Finite-Size and Illumination Conditions Effects in All-Dielectric Metasurfaces

Round 1

Reviewer 1 Report

The author studied the finite-size all-dielectric metasurfaces and compare with COMSOL.

This paper should be rejected unless the following question can be addressed properly:

In the title, the authors claimed that they studied the finite-size modelling of metasurface by mixing multipolar decomposition and T-matrix method. However, it seems that the authors simply employed a third-party python library (SMUTHI) which is based on multipolar decomposition and T-matrix method. There seems not enough original work that have been done by the authors. At the end of the day, you cannot claim that you studied something using FEM by just simulating with COMSOL or HFSS. (This is the most import issue. The authors should prove that they have done sufficient original work.)

Author Response

We thank the reviewers for their insightful comments and questions, which helped us to improve the quality of the manuscript. We highlighted in red the changes to the main text.

1. In the title, the authors claimed that they studied the finite-size modelling of metasurface by mixing multipolar decomposition and T-matrix method. However, it seems that the authors simply employed a third-party python library (SMUTHI) which is based on multipolar decomposition and T-matrix method.

 

We changed the title of the manuscript and the abstract to better match the content of the paper and to clarify the fact that the main focus in this work concerns the study of finite size effects rather than the details of the T-matrix method implementation used for this purpose. We also clarified that we did not develop the simulation tool, rather we employed the python library (SMUTHI) to show the importance of novel tools and the physics related to finite size structures.

 

2. There seems not enough original work that have been done by the authors. At the end of the day, you cannot claim that you studied something using FEM by just simulating with COMSOL or HFSS. (This is the most import issue. The authors should prove that they have done sufficient original work.)

 

To improve the quality of the manuscript, and thanks to the suggestions of the Reviewers, we added a study on the so-called high-Q structures. Based on the same approach, we added new results shown in figure 6 which includes simulations of metasurfaces of different size highlighting the emerging bound states in the continuum (BIC) and the dependence of the linewidth upon the system size.

In the Introduction and Results sections, we added several sentences. In particular, a brief description about bound states in the continuum, and a discussion on the importance of considering finite-size effects.

Reviewer 2 Report

In this manuscript, the simulation of all-dielectric structures 
with finite size and Gaussian beam incidence is conducted using 
SMUTHI, the results of which are also compared with those using 
COMSOL. It shows that SMUTHI is time saving. The less the array 
size, the weaker the collective interaction. With paraxial 
approximation, the simulated results are similar for the plane wave 
and Gaussian beam incidence. In my opinion, the manuscript may be 
considered for the publication in the Electrics.

Author Response

We thank the reviewers for their insightful comments and questions, which helped us to improve the quality of the manuscript. We highlighted in red the changes to the main text.

1. In this manuscript, the simulation of all-dielectric structures with finite size and Gaussian beam incidence is conducted using SMUTHI, the results of which are also compared with those using COMSOL. It shows that SMUTHI is time saving. The less the array size, the weaker the collective interaction. With paraxial approximation, the simulated results are similar for the plane wave and Gaussian beam incidence. In my opinion, the manuscript may be considered for the publication in the Electrics.
   
   We thank the Reviewer for appreciating our work. We corrected some typos and performed an accurate spell check of the manuscript.

Reviewer 3 Report

The question that the paper is trying to answer is interesting. However, several points have to address before considering the paper for publishing as follows:

1- What's really important is the size of the structures in wavelength, not number of unit cells. Also, if possible, if such a number is scalable to a different spectral region.

2- Can the authors answer this question: How many cells in wavelength are enough to mimic an infinite design? as the readers will be very interested in such an answer.

3- Can the authors present a structure with a high Q-factor? as this is very important for sensing applications.

4- Some more details about the simulation setting have to be included, such as the number of mesh cells, convergence criteria.

5- What could be the reasons behind the discrepancy in the results in Figs. 4&5 at small wavelengths compared to the large wavelengths?

6- Interestingly, in Fig. 5, even for the 3x3 structure, the match of R is quite good for the large wavelengths, any clue? 

7- Line 16: Some relevant references related to sensing biological substances must be added.

Author Response

We thank the reviewers for their insightful comments and questions, which helped us to improve the quality of the manuscript. We highlighted in red the changes to the main text.

• What's really important is the size of the structures in wavelength, not number of unit cells. Also, if possible, if such a number is scalable to a different spectral region.

 

We agree with the reviewer. However, metasurfaces with the same total dimensions and constituting resonators but different amount of unit cells will have very different behavior depending on the unit cell size. This derives from the fact that the unit cells size determines the interaction strength among the resonators. The stronger the interaction, the more important the number of unit cells will be. Indeed, a resonance related to the single pillar, like the one at 1610 nm shown in the paper, will be marginally affected by the number of resonators, while the resonance related to pillar-pillar interaction will be strongly affected. We have now further stressed this fact by adding several sentences at the end of the “Results” section.

Due to Maxwell equations invariance, if the materials involved have no dispersion, the structure can be resized and the same effects of finite size will be present in different spectral regions.

 

• Can the authors answer this question: How many cells in wavelength are enough to mimic an infinite design? as the readers will be very interested in such an answer.

 

The number of unit cells necessary to mimic an infinite design depends on the coupling between the resonators. As can be seen from Fig. 5, resonances related to isolated pillars can be reproduced with few unit cells (less than 5), while features related to the interaction between neighbor resonators necessitate more than 10 unit cells. Additionally, structures characterized by very distant resonators will resemble more closely the case of isolated structures, irrespectively of the number of unit cells considered in the simulation.

 

• Can the authors present a structure with a high Q-factor? as this is very important for sensing applications.

 

We added a brief description about bound states in the continuum and the importance of considering finite size effects. We added figure 6 which includes simulations of metasurfaces of different size highlighting the emerging BIC and the dependence of the linewidth upon the system size. We considered a suspended array of cylinders previously reported in literature which was employed as a sensor (ref. 44).

 

• Some more details about the simulation setting have to be included, such as the number of mesh cells, convergence criteria.

 

We employed the GMRES solver included in COMSOL Multiphysics and a tolerance of 10^-4. We employed a free tetrahedral meshing for all the environment with mesh size l_e/7, where l_e is the effective wavelength in the material. We enclosed the domain with Perfectly Matched Layers and scattering boundary conditions. We have now included this information in the main text.

 

• What could be the reasons behind the discrepancy in the results in Figs. 4&5 at small wavelengths compared to the large wavelengths?

 

The resonance at longer wavelength is related to the magnetic dipole resonance of the single pillar, thus it is well reproduced also with few resonators. As can be seen, increasing the number of resonators mainly affects the resonance at shorter wavelengths since it is related to the interaction between resonators.

• Interestingly, in Fig. 5, even for the 3x3 structure, the match of R is quite good for the large wavelengths, any clue? 

The resonance at larger wavelengths is related to a magnetic dipole inside the pillars. We note that this resonance is present also in the isolated pillar, thus it is well mimicked with few resonators, however the interaction with neighbor pillars results in a small blueshift.

 

• Line 16: Some relevant references related to sensing biological substances must be added.

 

We have now added references [10-12] related to biological sensing.

Round 2

Reviewer 1 Report

The author added contents to the paper which makes the  paper carry more weight. The paper can now be published in present form. 

Reviewer 3 Report

The authors have addressed the raised points and hence I recommend the publication of this paper in this journal.