High-Efficiency Mid-Infrared Transmission Modulator Based on Graphene Plasmon Resonance and Photonic Crystal Defect States

Comments 1: the authors mentioned that a low doped Ge layer is used for gate electrode. I am not sure whether all Ge layers are doped or not？

Response 1: Thank you for pointing this out. Initially, we intended to dope the germanium layer closest to the graphene nanoribbon to serve as the gate electrode. However, in our subsequent analysis of graphene gate modulation, we found that to achieve a Fermi level adjustment of 0.5 eV in graphene with a gate dielectric thickness exceeding 1 μm, the required voltage would reach 1 kV, which significantly limits the practical application of the device. We have now adopted a revised gate electrode strategy, using metallic slit antennas as gate electrode, with the thin spacer layer between graphene and the metal acting as the gate dielectric. This approach has enabled the gate voltage to be reduced to within 50 V. Corresponding revisions have been made in the manuscript:

“A thin dielectric layer, referred to as the spacer layer, is conformally grown over the metallic structure, creating suspended graphene regions above the slits (Figure 1b). The structure employs an electrical gating mechanism where graphene nanoribbons connect to the positive terminal of a voltage source, while the metal slit attenna serves as the gate electrode.”  (lines 107-111)

(lines 123)

Comments 2: as mentioned in line 118, the graphene is imbeded into CaF2. However, it looks like the graphene is positioned within a dielectric layer?

Response 2: Thank you for your question. We apologize for the confusion caused by our unclear description. In the paper, the graphene device is placed in the dielectric layer between the photonic crystals. It should be clarified that when selecting materials for the dielectric layer in our simulations, we used CaF₂, which is the same as the low-refractive-index material employed in the photonic crystals. We have now added an explanation in the main text to eliminate any ambiguity.：

“The PC cavity consists of alternating layers of calcium fluoride (n₁ = 1.35) and germanium (n₂ = 4), arranged symmetrically to form an optical cavity. The graphene plasmonic device is centrally positioned within a dielectric cavity layer (CL). In this paper, we select calcium fluoride as the dielectric material (n₃ = n₁) to simplify the design process and reduce the variety of materials required for device fabrication. This arrangement intentionally breaks the PC periodicity, generating a defect state that amplifies light intensity in the central slit antenna region, further enhancing light-plasmon interactions and improving modulation depth.” （lines 115-122）

Comments 3: the electric field is Y direction polarized, so the height h_d in figure 1b also affect the field enhancement but this is not mentioned in the paper

Response 3: Thank you for pointing this out. We have now supplemented the influence of the cavity layer thickness h_d on the electric field enhancement of AEGP, and also elaborated on how variations in h_d affect the overall modulation performance of the device in the manuscript:

“Notably, modulation characteristics exhibit higher sensitivity to CL thickness variations, as this parameter controls the cavity interference strength and thereby the electric field enhancement factor at the AEGP structure, as shown in Figure 7f.

Figure 7 (e) variations of modulation depth and operating frequency band with CL thickness; (f) average electric field gain factor at the AEGP structure under 28.3 THz after introducing photonic crystals with different CL layer thicknesses.” （lines,435-437 and 454-456）

Comments 4: in the introduction part, when talking about lithium niobate modulators, i recommend to cite the following papers: "Improving Linewidth and Extinction Ratio Performances of Lithium Niobate Ring Modulator Using Ring‐Pair Structure."Advanced Photonics Research 4.8 (2023): 2300169. "High-speed electro-optic modulators based on thin-film lithium niobate."Nanomaterials 14.10 (2024): 867.

Response 4: Thank you for your suggestion. We have carefully reviewed these two papers, which are representative in the research field of lithium niobate modulators. Therefore, we have cited them when first mentioning lithium niobate modulators and added them to the reference list：

“Although efficient modulators based on lithium niobate electro-optic technology have been successfully developed for near-infrared and visible light communications, enabling high-speed fiber optic systems [3-6], ...

5.Hou, S.; Hu, H.; Liu, Z.; et al. High-Speed Electro-Optic Modulators Based on Thin-Film Lithium Niobate. Nanomaterials 2024, 14 (10), 867.

6.Hou, S.; Hu, H.; Xing, W.; et al. Improving Linewidth and Extinction Ratio Performances of Lithium Niobate Ring Modulator Using Ring‐Pair Structure. Adv. Photonics Res., 2023, 4(8), 2300169.”

（lines,43-45 and 533-536）