Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The comments in the attached document

Comments for author File: Comments.pdf

Author Response

1. First, the manuscript frequently emphasizes operation in the "visible-frequency" regime, although part of the numeirical analysis entends into the near-infrared (up to 1000 nm). This does not detract from the results, but a clearer distinction between visible and near-infrared regimes would improve conceptual precision.

Response: We thank the reviewer for this comment. We have made the following modifications:

on line 19 of the first page：Owing to the exotic and ray-like propagating properties of HPPs, the negative refraction inspired superlens can easily reach into deep subwavelength scale, with spatial confinement of 800 nm near-infrared light wavelength to below 150 nm focal spots.

on line 71 of page 2：More recently, a new-type vdWs polaritons have been reported in thin-films of molybdenum dioxide chloride (MoOCl₂)[27-33], a natural vdWs crystal in the visible and near-infrared frequencies.

on line 79 of page 2：Within this context, here we study and unveil the counterintuitive negative refraction phenomena in such natural vdWs material based hetero-junctions in the visible and near-infrared frequency.

on line 249 of page 7：More importantly, owing to the large wavevector and ray-like propagating properties of HPPs, the negative refraction inspired superlens can reach into deep subwavelength scale, with spatial confinement of 800 nm near-infrared wavelengths to below 150 nm focal spots.

on line 281 of page 8：In summary, our research has achieved low-loss, ray-like deep subwavelength negative refraction highly confined HPPs within the visible and near-infrared light spectrum.

on line 285 of page 8：Moreover, the aforementioned focusing phenomena inherited the exceptional light squeezing capability of HPPs, enabling the confinement of 800-nanometer near-infrared light wavelengths into focal spots smaller than 150 nanometers with low loss.

2. Also, different MoOCl₂ thicknesses are used in dispersion analysis, heterojunction simulations and parameter sweeps. While this approach is reasonable, a short explanation of the reference configuration and the rationale for varying thickness would help the readers better interpret the reported trends.

Response: We sincerely appreciate the reviewer's valuable suggestion. 

In dispersion analysis, we simulated molybdenum oxide dichloride material with a thickness of 10 nm. At this thickness, the dispersion diagram was very clear, with the wavelength compression ratio reaching a maximum value of 5. In the heterojunction simulations, the structures composed of 20 nm and 30 nm thick MoOCl₂ both exhibited a good negative refraction effect, with the optimal performance observed at 20 nm. Therefore, the base thickness was fixed at 20 nm for the parameter sweep.

3. Moreover, the manuscript contains a number of issues including word misspellings and grammatical errors that occasionally interrupt the flow of the text:

One the other hand - on the other hand

negative refraction of surface plasmon polaritons have been extensively studied -negative refraction of surface plasmon polaritons has been extensively studied

focal sport - focal spot

Response: We sincerely appreciate the reviewer's suggestions. We have implemented corresponding modifications:

on line 12 of the first page：In the visible regime, negative refraction of surface plasmon polaritons has been extensively studied in conventional plasmonic and metamaterial systems, however the inherent metallic losses remain a challenge that hinder its practical applications.

on line 45 of page 2: On the other hand, such negative reflection rely on the extreme anisotropic properties of layered vdW materials, which largely reduce the fabricate difficulties.

on line 212 of page 6 (d): MoOCl₂ thickness = 30 nm; dipole wavelengths of 800 nm (top panel) and 950 nm (bottom panel). The line plots on the right of (c) and (d) show the electric field (E-field) distribution along the line perpendicular to the x-axis at the focal spot.

4. Moreover, Refs. 11 and 12 are not directly related to polariton optics or negative refraction. It is proposed that these references be removed or replaced with references directly relevant to nanophotonics or hyperbolic polaritons.

Response: We sincerely appreciate the reviewer's suggestions and have accordingly removed these references.

on line 35 of the first page：The past decades, negative refraction and superlensing have been predicted and demonstrated in a variety of metamaterial [7,8] and photonic crystal [9,10] systems, across electromagnetic and optical spectrum.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The authors proposed achieving deep subwavelength negative refraction in the visible light band within a MoOCl₂ lateral heterostructure, a study with significant innovation and potential applications. They verified the existence of the negative refraction effect through theoretical modeling and FDTD simulations, and explored the influence of wavelength, thickness, and crystal orientation on its properties. The article is clearly structured and the theoretical analysis is relatively complete, suitable for publication in 《Photonics》. However, several significant shortcomings exist and require further clarification and improvement in the revision. Specific issues are as follows:

1. The authors emphasize that their work achieved "low-loss negative refraction in the visible light band" and "tunable tilt focusing." However, there are already systematic reports in the literature on negative refraction, superlensing, and focusing behavior in vdW materials (such as α-MoO₃ and CrSBr). The main novelty of this manuscript seems to focus on extending the material system from infrared to visible light, and achieving focus deflection within the same material through crystal orientation rotation. Therefore, the authors need to strengthen and clarify their description of the innovative aspects.
2. The authors did not explicitly provide references or first-principles calculation details for key parameters such as the dielectric constant and Q-factor of MoOCl₂ used in the manuscript. In particular, the manuscript mentions "low loss in the visible light band," requiring data support for the loss term in the dielectric constant. Could you please provide a graph of the dielectric tensor of MoOCl₂ as a function of frequency in the supplementary materials? And could you clearly specify which data from references [27-33] were used?
3. The wave vector matching condition for negative refraction is only schematically illustrated in Figure 1(e), which is a qualitative analysis and lacks quantitative analysis (such as isofrequency plots and group velocity direction calculations).
4. The authors used a 0.25 nm spatial grid for the FDTD simulation, which is extremely rare in visible light FDTD simulations, requiring very high computational resources; and is prone to numerical dispersion and material parameter interpolation errors. Could the authors please confirm the simulation parameter settings?

Author Response

1. The authors emphasize that their work achieved "low-loss negative refraction in the visible light band" and "tunable tilt focusing." However, there are already systematic reports in the literature on negative refraction, superlensing, and focusing behavior in vdW materials (such as α-MoO₃ and CrSBr). The main novelty of this manuscript seems to focus on extending the material system from infrared to visible light, and achieving focus deflection within the same material through crystal orientation rotation. Therefore, the authors need to strengthen and clarify their description of the innovative aspects.

Response: We sincerely appreciate the reviewer's valuable input.

As the reviewer mentioned, the main innovations of this paper are concentrated on the following two points. First, we have achieved negative refraction in the visible light band, successfully extending the operational range from the infrared band. Second, we have realized active control over the deflection of the focal point.

Specifically, these contributions are detailed on line 81 of the second page.

2. The authors did not explicitly provide references or first-principles calculation details for key parameters such as the dielectric constant and Q-factor of MoOCl₂ used in the manuscript. In particular, the manuscript mentions "low loss in the visible light band," requiring data support for the loss term in the dielectric constant. Could you please provide a graph of the dielectric tensor of MoOCl₂ as a function of frequency in the supplementary materials? And could you clearly specify which data from references [27-33] were used?

Response: We sincerely appreciate the reviewer's valuable suggestions. Figure 1(c) illustrates the quality factor (Q factor) of MoOCl₂, highlighting its low-loss characteristics. Detailed calculations of permittivity and quality factors are provided in Ref. [29](Venturi et al. 2024).

The figure can be seen in the Word document.

Figure R1. Quality factor of MoOCl₂. The x-axis represents the wavelength, spanning the range from 500 nm to 900 nm.

The reference[31] (Gao et al. 2021) presents the dielectric constants of monolayer and bulk molybdenum oxychloride (MoOCl₂) calculated using density functional theory (DFT). The Drude-Lorentz (DL) model is described in the supplementary material of Ref. (Venturi, et al. 2024):

The figures and formulas can be found in the Word document.

Figure R2. The real part of the dielectric constant of molybdenum oxychloride (MoOCl₂). The permittivity model covers a wavelength range of 500 nm to 900 nm.

29. Venturi G, Mancini A, Melchioni N, et al., "Visible-frequency hyperbolic plasmon polaritons in a natural van der Waals crystal," Nat. Commun. 15(1), 9727 (2024).
30. Gao H, Ding C, Sun L, et al., "Robust broadband directional plasmons in a MoOCl₂ monolayer," Rev. B 104(20), 205424 (2021).

 

3. The wave vector matching condition for negative refraction is only schematically illustrated in Figure 1(e), which is a qualitative analysis and lacks quantitative analysis (such as isofrequency plots and group velocity direction calculations).

Response: We sincerely appreciate this valuable suggestion from the reviewer. The specific equal-frequency contour plots and group velocity direction calculations are described in detail in the supplementary material of Ref. (Venturi et al. 2024).

29. Venturi G, Mancini A, Melchioni N, et al., "Visible-frequency hyperbolic plasmon polaritons in a natural van der Waals crystal," Nat. Commun. 15(1), 9727 (2024).

 

4. The authors used a 0.25 nm spatial grid for the FDTD simulation, which is extremely rare in visible light FDTD simulations, requiring very high computational resources; and is prone to numerical dispersion and material parameter interpolation errors. Could the authors please confirm the simulation parameter settings

Response: We sincerely appreciate the valuable feedback from the reviewers. We confirm the adoption of a 0.25-nanometer spatial grid. Since the vdW MoOCl₂ is ultrathin, only with 10 nm.

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

Dear Editor,

The authors report a comprehensive numerical study of deep-subwavelength negative refraction of visible-frequency HPPs in lateral heterojunctions composed of the natural van der Waals crystal MoOCl₂. They claim MoOCl₂ as a good candidate for compact, low-loss, and visible-range nanophotonic devices. The manuscript needs to be polished based on the following comments to reach an acceptance level.

1. The discussion of experimental feasibility, tolerances (e.g., crystal alignment accuracy), and potential characterization methods is missing. Solve this problem toto strengthen the practical impact.
2. Sensitivity of obtained results to parameter variations would improve robustness.
3. It is necessary that a numerical comparison of propagation length or quality factor with conventional plasmonic systems be given in the visible regime.
4. I suggest an analytical or semi-analytical treatment of the wavevector matching condition to enhance the physical view.
5. Discuss more physical explanation for the weak dependence and effect of thickness.
6. Details on boundary conditions, simulation domain size, and potential edge reflections in the FDTD model should be given in the text.
7. Recheck the text for solving some grammatical issues and repetitive phrasing.

Kind regards,

Author Response

1. The discussion of experimental feasibility, tolerances (e.g., crystal alignment accuracy), and potential characterization methods is missing. Solve this problem toto strengthen the practical impact.

Response: We sincerely thank the reviewer for their valuable comments. The simulated heterojunction we studied demonstrates experimental feasibility.

As shown in the following figure, we have conducted additional simulations to study the case of discontinuous boundaries between two pieces of MoOCl₂. The numerical results of the simulations are presented in Figure R3.

According to the simulation results, when the gap between the left and right pieces of MoOCl₂ materials is more than 50 nm, it is difficult for polaritons to traverse this boundary discontinuity. Only a small portion undergoes negative refraction, while the vast majority experiences reflection. When the gap between the left and right pieces of MoOCl₂ materials is within 50 nm, although there is some reflection of polaritons, a considerable portion can still pass through this boundary discontinuity.

The image is available in the Word document.

Figure R3. Numerical simulation results for negative refraction with discontinuous boundaries. (a-f) Numerical simulations depicting scenarios where discontinuities exist between the left and right pieces of MoOCl₂. The thickness of each MoOCl₂ piece is 20 nm, and the dipole light source has a wavelength of 800 nm. The gaps between the two pieces of MoOCl₂ are 0 nm (Figure a), 25 nm (Figure b), 50 nm (Figure c), 75 nm (Figure d), 100 nm (Figure e), and 200 nm (Figure f), respectively.

Alternatively, we design a heterojunction by splicing two layers of molybdenum oxydichloride (MoOCl₂). The detailed simulation results are presented below:

The image is available in the Word document.

Figure R4. Heterojunction numerical simulation. (a) Heterojunction design. The lower layer consists of 10 nm thick molybdenum oxydichloride with the [100] crystal direction parallel to the y-axis. The upper layer consists of 10 nm thick molybdenum oxydichloride with the [100] crystal direction parallel to the x-axis. (b) Numerical simulation of the heterojunction. The dipole source s is set at 800 nm.

When the heterojunction is formed by splicing the upper and lower layers, a small portion of the energy is reflected at the interface, while the majority undergoes negative refraction. If the angular difference between the two molybdenum oxydichloride layers is not exactly 90 degrees, it will cause the focal point to deviate from the center. For a detailed discussion, please refer to the section in the main text regarding the angular dependence of negative refraction.

2. Sensitivity of obtained results to parameter variations would improve robustness.

Response: We appreciate the reviewer's valuable suggestion. The sensitivity to parameter variations has been presented in the main text:

As can be observed, for the simulated thicknesses mentioned above, both the focal length and the FWHM exhibit minor fluctuations within a small range, but the overall variations are relatively insignificant. From the analysis conducted, it is evident that the thickness has an impact on the focusing of negative refraction as well as on the FWHM of the focused spot. However, this influence is not particularly pronounced.

As clearly illustrated, the focal length (blue line) increases monotonically with the dipole wavelength. Among the simulated data, the shortest focal length of 40 nm is achieved at a dipole wavelength of 550 nm, while the longest focal length of 1530 nm occurs at 1000 nm. This demonstrates a larger focal length with increasing dipole wavelength. For the FWHM (red line), the initial value at 550 nm is 212 nm. As the di-pole wavelength increases, the FWHM first decreases, reaching a minimum of 135 nm at 650 nm. Beyond this point, further increases in dipole wavelength lead to a gradual rise in FWHM, culminating in a maximum value of 332 nm at 1000 nm. Therefore, the exciting wavelength plays a main role in both the focal length and FWHM of the in-plane superlens.

It is evident that both the deflection angle (i.e., the angle between the red arrow and the x-axis) and the focal length (i.e., the length of the red arrow) progressively increase with β from 0° to 60°. When β ranges from 75° to 90°, negative refraction phenomenon cannot occur.

3. It is necessary that a numerical comparison of propagation length or quality factor with conventional plasmonic systems be given in the visible regime.

Response: We appreciate the reviewer for this valuable suggestion. A detailed comparison of the quality factor between molybdenum oxydichloride and other materials in the visible spectral range is provided in the supplementary material of Ref. (Venturi et al. 2024).

29. Venturi G, Mancini A, Melchioni N, et al., "Visible-frequency hyperbolic plasmon polaritons in a natural van der Waals crystal," Nat. Commun. 15(1), 9727 (2024).

 

Existing hyperbolic materials face significant limitations, including high losses, low Q-factors, or narrow bandwidths. While GaTe, tetradymites, and metal diborides exhibit anisotropy, their Q-factors are below 1. CrSBr shows large dielectric anisotropy (~160) but requires low temperatures (20 K) and operates only in a narrow band (855–911 nm). Organic alternatives like QQT(CN)₄ and rr-P3HT also suffer from trade-offs between Q-factor and anisotropy.

In contrast, MoOCl₂ demonstrates outstanding performance across our experimental spectral region. It features an ultra-high Q-factor exceeding 32, low dielectric loss (ℑ(εy) ~0.5), and significant dielectric anisotropy (14–21). Crucially, its predicted in-plane hyperbolic region is exceptionally broad (500–3000 nm). These superior properties establish MoOCl₂ as an ideal, low-loss, and highly anisotropic material, holding great promise for visible light optics and polaritonics.

4. I suggest an analytical or semi-analytical treatment of the wavevector matching condition to enhance the physical view.

Response: We appreciate the reviewer's valuable suggestion.

Light is an electromagnetic wave. At the interface between two media, the complex amplitude vectors of the incident, reflected, and refracted light satisfy the electromagnetic boundary value relations. These boundary value relations are derived from Maxwell's equations, which describe the abrupt changes in electromagnetic fields at the interface between two media.

Maxwell's equations are as follows:

The formulas can be found in the Word document.

The simulation model in this study approximates the ideal dielectric model. Ideal dielectrics have no free electrons. At the interface between ideal dielectrics, there are no free surface charges () or surface currents ().

Boundary conditions can be derived from Maxwell's equations. The boundary conditions at the interface between ideal dielectrics are as follows:

The following boundary conditions are satisfied at the interface of the molybdenum oxydichloride (MoOCl₂) heterojunction:

As a quintessential example, negative refraction—one of the most counterintuitive optical phenomena that bends light in the opposite direction to conventional refraction—that requires opposite group velocity of two side HPPs. Through meticulous design (maintaining a 90-degree orientation difference between the two independent MoOCl₂ materials), we achieved an opposite group velocity for the incident and transmitted polaritons in the direction parallel to the interface. Since the direction of power flow is determined by the group velocity, the power flow components of the incident and transmitted polaritons exhibit opposite orientations in the direction parallel to the interface. In this configuration, when the hyperbolic polariton excited on the left side reaches the interface, it satisfies the wavevector matching condition, causing the polariton on the right side to focus at a single point, thereby realizing ray-like negative refraction.

5. Discuss more physical explanation for the weak dependence and effect of thickness.

Response: We highly appreciate this insightful and constructive suggestion from the reviewer.

When investigating the thickness dependence, we fixed the distance between the dipole source and the heterojunction interface, as well as the wavelength of the light source used to excite the hyperbolic polaritons. As the thickness was varied, the asymptotic angles of the excited hyperbolic polaritons remained largely consistent. Consequently, when they propagated to the interface and underwent negative refraction, the distance from the focal point to the interface also remained substantially unchanged.

When studying the wavelength dependence, we fixed the thickness of the polariton-supporting material. The asymptotic angles of the hyperbolic polaritons excited by the source at different wavelengths showed significant differences. This resulted in a considerable variation in the focal length when the polaritons propagated to the interface and were negatively refracted.

6. Details on boundary conditions, simulation domain size, and potential edge reflections in the FDTD model should be given in the text.

Response: We thank the reviewer for this valuable suggestion.

In the FDTD model, all boundary conditions are set as Perfectly Matched Layers (PMLs), specifically the stretched coordinate PML type. The PML is used to absorb electromagnetic waves in open space, thereby reducing edge reflections.

7. Recheck the text for solving some grammatical issues and repetitive phrasing.

Response: We appreciate the reviewer’s valuable suggestion. We have checked the text, revised the grammatical issues, and eliminated redundant expressions.

Author Response File: Author Response.docx

Reviewer 4 Report

Comments and Suggestions for Authors

Manuscript ID: photonics-4064483

Type: Article
Title: Deep-Subwavelength Negative Refraction of Hyperbolic Plas-2 mon Polariton at Visible-Frequency

Authors: Shuxin Qi, Xuanbin Chen, Haoran Lv, Yuqi Wang, Jihong Zhu,  Jiadian Yan, and Qing Zhang 

 

This manuscript reports negative refraction and tunable focusing of hyperbolic plasmon polaritons in MoOCl₂ heterojunctions in the visible regime. The topic is timely and relevant, and the work is clearly motivated by recent developments in polaritonics and hyperbolic materials. The manuscript is generally easy to follow, and the simulations provide visually appealing demonstrations of the proposed concepts.

However, in its current form, the paper remains primarily simulation-driven and descriptive, with insufficient theoretical depth and incomplete documentation of the numerical methodology. As a result, some of the conclusions appear stronger than what is demonstrated.

I believe the paper could become publishable after appropriate revision, provided the authors address the points below.

 

1. Light only propagates in specific directions, leading to reflections at the interface. The authors should also address reflection at the heterojunction.
2. The effect of the distance between the dipole and the interface is not addressed. This factor should also be considered, as the evanescent wave from the source may have an impact.
3. No details are provided regarding the orientation of the dipole, even though the results should depend on how it is oriented.
4. The dielectric permittivity tensor and its parameters are not specified.
5. The material's metallic properties make it dispersive, so FDTD methods need modification for this medium. The authors should address these issues thoroughly and include theoretical models such as the Drude model.
6. In addition to single source imaging, it's also important to consider imaging with two sources. If two dipoles are located within one wavelength of each other, is it still possible to distinguish their images?

Comments for author File: Comments.pdf

Author Response

1. Light only propagates in specific directions, leading to reflections at the interface. The authors should also address reflection at the heterojunction.

Response: We appreciate the reviewer's valuable comment. When two pieces of molybdenum oxydichloride are spliced together seamlessly, the reflected energy is extremely small and can be considered negligible.

2. The effect of the distance between the dipole and the interface is not addressed. This factor should also be considered, as the evanescent wave from the source may have an impact.

Response: We appreciate the reviewer’s valuable suggestion.

The negative refraction effect is limited by the propagation length of polaritons. The propagation of polaritons, in turn, is constrained by the q-factor. When the dipole is located far from the interface, the field becomes very weak by the time the polariton reaches the boundary. This results in a very weak negative refraction effect.

We have added a discussion regarding the distance between the dipole and the interface.

The image is available in the Word document.

Figure R5. Numerical simulation of negative refraction. (a–c) Numerical simulations of negative refraction at dipole-heterojunction interface distances of D = (a) 300 nm, (b) 750 nm, (c) 1350 nm.

3. No details are provided regarding the orientation of the dipole, even though the results should depend on how it is oriented.

Response: We appreciate the valuable comments from the reviewers. The dipole is configured as an electric dipole source with a phase of 0, a polar angle (theta) of 0, and an azimuthal angle (phi) of 0.

4. The dielectric permittivity tensor and its parameters are not specified.

Response: We appreciate the valuable comments from the reviewers.

The electric constant of moocl2 is from the supplementary material of Ref.(Venturi et al. 2024).

29. Venturi G, Mancini A, Melchioni N, et al., "Visible-frequency hyperbolic plasmon polaritons in a natural van der Waals crystal," Nat. Commun. 15(1), 9727 (2024).

The image is available in the Word document.

Figure R6. Real part of the dielectric function of MoOCl₂. Model dielectric function over the wavelength range from 500 nm to 900 nm.

5. The material's metallic properties make it dispersive, so FDTD methods need modification for this medium. The authors should address these issues thoroughly and include theoretical models such as the Drude model.

Response: We appreciate the reviewer's valuable comments. When implementing the MoOCl₂ material, we have taken into account its metallic nature. The Drude model is described in detail in the supplementary material of Ref.(Venturi et al. 2024).

29. Venturi G, Mancini A, Melchioni N, et al., "Visible-frequency hyperbolic plasmon polaritons in a natural van der Waals crystal," Nat. Commun. 15(1), 9727 (2024).

The formulas can be found in the Word document.

           Table R1 Parameters of the Drude-Lorentz model. Except for the dimensionless quantities ,  , and , all values are expressed in terahertz (THz). This table is from Reference [29](Venturi et al. 2024).
The table is available in the Word document.

6. In addition to single source imaging, it's also important to consider imaging with two sources. If two dipoles are located within one wavelength of each other, is it still possible to distinguish their images?

Response: We appreciate the reviewer’s valuable comments. As can be seen from the figure R7, the full width at half maximum (FWHM) of the negative refraction effect is the resolution limit. The full width at half maximum (FWHM) in Fig.R7. a is 180 nm.
The image is available in the Word document.

Figure R7. Numerical simulation of negative refraction. (a) Numerical simulations of negative refraction. Simulation details: MoOCl₂ thickness = 20 nm; dipole wavelengths of 800 nm (top panel). (b) Numerical simulations of negative refraction at dipole separations of D = 180 nm.

Author Response File: Author Response.docx

Round 2

Reviewer 4 Report

Comments and Suggestions for Authors

Since the authors have already addressed most of the issues raised in the previous version, now I decide to recommend this paper for publication.