Some Insights on Kerr Lensing Effects

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Kamel Aït-Ameur and Kamel Aït-Ameur summarized a  review titled " Some Insights on Kerr Lensing Effects. "This article presents a comprehensive analysis of the behavior of beams under the optical Kerr effect (OKE), with a focus on the comparative performance ofand.It systematically demonstrates that thebeam retains superior focusability compared to thebeam under OKE, a finding with two critical implications: (1) the design of high-intensity laser systems using-based architectures to surpass Gaussian beam limitations, and (2) the development of countermeasures against OKE-dependent optical limiters by leveraging the unique properties ofbeams. Overall, this article is valuable, timely, and suitable for publication in Photonics. I recommend to publish it after some minor revisions.

1. The introduction section insufficiently addresses the research background, particularly lacking references to recent critical advancements in the field.The authors should comprehensively review and cite high-impact literature from the past five years, focusing on key developments directly relevant to the research topic.This revision will better highlight the motivation and significance of the work.
2. Manuscript, page 1, line 24, “Before getting into the issue itself, we should start by recalling the optical KERR effect...” the term "optical KERR effect" is incorrectly formatted. The standard academic nomenclature for this phenomenon is "optical Kerr effect," with only the initial letter of "Kerr" capitalized.
3. Manuscript, page 1, line 37, “We will instead focus on the effect of a thin Kerr medium taking the form of a slice of nonlinear material having a thickness d as shown in Figure 1.” What is the difference between thin Kerr media and conventional Kerr media? The author should add some information about these.
4. In Figure 1 of the manuscript, the term "medium" in the label "Kerr medium" texhibits incomplete typographic specifications, resulting in unclear annotations. It is recommended to revise the figure by improving the font description to ensure clarity and legibility of all labels.
5. Manuscript, page 3, line 81, “with λ=1064 nm the wavelength,” The phrase "with λ=1064 nm the wavelength" contains formatting and grammatical errors. It should be revised to "with the wavelength λ = 1064 nm." It is recommended to revise this terminology throughout this article.
6. Manuscript, page 14, line 377, “Each focusability metric has its advantages and disad-vantages, and we would however prefer to use the Strehl ratio defined as follows:.” The authors should briefly describe the advantages and disadvantages of each mentioned focusability metric and provide a concise rationale for selecting the Strehl ratio.
7. Manuscript, page 18, line 476, Equation (34) has a formatting inconsistency. Please ensure it aligns with the style of other equations in the manuscript.
8. Manuscript, page 19, line 487, “Before getting into the issue itself, let us recall the basic principle of an optical limiter based on OKE.” This section should be supplemented with a brief description of the OKE-based optical limiter principle. Additionally, Figure 20 requires a brief analytical discussion rather than a mere description of its components.
9. The references cited in the manuscript lack recent publications, with most sources being over a decade old. This may lead to an incomplete representation of current advancements in the field. The authors are advised to incorporate high-quality literature from the past five years, particularly studies directly relevant to the research focus.

Comments for author File: Comments.pdf

Author Response

Answer to the Reviewer#1 report

Paper Photonics3660627 entitled “Some Insights on Kerr Lensing Effect”.

 

The authors would like to thank the Reviewers for their accurate reading and their suggestions.

 Comments and Suggestions for Authors

Kamel Aït-Ameur and Kamel Aït-Ameur summarized a review titled " Some Insights on Kerr Lensing Effects. "This article presents a comprehensive analysis of the behavior of beams under the optical Kerr effect (OKE), with a focus on the comparative performance ofand.It systematically demonstrates that thebeam retains superior focusability compared to thebeam under OKE, a finding with two critical implications: (1) the design of high-intensity laser systems using-based architectures to surpass Gaussian beam limitations, and (2) the development of countermeasures against OKE-dependent optical limiters by leveraging the unique properties ofbeams. Overall, this article is valuable, timely, and suitable for publication in Photonics. I recommend to publish it after some minor revisions.

 

1. The introduction section insufficiently addresses the research background, particularly lacking references to recent critical advancements in the field.The authors should comprehensively review and cite high-impact literature from the past five years, focusing on key developments directly relevant to the research topic.This revision will better highlight the motivation and significance of the work.

 

The Reviewer#2 has made the same comment and the following tet has been added at the end of the introduction with four new recent references:

 

The numerous publications on Kerr effect have been done in the seventies and eighties. They are essentially devoted to the problematic of small and large-scale self-focusing occurring in high-intensity laser chains. In the nineties, the research on OKE was mostly focused on Kerr Lens Mode-Locking (KLM) of lasers for generating ultrashort laser pulses. It seems that the studies on Kerr effect will not be soon exhausted, but are currently oriented to other fields of physics such as cold atoms [7], vacuum [8], gravitational waves [9], and black holes [10].

 

7. Levine, Z.H.; Du, Z. Semiclassical calculation of the power saturation of the Kerr effect in Rb vapor. JOSA B, 2023, 40, 3190-3195.
8. Robertson, S. Optical Kerr effect in vacuum. Rev. A. 2019, 100, 063831.
9. Hsieh, T.; Lee, D.S.; Lin, C.Y. Throat effects on strong gravitational lensing in Kerr-like wormholes. Rev. D. 2025, 111, 044051.

• Gralla, S.E.; Lupsasca, A. Lensing by Kerr black holes. Rev. D. 2020, 101, 044031.

 

 

2. Manuscript, page 1, line 24, “Before getting into the issue itself, we should start by recalling the optical KERR effect...” the term "optical KERR effect" is incorrectly formatted. The standard academic nomenclature for this phenomenon is "optical Kerr effect," with only the initial letter of "Kerr" capitalized.

 

This has been corrected

3. Manuscript, page 1, line 37, “We will instead focus on the effect of a thin Kerr medium taking the form of a slice of nonlinear material having a thickness d as shown in Figure 1.” What is the difference between thin Kerr media and conventional Kerr media? The author should add some information about these.

The assumption that the Kerr medium is thin means that the restructuring of the beam due to diffraction occurs outside the Kerr medium and not inside as in a “conventional Kerr medium” (thick medium).

 

4. In Figure 1 of the manuscript, the term "medium" in the label "Kerr medium" texhibits incomplete typographic specifications, resulting in unclear annotations. It is recommended to revise the figure by improving the font description to ensure clarity and legibility of all labels.

 

This has been corrected

5. Manuscript, page 3, line 81, “with λ=1064 nm the wavelength,” The phrase "with λ=1064 nm the wavelength" contains formatting and grammatical errors. It should be revised to "with the wavelength λ = 1064 nm." It is recommended to revise this terminology throughout this article.

 

This has been corrected

6. Manuscript, page 14, line 377, “Each focusability metric has its advantages and disad-vantages, and we would however prefer to use the Strehl ratio defined as follows:.” The authors should briefly describe the advantages and disadvantages of each mentioned focusability metric and provide a concise rationale for selecting the Strehl ratio.

 

We have added the reference [55] which carries out the comparison between the different metric characterizing the focusability of a laser beam

Power in the bucket [52], beam parameter product [53], Strehl ratio [54]. Each focusability metric has its advantages and disadvantages well described in [55],

• Jabczynski, J.K.; Kaskow, M.; Gorajek, L.; Kopczynski, K.; Zendzian, W. Modeling of the laser beam shape for high-poer applications. Eng. 2018, 57, 046107.

Our preference on Strehl ratio is based mainly on its definition which involves the on-axis intensity in the focal plane, and that is directly connected with the two considered applications.

 

7. Manuscript, page 18, line 476, Equation (34) has a formatting inconsistency. Please ensure it aligns with the style of other equations in the manuscript.

T

This has been corrected.

 

 

8. Manuscript, page 19, line 487, “Before getting into the issue itself, let us recall the basic principle of an optical limiter based on OKE.” This section should be supplemented with a brief description of the OKE-based optical limiter principle. Additionally, Figure 20 requires a brief analytical discussion rather than a mere description of its components.

 

We have added the following text in section 3.2 :

For high (low) input  intensities, the trajectory of the light follows the dashed (solid) line giving rise to a low (high) transmission through the diaphragm.

 

9. The references cited in the manuscript lack recent publications, with most sources being over a decade old. This may lead to an incomplete representation of current advancements in the field. The authors are advised to incorporate high-quality literature from the past five years, particularly studies directly relevant to the research focus.

See the answer to question N°1 for recent references about the Kerr effect research. However, for the two applications considered in this paper,.there is a lack in the literature which can be easily understood since these two applications are based on the use of a high order Laguerre-Gauss beams which have been considered as useless since a long time. This old point of view has been called into question in reference [56].

• Aït-Ameur, K. The advantages and disadvantages of using structured high-order but single Laguerre-Gauss LG_p0 laser beams. Photonics 2024, 11, 217.

 

 

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This paper presents an in-depth and insightful investigation into the behavior of high-order Laguerre-Gaussian beams (particularly the LG₁₀ mode) under the influence of the optical Kerr effect (OKE). The study demonstrates that LG₁₀ beams exhibit superior focusability compared to Gaussian beams (LG₀₀) in nonlinear media and explores their potential applications in high-intensity laser amplification and optical limiting countermeasures. While the research is innovative, several key aspects require further refinement to enhance the academic rigor and scientific merit of the work.

The specific points are as follows:

1. For the introduction section, it would be beneficial to incorporate key references from the last five years to better reflect the cutting-edge nature of the research.
2. While the study focuses on LG₀₀ and LG₁₀ beams, a brief comparative analysis with higher-order modes would provide more comprehensive insights into the observed advantages of LG₁₀.
3. Several formatting issues need attention, including non-centered equations (e.g., Eqs. 11 and 13) and small font sizes in some figures that affect readability.
4. To enhance readability, the authors might consider dividing this lengthy section into several subsections with clear headings. This would help guide readers through the complex material.
5. It may be beneficial to reorganize some of the figures into multi-panel formats, which often help readers make direct visual comparisons more effectively.

 

Author Response

Answer to the Reviewer#2 report

Paper photonics-3660627 entitled “Some Insights on Kerr Lensing Effect”.

The authors would like to thank the Reviewers for their accurate reading and their suggestions.

 

 Comments and Suggestions for Authors

This paper presents an in-depth and insightful investigation into the behavior of high-order Laguerre-Gaussian beams (particularly the LG₁₀ mode) under the influence of the optical Kerr effect (OKE). The study demonstrates that LG₁₀ beams exhibit superior focusability compared to Gaussian beams (LG₀₀) in nonlinear media and explores their potential applications in high-intensity laser amplification and optical limiting countermeasures. While the research is innovative, several key aspects require further refinement to enhance the academic rigor and scientific merit of the work.

 

The specific points are as follows:

1.For the introduction section, it would be beneficial to incorporate key references from the last five years to better reflect the cutting-edge nature of the research.

The following text has been added at the end of the introduction:

The numerous publications on Kerr effect have been done in the seventies and eighties. They are essentially devoted to the problematic of small and large-scale self-focusing occurring in high-intensity laser chains. In the nineties, the research on OKE was mostly focused on Kerr Lens Mode-Locking (KLM) of lasers for generating ultrashort laser pulses. It seems that the studies on Kerr effect will not be soon exhausted, but are currently oriented to other fields of physics such as cold atoms [7], vacuum [8], gravitational waves [9], and black holes [10].

 

7. Levine, Z.H.; Du, Z. Semiclassical calculation of the power saturation of the Kerr effect in Rb vapor. JOSA B, 2023, 40, 3190-3195.
8. Robertson, S. Optical Kerr effect in vacuum. Rev. A. 2019, 100, 063831.
9. Hsieh, T.; Lee, D.S.; Lin, C.Y. Throat effects on strong gravitational lensing in Kerr-like wormholes. Rev. D. 2025, 111, 044051.

• Gralla, S.E.; Lupsasca, A. Lensing by Kerr black holes. Rev. D. 2020, 101, 044031.

 

 

2. While the study focuses on LG₀₀ and LG₁₀ beams, a brief comparative analysis with higher-order modes would provide more comprehensive insights into the observed advantages of LG₁₀.

This comparative analysis is already done after Equation (27). Hereafter we recall our text:

The two quantities allowing to illustrate the Kerr lensing effect (KLE) are the relative focal shift , and the on axis intensity  which are, respectively shown in Figures (13) and (14). We cannot strictly speaking describe the plots, for , in Figure (14) as a focal zoom due to OKE since the value of  is less than one percent. It is as if the  beams for  are insensitive to Kerr effect or more precisely are much less sensitive than the usual Gaussian beam. This important property is confirmed by the plot in Figure (13) which shows that the on-axis intensity in plane  remains high even for large values of , and even greater that the focused intensity obtained for a Gaussian beam. This important feature is very similar to the relative insensitivity of high-order  beams subject to a spherical aberration [38,39], and finds as it will be later a promising application to optical limiters and amplification of pulses of high intensity.

 

 

3. Several formatting issues need attention, including non-centered equations (e.g., Eqs. 11 and 13) and small font sizes in some figures that affect readability.

 

The centering of cited Equations has been arranged. Concerning the small font sizes, this is imposed by the Photonics journal.

4. To enhance readability, the authors might consider dividing this lengthy section into several subsections with clear headings. This would help guide readers through the complex material.

We do not entirely agree with the feeling of the Reviewer#2 because we find that the subsections proposed are sufficiently clear. We recall below the subsections headings:

1. Introduction
2. Kerr lensing effect

    2.1 Kerr-lens effect induced by a Gaussian beam

    2.2 Kerr-lens effect induced by a LGp0 beam

3. LGp0 beams subject to OKE: Applications

    3.1 Improving the focusing properties of a laser beam subject to OKE

    3.2 A LG10 beam for weakening of the optical limiters protection

4. Conclusions

Appendix A

 

 

5. It may be beneficial to reorganize some of the figures into multi-panel formats, which often help readers make direct visual comparisons more effectively.

The remark of the Reviewer#2 is unfortunately not very clear. On our part we find that the figures are sufficiently clear for allowing the necessary comparisons between the different situations presented in the article.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

This paper presents an in-depth and insightful investigation into the behavior of high-order Laguerre-Gaussian beams (particularly the LG₁₀ mode) under the influence of the optical Kerr effect (OKE). The study demonstrates that LG₁₀ beams exhibit superior focusability compared to Gaussian beams (LG₀₀) in nonlinear media and explores their potential applications in high-intensity laser amplification and optical limiting countermeasures. While the research is innovative, several key aspects require further refinement to enhance the academic rigor and scientific merit of the work.

The specific points are as follows:

1. While the study focuses on LG₀₀ and LG₁₀ beams, a brief comparative analysis with higher-order modes would provide more comprehensive insights into the observed advantages of LG₁₀.
2. There are still many formulas in the article that do not meet the formatting requirements and are obviously misaligned.

Author Response

1. While the study focuses on LG₀₀ and LG₁₀ beams, a brief comparative analysis with higher-order modes would provide more comprehensive insights into the observed advantages of LG₁₀.

This question has been raised by Reviewer#2 in his first report and our answer was as follows

In fact, the asked comparative analysis has been made in the paper through figures 13 and 14. Figure 14 demonstrates that the focal zoom for p greater or equal to one is negligible compared to that of the LG00 beam. However, Figure 13 shows that the highest focused intensity is obtained for p=1. Since the paper is center on two applications based on the efficiency of focusing of a LGp0 beam in the focal plane of the focusing lens, it is clear that the LG10 beam is the best candidate. All these arguments are expressedby Figures 13 and 14.

Answer to the first report:This comparative analysis is already done after Equation (27). Hereafter we recall our text:

The two quantities allowing to illustrate the Kerr lensing effect (KLE) are the relative focal shift , and the on axis intensity  which are, respectively shown in Figures (13) and (14). We cannot strictly speaking describe the plots, for , in Figure (14) as a focal zoom due to OKE since the value of  is less than one percent. It is as if the  beams for  are insensitive to Kerr effect or more precisely are much less sensitive than the usual Gaussian beam. This important property is confirmed by the plot in Figure (13) which shows that the on-axis intensity in plane  remains high even for large values of , and even greater that the focused intensity obtained for a Gaussian beam. This important feature is very similar to the relative insensitivity of high-order  beams subject to a spherical aberration [38,39], and finds as it will be later a promising application to optical limiters and amplification of pulses of high intensity.

 

 

 

1. There are still many formulas in the article that do not meet the formatting requirements and are obviously misaligned.

The alignement of the equations is at the final step finalized by the Edition board of photonics.

Submission Date

08 May 2025

Date of this review

03 Jun 2025 04:24:22

 

Author Response File: Author Response.docx