Brillouin Zone Folding-Induced Magnetic Toroidal Dipole Metasurfaces for Tunable Mid-Infrared Upconversion

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript proposes a theoretical and numerical investigation of a gallium phosphide (GaP) dimer metasurface that exploits Brillouin-zone-folding-induced magnetic toroidal dipole quasi-guided modes (MTD-QGM) to achieve tunable mid-infrared (MIR) upconversion via sum-frequency generation (SFG). Using COMSOL-based electromagnetic simulations and multipolar decomposition analysis, the authors demonstrate that the metasurface supports a high-Q MTD resonance around 3101.8 nm and a pump resonance near 1273.2 nm. Through spatial mode overlap between these resonances, an SFG conversion efficiency of 7.9×10−4 is obtained, enabling the conversion of MIR radiation into the near-infrared region (~903 nm).

The work explores an interesting mechanism for nonlinear frequency conversion using toroidal multipolar resonances and Brillouin zone folding, and it attempts to address the narrow bandwidth limitation of symmetry-protected resonances by exploiting k-space stability. Overall, the manuscript is clearly structured and contains extensive numerical analysis. However, several issues should be addressed before the work can be considered for publication.

1. The entire study is based solely on numerical simulations without experimental validation. Since the proposed metasurface targets practical MIR detection and imaging applications, the authors should discuss the feasibility of fabrication and experimental realization, including potential fabrication tolerances for the GaP nanorod dimer structure.
2. The reported SFG conversion efficiency is relatively high for dielectric metasurfaces under the given conditions. The manuscript should more clearly justify whether the assumed input intensities (30 MW/cm² for the signal and 50 MW/cm² for the pump) are experimentally realistic and whether thermal or material damage effects could arise under such excitation levels.
3. The authors attribute the enhanced nonlinear response primarily to the MTD-QGM resonance induced by Brillouin zone folding. While the multipole decomposition supports this claim, additional quantitative analysis—such as field enhancement factors or comparison with structures lacking toroidal resonances—would strengthen the physical interpretation.
4. The discussion comparing Mode A, Mode B, and Mode C is useful, but the physical reasoning could be clearer. In particular, the explanation of the accidental BIC behavior of Mode C and its impracticality for nonlinear conversion would benefit from a more concise and physically intuitive discussion.
5. The method used to compute the SFG signal involves sequential electromagnetic simulations under the undepleted pump approximation. The authors should clarify the assumptions and limitations of this approach, especially regarding pump depletion, nonlinear back-action, and potential coupling between generated fields and resonant modes.
6. The definition of the SFG conversion efficiency should be discussed more carefully. It is unclear whether the calculated output power accounts for all radiated directions or only the transmitted component toward the substrate. A clarification of how the Poynting vector integration is implemented would improve reproducibility.
7. The manuscript claims that the MTD-QGM exhibits “exceptional k-space stability,” enabling broadband upconversion through angle tuning. It would be helpful to quantify the achievable tuning bandwidth and compare it with conventional quasi-BIC metasurfaces.
8. The polarization dependence of the SFG process is attributed to both metasurface geometry and the 𝜒(2) tensor symmetry of GaP. However, the manuscript does not explicitly state the crystal orientation used in the simulations. Providing this information and the corresponding nonlinear tensor components would improve clarity.
9. The manuscript would benefit from a broader comparison with existing nonlinear metasurface upconversion platforms, particularly those based on GaP, AlGaAs, or lithium niobate, to better position the novelty and performance of the proposed design.
10. Some recent related works (photonic BICs) could be cited to better contextualize this study and enrich the landscape of recent developments in this area, such as Chinese Optics Letters, 2025, 23(10): 103602

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This study investigates the enhancement of nonlinear frequency conversion efficiency via Brillouin-folded quasi-guided modes. The research is substantial and merits publication. Several comments are provided as follows:

How to distinguish between guided modes and bound states in the continuum (BICs).

How to identify the idler and signal waves.

What are the main factors affecting sum-frequency conversion efficiency?

Please check the format of the references for consistency and to update the bibliography with the latest research on nonlinear frequency conversion, such as Advanced Optical Materials 14 (3), e03449 (2026); Physical Review B 111 (7), 075301 (2025); Applied Physics Letters 127 (6), 061701 (2025).

Author Response

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Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

The paper presents a theoretical analysis of GaP toroidal dipole metasurfaces for tunable mid-infrared upconversion. The obtained results show that the all-dielectric metasurface demonstrates highly efficient mid-infrared (MIR) nonlinear upconversion due to high-Q magnetic toroidal dipole quasi-guided modes within a relatively wide wavelength range. These findings may be useful for applications in MIR molecular spectroscopy and environmental monitoring. However, a significant drawback of the work is the lack of experimental validation.

The manuscript requires improvement before it can be considered for publication:

1. The statement “The excitation mechanism of the MTD is depicted in Figure 1(b)” is incorrect, as the figure only illustrates the geometric dimensions of one metasurface period rather than the excitation mechanism.
2. The sentence “Each nanorod features a length of l = 1180 nm, a width of w = 580 nm, and a height of t = 555 nm” introduces parameters that are not clearly indicated in any schematic. The geometrical dimensions of the metasurface structure should be explicitly shown in the corresponding figure.
3. In the statement “while the dispersion of GaP is obtained from reference data [32],” it would be beneficial to include the dispersion curve directly in the paper for clarity.
4. The value of ΔL used in the simulation for determining the Q-factor is not specified and should be provided.
5. In the text: “Combined with its near-field distribution, which is shown in Figure 4(e) and (f), the electric field of Mode C is primarily localized at the interface between the nanorods and the substrate,” there is an inconsistency. According to the caption of Figure 4, panels (e) and (f) correspond to Mode B, not Mode C.
6. It is unclear which value of ΔL was used in the simulations presented in Figures 5–9. This should be clarified.
7. The reference  in  the paper text “[11,2,3]” is not correct.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

None.