Analysis of Faceted Gratings Using C-Method and Polynomial Expansion

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In my opinion, the work does not fit the journal scope. Just grating theory and its numerical modeling was described in this work without any relation to the sensors. Hence, I found no overall benefit to publishing this work.

Comments on the Quality of English Language

In my opinion, the work does not fit the journal scope. Just grating theory and its numerical modeling was described in this work without any relation (or applications) to the sensors. Hence, I found no overall benefit to publishing this work.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

1. I see. If you would like to improve the English language in your manuscript, removing instances of the pronoun "we" can make the language more objective and formal. In academic or technical writing, it is common practice to avoid personal pronouns and instead use more neutral language such as "the authors" or "the researchers". This can help to improve clarity and avoid any potential bias or subjectivity in the language used.

2. The abstract and conclusion sections need to provide more information on the novel numerical solution. Examples of numerical comparisons in the literature survey section can also help improve clarity.

3-I understand that mathematical equations can be complex and challenging to comprehend, especially for those who are new to numerical methods. Simplifying them and focusing on the most important equations can make the learning process easier and more effective.

4. Figure 5 needs more explanation on why the error function exists and how it can be eliminated. 

Overall, it would be beneficial to provide more information and detail regarding the technical aspects of the report or paper.

Comments on the Quality of English Language

I see. If you would like to improve the English language in your manuscript, removing instances of the pronoun "we" can make the language more objective and formal. In academic or technical writing, it is common practice to avoid personal pronouns and instead use more neutral language such as "the authors" or "the researchers". This can help to improve clarity and avoid any potential bias or subjectivity in the language used.

Author Response

please see the attachment

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

In their paper titled "Analysis of Faceted Gratings using C-method and Polynomial Expansion," G. Granet and K. Edee explore the nuanced domain of faceted gratings. Despite the paper's intriguing subject matter, the introductory section lacks clarity in delineating the distinctiveness of their work compared to recent contributions, particularly those by Ming and Sun [1] and Xu and Li [2]. The presence of equation-related issues throughout the manuscript, such as equations exceeding text width and missing punctuation, raises concerns about the overall precision of the presented analyses. The reliance on comparisons with Plumey's work from 1999 and 1997 may appear somewhat outdated given the field's recent advancements. The absence of illustrated axes in Figure 1 adds ambiguity to the statement in line 96 regarding a "cylindrical surface invariant along the Oy axis," leaving readers pondering the nature of the structures described. Additionally, the authors may consider the potential benefits of sharing their source code, as it could aid readers in identifying and rectifying equation-related errors and contribute to the transparency and reproducibility of their findings.

 

 

I am inclined to endorse the publication of this paper once a revised version has been submitted and reviewed.

 

 

[1] X. Ming and L. Sun, Simple Reformulation of the Coordinate Transformation Method for Gratings with a Vertical Facet or Overhanging Profile, Appl. Opt., AO 60, 4305 (2021).

[2] X. Xu and L. Li, Numerical Instability of the C Method When Applied to Coated Gratings and Methods to Avoid It, J. Opt. Soc. Am. A, JOSAA 37, 511 (2020).

Author Response

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Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

In the paper, the authors formulated the C-method using the new coordinate transformation system and Legendre polynomial expansion. The presented approach and its implementation enable to deal efficiently with triangular and trapezoidal (slanted) grating groove profiles. The method was compared to the Rigorous Coupled Wave Analysis (RCWA or FMM) and it substantially outperformed RCWA in calculation speed and accuracy for the problems of a practical importance. The manuscript is well-written and clear understandable. I could recommend its possible publication in Sensors, however, there is a couple of important revisions, which must be addressed prior to a publication.

Line 26: “In recent years, the advancement of computers has facilitated the application of the finite element method (FEM) to solve Maxwell’s differential equations. This method is particularly well-suited for addressing periodic structures or models with arbitrary shapes.” I think, the boundary integral equation method (BIEM) is also should mentioned here, at least, briefly. Because, on the basis of this theory all the well-known problems of diffraction by periodic and non-periodic structures in optics and other fields have been solved.

Line 360: “Remarkably, for the same level of precision, CPE significantly outperformed FMM in terms of computational speed. While no single method can efficiently address all diffraction problems related to gratings, CPE stands out as an excellent candidate, particularly for faceted profiles.” I believe, the most useful method to compare diffraction efficiencies of gratings with faceted groove profiles is BIEM. It is much accurate and faster than FMM for such type of gratings, especially in the TM polarization and high conductivity. See, e.g., in [E. Popov (Ed.), Gratings: Theory and Numeric Applications, 2nd rev. ed., Presses Universitaires de Provence, Marseille (2014), https://www.fresnel.fr/files/gratings/Second-Edition/index.htm  ]. So, the BIEM is a better candidate for comparisons and such a comparison should made in the manuscript.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

One other approach to successfully analyze surface relief gratings is the coordinate transformation method developed by Chandezon et al. (C-method) . Although this method outsmarts the rigorous coupled-wave analysis in the analysis of surface relief gratings, it has two intrinsic problems that make it inappropriate for some important structures. In this paper, authors present a novel numerical solution using Legendre polynomial expansion, enabling us to deal with faceted gratings. In the previous instance, I mentioned that the article is beyond the scope of the Sensor Journal. However, this time I can say that the article is entirely within the scope of the Photonics journal, and considering strengths and weaknesses, I recommend publishing the article in its current form.

Comments on the Quality of English Language

One other approach to successfully analyze surface relief gratings is the coordinate transformation method developed by Chandezon et al. (C-method) . Although this method outsmarts the rigorous coupled-wave analysis in the analysis of surface relief gratings, it has two intrinsic problems that make it inappropriate for some important structures. In this paper, authors present a novel numerical solution using Legendre polynomial expansion, enabling us to deal with faceted gratings. In the previous instance, I mentioned that the article is beyond the scope of the Sensor Journal. However, this time I can say that the article is entirely within the scope of the Photonics journal, and considering strengths and weaknesses, I recommend publishing the article in its current form.

Reviewer 2 Report

Comments and Suggestions for Authors

accepted in present form 

Reviewer 4 Report

Comments and Suggestions for Authors

It is ready for publishing.