Boundary Integral Equations Approach for a Scattering Problem of a TE-Wave on a Graphene-Coated Slab

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript photonics-3558777 “Boundary integral equations approach for a scattering problem of a TE-wave on a graphene-coated slab, accounting for the nonlinearity of graphene”， describing the scattering of a TE-wave on a slab having an absolutely conducting wall at the bottom and covered with graphene at the top, accounting for the optical nonlinearity of graphene on a transmission problem.The model of this paper is innovative to some extent.In order to better improve the quality of the paper, my suggestion is as follows:

1. The paper does not provide a schematic of the physical model, which makes it difficult for the reader to understand the physical mechanism.
2. This paper is based on the boundary conditions of the interface between the linear medium and graphene in restricted directions. It is clear that the thickness of the graphene, the thickness of the linear medium, and the beam width of the transmitted beam have a large effect on the physical model, but this is not described in detail in this paper. Therefore, it is better to give the relevant schematic diagram in the revised draft, and explain the rationality of the physical mechanism in detail.

When the above comment was added on the revised manuscript, I can recommend this paper for publication.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The problem of reflection of an electromagnetic wave from a dielectric layer shielded from below, covered with graphene, has been solved. Graphene is described using conductivity determined by the Kubo formula plus the nonlinear term according to the Mikhailov formula. The boundary value problem is reduced to the solution of the bisingular integral equation (BSIE) defined in the segment [-1,1]. A fairly effective solution method based on the decomposition of an unknown function into a series by polynomials, Chebyshev of the second kind, was applied to the solution of the BSIE.   Bisingular integrals from Chebyshev polynomials are computed explicitly. This allowed the BSIU to be transformed into the Fredholm equation, which is solved by the collocation method. As a result, a system of nonlinear algebraic equations is obtained, which, with a small nonlinearity, is solved by the iteration method.

The work can be published. As a wish, the authors in the future should study not only the effect of self-influence, but also the generation of the third harmonic.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

In the work entitled with “Boundary integral equations approach for a scattering problem of a TE-wave on a graphene-coated slab, accounting for the nonlinearity of graphene”, the authors studied the scattering of a monochromatic TE-polarized electromagnetic wave by an infinite dielectric slab with specific design: conducting wall at the bottom, graphene coated top for which the y attempted to solve the transmission problem.

I found the work in a very strong point in mathematical point of view and with a great impact on the field of the nonlinear optical response at THz band. Additionally, by tuning the chemical potential of graphene and modulating  both the phase and amplitude of the reflected T-waves, they can potentially impact the field of active photonic devices

I would like to thank the authors for their strong work from the mathematical point of view. I find their work interesting and worthy to publish on photonics after some minor changes.

1. The title is too long and technical. To attract readers' attention, it would be beneficial to consider a shorter, more informative title.
2. In the abstract, from line 5 to 12, the authors mentioned the steps they took to solve the transmission problem, which I find dense and unnecessary.
3. “The graphene coated slab filled by silica”. I would like to ask the authors to provide more information on the waveguide, the design, and the choice of materials. They may also provide a sketch of the waveguide.
4. The figures suffer from low quality.
5. In all figures the label of y-axis is missing.
6. The captions suffer from low clarity.
7. Figures 1, 6, and 7 need to be better presented. I suggest adding a colorbar to these figures.
8. In the method section, the transformation from the original Maxwell’s equation to the final solution can be better visualized if the authors add a flowchart or diagram to this section.

 

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

In the revised version of photonics-3558777, the paper has been modified according to the review comments, thus enabling readers to understand the design of the paper model more clearly and easily. I recommend this paper for publication.