Scattering of Radiation by a Periodic Structure of Circular and Elliptical Microcavities in a Multimode Optical Waveguide

Round 1

Reviewer 1 Report (Previous Reviewer 1)

Comments and Suggestions for Authors

The request regarding the text modification has been addressed. However, the authors did not answer the main objection of the manuscript regarding the novelty of manuscript. The manuscript seems a small step forward respect to the previous work of the same authors (ref. 17).  The novelty is simply the linear regression of linear power density of scattered radiation to evaluate the uniformity. 

Author Response

The request regarding the text modification has been addressed. However, the authors did not answer the main objection of the manuscript regarding the novelty of manuscript. The manuscript seems a small step forward respect to the previous work of the same authors (ref. 17).  The novelty is simply the linear regression of linear power density of scattered radiation to evaluate the uniformity. 

Answer: We would like to thank you for the careful consideration of the manuscript and the remark regarding the novelty of the research. The scientific novelty of our work lies in a comprehensive approach to studying light scattering processes in multimode mode, which includes a detailed analysis of radiation power dependence on changing structural parameters, an investigation of various microcavity shapes (spherical, elliptical) impact on scattering characteristics, the development of a methodology for quantitative assessment of radiation distribution uniformity, and the determination of optimal structural parameters to achieve uniform scattering. Unlike the previous publication, this research significantly expands the understanding of scattering processes through a more in-depth analysis of multimode radiation propagation characteristics, exploration of an extended range of geometric parameters, and development of practical recommendations for designing optical structures with specified scattering characteristics.

Author Response File: Author Response.docx

Reviewer 2 Report (Previous Reviewer 2)

Comments and Suggestions for Authors

In the revised manuscript, I see the efforts made by the author. The questions I raised before have been basically answered and revised. The current version basically meets the standards of Photonics, but the author still needs to optimize the layout of the figures. I am not worried about the originality of the paper, but the technical details are not within my professional scope, which requires a comprehensive judgment based on the comments from other reviewers.

Author Response

In the revised manuscript, I see the efforts made by the author. The questions I raised before have been basically answered and revised. The current version basically meets the standards of Photonics, but the author still needs to optimize the layout of the figures. I am not worried about the originality of the paper, but the technical details are not within my professional scope, which requires a comprehensive judgment based on the comments from other reviewers.

Answer: We would like to thank you for reviewing the revised version of our manuscript and for your positive assessment of the work done. The comments have been taken into account, and the authors have carried out a complete optimization of the illustrative material, ensuring its logical placement in accordance with the text and improving the overall perception of the work.

Reviewer 3 Report (Previous Reviewer 4)

Comments and Suggestions for Authors

The comments have been addressed accordingly. But the format of the manuscirpt is still strange.

Author Response

The comments have been addressed accordingly. But the format of the manuscirpt is still strange.

 

Answer: Thank you for your assessment, the manuscript format has been finalized.

Author Response File: Author Response.docx

Reviewer 4 Report (New Reviewer)

Comments and Suggestions for Authors

The manuscript could be considered for publication after a major revision

 

Major issues

It is not clear what is the reason of investigation of waveguide breakdown. As the reader can understand from the introduction, in case the breakdown happens, the waveguide should be replaced, isn't it? Please, clearly state the necessity of simulation and investigation of radiation scattering in microcavities.

Did the authors make a unique research in this field? The introduction does not provide the information about similar works dedicated to the simulations. Please, improve the introduction and provide relevant research works in the field.

As authors stated, current manuscript differs from [20] in three aspects, namely, multiple mode radiation, wavelength and core diameter. I believe, the main difference is the addition of multiple mode radiation support. Why is it necessary?

A few minor issues also found:
- Please, provide the reference to COMSOL software.
- Please, consider reducing self citations number.
- Equation (1) - "where I = 1,2,3" - I believe it should be lower-case "i".
- Fig. 1,2,3 - what does the colorbar mean? What is the measurement unit? Please, clearly state it in figures.
- Please, provide a description for each term used after equation (8). What is r_PML, d_PML, etc.?
- Fig. 4 is not referenced in the text.
- Please, also consider reducing the size of FIg. 4 or even place it as the inset to some of previous figures.

Author Response

1. Major issues

It is not clear what is the reason of investigation of waveguide breakdown. As the reader can understand from the introduction, in case the breakdown happens, the waveguide should be replaced, isn't it? Please, clearly state the necessity of simulation and investigation of radiation scattering in microcavities.

Did the authors make a unique research in this field? The introduction does not provide the information about similar works dedicated to the simulations. Please, improve the introduction and provide relevant research works in the field.

As authors stated, current manuscript differs from [20] in three aspects, namely, multiple mode radiation, wavelength and core diameter. I believe, the main difference is the addition of multiple mode radiation support. Why is it necessary?

Answer: We thank you for your valuable comments.

The study of waveguide breakdown has significant practical importance, as after optical breakdown, a microcavity structure is formed that preserves the basic waveguide properties (mechanical and waveguiding characteristics). These modified fibers find application in the following areas:

1. Medical diagnostics and surgery — creation of special probes for operations requiring additional lighting and uniform irradiation of affected areas.
2. Optical sensors — development of sensitive elements for fiber-optic sensors. Each microcavity individually and the periodic structure as a whole represent a set of Fabry-Pérot microinterferometers; when radiation passes through, multibeam interference is observed. This property can be used for sensor creation. In areas of maximum radiation reflection, power increases, which may further enhance sensor quality factor.
3. Radiation diffusers — uniform distribution of light flux in various diagnostic devices.
4. Optical systems — creation of new device types with specified scattering characteristics.

Modeling and studying radiation scattering by a microcavity structure is necessary to determine optimal microcavity structure parameters, ensure uniform distribution of scattered radiation, predict fiber element characteristics, and develop methods for controlling light flows. While the authors agree that broken fiber is not suitable for fiber-optic communication lines, it opens new possibilities for use as a functional element in optical systems.

Reference [12] (in the previous version of the article it was [20]) considered single-mode optical fibers for medical applications, but their use is significantly limited. Experimental data show that when using single-mode fibers, rapid attenuation of scattered radiation occurs on formed structures after the first defects appear, which significantly limits their application.

In contrast, our research focuses on a deep understanding of light scattering processes in multimode mode, where a more diverse shape of formed microcavities and significantly more uniform radiation distribution along the fiber lateral surface is observed. The important advantage of multimode mode is the ability to increase scattering power, which is critical for medical applications requiring high illumination intensity. Additionally, spectrum broadening (wavelength change) allows adapting the device to various tasks, while changing the core diameter affects light capture efficiency and scattering characteristics. The obtained results expand theoretical understanding of scattering mechanisms for developing medical probes and optical sensors with uniform radiation distribution.

There are similar studies on this topic [references provided below], which are usually related to Bragg gratings. These references have been added to the list of literature and the article text.

Publications on similar topics:

• Kashaganova, G. B.; Amirgalieva, S. N.; Kalizhanova, A. U. et al. Numerical modeling of a fiber Bragg grating in MATLAB environment // Proceedings of the International Symposium “Reliability and Quality”. 2018, 1, 329-333.
• Nuerev, I. I. Modeling of spectral characteristics of fiber Bragg gratings with phase shift for solving problems of optomechanics in sensor systems. Information Technologies. Radioelectronics. Telecommunications. 2015, 5(2), 127-133.
• Safaryan, K. A.; Goldobin, A. A.; Trefilov, I. A.; Goncharov, M. M. Modeling of a fiber-optic vibration sensor based on a fixed Bragg grating. Applied Photonics. 2024, 11(1), 123-135.
• Matveenko, V. P.; Serovaev, G. S.; Kosheleva, N. A. Results of mathematical modeling supporting the reasonable use of fiber-optic strain sensors based on Bragg gratings // XII All-Russian Congress on Fundamental Problems of Theoretical and Applied Mechanics. 2019, 3, 1333-1335.
• Zakharov, V. N. Modeling of fiber-optic sensors for electrical quantities based on Bragg gratings with instrumental error correction // Proceedings of ITNT-2019. New Technology. 2019, 1, 499-504.
• Glushkov, E. V.; Glushkova, N. V. and Evdokimov, A. A. Hybrid numerical-analytical scheme for calculating elastic wave diffraction in locally inhomogeneous waveguides. Acoustical Physics. 2018, 64, 1–9. https://doi.org/10.1134/S1063771018010086.

2. A few minor issues also found:
- Please, provide the reference to COMSOL software.

Answer: The link https://www.comsol.com/release/6.1 has been added to the article text, line 47.

- Please, consider reducing self citations number.
Answer: We consider the number of self-citations to be justified due to the rather high originality of the research direction.

- Equation (1) - "where I = 1,2,3" - I believe it should be lower-case "i".

Answer: Changes have been added to the text (line 151), the designations have been corrected.

- Fig. 1,2,3 - what does the colorbar mean? What is the measurement unit? Please, clearly state it in figures.

Answer: Thank you for your valuable comments. The displayed physical quantity and its dimension are indicated above the figures. The color bar serves as a scale for the electric field strength/electric field amplitude value, with the unit of measurement being V/m (volts per meter).

- Please, provide a description for each term used after equation (8). What is r_PML, d_PML, etc.?

Answer: Changes have been made to the text (lines 196–199); r_PML = 0.5 μm ∙ s — the distance from the PEC edge to the current PML layer, where s is the layer number, d_PML is the total thickness of the PML layer.

- Fig. 4 is not referenced in the text.

Answer: A description has been added to the text (lines 213–215).

- Please, also consider reducing the size of Fig. 4 or even place it as the inset to some of previous figures.

Answer: The size of Figure 4 has been reduced.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report (Previous Reviewer 1)

Comments and Suggestions for Authors

The authors have extended the introduction puttin in evidence the novelty of work. Now the potential application and the motivation are more cleaner. The manuscript can be published as is it.

Reviewer 4 Report (New Reviewer)

Comments and Suggestions for Authors

The authors addressed all issues

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript reports a method o evaluate the scattered radiation by a periodic structure of circular and elliptical microcavities.

The novelty of manuscript is limited respect to the previous work of the same authors (ref. 17). Here it has been proposed a simple linear regression of linear power density of scattered radiation to evaluate the uniformity.

in Material and Methods

The authors explain the details of the 2D electromagnetic simulation by means Comsol Multiphysics. In line 100-102 it is report the following unclear sentence:

"In this work, the microcavities, characterised by circular and elliptical cross-sections, are considered to be infinitely extended along the z-axis, thereby representing spheres or ellipsoids within a real optical fibre"

a circular cross-section extended along the z-axis is not a sphere is a cylinder.

In line 129: The formula of wavevector should be revised. Probably ni, refractive index, must be removed.

The paragraph in lines 179-183 sholud be rewritten in a more clear form.

Figure 5 must be improved. Probably it is better to do more plot in same graph using indexing procedure with a), b),...

 

 

Typos:

In line 48: λ0 should be λ₀ 

In lines 84-86: Region 1 should be waveguide core and Region 2 waveguide cladding

in line 236 Figure 5 instead of Figure 4

in line 277-282 The sentences have not been supported from the graph.

The discussion paragraph is a recap of the work done. There is no comments at numerical results. 

 

 

Author Response

1. In line 100-102 it is report the following unclear sentence: "In this work, the microcavities, characterised by circular and elliptical cross-sections, are considered to be infinitely extended along the z-axis, thereby representing spheres or ellipsoids within a real optical fibre" a circular cross-section extended along the z-axis is not a sphere is a cylinder.

Answer: The authors have changed the text (in the new version lines 100-104, p.3) “In the proposed mathematical model, the solution is performed in the section of a flat infinitely long along the z-axis waveguide. The microcavities of the spherical and elliptical sections are assumed to be infinitely extended along the z-axis”.

2. In line 129: The formula of wavevector should be revised. Probably n_i, refractive index, must be removed.

Answer: n_i is removed from the wave vector formula (5), p.4.

3. The paragraph in lines 179-183 should be rewritten in a more clear form

Answer: The authors have made changes to the paragraph (in the new version it is lines 185-191, p.6)

4. Figure 5 must be improved. Probably it is better to do more plot in same graph using indexing procedure with a), b),...

Answer: The authors have made changes to Figure 5, added indexing with (a) and (b) (p.8)

Typos:

• In line 48: λ0 should be λ0

Answer: The authors have made changes to the text (line 48, p.2)

• In lines 84-86: Region 1 should be waveguide core and Region 2 waveguide cladding

Answer: The text has been corrected (lines 84-86, p.2)

• in line 236 Figure 5 instead of Figure 4

Answer: The authors have changed the text (line 245, p.10 in the new version)

• in line 277-282 The sentences have not been supported from the graph.

Answer: An example of such a graph is shown in Figure 5, p.8. To avoid cluttering the manuscript, it was decided to describe the observations in writing without attaching a figure.

• The discussion paragraph is a recap of the work done.

Answer: We thank the reviewer for the comment regarding the discussion section. The authors clarify that this section indeed contains not only an overview of the work done, but also a discussion of future directions in the study of radiation scattering by microcavities in a periodic structure.

• There is no comments at numerical results.

Answer: All the numerical data obtained were analyzed and commented in detail in [Petukhova, A. Y. Mathematical Model of Radiation Scattering on Quasi-Periodic Microstructure in Optical Fiber / A. Y. Y. Petukhova, A. V. Perminov, V.A. Starikova, Y. A. Konin. - DOI 10.1134/S1062873824706986. - Text: electronic // Bulletin of the Russian Academy of Sciences: Physics. - 2024. - Vol. 88, No. 6. pp. 1000-1009. - URL: https://doi.org/10.1134/S1062873824706986;]. The authors referred to this paper in the article.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

Yu, et al. proposed a periodic structure of circular and elliptical microcavities in a multimode optical waveguide, and investigated its scattering property of radiation. This work is based entirely on simulations. Although the structural design is interesting, the performance obtained through simulation is difficult to judge. In addition, the organization of the article is difficult to understand. Therefore, I will not make a final judgment on this article. The editor can refer to the suggestions of other reviewers to make a final decision. Some specific suggestions are as follows:

1. Problem Statement should be in Introduction, not in the Materials and Methods
2. In figure 1, authors assumed that both the waveguide and the microcavities are infinite along the z-axis. What is the basis for this assumption? Is it reasonable?
3. Many formulas between formula 3 and 4 are not numbered.
4. In figure 6, what does the comma between the numbers on the axis mean?
5. In figure 9, the quantitative information in the figure legend should be T and l.

Author Response

Response to Reviewer 2

Dear reviewer, thank you for the review of the paper and for possibility to expand it. We will give the answers below for each question.

All changes in the manuscript are highlighted in green.

 

Yu, et al. proposed a periodic structure of circular and elliptical microcavities in a multimode optical waveguide, and investigated its scattering property of radiation. This work is based entirely on simulations. Although the structural design is interesting, the performance obtained through simulation is difficult to judge. In addition, the organization of the article is difficult to understand. Therefore, I will not make a final judgment on this article. The editor can refer to the suggestions of other reviewers to make a final decision. Some specific suggestions are as follows:

1. Problem Statement should be in Introduction, not in the Materials and Methods

Answer: problem formulation and description of the numerical method are described in Section 2, which is renamed. The authors believe that this structure of the paper is more appropriate than suggested by the reviewer.

2. In figure 1, authors assumed that both the waveguide and the microcavities are infinite along the z-axis. What is the basis for this assumption? Is it reasonable?

Answer: A real fiber has a cylindrical geometry. If we assume strict axisymmetric of microcavities and radiation propagating along the fiber, then the solution of the problem does not depend on the polar angle around the symmetry axis (x-axis in Figure 1). In fact, the problem for the fiber can be solved in a planar formulation in a region representing an arbitrary diametric cross-section. For more correct realization of the numerical procedure in the chosen version of the computational package it is possible without loss of accuracy of the results to go to a simpler geometry of a flat infinite along the z-axis waveguide, allowing the use of Cartesian coordinate system. The microcavities are also assumed to be infinitely extended along the z axis. All calculations are performed in the x - y plane, as shown in Figure 1. The solution of the wave equation in a plane waveguide for each mode is sought in the form of a plane wave propagating along the x-axis and polarized along the z-axis.

3. Many formulas between formula 3 and 4 are not numbered.

Answer: Numbers have been added to the formulas on pages 3-6.

4. In figure 6, what does the comma between the numbers on the axis mean?

Answer: The authors have modified Figure 6, page 9.

5. In figure 9, the quantitative information in the figure legend should be T and l.

Answer: The caption for Figure 9 has been changed, p.12.

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript presents a mathematical model to investigate the scattering of light by periodic circular and elliptical microcavities embedded in a planar waveguide, simulating the behavior of a multimode optical fiber. The use of periodic microcavities for light scattering in multimode waveguides is a well-established concept. The manuscript does not sufficiently distinguish its approach from existing work or provide a clear innovation in terms of modeling strategy or physical insight. Secondly, the authors use commercial software COMSOL for simulations without proposing a new mathematical model. Therefore, I believe the manuscript does not meet the requirements for publication.

Author Response

Response to Reviewer 3

 

Dear reviewer, thank you for the review of the paper and for possibility to expand it. We will give the answers below for each question.

All changes in the manuscript are highlighted in green.

 

The manuscript presents a mathematical model to investigate the scattering of light by periodic circular and elliptical microcavities embedded in a planar waveguide, simulating the behavior of a multimode optical fiber. The use of periodic microcavities for light scattering in multimode waveguides is a well-established concept. The manuscript does not sufficiently distinguish its approach from existing work or provide a clear innovation in terms of modeling strategy or physical insight. Secondly, the authors use commercial software COMSOL for simulations without proposing a new mathematical model. Therefore, I believe the manuscript does not meet the requirements for publication.

Answer: The authors agree with the reviewer that the effects of radiation scattering on periodic structures in optical waveguides have long been studied and applied in practice. Such structures include, for example, Bragg gratings in the core of optical fibers. The scattering of radiation on quasi-periodic structures inside optical waveguides is relatively poorly studied. For such structures, many questions arise related to the control of optical breakdown. The answers to these questions will allow to obtain structures with specified properties of scattered radiation. The aim of the present work is to understand how microcavities of different shapes scatter radiation. The authors are not aware of any work where such studies have been carried out. Indeed, the authors use commercial modelling software. However, the modelling strategy, the geometrical parameters of the model and the physical interpretation of the results are novel.

Author Response File: Author Response.docx

Reviewer 4 Report

Comments and Suggestions for Authors

Yu and co-authors investigate the scattering characteristics of periodic circular and elliptical microcavity structures in a multimode optical waveguide by employing numerical simulations to identify optimal geometric parameters for uniform scattering. The research topic holds practical value, particularly in medical probe illumination and fiber-optic sensing. The manuscript is well-structured, with clear methodological descriptions and systematic result analyses. However, several critical issues require major revision to enhance the rigor and applicability of the conclusions. Detailed comments are provided below.

1. The study relies entirely on numerical simulations. Experimental validation (e.g., scattering measurements in fabricated fibers with microcavities) is critical to confirm the model’s accuracy. The authors should either supplement experimental data or explicitly reference prior experimental results to strengthen credibility.
2. The 2D planar approximation of a cylindrical fiber neglects 3D effects (e.g., mode coupling, axial microcavity distribution). An analysis or discussion of how axisymmetric assumptions impact results is necessary.
3. Some serial number of the equations are missing, please add.
4. Briefly compare the proposed model with existing scattering theories (such as Mie scattering for spherical cavities) to contextualize the novelty of the approach.
5. Minor grammatical errors.
6. Please modify the figure sizes and font sizes in all the figures to improve the readability.

Comments for author File: Comments.pdf

Author Response

Response to Reviewer 4

 

Dear reviewer, thank you for the review of the paper and for possibility to expand it. We will give the answers below for each question.

All changes in the manuscript are highlighted in green.

 

Yu and co-authors investigate the scattering characteristics of periodic circular and elliptical microcavity structures in a multimode optical waveguide by employing numerical simulations to identify optimal geometric parameters for uniform scattering. The research topic holds practical value, particularly in medical probe illumination and fiber-optic sensing. The manuscript is well-structured, with clear methodological descriptions and systematic result analyses. However, several critical issues require major revision to enhance the rigor and applicability of the conclusions. Detailed comments are provided below.

1. The study relies entirely on numerical simulations. Experimental validation (e.g., scattering measurements in fabricated fibers with microcavities) is critical to confirm the model’s accuracy. The authors should either supplement experimental data or explicitly reference prior experimental results to strengthen credibility.

Answer: Experimental studies of scattered radiation on the structure of microcavities (there are significantly more than four of them in the experiments) were described in the following articles:

1. Konin Yu.A., Bulatov M.I., Shcherbakova V.A., Garanin A.I., Tokareva Ya.D., Mosheva E.V. Investigation of the properties of the tsssno-volokonnyi temperature sensor created by the melting effect // Instrumentation and Technique of Experiment, 2020, 4. 7882. doi: 10.31857/S003281622004028Х
2. Konin Y. A., Shcherbakova V.A., Garanin A.I., Mosheva E.W., Grachev N.A. The Development of All-fiber Temperature Sensor for Extreme Conditions // 2021 IEEE Conference of Russian Young Researchers in Electrical and Electronic Engineering (ElConRus). IEEE, 2021, 1317-1320. doi: 10.1109/ElConRus51938.2021.9396393
3. Konin Y.A., Garanin A.I., Scherbakova V.A. Research the thermal sensitivity of a fiber optic sensor created with the catastrophic fuse. // PNRPU Bulletin. Electrotechnics, Informational Technologies, Control Systems. 2019, 32, 90-104.

The described experimental verification allows us to believe that the calculation gives the correct distribution of the wave field.

In [Mathematical model of radiation scattering on a quasi-periodic structure in an optical fiber / Y.A. Konin, V.A. Starikova, A.Yu. Petukhova, N.A. Grachev, A.A. Petrov, A.V. Perminov // Applied Photonics. - 2023. - Т. 10, № 2. - С. 42-55.] calculations were performed on the basis of a similar mathematical model in the COMSOL environment, the experimental and calculated spectra of radiation reflected from the microcavity structure were compared. The comparison showed quite satisfactory results.

The COMSOL environment itself is a proven means of numerical modeling. In addition, the convergence of the numerical solution was verified by changing the grid spacing.

2. The 2D planar approximation of a cylindrical fiber neglects 3D effects (e.g., mode coupling, axial microcavity distribution). An analysis or discussion of how axisymmetric assumptions impact results is necessary.

Answer: The two-dimensional flat approximation allowed us to simplify the mathematical model considerably and provided an understanding of the main scattering mechanisms. The three-dimensional approximation is planned in future works.

3. Some serial number of the equations are missing, please add.

Answer: The authors have modified and added missing ordinal numbers to the equations

4. Briefly compare the proposed model with existing scattering theories (such as Mie scattering for spherical cavities) to contextualize the novelty of the approach.

Answer: Mie theory is well developed to describe the scattering of radiation on a single spherical object. However, applying this theory to analyze scattering on a group of microcavities or on a nonspherical microcavity is significantly difficult. The essence of the Mie theory is that each particle is treated as an independent scatterer, and the interaction between particles (e.g., the re-scattering of light from one particle to another) and the interference of waves scattered by different particles are not taken into account.

In the initial stages of the study, the authors performed a qualitative comparison of the calculated scattered radiation fields for a single microcavity. The comparison of the results obtained using Mie theory and COMSOL tools showed a satisfactory correspondence. It should be noted that quantitative analysis was not performed.

5. Minor grammatical errors.

Answer: Corrected

6. Please modify the figure sizes and font sizes in all the figures to improve the readability.

Answer: Corrected

 

Author Response File: Author Response.docx