Design of a Tunable Metamaterial Absorption Device with an Absorption Band Covering the Mid-Infrared Atmospheric Window
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsDear Editor,
This manuscript proposes a light absorber for IR wavelengths using a VO2 layer. The authors need to address important challenges, so I suggest a major revision at this stage.
1. The proposed geometry for VO2 is complex in terms of fabrication. Discuss the fabrication.
2. On what basis were the dimensions in Table 1 chosen? There is a need to optimize the structure effectively.
3. I feel that artificial intelligence has been used in this manuscript because some complex words have been used. It is suggested that the text be revised and the sentences simplified.
4. Write the wave propagation equations in the structure and explain the boundary conditions.
5. What is the temperature range and radiation power required for proper structure performance?
Kind regards
Author Response
Dear editor and reviewer:
We are grateful to the editor and reviewers for their constructive comments and suggestions on the revision of the manuscript. We have made all the necessary changes as suggested by the editor and reviewers. All the revisions in the manuscript and the supporting information have been highlighted in underline.
Reviewer #1:
Comment 1: The proposed geometry for VO2 is complex in terms of fabrication. Discuss the fabrication.
Response: Thanks for your valuable counsel and reading the manuscript carefully. As per your suggestion, I have given the preparation of VO2 structural shapes in the paper.
To enable practical implementation, we have outlined a fabrication methodology for the proposed absorption device. Initially, a 0.5 μm titanium (Ti) film is deposited onto a silicon (Si) substrate via magnetron sputtering. Subsequently, a 0.5 μm silicon dioxide (SiO2) layer is deposited onto the Ti film using ion beam sputtering. Following this, a 1.38 μm vanadium dioxide (VO2) layer is deposited onto the SiO2 film through magnetron sputtering. Finally, a dart-shaped VO2 structure is fabricated employing electron beam evaporation in conjunction with photolithography techniques.
Comment 2: On what basis were the dimensions in Table 1 chosen? There is a need to optimize the structure effectively.
Response: Thanks for your valuable counsel and reading the manuscript carefully. The dimensions in Table 1 were mainly obtained by parametric scanning of the structure of the absorption device. The following are the results of the parametric scanning.
Figure 6. (a) Absorption spectra of the absorbing device at different cycle lengths. (b) Absorption spectra of the absorption device at different distances between neighboring darts. (c) Absorption spectra of the absorption device at different dart lengths.
In the preceding section, we explored the electromagnetic field distribution of the absorption device. Here, we delve into the impact of the shape parameters of the absorption device. Figure 6. (a) illustrates the influence of the period length (P) of the unit structure of the absorption device on its absorption rate. The absorption peaks in the absorption curves experience a blueshift with an increase in period length, as depicted in the figure. For period lengths of P = 2.83 μm and 2.93 μm, the absorption device fails to achieve continuous absorption exceeding 90%. Conversely, at P = 3.13 μm and 3.23 μm, the absorption bandwidth of over 90% absorption narrows compared to that at P = 3.03 μm. Hence, we have selected P = 3.03 μm as the optimal cycle length for the unit structure of the absorption device. Figure 6. (b) demonstrates the impact of the blade length (L) of the top dart-shaped VO2 layer of the absorption device on its absorption rate. Absorption rates above 90% continuous absorption were not attainable at L = 0.66 μm, L = 0.86 μm, and L = 0.96 μm. Additionally, the absorption bandwidth at L = 0.56 μm is narrower than that at L = 0.76 μm. Consequently, L = 0.76 μm has been identified as the optimal parameter. Figure 6. (c) showcases the effect of the distance (W) between neighboring dart blades of the dart-shaped VO2 layer of the absorption device on its absorption. Notably, at W = 0.62 μm and 0.72 μm, the absorption bandwidth narrows compared to that at W = 0.82 μm. Furthermore, at W = 0.92 μm and 1.02 μm, the absorption rate mostly remains below 90%. Thus, W = 0.82 μm has been selected as the optimal parameter for the absorption device.
Figure 7. (a) Absorption spectra of the absorption device at different VO2 thicknesses. (b) Absorption spectra of the absorption device at different SiO2 thicknesses.
In the preceding section, we examined the shape parameters of the absorption device. In this section, we will delve into the thickness parameters of the absorption device. Figure 7. (a) and (b) display the absorption spectra of the absorption device for varying thicknesses of the VO2 layer and SiO2 layer, respectively. From Figure 7. (a), it is observed that the absorption bandwidth of the absorption device exceeds 90% as the VO2 thickness (H1) increases from 1.18 μm to 1.38 μm. However, the absorption bandwidth narrows as H1 is further increased to 1.58 μm. Consequently, the optimal parameter for the VO2 thickness H1 is determined to be 1.38 μm. Figure 7. (b) illustrates the impact of SiO2 thickness on the absorption rate. The absorption bandwidth of the absorption device exceeds 90% initially as the SiO2 thickness increases from H2 = 0.20 μm to H2 = 0.80 μm, reaching optimal absorption characteristics at 0.50 μm. Therefore, the optimal parameter for SiO2 thickness (H2) is chosen as 0.50 μm. Furthermore, upon comparing Figures 7. (a) and (b), it is noted that the absorption peaks of the absorption device undergo red-shifting as the thicknesses of both VO2 and SiO2 layers increase. This red-shifting phenomenon is attributed to interference theory. An increase in the thickness of the absorption device results in a greater phase difference of the electromagnetic wave, leading to a lengthening of the wavelength during resonance. In conclusion, the structural parameters of the absorption device have been optimized through an analysis of absorption rates at different structural parameters.
Comment 3: I feel that artificial intelligence has been used in this manuscript because some complex words have been used. It is suggested that the text be revised and the sentences simplified.
Response: Thanks for your valuable counsel and reading the manuscript carefully. I've made changes to the complex vocabulary in the paper.
Comment 4: Write the wave propagation equations in the structure and explain the boundary conditions.
Response: Thanks for your valuable counsel and reading the manuscript carefully. In response to your suggestions, I have made the following changes.
When the electromagnetic wave is incident into the absorbing device, the wave number at this point can be expressed by equation (7) because the material has loss:
(7)
Here is the angular frequency. is the equivalent magnetic permeability of the absorbing device. is the equivalent dielectric constant of the absorbing device. At this point, the electromagnetic wave is absorbed during propagation, as shown in Equation (8):
(8)
Here is the attenuation constant, which is related to the loss characteristics of the material. We use Perfectly Matched Layer (PML) boundary conditions in the Z-direction when designing the absorber device. Periodic boundary conditions are used in the X and Y directions.
Comment 5: What is the temperature range and radiation power required for proper structure performance?
Response: Thanks for your valuable counsel and reading the manuscript carefully. I give the following answer to this question.
VO2 has a phase transition temperature of 340 K, which is critical for its thermochromic properties. For optimum performance of an infrared absorber device, the operating temperature should be maintained within a range that allows VO2 to transition between insulating and metallic phases. Typically, this range is between 30°C and 100°C, depending on the specific design and application. Below 30°C, VO2 remains in the insulating phase; above 100°C, VO2 may degrade or lose the desired properties. Absorption devices also have requirements for the radiant power of the incident light. In the low power range (< 10 mW/cm²) VO2 can operate normally, the phase change behaviour is reversible and the material does not degrade. In the medium power range (10-100 mW/cm²), the temperature of VO2 increases significantly with increasing incident light power. If the temperature exceeds the phase transition temperature but is below the degradation temperature, VO2 may temporarily lose its properties (e.g., dynamic optical properties), but this can be restored upon cooling. In the high power range (> 100 mW/cm²), where the incident optical power is too high, the temperature of VO2 may exceed its degradation temperature, resulting in irreversible oxidation or structural damage of the material, which can lead to loss of its properties. Taken together, the incident light power was controlled in the range of 10-50 mW/cm² to avoid overheating and degradation.
Thank you for your attention and patience, and if you have any questions, please don't hesitate to contact me.
Yours sincerely
Yougen Yi
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for Authorshe manuscript photonics-3429736 mainly presents a study about a particular metamaterial absorption system. The authors considered and absorption band covering the mid-infrared atmospheric window in the device proposed. Please see below a list of comments to the authors:
1. The unit structure of the absorption unit proposed should be justified with better details.
2. The selection of the materials for this research should be justified.
3. How is the influence of the size of the structure proposed? How the authors proposed the parameters shown in table 1?
4. Do the system is dependent on incident polarization?
6. How is the vectorial behavior if the system? The angle of incidence can be neglected?
7. The label in the color bars are missing.Moreover, absorption and absorbance is different, please correct.
8. The authors could improve the perspectives described. The authors are invited to see and discuss about fractional thermal transport in advanced materials for future work. You can see for instance: https://doi.org/10.1016/j.ijthermalsci.2019.106136
9. The main findings should be confronted with updated publications in the topic. You can see for instance: https://doi.org/10.1016/j.optcom.2024.130816
10. The importance of the publications cited in the text could be better visualized if collective form of citation is avoided in the text.
Author Response
Dear editor and reviewer:
We are grateful to the editor and reviewers for their constructive comments and suggestions on the revision of the manuscript. We have made all the necessary changes as suggested by the editor and reviewers. All the revisions in the manuscript and the supporting information have been highlighted in underline.
Reviewer #2:
Comment 1: The unit structure of the absorption unit proposed should be justified with better details.
Response: Thanks for your valuable counsel and reading the manuscript carefully. Following your suggestion, I have described the unit structure of the absorption unit in more detail.
Our proposed absorption device is a three-layer structure. Its bottom layer is a titanium substrate. The middle layer is a silica dielectric layer. The top layer is a dart-shaped VO2 resonator layer. VO2 undergoes a reversible phase transition from the insulating to the metallic state at ~68°C, which significantly alters its optical and electrical properties. Tunable absorption of electromagnetic waves can be achieved using its phase transition properties. Moreover, in the infrared band, VO2 can effectively absorb infrared radiation at specific wavelengths, thus achieving efficient infrared absorption. Titanium, with its high reflectivity, is used as a substrate material to enhance the overall performance of the IR absorption device.SiO2, with its low refractive index, is used as a dielectric layer to reduce the reflection loss of the incident light, thus improving the absorption efficiency. In Figgure 1, H3 is the thickness of the titanium substrate, H2 is the thickness of the middle SiO2 layer, H1 is the thickness of the top VO2 layer, P is the period length of the absorber unit structure, L is the horizontal distance between two adjacent dart edges of the dart-shaped VO2 structure, and W is the length of each dart edge. Specific values for these structural parameters are given in Table 1.
Comment 2: The selection of the materials for this research should be justified.
Response: Thanks for your valuable counsel and reading the manuscript carefully. I have made changes in the paper as per your suggestion.
VO2 undergoes a reversible phase transition from the insulating to the metallic state at ~68°C, which significantly alters its optical and electrical properties. Tunable absorption of electromagnetic waves can be achieved using its phase transition properties. Moreover, in the infrared band, VO2 can effectively absorb infrared radiation at specific wavelengths, thus achieving efficient infrared absorption. Titanium, with its high reflectivity, is used as a substrate material to enhance the overall performance of the IR absorption device.SiO2, with its low refractive index, is used as a dielectric layer to reduce the reflection loss of the incident light, thus improving the absorption efficiency.
Comment 3: How is the influence of the size of the structure proposed? How the authors proposed the parameters shown in table 1?
Response: Thanks for your valuable counsel and reading the manuscript carefully. The dimensions in Table 1 were mainly obtained by parametric scanning of the structure of the absorption device. The following are the results of the parametric scanning.
Figure 6. (a) Absorption spectra of the absorbing device at different cycle lengths. (b) Absorption spectra of the absorption device at different distances between neighboring darts. (c) Absorption spectra of the absorption device at different dart lengths.
In the preceding section, we explored the electromagnetic field distribution of the absorption device. Here, we delve into the impact of the shape parameters of the absorption device. Figure 6. (a) illustrates the influence of the period length (P) of the unit structure of the absorption device on its absorption rate. The absorption peaks in the absorption curves experience a blueshift with an increase in period length, as depicted in the figure. For period lengths of P = 2.83 μm and 2.93 μm, the absorption device fails to achieve continuous absorption exceeding 90%. Conversely, at P = 3.13 μm and 3.23 μm, the absorption bandwidth of over 90% absorption narrows compared to that at P = 3.03 μm. Hence, we have selected P = 3.03 μm as the optimal cycle length for the unit structure of the absorption device. Figure 6. (b) demonstrates the impact of the blade length (L) of the top dart-shaped VO2 layer of the absorption device on its absorption rate. Absorption rates above 90% continuous absorption were not attainable at L = 0.66 μm, L = 0.86 μm, and L = 0.96 μm. Additionally, the absorption bandwidth at L = 0.56 μm is narrower than that at L = 0.76 μm. Consequently, L = 0.76 μm has been identified as the optimal parameter. Figure 6. (c) showcases the effect of the distance (W) between neighboring dart blades of the dart-shaped VO2 layer of the absorption device on its absorption. Notably, at W = 0.62 μm and 0.72 μm, the absorption bandwidth narrows compared to that at W = 0.82 μm. Furthermore, at W = 0.92 μm and 1.02 μm, the absorption rate mostly remains below 90%. Thus, W = 0.82 μm has been selected as the optimal parameter for the absorption device.
Figure 7. (a) Absorption spectra of the absorption device at different VO2 thicknesses. (b) Absorption spectra of the absorption device at different SiO2 thicknesses.
In the preceding section, we examined the shape parameters of the absorption device. In this section, we will delve into the thickness parameters of the absorption device. Figure 7. (a) and (b) display the absorption spectra of the absorption device for varying thicknesses of the VO2 layer and SiO2 layer, respectively. From Figure 7. (a), it is observed that the absorption bandwidth of the absorption device exceeds 90% as the VO2 thickness (H1) increases from 1.18 μm to 1.38 μm. However, the absorption bandwidth narrows as H1 is further increased to 1.58 μm. Consequently, the optimal parameter for the VO2 thickness H1 is determined to be 1.38 μm. Figure 7. (b) illustrates the impact of SiO2 thickness on the absorption rate. The absorption bandwidth of the absorption device exceeds 90% initially as the SiO2 thickness increases from H2 = 0.20 μm to H2 = 0.80 μm, reaching optimal absorption characteristics at 0.50 μm. Therefore, the optimal parameter for SiO2 thickness (H2) is chosen as 0.50 μm. Furthermore, upon comparing Figures 7. (a) and (b), it is noted that the absorption peaks of the absorption device undergo red-shifting as the thicknesses of both VO2 and SiO2 layers increase. This red-shifting phenomenon is attributed to interference theory. An increase in the thickness of the absorption device results in a greater phase difference of the electromagnetic wave, leading to a lengthening of the wavelength during resonance. In conclusion, the structural parameters of the absorption device have been optimized through an analysis of absorption rates at different structural parameters.
Comment 4: Do the system is dependent on incident polarization?
Response: Thanks for your valuable counsel and reading the manuscript carefully. The absorption device we have designed is insensitive to the polarisation of the incident light. Here are the results of the simulation.
Figure 8. (a) Absorption spectra of the absorbing device in TE mode at different incidence angles (0°-60°). (b) Absorption spectra of the absorption device at different incidence angles (0°-60°) in TM mode. (c) Absorption spectra of the absorption device at different polarization angles (0°-90°).
Figure 8. (c) illustrates the absorption spectra of the absorption device at various polarization angles, demonstrating minimal changes in absorption characteristics within the 0°-90° polarization angle range.
Comment 6: Do the system is dependent on incident polarization?
Response: Thanks for your valuable counsel and reading the manuscript carefully. Here are the answers to the question.
Figure 8. (a) Absorption spectra of the absorbing device in TE mode at different incidence angles (0°-60°). (b) Absorption spectra of the absorption device at different incidence angles (0°-60°) in TM mode. (c) Absorption spectra of the absorption device at different polarization angles (0°-90°).
The sensitivity to the angle of incidence and polarization plays a crucial role in the functionality of the device. Hence, we explore the impact of varying angles of incidence and polarization on the absorption device in Figure 8, utilizing 5° steps to scan the incidence and polarization angles. In Figure 8. (a), the absorption spectra of the absorption device at different incidence angles in TE mode are depicted. It is observed that the absorption bandwidth remains relatively consistent within the incidence angle range of 0°-30°. Subsequently, the absorption bandwidth shortens between 30°-50°, with minimal changes in absorption. Beyond 50°, specifically within 50°-60°, both the absorption bandwidth and absorption of the absorption device decrease. Figure 8. (b) showcases the impact of different incidence angles on the absorption device in TM mode, revealing a similar trend to TE mode, as observed in Figure 8. (a). Figure 8. (c) illustrates the absorption spectra of the absorption device at various polarization angles, demonstrating minimal changes in absorption characteristics within the 0°-90° polarization angle range. Based on the analysis, it can be concluded that our designed absorption device displays excellent insensitivity to both the angle of incidence and polarization. This insensitivity signifies the high potential applicability of our design.
Comment 7: The label in the color bars are missing.Moreover, absorption and absorbance is different, please correct.
Response: Thanks for your valuable counsel and reading the manuscript carefully. I have corrected and highlighted the errors.
Comment 8: The authors could improve the perspectives described. The authors are invited to see and discuss about fractional thermal transport in advanced materials for future work. You can see for instance: https://doi.org/10.1016/j.ijthermalsci.2019.106136
Response: Thanks for your valuable counsel and reading the manuscript carefully. Based on your suggestions, I have made the following changes.
By rationally designing the structural parameters and material composition of metamaterial absorption devices, selective absorption and suppression of electromagnetic waves in specific frequency bands can be realized[16].
Comment 9: The main findings should be confronted with updated publications in the topic. You can see for instance: https://doi.org/10.1016/j.optcom.2024.130816
Response: Thanks for your valuable counsel and reading the manuscript carefully. Based on your suggestions, I have made the following changes.
And most of the metamaterial infrared absorbers have a narrow absorption bandwidth and the absorption characteristics are not tunable[21].
Comment 10: The importance of the publications cited in the text could be better visualized if collective form of citation is avoided in the text.
Response: Thanks for your valuable counsel and reading the manuscript carefully. I've made changes to the quotes in the paper.
Thank you for your attention and patience, and if you have any questions, please don't hesitate to contact me.
Yours sincerely
Yougen Yi
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsThe authors designed and theoretically studied thermally tunable VO2-based metamaterial absorption device at infrared frequencies. Importantly, at a temperature of 342 K, the absorption bands with over 90% absorption range from 6.10 μm to 17.42 μm, featuring an absorption bandwidth of 11.32 μm that covers the mid-infrared atmospheric window (8 μm-14 μm).
In general, the manuscript is interesting and carefully thought out. Nevertheless, I believe that additional discussion covering the following points could have increased its substantive value:
1. In the introduction, the authors mention that “Metamaterials have been subject to extensive research and dramatic advances over the past few decades, and have attracted interest for their various exotic properties and potential application areas.”. It is worth mentioning here several concepts of such metamaterials, i.e.: Advanced Optical Materials 10.19 (2022): 2200750; Materials & Design 221 (2022): 110920, etc.
2. Why was this particular meta-surface model proposed, i.e. a particular cross-shaped element? What is its unique property from a physical point of view in terms of the proposed application? Please explain.
3. What tool was used to implement the theoretical model?
Comments for author File: Comments.pdf
Author Response
Dear editor and reviewer:
We are grateful to the editor and reviewers for their constructive comments and suggestions on the revision of the manuscript. We have made all the necessary changes as suggested by the editor and reviewers. All the revisions in the manuscript and the supporting information have been highlighted in underline.
Reviewer #3:
Comment 1: In the introduction, the authors mention that “Metamaterials have been subject to extensive research and dramatic advances over the past few decades, and have attracted interest for their various exotic properties and potential application areas.”. It is worth mentioning here several concepts of such metamaterials, i.e.: Advanced Optical Materials 10.19 (2022): 2200750; Materials & Design 221 (2022): 110920, etc.
Response: Thanks for your valuable counsel and reading the manuscript carefully. I have read the literature and made changes to the article.
Metamaterials have witnessed tremendous progress over the past few decades, capturing widespread interest owing to their extraordinary properties and vast potential for diverse applications[16-18].
- Kowerdziej, R.; Ferraro, A.; Zografopoulos, D.C.; Caputo, R. Soft-Matter-Based Hybrid and Active Metamaterials. Advanced Optical Materials 2022, 10, 2200750. https://doi.org/10.1002/adom.202200750.
- Esfandiari, M.; Lalbakhsh, A.; Shehni, P.N.; Jarchi, S.; Ghaffari-Miab, M.; Mahtaj, H.N.; Reisenfeld, S.; et al. Recent and emerging applications of Graphene-based metamaterials in electromagnetics. Materials & Design 2022, 221, 110920. https://doi.org/10.1016/j.matdes.2022.110920.
- Lee, Y. Metamaterials and Their Devices. Crystals 2025, 15, 119. https://doi.org/10.3390/cryst15020119.
Comment 2: Why was this particular meta-surface model proposed, i.e. a particular cross-shaped element? What is its unique property from a physical point of view in terms of the proposed application? Please explain.
Response: Thanks for your valuable counsel and reading the manuscript carefully. I have already answered the questions posed and highlighted them in the paper.
Figure 9. Different surface shapes and corresponding absorption curves.
In this study, we initially considered other surface shapes as well, such as circular or square structures. We exemplify several shapes in Figure 9 and give their absorption curves. As shown in the figure, the dart surface shape we designed consistently exhibits excellent performance in terms of absorption bandwidth and absorption efficiency. The sharp edges and corners of the surface structure of this dart shape enhance the local electromagnetic field strength, leading to stronger photomatter interactions. This property is essential for achieving high absorption rates, as it maximises the dissipation of energy within the metasurface structure. Moreover, this dart-like structure has a high degree of symmetry, making it inherently independent of polarisation. This is a key feature for infrared absorption applications as it ensures consistent performance regardless of the polarisation state of the incident light. This property is particularly advantageous in practical applications where the polarisation of the incident radiation may change.
Comment 3: What tool was used to implement the theoretical model?
Response: Thanks for your valuable counsel and reading the manuscript carefully. I give the following answer to this question.
We used FDTD solutions simulation software for simulation.
To enable practical implementation, we have outlined a fabrication methodology for the proposed absorption device. Initially, a 0.5 μm titanium (Ti) film is deposited onto a silicon (Si) substrate via magnetron sputtering. Subsequently, a 0.5 μm silicon dioxide (SiO2) layer is deposited onto the Ti film using ion beam sputtering. Following this, a 1.38 μm vanadium dioxide (VO2) layer is deposited onto the SiO2 film through magnetron sputtering. Finally, a dart-shaped VO2 structure is fabricated employing electron beam evaporation in conjunction with photolithography techniques.
Thank you for your attention and patience, and if you have any questions, please don't hesitate to contact me.
Yours sincerely
Yougen Yi
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsDear Editor,
The manuscript has been polished based on the raised comments, so I think it meets the acceptance level. At this round, I recommend the manuscript for publication.
Kind regards
Author Response
Dear reviewer
Thank you very much for your help.
Reviewer 2 Report
Comments and Suggestions for AuthorsI appreciate the effort of the authors to improve the presentation of their work; however, fundamental issues are still present, please see below:
*It is not clear how this material cannot be dependent on incident polarization. Experimental evidences or comparative methods should be employed.
**The following two points raised in the initial review stage were avoided: 5. How is the vectorial behavior if the system? 6. The angle of incidence can be neglected?
***The perspectives were not properly discussed as suggested.
Author Response
Dear editor and reviewer:
We are grateful to the editor and reviewers for their constructive comments and suggestions on the revision of the manuscript. We have made all the necessary changes as suggested by the editor and reviewers. All the revisions in the manuscript and the supporting information have been highlighted in underline.
Reviewer #2:
Comment 1: It is not clear how this material cannot be dependent on incident polarization. Experimental evidences or comparative methods should be employed.
Response: Thanks for your valuable counsel and reading the manuscript carefully. Based on your suggestions, I have made changes to the relevant content, please see below.
Figure 8. (a) Surface electric field distribution of the absorbing device in TE mode at an incident wavelength of 6.57 µm. (b) Surface electric field distribution of the absorbing device in TM mode at an incident wavelength of 6.57 µm. (c) Absorption spectra of the absorption device at different polarisation angles (0°-90°).
The sensitivity to the angle of incidence and polarization plays a crucial role in the functionality of the device [59-63]. In contrast, the vector behaviour of this infrared absorbing system of our design is characterized precisely by a polarisation-insensitive response. This is attributed to the highly symmetric structure of the surface of the proposed infrared absorbing device. Due to the geometrical symmetry, light of different polarisation directions excites similar electromagnetic resonance modes, and the electric field distribution and resonance modes are homogeneous, independent of the incident polarisation direction. We give in Figure. 8(a) and (b) the electric field distributions of the absorbing device in TE and TM modes for an electromagnetic wavelength of 6.57 µm. As shown, the surface electric field maps of the absorber device in TE and TM modes are rotationally symmetric and have the same intensity. This indicates that the electric field vectors exhibit the same pattern for TE polarisation and TM polarisation, which suggests that the electromagnetic response of the absorber device is consistent across polarisation states. We scanned the polarisation angle in 5° steps using FDTD simulation software. The scanning results are shown in Figure. 8(c). The results further confirm that the absorption spectra of randomly polarised light are almost identical, thus validating the polarisation-independent nature of the system.
Comment 2: The following two points raised in the initial review stage were avoided: 5. How is the vectorial behavior if the system? 6. The angle of incidence can be neglected?
Response: Thanks for your valuable counsel and reading the manuscript carefully. We apologise for the omission in our previous response. We hereby reissue our response.
Regarding comment 5 we give the following response:
Figure 8. (a) Surface electric field distribution of the absorbing device in TE mode at an incident wavelength of 6.57 µm. (b) Surface electric field distribution of the absorbing device in TM mode at an incident wavelength of 6.57 µm. (c) Absorption spectra of the absorption device at different polarisation angles (0°-90°).
The sensitivity to the angle of incidence and polarization plays a crucial role in the functionality of the device [59-63]. In contrast, the vector behaviour of this infrared absorbing system of our design is characterized precisely by a polarisation-insensitive response. This is attributed to the highly symmetric structure of the surface of the proposed infrared absorbing device. Due to the geometrical symmetry, light of different polarisation directions excites similar electromagnetic resonance modes, and the electric field distribution and resonance modes are homogeneous, independent of the incident polarisation direction. We give in Figure. 8(a) and (b) the electric field distributions of the absorbing device in TE and TM modes for an electromagnetic wavelength of 6.57 µm. As shown, the surface electric field maps of the absorber device in TE and TM modes are rotationally symmetric and have the same intensity. This indicates that the electric field vectors exhibit the same pattern for TE polarisation and TM polarisation, which suggests that the electromagnetic response of the absorber device is consistent across polarisation states. We scanned the polarisation angle in 5° steps using FDTD simulation software. The scanning results are shown in Figure. 8(c). The results further confirm that the absorption spectra of randomly polarised light are almost identical, thus validating the polarisation-independent nature of the system.
Regarding comment 6 we give the following response:
Figure 9. (a) Absorption spectra of the absorbing device in TE mode for different angles of incidence (0°-60°). (b) Surface electric field distribution of the absorption device at = 0° incidence in TE mode. (c) Surface electric field distribution of the absorption device in TE mode at = 60° incidence. (d) Absorption spectra of the absorption device in TM mode at different angles of incidence (0°-60°). (e) Surface electric field distribution of the absorption device in TM mode at = 0° incidence. (f) Surface electric field distribution of the absorption device in TM mode at = 60° incidence.
In this section, we explore the effect of the angle of incidence of electromagnetic waves on the absorbing device in different modes. Figure. 9 (a) shows the absorption spectra of the absorber device in TE mode for different incidence angles. It is observed that the absorption bandwidth remains relatively uniform in the range of 0°-30° incidence angle. Subsequently, the absorption bandwidth shortens between 30° and 50° with very little change in absorption. As the angle of incidence exceeds 50°, especially between 50° and 60°, the absorption bandwidth and absorbance of the absorber decreases. Figure. 9 (b) and (c) show that the excitation position of the electric field on the surface of the absorber device does not change significantly as the angle of incidence increases, but the excitation intensity changes. Figure. 9 (d) illustrates the effect of different incidence angles on the absorber device for TM mode, which is similar to the trend observed in Figure. 9 (a) for TE mode. Figure. 9 (e) and (f) are also similar to the features in TE mode. Based on the above analyses, it can be concluded that the electromagnetic wave excites similar electromagnetic resonance (EMR) modes at varying angles of incidence, with only a slight change in intensity. Therefore, our designed absorber device is able to maintain excellent absorption characteristics even at larger incidence angles. This performance indicates the high potential applicability of our design [64-66].
Comment 3: The perspectives were not properly discussed as suggested.
Response: Thanks for your valuable counsel and reading the manuscript carefully. We have discussed fractional heat transfer appropriately in the paper. In our future work, we will improve the descriptive perspective to improve the quality of our work.
This study used a general analytical approach and only explored the absorption effect of the absorber device. We can also use fractional heat transport models to enhance the analysis of transient heat dissipation in infrared absorbing devices. For example, the modified Caputo fractional derivative can capture the memory effect in thermal diffusion, especially under pulsed laser irradiation. Furthermore, the size-dependent thermal conductivity observed in 2D materials suggests that the fractional model may be useful for optimising nanostructured absorber layers with controlled defects. Moreover, the fractional heat transport model has many applications not only in thermal management of infrared absorbers as well, but also has advantages in material design and thermal transport modulation. In future studies, the use of fractional heat transport models will be focused to increase the depth of the work.
Thank you for your attention and patience, and if you have any questions, please don't hesitate to contact me.
Yours sincerely
Yougen Yi
Author Response File: Author Response.pdf
Round 3
Reviewer 2 Report
Comments and Suggestions for AuthorsI agree with the reviewed version of the work. Then I can recommend this manuscript for publication in present form.
