Refinement of the Heuristic Solution for the Problem of TE-Polarized Electromagnetic Wave Diffraction on a Half-Plane with Two-Sided Impedance Boundary Conditions
Round 1
Reviewer 1 Report (Previous Reviewer 1)
no comments
Author Response
Thank you very much
Reviewer 2 Report (Previous Reviewer 2)
Dear Authors,
Unfortunately, you did not answer any of my questions.
So, I think the current version still needs major modification.
Regards
The following is my previous comments:
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The author applies a heuristic method which is a combination of the generalized diffraction coefficient (GDC) and the generalized diffraction coefficient in the approximation of physical optics (PODC) to a conducting half-plane with two-sided impedance boundary conditions. The paper is interesting. However, there are some issues in the paper that should be addressed before publication.
1- Why only TE-polarized solution is investigated in the paper? What is the problem to complete the solution for TM-Polarized?
2- What is the vertical axis in Figure 2?
3-What is the difference between this paper and following papers:
a- Ref [21]
b- DOI : https://doi.org/10.1080/17455030.2022.2108160
What are the limitations of these works and what are the advantages of this work?
4-The contribution of Z for two-sided impedance boundary conditions should be investigated in the paper. Please note that the last paragraph of the introduction section needs to be supported with more references. For example, the author has mentioned that " .... two-sided impedance boundary conditions is chosen as a semi-transparent object, ...", this phrase needs some proper references. Below there are suitable suggestions.
a- DOI: 10.1109/TAP.2022.3187510
b- https://doi.org/10.1029/RS011i001p00049
5- The numerical examples to validate the method are not enough The validation should be more strength. The validation part should be done for a case with different impedances on both sides.
6-It would be nice if the author can compare the numerical property (the accuracy, the memory cost, the CPU time) of different methods to show the capability of the proposed method.
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Author Response
- In this article, we describe only the MFC technique. Specific boundary conditions are used only to verify the heuristic solution. Accurate heuristic solutions for a specific type of boundary conditions are given in [27].
- Scattering diagram – indicated in the figure and said in the caption.
- (a) Different polarization and different tuning function
(b) Indeed, very precise solutions for both polarizations are given in this paper. But such solutions are possible only in some rare cases, while the technique described in this paper is much more general.
The technique described in this paper is much more general.
- Boundary conditions are not studied in this article. We study only a heuristic technique that allows us to refine the heuristic solution. Additional comments are given in the "Discussion" section.
- Malyuzhinets' solution for different face impedances is different from this work. We do not study boundary conditions here.
6. Yes, it would be interesting, but not necessary, since the described technique can be applied to various practical problems for which these data are different. And for a specific type of boundary conditions, heuristic solutions of high accuracy already exist [27].
Author Response File: 
Author Response.pdf
Reviewer 3 Report (Previous Reviewer 3)
The author claims that the novelty of the manuscript is not the solution to the diffraction problem, it is in the development of the heuristic approach. Probably, it will be interesting for readers of this journal to know about the heuristic approximation. So, I recommend accepting the manuscript
Author Response
Thank you very much
Reviewer 4 Report (New Reviewer)
The manuscript is devoted to the construction of approximate heuristic solutions for the diffraction on a half-space. Despite progress in the creation of numerical methods for solving these problems, the construction of approximations in the form of simple analytical formulas remains an urgent problem in the diffraction theory. The constructed approximate solution is analyzed in great detail both analytically and numerically through comparison with the Wiener-Hopf method.
I believe that the manuscript fits the thematics of the journal and can be published.
Author Response
Thank you very much
Round 2
Reviewer 2 Report (Previous Reviewer 2)
The proposed method should be validated by a strong numerical or analytical method.
Author Response
"The proposed method should be validated by a strong numerical or analytical method."
Yes, I agree with this statement. That is why this paper presents the results of a quantitative assessment of the accuracy (Figure 4), which showed the success of the method used. The approach described in this article (namely, the numerical determination of tuning parameters) is universal and suitable for any type of boundary conditions.
For some types of boundary conditions, the application of the method of fundamental components can lead to obtaining the analytical formulas [27], but this approach is less universal.
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 on Vesnik’s article eng-2084830
This article presents a further development of the heuristic approach presented earlier in the author’s publications. It consists in a successive improvements of the initially chosen approximations. The proposed method is demonstrated on the problem of diffraction by a semi-transparent half-plane. It can also be applied to other, more complex diffraction problems.
In this article, it is appropriate to refer to and comment on the paper
G.D. Maluzhinetz, “Das Sommerfeldische integral und die Losung von Beugungsaufgufgaben in Winkelgebieten,” Annalen der Physik, Folge 7, Band 6, Heft 1-2, 1960, pp. 107-112.
This paper contains an exact solution of the diffraction problem for a wedge with arbitrary face impedances. In a particular case, it is valid for a half-plane with different impedances on its two faces.
Question: Can this theory work for a semitransparent half – plane?
Conclusion: the manuscript is recommended for publication with appropriate changes.
Reviewer 2 Report
The author applies a heuristic method which is a combination of the generalized diffraction coefficient (GDC) and the generalized diffraction coefficient in the approximation of physical optics (PODC) to a conducting half-plane with two-sided impedance boundary conditions. The paper is interesting. However, there are some issues in the paper that should be addressed before publication.
1- Why only TE-polarized solution is investigated in the paper? What is the problem to complete the solution for TM-Polarized?
2- What is the vertical axis in Figure 2?
3-What is the difference between this paper and following papers:
a- Ref [21]
b- DOI : https://doi.org/10.1080/17455030.2022.2108160
What are the limitations of these works and what are the advantages of this work?
4-The contribution of Z for two-sided impedance boundary conditions should be investigated in the paper. Please note that the last paragraph of the introduction section needs to be supported with more references. For example, the author has mentioned that " .... two-sided impedance boundary conditions is chosen as a semi-transparent object, ...", this phrase needs some proper references. Below there are suitable suggestions.
a- DOI: 10.1109/TAP.2022.3187510
b- https://doi.org/10.1029/RS011i001p00049
5- The numerical examples to validate the method are not enough The validation should be more strength. The validation part should be done for a case with different impedances on both sides.
6-It would be nice if the author can compare the numerical property (the accuracy, the memory cost, the CPU time) of different methods to show the capability of the proposed method.
Reviewer 3 Report
The author presents a heuristic approximation of a cylindrical wave scattered by a semitransparent half-plane. The incident field has only one polarization. I have some concerns about the scientific value of the results:
1) to verify the heuristic approximation, the author uses an exact solution obtained using the Wiener-Hopf technique. The author claims that the heuristic solution is in an analytical form, so it is more convenient for the determination of the scattering pattern. I partially agree with that because the Wiener-Hopf solution contains integrals, which should be calculated numerically. It is much better to use an analytic formula containing trigonometric formulae. However, another exact solution to the considered problem is available in [10]. The solution from [10] is based on the Sommerfeld integral method, and it is for both TE and TM polarizations of the incident field. It is represented using a product of trigonometric functions and the Maliuzhinets function. The Maliuzhinets function can be calculated very easily because it is a double product of an algebraic function. Thus, if an exact solution represented using a simple analytical equation is presented in [10] for both TM and TE polarizations, what is the advantage of the heuristic approximation for only single polarization of the incident field?
2) the author considers boundary conditions (1) when the impedance Z is fully reactive. This is one more limitation because in [10] authors consider any kinds of semitransparent impedances including both reactive and resistive parts. After figure 1, the author claims that real physical objects as ones made of resistive materials can be described using the semitransparent boundary conditions. But as the author considers only reactive impedances, the presented heuristic approximation is inappropriate for describing resistive materials.
In a conclusion, I do not see any advantages of the presented heuristic solution as compared with the previously published exact solution from [10].
Reviewer 4 Report
Article is interesting. The problem statement is clear, novelty is shown, the compariosn with other methods is given, the effectivneness of the heuristic approach is shown. the english language is normal. I don't see any typos or grammar errors. I give recommendation to be published in this journal.
