Spectral Analysis of Electromagnetic Diffraction Phenomena in Angular Regions Filled by Arbitrary Linear Media
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe authors develop a spectral domain analysis for the problem of diffraction by a PEC or penetrable wedge in linear media. Here they refer to "spectral domain" as the Laplace transform domain. The longstanding challenge with wedge diffraction is being able to treat a wedge of some dielectric material immersed in a medium of some other material. They implement a new approach they call the "Direct Fredholm Factorization" approach in order to accomplish this; more specifically they create a "generalized" Wiener Hopf type problem that can in principle be solved for the general case. They develop the theoretical equations in the form of their generalized Wiener Hopf problem. They provide some validation for PEC wedges, and some asymptotic results, but do not carry out a full demonstration of their theory.
Overall, this development is quite vigorous and it is essentially impossible to verify its correctness in the period of time one normally expends reviewing a paper. I believe that the authors have done a reasonable job of extending their theory and feel that the paper can be published in its present form.
Comments on the Quality of English LanguageThe English is very good but not perfect, there are missing articles in some places.
Author Response
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Author Response File: Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsReview report for the paper titled "Spectral Analysis of Electromagnetic Diffraction Phenomena in Angular Regions Filled by Arbitrary Linear Media" by Vito G. Daniele, Guido Lombardi.
The authors study a new general theory for solving electromagnetic diffraction problems in the case of impenetrable/penetrable wedges immersed in an arbitrary linear medium. The paper is quite extensive and well written, explicitly discussing various details. The authors start from the transversal equations in the case of angular structures. The paper also uses various methods, the Green’s procedure, the Wiener-Hopf technique and a new Fredholm factorization.
However, before writing something like ["According to our opinion, for the first time, the proposed mathematical technique extends the possibilities of spectral analysis of electromagnetic problems in presence of angular regions filled by complex arbitrary linear media characterized by multiple propagation constants."], I think that the authors should explain an up to date mathematical context. Hence, the authors should add more material in the paper, explaining the relevance of the present study with respect to similar works/alternative direction. From this point of view, the last part of the paper (Conclusions) in very weak. I also think that before the Conclusion section another section should be added, related to the discussion of the results. The results are quite interesting, but the paper lacks an extensive discussion.
Another comment is related to the Fig. 9, can the authors explain the difference in slopes for larger phi's and for ~0.4 pi's. Why we see two maxima in this case?
Author Response
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Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsPlease see the report.
Comments for author File: Comments.pdf
Author Response
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Reviewer 4 Report
Comments and Suggestions for AuthorsIn this work, the authors present a general theory for solving electromagnetic diffraction problems involving impenetrable and penetrable wedges submerged in arbitrary linear media. The proposed mathematical techniques extend the possibility of spectral analysis of electromagnetic problems in angular regions filled with complex arbitrary linear media, introducing new mathematical tools. The approach has been validated through fundamental examples. While this work is compelling, profound, and novel, there are still several areas for improvement.
1. What advantages and potential limitations does the proposed mathematical technique have compared to traditional Sommerfeld-Malyuzhinets (SM) methods and Kontorovich-Lebedev (KL) transform methods when dealing with electromagnetic diffraction problems in angular regions filled with arbitrary linear media?
2. How does the "Direct Fredholm Factorization" method overcome the challenge of mapping Generalized Wiener-Hopf Equations (GWHEs) to Classical Wiener-Hopf Equations (CWHEs) in arbitrary linear media? What are the mathematical and physical innovations of this method?
3. What basic examples did the authors use to validate the effectiveness of the proposed theoretical framework? Are these examples sufficient to cover the range of applications of the theory in various electromagnetic problems?
4. How does the network formalism mentioned in the paper aid in systematically analyzing and solving electromagnetic scattering problems in anisotropic media? How does it differ from traditional transmission line theory?
5. How does the author ensure the stability and accuracy of the proposed mathematical models and methods in numerical computations for complex electromagnetic scattering problems? Are there specific numerical analysis techniques used to enhance computational efficiency or address numerical instability issues?
Author Response
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Author Response File: Author Response.pdf
Round 2
Reviewer 3 Report
Comments and Suggestions for AuthorsThe authors revised the paper correctly. I recommend that this paper is accepted in Applied Sciences