for compact radiation sources.
• The authors provide a range of parametric studies to explore the effects of intensity and beam waist coupling.

Critical Issues:

Despite the merits of the topic, several major issues must be addressed:

1. Figure 1:
• The figure is referenced but has no proper caption explaining the content or context.
• The resolution is extremely poor, making it difficult to interpret. A high-quality, vector-based rendering with labels is necessary.
2. Formatting Anomaly (Line 68 onwards):
• The main body text from line 68 is inexplicably bold. This formatting inconsistency is distracting and needs correction.
3. Figure 2:
• This figure is unreadable and does not meet academic standards.
• Axis labels are too small, units are missing, and the caption lacks any substantive explanation.
• The complexity of the information requires it to be split into at least two clearer sub-figures, each with descriptive captions.
4. Figures 3 and 4:
• These figures also fall short of scientific visualization norms.
• Fonts are inconsistent, axis ticks are too small, and again, there is a lack of clear explanation of what is shown.
• The use of 3D rendering seems unnecessary and obfuscates trends that might be clearer in simpler 2D plots.
5. Figures 5-1, 5-2, 5-3, and Figure 6:
• These are clearly screenshots from MATLAB or similar environments.
• They are not final-quality scientific figures and suffer from pixelation, poor label placement, and lack of annotation.
• Axis labels are small, sometimes missing units, and titles do not adequately explain the data.
6. Figure 7:
• It is unclear what this figure shows. The caption is vague, the content is densely packed, and no guidance is given on how to interpret the patterns.
• More sub-figures or separated plots are required, with clear explanations and units.

Recommendation:

Reject in current form.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript presents a systematic numerical investigation of nonlinear Thomson scattering (NTS) with emphasis on how laser intensity (a₀) and beam waist radius (ω₀) jointly affect radiation power, electron trajectories, and time-frequency spectra. The study is well-structured and covers a broad parametric space, but several areas require improvement before the manuscript is suitable for publication.

1. The radiation transitions (e.g., from “saddle-shaped” to “dual-peak”) are described in detail, but the underlying electrodynamic mechanisms are not fully explained. Please elaborate on how ponderomotive forces, relativistic motion, or field asymmetries contribute to these observed trends.

2. While the coupling of a₀ and ω₀ is novel in its parameter sweep, the manuscript would benefit from comparison to key prior works. Please include and discuss recent references to help clarify how your model builds upon or differs from prior NTS studies.

3. The manuscript suggests the generation of ultrashort radiation pulses, potentially in the attosecond regime. To support this claim, consider providing time-domain pulse duration estimates (e.g., from inverse spectral bandwidth) or simulated field envelopes.

4. Currently, all simulations use normalized parameters. Please provide at least one example mapping a₀ and ω₀ to real-world units (e.g., intensity in W/cm² and spot size in μm at λ = 800 nm). This will improve the paper’s accessibility to experimentalists.

5. The manuscript contains several redundant phrases and awkward sentence constructions. A thorough English edit is recommended. Also, please enhance figure captions with parameter details and ensure all axes have units.

6. Sections 3.1 to 3.4 include overlapping descriptions and similar trends. Streamlining these parts for conciseness while emphasizing the most insightful findings will improve clarity and focus.

With these major revisions, your work will be more impactful and can be considered for publication in Applied Sciences.

Comments on the Quality of English Language

The manuscript would benefit from thorough English language editing. Several sections contain repetitive phrasing, awkward sentence structures, and inconsistent verb tenses. Improving the clarity and flow of the text, especially in the Abstract, Results, and Conclusion sections will help readers better understand the technical contributions and key findings. Additionally, ensure all figure captions are grammatically correct and provide complete descriptions of the visual content. A professional language edit is recommended before publication.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Summary: 
                In this work, the respected authors systematically reveal the synergistic control mechanisms of linearly polarized laser intensity and beam waist radius on radiation power, electron dynamics, and temporal spectra in nonlinear Thomson scattering. They found the sensitivity of radiation power symmetry to beam waist radius increased significantly. 

Comments: 
1.    Abstract section: Line 14, correct the translated word into English. 
2.    Please highlight Thomson scattering and its principles with diagram. Also, about correlation with laser parameters. 
3.    Under methods section: Make it properly arranged with equations and its terminologies. 
4.    What is the significance of Eq. 11 and 12. How it affects or controls the lasing parameters which the author wants to discuss.
5.    Which medium is used for numerical simulation.
6.    Fig. 2 is not clear enough to understand its contents. Please make it readable with clear message. 
7.    Fig. 2 analysis is not mentioned in the text. Please specify it.
8.    How Fig. 3 and 4 is obtained and discuss its analysis. Also specify the units into which the x and y axis are being measured. Any specific reason to choose a0=7. 
9.    For fig. 5, mention the analysis part to the proper figure number in the text.
10.    Fig. 6 and 7: make it visible enough to understand its significance. Please discuss properly in the text with analysis of each part. 
11.    Provide some numerical values (if any) which show improvement in comparison with previous studies, in this regard. 
12.    Compare these aspects: high-energy, high-frequency, high-collimation, good directivity, and supercontinuum X-rays with previous studies related to Thomson scattering. 
13.    Compare the numerical and experimental aspects, if they are in agreement. 
14.    Correct the figure captions with spellings etc. 
15.    Major English checks required. Correct the fonts size and styles. 

 

Thanks

Comments on the Quality of English Language

Needs major improvement. 

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

A topic of current relevance with high relevance to the generation of high-energy X-ray and photon sources is addressed. However, work can be done to improve the quality of the manuscript.

 

1. The rationale for the choice of 𝒂₀ and ω₀ ranges needs to be expanded, what is the practical relevance of these values in real experiments or applications?
2. More clarity is needed in the exposition of the equations. In expressions (1) to (6), precise definitions of all variables, units and constants involved should be included to avoid ambiguities.
3. In the methods section add a flowchart or schematic that summarizes the simulation chain and the handling of boundary conditions.
4. In the explanation on the decomposition of the field in terms of sines and cosines (equations (8) and (9)) clarify the relationship with the angle of incidence and the Guoy phase shift, thus improving understanding.
5. The translation of some technical terms (e.g., “beam waist” vs. “waist radius” or “collimation” vs. “collimation”) should be standardized throughout the text.
6. The language is generally correct, however, there are errors to be corrected, in particular the use of commas and periods in the descriptions of equations, which would make for smoother reading.
7. The references present inconsistent formats (for example, differences in the order of the elements and in the separators), it is recommended to standardize the bibliographic style.
8. Enrich the bibliography by including experimental studies that corroborate the numerical models presented, in order to reinforce the validity of the results and present a better comparison with empirical data.
9. Authors and studies are mentioned without deepening in a critical discussion of their findings. Extend the comparative analysis with previous works.
10. Include legends and scales more explicitly in each figure, so that each axis and each symbol can be clearly identified without the need to constantly refer to the main text.
11. In figures with numerical results (such as exponential and quadratic variations), add fit curves or trend lines, together with error or uncertainty indicators, to evaluate the robustness of the observed relationships.
12. In some diagrams, font and label sizes are small, increase the size to make it readable.
13. The discussion section can be expanded to link the numerical results more critically with existing literature and to raise possible applications or future developments.
14. What are the possible constraints on the model (e.g., single electron approximation and simulation in the absence of collisional effects)?

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have clearly tried to improve the manuscript, but many issues still exist.

1. The introduction should be expanded to include recent trends in the field such as:
   -    "Dispersion of organic exciton polaritons—A novel undergraduate experiment." European Journal of Physics3 (2022): 035301.

• Yang, Minye, et al. "Electronic CPA‐Laser Having Enhanced Sensitivity and Tunability." Advanced Electronic Materials (2025): 2400722.

2. Why are all the equations are still in bold format?
3. There is still no full caption in Figure. 1, 2.2.
4. Labels such as “w0” should be fixed to “\omega_{0}”, etc.
5. Figures 5.1, 5.2 and 5.3 are Matlab screenshots, you should save it in an eps or pdf format and make a proper scientific figure.
6. What are the units in figure 6 and 7?

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Comments well addressed. 

Author Response

Thank the reviewers for their guidance on our article.

Reviewer 3 Report

Comments and Suggestions for Authors

Thanks to authors for considering the comments. The current revised manuscript is ok for me. 

Comments on the Quality of English Language

Can be improved a bit further. 

Author Response

Thank the reviewers for their guidance on our article.

Reviewer 4 Report

Comments and Suggestions for Authors

The revised manuscript meets the necessary standards for publication.

The suggestions made by the reviewers were considered.

Author Response

Thank the reviewers for their guidance on our article.

Round 3

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have made substantial steps towards improving the quality and readability of the manuscript. 

The manuscript is in much better shape now but there are some minor issues that should be addressed:

• In line 28: "

(10... power 20W / superscript baseline, cm, end baseline, square)" 
What is going on here? it's a latex compilation problem?

• line 61: no space after [26]
• In all figures, you need space between "Figure" and the number. i.e., Figure1>Figure 1.
• I still think you should provide a full caption in Figure 1, something like:
  Schematic illustration of the interaction between a chirped laser pulse and a relativistic electron in a tightly focused beam geometry. The diagram outlines the key physical elements considered in the simulation, including laser polarization, beam waist radius (ω₀), and the electron trajectory along the z-axis. 
• Figure 2.2 still shows w_{0} instead of ω₀ in the axis.

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf