Electromagnetic Guided Wave in Goubau Line with Graphene Covering: TE Case
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe manuscript proposes a graphene-based circle cylindrical waveguide and studies the propagation of monochromatic terahertz TE-polarized wave. I would like to recommend it to be published in Photonics if the authors can address my following comments:
1. Line 172: Please provide the source references for the relevant parameters;
2. Figure 1: The schematic diagram of graphene and the polarization direction of incident light should be supplemented.
3. Line 210-222: For a more intuitive understanding of the field distribution under different conditions, please supplement the relevant local field distribution.
Author Response
Dear Reviewer,
Our reply is attached as a pdf file.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsWhen mentioning equations in the paper can be unify to be Eq, (#)
Don't quite understand the last sentence in abstract: the nonlinear case, the case, doesn't contain nonlinear term and completely linear case.
Line 21, just mark with reference number.
Line 35-37, can be rewritten to make it easier to understand.
Line 61, the inner radius should be r0 and outer radius is r1 corresponding to R1 and R2 in the Fig. 1?
Line 185 the unit for sqrt(µε) should be s/m, and the unit for frequency ω is Hz, so the unit for k0 should be 1/m?
The conclusion can be stronger and can put more emphasis on the directive role on application.
Comments on the Quality of English LanguageLine 132 equivalent
Line 159 auxiliary
Line 166 can choose
Some of the sentence is not easy to understand, it would be better to ask some other colleagues to help to improve.
Author Response
Dear Reviewer,
Our reply is attached as a pdf file.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsS. Tikhov et al. presents an interesting and highly specific problem concerning wave propagation in cylindrical waveguides, particularly the Goubau line. Overall, the topic appears to be within the realm of electromagnetism, which is somewhat divergent from your areas of expertise listed in your profile—namely biostatistics, bioinformatics, genomics, and data science.
Though this work has obtained promising results, many aspects still need to be improved. Therefore, the following issues are recommended for further justification and clarification.
1. The study attempts to build upon existing literature by considering cubic nonlinearity in graphene. This is an interesting twist that could offer new insights into TE-polarized wave propagation. While the paper states that the study is novel, it fails to articulate clearly what gap in the existing literature is being filled.
2. The paper seems to focus on a well-defined problem—determining eigenmodes of the waveguide. This clear scope can be beneficial for concentrated study. The paper neglects energy losses in the dielectric and absorption in graphene. While the abstract states that this is a reasonable approximation, it would strengthen the paper to include a justification or a sensitivity analysis.
3. The paper could benefit from directly comparing its results with those in existing literature, especially with the study cited in [30] which also deals with a similar nonlinear problem.
4. The statement "there is no qualitative difference in the cases with nonlinear graphene covering and without it" could benefit from further elaboration. What are the implications of this result? Does it suggest that the cubic nonlinearity of graphene is not as significant as initially thought? While the paper suggests that "theoretical results and approach used need to be developed further," it would be beneficial to be more explicit about what those developments might entail.
5. Besides the paper mentioned in previous comments, the other several papers will help authors analyze the applications of 2D materials. The papers with a recent study on 2D materials can be parts of the reference of this manuscript, which will help to fill in the details (Haoran Mu et al 2022 Mater. Futures 1 012301; Han Song et al SusMat, 3 (4), 2023, 543-554; Renzhong Zhuang et al Nat. Commun. 2023, 14 (1), 1621.).
Author Response
Dear Reviewer,
Our reply is attached as a pdf file.
Author Response File: Author Response.pdf
Reviewer 4 Report
Comments and Suggestions for AuthorsThis is an interesting article in an actual research field. The paper fulfils the journal conditions for acceptance and I recommend its publication in Photonics.
I have just a few observations about typos that authors should check before a manuscript is ready for publication:
1. Page 1, line 4, "propgation" should be "propagation"
2. Page 1, line 6, "numercial" should be "numerical"
3. Page 2, line 61, "perfectrly" should be "perfectly"
4. Page 2, line 67, "filed" should be "field"
5. Page 5, line 132, "equivakent" should be "equivalent"
6. Page 6, line 154, "exisntence" should be "existence"
7. Page 6, line 159, "auxiiliary" should be "auxiliary"
8. Page 6, line 159, "origianl" should be "original"
9. Page 12, line 289, "2015, 107" should be "2015, 107, 091602"
10. Page 12, line 295, "2013, 113" should be "2013, 113, 053701"
11. Page 12, References [40] and [41] should be deleted because they are not mentioned in the text!
12. Page 12, line 329, "91, 013840 (6 pages), 2015" should be "2015, 91, 013840"
13. Page 12, line 331, "367, 804-833, 2023" should be "2023, 367, 804-833"
Author Response
Dear Reviewer,
Our reply is attached as a pdf file.
Author Response File: Author Response.pdf
Reviewer 5 Report
Comments and Suggestions for AuthorsA. General idea of the presented scientific work
The article deals with the analytical solution of the wave propagation problem in a rather typical model: a cylindrical waveguide, and the EM equations defined in cylindrical coordinate system.
The authors presented solution of a specific case where nonlinear material constitutive data is nonlinear.
Formulation and presentation of solution of analytical solution of wave propagation in time harmonic (monochromatic) mode is the main part of the paper. The solution of the wave equation in cylindrical coordinates is well known. No new idea is presented in this part.
A new aspect can be found in the assumption on the nonlinear properties of one material. In this case nonlinearity of outer electrode of the waveguide is assumed (i.e. nonlinearity of boundary condition). The conductivity of graphene is expressed using second order polynomial. This formal assumption enables to find the modified (general) analytical solution of the problem. At the end paper this assumption is verified. As we can see nonlinearity of graphene has no significant influence on the final solution.
The article deals with well known theoretical case, where nonlinearity of material (i.e. boundary condition) is applied. The presented paper is fully theoretical, and it has a very limited practical sense.
My overall assessment of the article is conditionally, weak positive.
The added value of the article is the presentation of a well-known analytical method, rarely used in technical work today (archaic in applied sciences). Based on the theoretical solution, the authors proved that influence of nonlinearity was very limited. This is also information somehow.
B. Assessment of methodology
The discussion of the other works is very short (lines 31 – 55). This part of the paper can be extended.
I assess correctly the general methodology of the research.
The basic components of the formulation have been presented. The mathematical formalism, explanation of equations, are presented correctly.
In the concluding section the authors writes “… analytical and numerical approaches.”. This is misleading information. In this article the analytical solutions is developed, presented and discussed. In order to demonstrate the obtained solutions, numerical method was used to determine the solutions of the obtained analytical equations. In this article does not use two different methods to compare and verify the results.
The strength of the paper is the theoretical part. A practical effect of the research is the information about influence of nonlinearity on the solution of wave equation.
C. Form, layout of the paper
The general structure and layout of the paper is correct (including body of the text, figures, tables, and equations), but some components must be improved.
The implemented notation is correct and consistent. The language of the paper is correct.
Please adjust the form of presentations of references to the requirements of the journal.
The list of publications has 46 items. One of them was printed 50 years ago and the other one 70 years ago. We can find essential information in these references, but I think we can omit historical books.
D. Some questions / critical comments on the work.
1. The graph of the wave number (Figs. 2, 4, 6) are presented with modified vertical axis. From practical point of view, authors should discuss real values, and real differences between curves (using absolute or relative values on the vertical axis). Can the author add three figures (form scale form 0) or present some result in tables. It interesting to compare real differences in the analyzed three cases. Is it important or (unfortunately) can it be neglected.
2. In lines 205 – 207 authors write that “nonlinearity leads to better localization of field in the waveguide”. Is it a result of nonlinearity or rather larger value of conductivity (according to the nonlinear model). If the second component in (4) is neglected (for signals with low magnitude) the properties of waveguide are not changed. We can observe tis effect only for signals with larger magnitude.
3. As the result of formulation of nonlinear model, we always obtain some distortion of signals (amplitude distortions). Can the author discuss this problem?
4. As the result of formulation of nonlinear model, the output signal is distorted in frequency too. We can observe some additional harmonics. It is a typical effect of electromagnetic dispersion. How this effect can be discussed using the presented formulations? The authors used monochromatic formulation (in frequency domain, with a prescribed frequency).
5. Can the authors can write something about computational cost of the algorithm.
E. Final opinion
Once again, I would like to stress, this is the paper, with analytical solution for the known cylindrical waveguide.
My overall assessment of the article is conditionally, weak positive.
The added value of the article is the presentation of a well-known analytical method, rarely used in technical work today (archaic in applied sciences). Based on the theoretical solution, the authors proved that influence of nonlinearity was very limited. This is also information somehow.
The authors should introduce some modifications. In my opinion the scientific level of the paper is acceptable, but the authors should improve some parts of it. The answer to my comments (five points with some remarks) can improve the quality of the paper and deliver more information for readers.
Comments on the Quality of English Language
The language of the paper is correct. Here are some errors, mistakes and suggestions.
1. Line 56: instead of “Now we pass …” please begin the new section.
2. Lines 59-62 and Fig. 1: r0 and r1 were not presented in the figure.
3. Line 67: in this sentence the boundary conditions are presented. The new sentence should begin after eq. (1).
4. Lines 75 – 78 and eq. (3): “n” is vector, then write it bold.
5. Lines 79 – 81: instead of one sentence with semicolon, write some separated sentences.
6. Line 83: “… formulas [31, 32]”. Please write this formula or ad “in”.
7. Lines 85 – 88: instead of one sentence with semicolon, write some separated sentences.
8. Line 92: parameter gamma has a physical sense. Could you write the right physical name, instead of mathematical babble.
9. Line 154: “exisntence”?
10. Line 159: “auxiiliary”?
11. Line 159: “origianl”?
12. Line 154: “chose” ïƒ “choose”.
13. Lines 176 – 182: instead of one sentence with semicolon, write some separated sentences.
14. Figure 5: “… denoted in 4 …”, before “4” write “Fig.”
15. Figure 7: “… denoted in 6 …”, before “6” write “Fig.”
Author Response
Dear Reviewer,
Our reply is attached as a pdf file.
Author Response File: Author Response.pdf
Round 2
Reviewer 5 Report
Comments and Suggestions for AuthorsA. General idea of the presented scientific work
Formulation and presentation of solution of analytical solution of wave propagation in time harmonic (monochromatic) mode is the main part of the paper. The solution of the wave equation in cylindrical coordinates is well known. No new idea is presented in this part. A new aspect can be found in the assumption on the nonlinear properties of one material. This formal assumption enables to find the modified (general) analytical solution of the problem. At the end paper this assumption is verified. As we can see nonlinearity of graphene has no significant influence on the final solution.
B. Positive evaluation components
The authors has made changes to the content of the paper, in accordance with the previously submitted comments. They add some additional comments, improved notations and figures. The description of the problem is better. The layout of the paper became better.
The general structure of the paper is right. The previous evaluation was conditionally positive due to the description of the issues, the explanation of the performed work.
The methodology of simulation, evaluation is explained. The additional comments and results presented in tables enable quantitative analysis of results.
C. Negative evaluation components
My overall assessment of the article is conditionally, weak positive.
The added value of the article is the presentation of a well-known analytical method, rarely used in technical work today (archaic in applied sciences). Based on the theoretical solution, the authors proved that influence of nonlinearity was very limited. This is also information somehow.
In my opinion, the analytical methods are out of scope of current science (unfortunately).
D. Conclusions
The scientific quality of the paper is better, in my opinion it fulfills the requirements of the journal.
The presented paper is fully theoretical, and it has a limited practical sense.
The scientific level of the paper is on the accepted level. In my opinion, the second version of the paper can be printed.
