Frequency-dependent topological polaritons in carbon nanotube array/hBN heterostructures

Domain: physics
Published: 2026-03-24
Editorial outcome: major_revision

Abstract
Plasmons in carbon nanotubes (CNTs) have attracted significant attention due to their strong spatial confinement and high-quality factors. However, constrained by CNTs’ intrinsic electronic characteristics, modulation of their plasmon dispersion relations remains a significant challenge. Here, we report frequency-dependent topological polaritons arising from the coupling between hyperbolic plasmons and phonon polaritons in CNT-array/hexagonal boron nitride (hBN) heterostructures. In particular, we achieved a controllable topological transition of the polariton wavefront from hyperbolic to elliptical. Moreover, we demonstrated a whispering-gallery polaritonic mode confined in closed-loop CNT array on hBN. Our findings provide fundamental insights into optical topological transitions in low-dimensional heterostructures, and a promising route to manipulate light propagation and energy transfer at the nanoscale.

Introduction
Polaritons, hybrid quasiparticles resulting from the coupling between collective oscillations of particles in materials and electromagnetic waves, have demonstrated remarkable potential of nanophotonic engineering for manipulating light-matter interactions1, 2, 3. Notably, in hyperbolic media, such as hexagonal boron nitride (hBN)4, 5, 6, 7, 8, 9 and α-phase molybdenum trioxide (α-MoO3)10, 11, 12, 13, 14, 15, 16, 17, 18, phonon polaritons exhibit pronounced directional anisotropy, with their isofrequency curves and propagation wavefronts forming distinct hyperbola-like shapes. Furthermore, control over the propagation direction of these hyperbolic polaritons through layer stacking and twist angles has been widely reported19, 20, 21, 22, 23, 24, 25, 26. Yet, the limited spectral range of these phonon polaritons has significantly hindered their practical applications. Plasmon polaritons27, 28, particularly in one-dimensional carbon nanotubes (CNTs)29, 30, 31, 32, 33, 34, 35, present exceptional properties, including deep subwavelength confinement and broad spectral range. Recently, closely packed homochiral CNT arrays have been successfully fabricated36, and signature of hyperbolic Luttinger-liquid plasmons have been reported in this distinct material structure37. However, despite their extraordinary properties, control of the dispersion relation or isofrequency contour of the plasmons in CNT arrays has so far remained unexplored yet.

Here, with a homemade scattering-type scanning near-field optical microscope (s-SNOM), we experimentally demonstrate nanoscale frequency-dependent topological polaritons—specifically, the topological transition of polariton iso-frequency contours between open and closed-loop shapes, in CNT-array/hBN heterostructures. Our results achieved control over the polariton dispersion, topology, and propagation by simply tuning the excitation frequency. The control is achieved through strong coupling between anisotropic Luttinger-liquid plasmons in close-packed identical CNT arrays and in-plane isotropic phonon polaritons in hBN when the excitation frequency lies within the Reststrahlen band of hBN substrate, leading to a topological transition of plasmon isofrequency contour that evolves from hyperbolic to elliptical. Furthermore, using closed-loop CNT arrays as circular nanoscale resonators and leveraging the high-quality factor of the coupled mode, we demonstrated polaritonic whispering-gallery modes in these closed-loop CNT arrays. Our study offers an alternative avenue to control nanoscale light through strong light-matter interaction, and a paradigm for applications in compact nanophotonic devices.

Results
Material structure, measurement scheme, and working principle

Our material structure composed of a close-packed array of identical CNTs on hBN substrate, a schematic of which is depicted in Fig. 1a. To quantitively analyze polariton modes within the CNT-array/hBN heterostructure, we carried out numerical simulations of the eigen electromagnetic modes in the structure using a finite element method (COMSOL Multiphysics). The structure is modeled as a dielectric medium composed of an in-plane strongly anisotropic layer38, 39, 40—representing the CNT array, and an in-plane isotropic layer—representing the hBN flake. The specific dielectric function used in our simulation can be found in Fig. 1b (see more details in Supplementary Note 2). An electrical dipole is placed at the center of the plane and serves as the excitation source. Numerically simulated field distributions of hybrid polariton modes at two representative excitation frequencies (943 cm-1 and 1538 cm-1) are shown in Figs.1c and 1d, respectively. At excitation frequency of 943 cm-1, the wavefront of the polariton mode exhibits hyperbolic. The hyperbolic plasmon originates from the strongly anisotropic conductivities of the layer of CNT array between the axial direction (x-direction) and the radial direction (y-direction). At excitation of 1538 cm-1, the wavefront becomes elliptical. The topological change of the wavefront is a result of the dramatic change in the dielectric function of the hBN layer.

It has been widely known that the two Reststrahlen bands (type I and II) of hBN support the propagation of phonon polaritons4, 7, 8. The type I band with out-of-plane dielectric function 𝜀 < 0 and in-plane dielectric function 𝜀 > 0 , extends over the frequency range 𝜔 = 760~825 cm−1 , and the type II band with 𝜀 > 0 and 𝜀 < 0 , spans the range 𝜔 = 1360~1614 cm−1. In this study, we focus exclusively on the analysis of polaritons at frequency range around the type II band. When the frequency is outside the type II Reststrahlen band, hBN exhibits positive in-plane permittivity (depicted in Fig. 1b), and no phonon polaritons are supported. As a consequence, the wavefront of plasmons in the CNT array is hyperbolic, representing the intrinsic plasmon mode of the CNT array. Once the frequency (e.g., 1538cm-1) falls into the type II Reststrahlen band, a topological transition occurs and the wavefront transforms into an elliptical shape, owing to the negative isotropic in-plane permittivity of hBN. Noted that the frequency at which this topological transition occurs is conditioned to the appearance of well-defined phonon polaritons in hBN. The strong coupling between hyperbolic plasmons in CNT array and isotropic in-plane phonon polaritons in hBN results in the elliptical-shaped wavefront. Figs.1e and 1f illustrate the corresponding Fourier transform of Figs.1c and 1d, where the yellow lines represent the fitted hyperbolic and elliptical isofrequency contour, respectively.

To experimentally demonstrate the inter-layer polariton coupling and the topological transition, we grew close-packed CNT arrays on hBN substrate using chemical vapor deposition (CVD)36, 41, 42; further details are provided in the Method section. Notably, the CNTs within each array exhibit uniform chirality and a close-packed arrangement, allowing the CNT array to be effectively described and modeled as an effective anisotropic medium36 (see more details in Supplementary Note 1). Infrared nano-imaging of the polariton response in the CNT array is achieved through a home-made s-SNOM, as illustrated in Fig. 2a. A gold-coated atomic force microscope (AFM) tip, illuminated by an infrared beam, serves as an exciter to launch polaritons in the CNT arrays. The excited polaritons propagate along the surface and reflect at the ends of the CNT array. The reflected polariton waves alter the local electromagnetic field beneath the tip apex, which is then scattered into the far field and detected by a mercury cadmium telluride (MCT) detector. In order to better capture the polariton interference pattern, an additional AFM cutting process43 is typically applied to the CNT array to create a sharp terminal boundary that reflects polariton waves with a well-defined phase (see Methods for more details).

Coupling between CNT plasmons and hBN phonon polaritons

To effectively visualize the polaritons within the CNT arrays, it is experimentally necessary to reduce the intensity of the hBN phonon polaritons to match that of the CNT plasmons. Therefore, we selected a relatively thin hBN flake, measuring 55 nm in thickness, to demonstrate the polaritonic coupling. Figure 2c shows the near-field optical image of the CNT-array/hBN heterostructure at excitation frequency of 952 cm-1, while Fig. 2b presents the corresponding topography image. Notably, the polaritons exhibits a hyperbolic wavefront, a result of the intrinsic hyperbolic plasmons in the CNT array. The polariton oscillation profiles along the x-axis (the tubes’ axial direction) at various frequencies are plotted in Fig. 2d, revealing a clear change in the oscillation period. It should be noted that in our reflection imaging scheme, the polariton oscillation period corresponds to half the polariton wavelength. As the frequency decreases, the polariton wavelength generally increases, but exhibits two abrupt decreases at specific frequencies, dividing the behavior into three distinct regimes. This unusual behavior presumably results from the coupling between CNT array plasmons and the hBN phonon polaritons.

The near-field infrared response of the CNT-array/hBN system is vividly illustrated by the calculated false color map of the imaginary part of the reflectivity (Fig. 2e), highlighting the frequency (𝜔)-momentum (𝑘x) dispersion relation of the eigen polariton modes. In contrast to isotropic materials, the hyperbolic hBN supports multiple distinct branches of phonon polaritons between its 𝜔TO and 𝜔LO frequency range, corresponding to quantized waveguide modes oscillating between the top and bottom surfaces of the hBN slab, as detailed in Supplementary Note 3. As a result, the coupled modes of hybrid polaritons exhibit multiple branches within the frequency range. The CNT array plasmons induce significant modifications to the coupled modes, causing the hybrid modes to display a clear blue shift relative to the original phonon polariton frequencies (see the hBN phonon polariton dispersion relations in Supplementary Fig. 2). The experimental results, represented by blue dots extracted from the polariton oscillation profiles, are distributed across three distinct bands and show excellent agreement with the theoretical calculations. The second experimental band fits with mode with the second-lowest momentum within the Reststrahlen band. The discrepancy between the experimental data and the calculated dispersion in the Reststrahlen band arises because our measurement captures a superposition of the fundamental and second-order modes of the hybrid polariton. Besides, the oscillation profiles of this second band (the three middle curves in Fig. 2d) seem to originate from multiple momentum components, corresponding to several sub-branches within the Reststrahlen band. These multiple sub-branches arise from various hBN phonon-polariton modes4, 44. Moreover, we calculated the hybrid polariton dispersion using the finite element method and obtained consistent results (Supplementary Note 4). All these findings closely correspond with the dispersion characteristics of graphene/hBN plasmon-phonon polaritons reported in previous studies45, demonstrating subtle but noticeable differences.

Coupling induced topological transition in polariton

We then carried out an in-depth investigation into this coupled polariton mode, which led to the observation of an intriguing topological wavefront transition. The detailed, step-by-step process of this transition is thoroughly illustrated in Fig. 3a. Remarkably, as the frequency decreases and enters the Reststrahlen band, coupling with hBN polaritons causes the wavefront of polaritons to undergo a clear transition from convergent to divergent propagation. Consequently, the interference pattern changes distinctly from a hyperbolic to a rectangular (or parallel) geometry, signaling a topological transition. Figures 3c and 3d show the isofrequency contours of the hybrid polaritons at 1639 cm-1 and 1575 cm-1, corresponding to the hyperbolic and elliptical curves, respectively. The green and blue arrows indicate the wavevectors and Poynting vectors. Importantly, because the hyperbolic plasmon isofrequency curve is open, energy flow tends to converge, whereas in the elliptical case it diverges. Our experimental results suggest a characteristic transition of polaritonic wavefront from hyperbolic to elliptical, which reverts back to hyperbolic upon exiting the Reststrahlen band. Numerical simulations supporting these findings are presented in Figure 3b and show excellent agreement with the experiments. Additionally, Supplementary Figure 6 illustrates the progression of the calculated isofrequency contours for the hybrid polaritons at various frequencies, demonstrating the complete transition of the polariton topology from elliptical to hyperbolic.

To further confirm this topological transition, we fabricated a hole in the CNT arrays using AFM etching to serve as a point reflector for polaritons. The tip-launched polaritons reflect off this hole and produce interference patterns, yielding standard near-field images of hyperbolic and elliptical polaritons, as depicted in Supplementary Figure 4. The top image shows the hyperbolic plasmon wavefront at an excitation frequency of 943 cm-1, while the bottom image shows the elliptical wavefront coupled with hBN phonon polaritons at 1563 cm-1. It is important to note that hyperbolic plasmons in CNT arrays originate from their ability to propagate in the x-axis (the axial direction) but not the y-axis. Thanks to the well-defined phonon polaritons along the tube’s radial direction, when the in-plane permittivity of hBN turns negative, hybrid polariton propagation is enabled even in the previously restricted direction, resulting in an elliptical wavefront.

To clarify this transition further, we performed numerical simulations of polaritons on CNT arrays of varying widths. Since our CNT arrays are limited in size along the tube radial direction, we demonstrate the polariton patterns in arrays with different numbers of CNTs, as depicted in Supplementary Figure 5. Polaritons were excited at the array boundary (marked by a dashing line) by an incident plane electromagnetic wave polarized along the nanotubes. When the array is sufficiently wide, the polariton wavefronts becomes obviously hyperbolic and elliptical, at excitation frequencies of 952 cm-1 and 1575 cm-1, respectively. With a reduction in the array width, the polariton pattern gradually changes and aligns more closely with our experimental images, which further confirms the polariton wavefronts in Fig. 3a are hyperbolic at 952 cm-1 and 1639 cm-1, while elliptical at 1575 cm-1.

Observation of a tunable whispering-gallery polaritons

Next, we demonstrate a tunable whispering-gallery mode within the CNT-array/hBN heterostructure. Due to the absence of electronic Ohmic loss44, 46, 47, hBN phonon polaritons are characterized by exceptionally long lifetimes and high-quality factors, thereby enhancing the propagation length of the hybrid polaritons in the CNT arrays. On the other hand, according to the calculated dispersion results (Fig. 2e), multiple distinct branches of hybrid polaritons exists in the CNT-array/hBN heterostructure, which leads to the polariton wavelength changes significantly with the excitation frequency. This in turn facilitates the design of polaritonic resonators. To test this idea, we fabricated closed-loop CNT arrays on hBN substrate. This distinct structure was created by repeatedly winding a nanotube in a spiral pattern resembling a mosquito coil, ultimately forming a circular, donut-like architecture, as illustrated in Fig. 4b and Supplementary Figure 8. We then performed infrared nano-imaging on these closed-loop structures and successfully observed polaritonic whispering-gallery modes (Fig. 4a). The AFM topography of the CNT array is shown in Fig. 4b, while Fig. 4c and Supplementary Figure 7 are near-field optical images with varying excitation frequencies. Remarkably, near the frequency 𝜔LO, the polariton interference pattern in the CNT array changed sharply with frequency.

At a frequency of 1563 cm-1, the inner ring exhibited almost no near-field optical response (dark), whereas the outer ring displayed strong response (bright). This phenomenon is presumably caused by destructive interference in the inner ring and constructive interference in the outer ring, as the closed-loop array can be divided into several sub-rings with different perimeters. Based on the polariton dispersion relations, we estimated that the perimeter of the outer tubes is approximately the wavelength of the polaritons, while that of the inner tubes is roughly half the wavelength. Notably, as frequency increasing, the constructive interference ring first contracted and then expanded. To clearly illustrate this behavior, we extracted and plotted the polariton line profiles along the dashed line marked in Fig. 4b. These profiles reveal that the constructive polariton interference peaks vary significantly with the excitation frequency, as shown in Fig. 4d. By aligning one of these peaks, we provided a more intuitive comparison of the peak-to-peak distance and intensity variations between the two peaks. Firstly, the distances between the two peaks exhibited clear oscillations with frequency, demonstrating the resonance of polariton waves in nanotube rings of varying diameters. Secondly, as the two interference peaks move closer together, the interference pattern becomes more strongly constructive (as shown in Fig. 4e). This phenomenon can be attributed to the fact that smaller peak spacing corresponds to shorter propagation lengths, which are typically associated with lower energy losses, leading to the more strongly constructive interference. Another CNT ring exhibiting similar polaritonic resonant behavior can be found in Supplementary Note 9, and further evidence for whispering-gallery modes is provided in Supplementary Note 11.

The realization of these remarkable features stems from the unique physical properties of the materials and the precisely controlled geometric design of the nano-ring structures. Specifically, within the closed-loop arrays of natural CNT crystals, the synergy of the low-loss characteristics of the Luttinger liquid electronic state, uniform chirality, and near-atomic-level smooth, low-loss ring-shaped interfaces enables efficient optical field confinement and the formation of strong optical resonances (see more details in Supplementary Note 10). These properties create ideal conditions for the generation and high-fidelity propagation of whispering-gallery modes. This on-chip natural whispering-gallery nanocavity structure features a diameter reduced to approximately one hundred nanometers. Compared to traditional low-dimensional polaritonic whispering-gallery nanocavities48, its characteristic dimensions have improved by nearly an order of magnitude. Its mode volume is as small as on the order of 10-6. The high compression ratio and quality factor not only preserve optical state coherence, but also provides robust support for exploring strong light–matter interactions. Furthermore, by adjusting geometric parameters or applying external fields, the resonant frequency and mode distribution of the whispering-gallery nanocavity can be precisely tuned, providing a promising pathway for achieving integrated optoelectronic systems. Consequently, single-chirality CNT-based whispering-gallery nanocavities advance our understanding of light–matter interactions and showcase the unique benefits of Luttinger liquid plasmons in low-loss optics, offering vital theoretical and experimental support for high-performance integrated optoelectronics.

Methods
Growth of CNT arrays

The hBN flakes were initially mechanically exfoliated onto SiO2/Si substrates. To ensure surface cleanliness, the samples were subsequently exposed to hydrogen plasma at 300 ℃, effectively removing all organic residues. Following this pretreatment, a precisely controlled 0.05 nm-thick iron (Fe) film was deposited onto the hBN-coated SiO2/Si surfaces using thermal evaporation, which served as catalytic nanoparticles for subsequent CNT arrays growth. The prepared substrates were then transferred into a quartz tube furnace (Anhui BEQ Equipment Technology) and subjected to a controlled heating process under a mixed atmosphere of hydrogen and argon at atmospheric pressure, gradually elevating the temperature to the optimal growth temperature of ~850 ℃ 41, 42. Upon reaching this temperature, the argon gas flow was replaced with methane to initiate the CNT arrays growth process. After a standard growth period of 30 minutes, the system was systematically cooled down to room temperature while maintaining a protective atmosphere of hydrogen and argon.

AFM cutting of CNT arrays

The cutting of CNT arrays for designed structures is performed in the atmosphere using a standard atomic force microscope (AFM). First, AFM is used to locate the CNT arrays grown on hBN/SiO2/Si substrate. Then, a 50 kHz AC voltage with an amplitude of 10V is applied between the conductive AFM tip and the Si layer of the substrate. The tip scans very slowly across the CNT array in tapping mode with a lift-down distance of 90~120 nm. Local anodic oxidation only occurs for CNTs underneath the tip with the assistance of a water bridge. Therefore, the array along the tip’s path is etched to be a smooth artificial boundary. The point hole is etched in the same way.

Infrared nano-imaging

For near-field infrared nano-imaging, we employed a custom-built scattering-type scanning near-field optical microscope (s-SNOM) that integrates a tapping-mode atomic force microscope (AFM, Bruker Innova) with a CO2 laser and a Daylight Solution quantum cascade laser (QCL). The system operates by focusing a mid-infrared wavelength laser (900~1650cm-1) beam onto the apex of a conductive AFM probe, generating a highly localized enhanced optical field. This near-field interacts with the sample, and the resulting scattered light, which encodes local optical information, is collected in the far field using a mercury cadmium telluride (MCT) detector (KLD-0.1-J1, Kolmar). To suppress background scattering, the collected signal is demodulated using a lock-in amplifier (Zurich Instruments HF2LI). This configuration allows for the simultaneous acquisition of high-resolution near-field optical images alongside topography information during measurements.

Numerical simulations

COMSOL Multiphysics is used to simulate the polariton patterns in CNT-array/hBN heterostructure. CNT array is modeled by a plane with the same size of experimental samples. We estimated the conductivity of CNTs utilizing the method reported by previous literature and selected appropriate value as the complex permittivity49. For the simulations shown in Figs.1c, d, a point electric dipole was placed at the center of CNT arrays to excite polaritons at a varying oscillating frequency. For the simulations shown in Fig. 3b, a beam of light polarized perpendicularly to the vertical boundary was irradiated onto the plane surface to excite polaritons at a varying oscillating frequency. The electric field component perpendicular to the plane (Ez) was recorded over the plane surface.

Dispersion calculations

The calculations of the dispersion shown in Fig. 2e and Supplementary Figure 2 were performed using a generalized 4 × 4 transfer matrix formalism50. In short, by incorporating the permittivity of CNT arrays and hBN, the solution of reflectivity, rp(q,𝜔), can be determined. Polariton mode corresponds to the frequencies at which the imaginary parts of rp(q,𝜔) reach the maximum. For each frequency, the corresponding polariton wavevector can be extracted.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In their work, “Configurable plasmon polaritons in carbon nanotube array/hBN heterostructures”, Y. Xie et al. report on coupled polaritons in heterostructures of carbon nanotubes (CNT) arrays and hexagonal boron nitride (hBN). They carefully study a frequency-dependent transition of the polaritons from hyperbolic to elliptical propagation and show indications of a whispering-gallery plasmonic mode in a closed-loop CNT array structure. I feel their work is particularly interesting as it explores polaritons of a relatively new material structure (CNT arrays), which here are hybridized with hBN phonon polaritons.\nOverall, I think the results are interesting, novel, and worth publishing. It appears that most of the findings presented are well-supported by an instructive combination of experimental results, numerical simulations, and comparison with literature.\nWhile the final section of the manuscript — on whispering-gallery modes — presents interesting findings, it does not yet match the quality and clarity of the rest of the manuscript and should be revised before publication.\nPlease find below some detailed comments:\n1. The manuscript presents experimental results in a relatively broad spectral range from around 900 to >1600 cm-1, which requires a tunable or broadband light source. However, the methods section mentions that the results have been obtained with a CO2 laser at a single wavelength of 10.6 um. Please add relevant information on the laser used for the experiments.\n2. As shown in Fig. 1b and described in Supplementary Note 2, the authors simply assume the conductivity of air for the radial direction (y-direction) of the CNT permittivity. While they state that this is consistent with previous research on CNT arrays, the authors do not provide specific references. The permittivity is an essential assumption that should be discussed in more detail. If the permittivity along the y-direction was in fact slightly negative, would this mean that the behavior qualitatively more resembled the well-studied case of graphene and the “topological transition” with frequency may disappear?\n3. Regarding the whispering-gallery modes, the authors mention “the intensity of the constructive interference peaks also oscillates with changes in frequency, revealing an inverse relationship between peak spacing and intensity: the smaller the peak spacing, the higher the intensity”. However, Fig. 4d shows “IR intensity” in arbitrary units. How is “intensity” defined here? I.e., how do the authors make sure that their definition of “intensity” is consistent across different frequencies and a frequency-dependent comparison of “intensity” is useful?\n4. While all figures in the main manuscript use false-color maps, none of these includes a color bar. It would be helpful to either include color bars for all false-color maps or at least provide a more detailed description of the displayed quantities in the caption.\n5. The section on the on the whispering-gallery modes appears to include several claims that are not well supported. Specifically, the following claims should be supported by a quantitative analysis:\na. The authors mention “near-atomic-level smooth, lossless ring-shaped interfaces”. While “lossless” is a strong claim, no quantitative analysis of losses is provided.\nb. “The high compression ratio (…) preserves quantum state coherence”. “quantum state coherence” appears vague here and it is not clear how this statement is supported by the data.\nc. The authors mention that their structures “showcase the unique benefits of Luttinger liquid plasmons”. This should be discussed in more detail. Specifically, how are the benefits “unique” compared to other plasmonic systems?\nd. The authors mention “Compared to traditional low-dimensional plasmonic whispering-gallery nanocavities38, its characteristic dimensions and performance have improved by nearly an order of magnitude.” They refer to reference 38 here. As the authors claim that the performance has increased by nearly an order of magnitude, this should be quantified by comparing suitable figures of merit such as the quality factor. At first glance, the whispering gallery modes shown in Fig. 4 do not appear to have a significantly higher quality compared to the ones shown in reference 38, making a quantitative comparison important.\ne. It might be helpful to support the experimental findings on the whispering-gallery modes in Fig. 4 with numerical simulations (e.g., similar to those provided in Fig. 3).", "reviewer_2": "This manuscript presents an approach to modulate the dispersion of hyperbolic Luttinger-liquid plasmon polaritons (HLLPPs) in carbon nanotube (CNT) arrays through coupling with phonon polaritons (PhPs) in hexagonal boron nitride (h-BN). The authors demonstrate a frequency-controlled topological transition from hyperbolic to elliptic polariton wavefronts and report the observation of a whispering-gallery confined plasmonic mode in the coupled CNT/h-BN heterostructure. The study addresses a topic of clear relevance to the fields of nanophotonics and polaritonics, potentially contributing to the development of tunable hybrid polaritonic systems. However, in my opinion, this manuscript in its current form requires major revisions to become acceptable for publication in Nature Communications.\nFirst, the novelty and physical interpretation need to be clarified, several claims must be quantitatively supported, and the results should be better addressed considering previous works. In addition, several figures and methodological descriptions require improved clarity. Addressing these issues would significantly enhance the scientific quality and overall impact of the manuscript. Please, find detailed comments below.\n1. The authors should carefully revise the manuscript to ensure consistent and precise use of polaritonic terminology. Terms such as “plasmon polaritons”, “hybrid polaritons”, and “phonon polaritons” appear to be used interchangeably, which can lead to conceptual ambiguity. Each polariton type should be clearly defined and used consistently according to its physical origin and distinctive characteristics.\n2. In Supplementary Information Note 4, the authors state: “The dispersion relations are similar to Fig. 3e, indicating reliable and accurate results.” This appears instead to refer to Figure 2e. The authors should verify the accuracy of all internal references (figures, tables, and text sections) throughout the manuscript.\n3. In the Introduction, the authors compare plasmon polaritons in CNTs with phonon polaritons in materials such as h-BN and α-MoO3. They mention that plasmon polaritons exhibit superior properties, including low loss and broad spectral range. This claim should be quantitatively supported with comparative metrics such as propagation length, lifetime, and confinement, or otherwise tempered. Moreover, phonon polariton systems, though spectrally limited to the Reststrahlen bands, are typically characterized by longer lifetimes and reduced losses compared to plasmonic systems due to their distinct scattering mechanisms. I would recommend the authors to reference prior reports on controlled polariton propagation in phonon-polariton systems (Nano Lett. 2020, 20, 5301–5308; Nano Lett. 2020, 20, 5323–5329; Nat Commun 2024, 15, 9042).\n4. The authors report a topological transition of hybrid polaritons from hyperbolic to elliptic wavefronts. Such transitions have been extensively investigated in recent literature, as they can lead to the emergence of the so-called canalized propagation regime. It would be expected that this system also exhibits polariton canalization at the precise topological transition frequency (Optica 2025, 12, 343-349; Nano Lett. 2025, 25, 6, 2203–2209). The authors should discuss whether such canalized regime is expected in the topological transition observed in the CNT array/h-BN system. Also, the qualitative explanation of the hyperbolic-to-elliptic transition based on the sign change of hBN’s in-plane permittivity is reasonable and consistent with established polaritonic behavior. However, the authors show only two discrete frequency cases. A continuous evolution of isofrequency contours across the transition region would more convincingly demonstrate the claimed topological change.\n5. The authors describe the observed phenomena as resulting from “strong coupling” between CNT plasmons and h-BN phonon polaritons yet no quantitative coupling parameters (e.g., mode splitting, coupling rate, or linewidth analysis) are provided. This statement should be substantiated with a detailed discussion of the mode splitting visible in the dispersion (Fig. 2e). For completeness, I recommend including the individual dispersions of the CNT array and of h-BN (plots shown in the Supplementary Information), alongside their coupled dispersion, to help the reader clearly visualize the hybridization effect.\n6. In Figure 1b, the notation “x4” is unclear. Please define this multiplier explicitly. The authors should also indicate on this panel the excitation frequencies corresponding to the simulated distributions shown in panels c and d.\n7. In Figure 1, all panels should include scale bars. If the same scale applies to multiple panels, this should be clearly stated in the caption. Panels c and d should include a shared colorbar indicating the plotted quantity (Re(Ez)), and panels e and f should include a grayscale colorbar for the corresponding magnitude. Please, see, for example, (Nanophotonics 2024, 13, 4761–4770). The use of the term “measured” in the caption is misleading, as Figure 1 presents simulated data. Please replace it with a term such as “calculated” or “simulated”.\n8. In Figure 2e, the authors should explain the discrepancy observed near 1400 cm-1 in the experimental data points (high-order mode). Additionally, it would strengthen the analysis to include error bars in the experimental estimations (blue dots) and overlay the analytical dispersion (for example, with a dashed line) on the colorplot derived from the transfer-matrix model for comparison.\n9. In the experimental measurement panels (Figure 2c, Figure 3a, Figure 4c, Supplementary Figures 4a,b, and Supplementary Figure 6a), the authors should add a colorbar and clearly specify which experimentally extracted quantity is plotted in each case (amplitude, phase). Was the signal demodulated at higher harmonics? If so, up to which harmonic order?\n10. In Figure 3a,b, the authors present an experimental-simulation comparison. First, as previously noted, the authors should indicate which experimentally obtained magnitude is plotted in Figure 3a. Second, please, ensure that the aspect ratios of the experimental and simulated subpanels are identical for a fair visual comparison. Third, I assume that in Figure 3b the authors plot the simulated Re(Ez) … if so, this should be explicitly stated. The authors should note that the only physically meaningful magnitude comparable to Re(Ez) is the real part of the near-field signal, Re(σ_n). If the experiment cannot independently and simultaneously extract s_n and ϕ_n, the only valid comparison with simulations would be between |Ez| and s_n. Finally, this experiment-simulation correspondence could be made clearer by comparing field profiles. Since the dispersion is already shown in Figure 2e, the authors could overlay the experimental data points on the isofrequency contour (IFC) plots in Figure 3c,d as another direct comparison.\n11. The authors state: “In this study, we focus exclusively on the analysis of polaritons at frequencies around the type-II band.” To strengthen this discussion, they should include numerical simulations showing the spatial distributions of Re(Ez) across three distinct regions: i) the frequency range where CNT plasmons does not intersect with h-BN phonon polaritons; ii) the frequency range where CNT plasmons intersect with h-BN type I RB phonon polaritons; and iii) the frequency range where CNT plasmons intersect with h-BN type II RB phonon polaritons. What do the authors expect to observe in s-SNOM nano-imaging for type I RB frequencies in this system?\n12. Are the authors able to grow or transfer the CNT array onto different substrates (e.g. BaF2 or SiO2) and perform nano-imaging measurements there? I believe it would be highly beneficial for the manuscript to show a direct experimental and numerical comparison between the coupled system (CNT arrays/h-BN) and its individual constituents (CNT array on one side, h-BN on the other) including dispersion plots, Re(Ez) simulations, and s-SNOM measurements.\n13. Regarding the sample fabrication process, the authors could clarify whether CNT arrays could be integrated with other 2D van der Waals materials such as graphene, α-MoO3 or α-V2O5.\n14. The coupling strength and dispersion modification in plasmon–phonon systems are known to depend sensitively on the hBN thickness. The authors mention using a 55 nm-thick flake “to reduce phonon intensity,” but no data or criteria are shown to justify this choice or demonstrate systematic thickness dependence. I believe that presenting simulations or experiments across several hBN thicknesses would greatly strengthen the coupling interpretation.\n15. As pointed out in previous comments, the comparison between experiment and simulation throughout the work is mostly qualitative (“good agreement”). The authors should provide quantitative comparisons to substantiate the agreement. Also, regarding the experimental results, several statements refer to “low loss” “long lifetime”, and “high-quality factor” without quantitative support. Extracted propagation lengths or damping constants from s-SNOM data would be welcome and allow comparison with other polaritonic materials.\n16. The interpretation of the observed near-field patterns in Figure 4 as whispering-gallery modes remains highly speculative. The near-field images presented in Figure 4 and the Supplementary Information are consistent with frequency-dependent interference effects, but they do not constitute conclusive evidence of resonant mode confinement. To substantiate the claim of whispering-gallery plasmonic modes, the authors should (i) perform full-wave electromagnetic simulations of the circular CNT-array/hBN structure to visualize the modal field distributions and confirm the existence of azimuthally confined resonances; (ii) provide frequency-dependent spectral data from s-SNOM amplitude or phase measurements to identify discrete resonance peaks; and (iii) estimate the corresponding quality factors (Q) to demonstrate true cavity behavior. Additionally, a systematic comparison across rings of different diameters would enable verification of the expected quantized angular momentum dependence (mode number scaling with circumference). Without such quantitative analysis and modeling, the evidence remains insufficient to support the claim of an “on-chip whispering-gallery nanocavity” and the observed oscillations could alternatively arise from simple standing-wave interference in the hybrid polariton field.\n17. The Discussion section includes numerous overstatements (“approached physical limits”, “unprecedented capabilities”, “lays a solid foundation”). These claims should be revised or supported by quantitative metrics.", "reviewer_3": "Response to Reviewers' Comments (NCOMMS-25-86882)\nWe sincerely thank all the referees for their careful review of our work and for providing insightful\nand constructive comments. Below, please find our detailed point-by-point responses.\nResponse to Reviewer #1\nIn their work, “Configurable plasmon polaritons in carbon nanotube array/hBN heterostructures”,\nY. Xie et al. report on coupled polaritons in heterostructures of carbon nanotubes (CNT) arrays and\nhexagonal boron nitride (hBN). They carefully study a frequency-dependent transition of the\npolaritons from hyperbolic to elliptical propagation and show indications of a whispering-gallery\nplasmonic mode in a closed-loop CNT array structure. I feel their work is particularly interesting as\nit explores polaritons of a relatively new material structure (CNT arrays), which here are hybridized\nwith hBN phonon polaritons.\nOverall, I think the results are interesting, novel, and worth publishing. It appears that most of the\nfindings presented are well-supported by an instructive combination of experimental results,\nnumerical simulations, and comparison with literature. While the final section of the manuscript —\non whispering-gallery modes — presents interesting findings, it does not yet match the quality and\nclarity of the rest of the manuscript and should be revised before publication.\nPlease find below some detailed comments.\nOur reply: We thank the reviewer for his/her appreciation of our work and for the positive\nevaluation. We are also very grateful for the constructive comments provided by the reviewer that\nhave helped us improve the manuscript. Below, we address the questions and comments raised by\nthe reviewer one by one.\n1. The manuscript presents experimental results in a relatively broad spectral range from around\n900 to >1600 cm-1, which requires a tunable or broadband light source. However, the methods\nsection mentions that the results have been obtained with a CO laser at a single wavelength of\n2\n10.6 um. Please add relevant information on the laser used for the experiments.\nOur reply: We thank the reviewer for pointing out our mistake in the Methods section.\nIn addition to the CO laser, we also used a quantum cascade laser (QCL) with a tunable frequency\n2\nranging from 900 cm-1 to 1600 cm-1 in our near-field optical measurement. We have revised the\nMethods section of the manuscript and added the relevant information as follows.\n“For near-field infrared nano-imaging, we employed a custom-built scattering-type scanning near-\nfield optical microscope (s-SNOM) that integrates a tapping-mode atomic force microscope (AFM,\nBruker Innova) with a CO laser and a Daylight Solution quantum cascade laser (QCL). The system\n2\noperates by focusing a mid-infrared laser (900~1650cm-1) beam onto the apex of a conductive AFM\nprobe, generating a highly localized enhanced optical field. This near-field interacts with the sample,\nand the resulting scattered light, which encodes local optical information, is collected in the far field\nusing a mercury cadmium telluride (MCT) detector (KLD-0.1-J1, Kolmar). To suppress background\nscattering, the collected signal is demodulated using a lock-in amplifier (Zurich Instruments HF2LI).\nThis configuration allows for the simultaneous acquisition of high-resolution near-field optical\nimages alongside topography information during measurements.”\n2. As shown in Fig. 1b and described in Supplementary Note 2, the authors simply assume the\nconductivity of air for the radial direction (y-direction) of the CNT permittivity. While they state that\nthis is consistent with previous research on CNT arrays, the authors do not provide specific\nreferences. The permittivity is an essential assumption that should be discussed in more detail. If\nthe permittivity along the y-direction was in fact slightly negative, would this mean that the\nbehavior qualitatively more resembled the well-studied case of graphene and the “topological\ntransition” with frequency may disappear?\nOur reply: We sincerely thank the reviewer for his/her insightful comments and suggestions.\nFor the selection of the radial dielectric constant of carbon nanotube (CNT) arrays, we adopted a\nstrategy that combines referencing parameters from the literature with fitting experimental\nobservations. Theoretically, based on the coupled Luttinger liquid theory, CNT arrays exhibit\ncharge-insulating properties in the radial direction [Phys. Rev. Lett. 86, 676 (2001)], which aligns\nwith our previous studies on the material properties of CNT arrays [Science, 387, 1310 (2025)].\nBased on this, we treated the radial direction as a quasi-air medium (insulating assumption). This\nsimplified approach has been widely adopted in the field of CNT array research [IEEE Trans.\nAntennas Propag. 57 1412(2009)] [Phys. Rev. B 82 155423(2010)] [IEEE Trans. Nanotechnol. 11\n964(2012)]. It has been confirmed that this parameter setting achieves excellent agreement in\nreproducing the CNT hyperbolic experimental phenomena [Chinese Phys. Lett. 42, 090710 (2025)]\nas well as in fitting the topological hybridization experiments in this study, thereby verifying the\nrobustness of the theoretical model.\nRegarding the comment on the possibility that the dielectric constant in the y-direction might be\nslightly negative, we conducted an in-depth analysis. In the mid-infrared range, the response of\nCNT arrays in the radial (y) direction to external fields is extremely weak (the magnitude of the\ndielectric constant is very small), and the dominant characteristic of the system is hyperbolic\nplasmonic behavior. Simulations and corresponding iso-frequency contours (see Fig. R1 below)\nshow that setting the radial dielectric constant to small negative values (e.g., -2) yields results that\nare nearly identical to those obtained with a value of +1. Physically, while a negative dielectric\nconstant supports high-momentum radial modes (manifested as short-period oscillations), these\nmodes are distinct from the characteristics of axial hyperbolic modes and do not significantly affect\nthe propagation behavior of the hyperbolic wavefront.\nIt is important to emphasize that only when the absolute value of the radial dielectric constant\nbecomes sufficiently large does the momentum of the radial mode significantly decrease, leading\nto a topological phase transition from hyperbolic polaritons to elliptical polaritons (as shown in Fig.\nR1f). Only under such extreme conditions would the frequency-dependent topological transition\ndisappear, and the system would exhibit isotropic behavior similar to graphene. Therefore, within\nthe current parameter range, our conclusions remain robust.\nFigure R1. The influence of radial dielectric constant on the topological transition. The numerical simulated spatial\ndistribution of the real part of the polariton field Re(E) (top)measured above the CNT-array/hBN at frequencies of\nz\n1639cm-1 and corresponding iso-frequency contours (bottom) with different radial dielectric constants.\n3. Regarding the whispering-gallery modes, the authors mention “the intensity of the constructive\ninterference peaks also oscillates with changes in frequency, revealing an inverse relationship\nbetween peak spacing and intensity: the smaller the peak spacing, the higher the intensity”.\nHowever, Fig. 4d shows “IR intensity” in arbitrary units. How is “intensity” defined here? I.e., how\ndo the authors make sure that their definition of “intensity” is consistent across different\nfrequencies and a frequency-dependent comparison of “intensity” is useful?\nOur reply: We appreciate the reviewer's insightful comments.\nIn our study, \"intensity\" is defined as the relative difference between the near-field signal—\nspecifically, the magnitude of the electric field perpendicular to the surface (|E|)—at the\nz\ninterference-enhanced peak of CNT-array/hBN polaritons and the background level observed in\nthe pure hBN region. Given that hBN forms a substantial part of the substrate, providing an\noverarching background, we believe this definition of intensity is appropriate. Throughout the\nexperiments, we maintained a consistent intensity of incident light across varying frequencies to\nensure comparability.\nTo enhance clarity, we have refined our statement to:\n“As the two interference peaks move closer together, the interference pattern becomes more\nstrongly constructive.”\n4. While all figures in the main manuscript use false-color maps, none of these includes a color bar.\nIt would be helpful to either include color bars for all false-color maps or at least provide a more\ndetailed description of the displayed quantities in the caption.\nOur reply: We thank the reviewer for his/her kind reminder.\nIn our revised manuscript, we have added color bars to all false-color maps to enhance clarity.\nAdditionally, we have provided more detailed descriptions of the displayed quantities in the figure\ncaptions.\n5. The section on the on the whispering-gallery modes appears to include several claims that are\nnot well supported. Specifically, the following claims should be supported by a quantitative analysis:\na. The authors mention “near-atomic-level smooth, lossless ring-shaped interfaces”. While “lossless”\nis a strong claim, no quantitative analysis of losses is provided.\nb. “The high compression ratio (…) preserves quantum state coherence”. “quantum state coherence”\nappears vague here and it is not clear how this statement is supported by the data.\nc. The authors mention that their structures “showcase the unique benefits of Luttinger liquid\nplasmons”. This should be discussed in more detail. Specifically, how are the benefits “unique”\ncompared to other plasmonic systems?\nd. The authors mention “Compared to traditional low-dimensional plasmonic whispering-gallery\nnanocavities38, its characteristic dimensions and performance have improved by nearly an order of\nmagnitude.” They refer to reference 38 here. As the authors claim that the performance has\nincreased by nearly an order of magnitude, this should be quantified by comparing suitable figures\nof merit such as the quality factor. At first glance, the whispering gallery modes shown in Fig. 4 do\nnot appear to have a significantly higher quality compared to the ones shown in reference 38,\nmaking a quantitative comparison important.\ne. It might be helpful to support the experimental findings on the whispering-gallery modes in Fig.\n4 with numerical simulations (e.g., similar to those provided in Fig. 3).\nOur reply: We thank the reviewer for his/her constructive comments. We have addressed each\ncomment and suggestion point by point as outlined below.\na-c: The plasmons in CNTs have been reported to exhibit characteristics of Luttinger liquid\nplasmons, demonstrating excellent properties of high spatial confinement and high quality factors,\nas detailed in previous literature [Nature Photon. 9, 515-519 (2015)]. We have quantitatively\nanalyzed these properties using the quality factor 𝑄 =𝑅𝑒(𝑞)/𝐼𝑚(𝑞) and the compression factor\n𝑁 =𝑅𝑒(𝑞)/𝑘 . Additionally, we fitted the experimental near-field profile with the following\n0\nformula,\n1 −2𝑥\n𝐼 =|𝜂 +𝜂 𝑒 𝑎 𝑒𝑖(2𝑞𝑥+𝜙𝑅)|\n𝑠 𝑅\n√2𝑥\nwhere 𝜂 represents the scattering rate of incident light back into the detector, 𝜂 is the\n𝑠 𝑅\nreflectivity of HPs at the edge, 𝑞 is the plasmon wavevector, a is the decay length, and 𝜙 is the\n𝑅\nreflection phase. This formula is derived from the literature [Adv. Funct. Mater. 2019, 29, 1904662].\nWe selected experimental data at frequencies of 1111 cm-1 and 1639 cm-1 for fitting, as shown in\nFig. R2 below. Notably, the quality factor of the CNT array plasmons reaches up to 21, while the\ncompression factor is 21.57. These results highlight that even structured into whispering-gallery-\nmode oscillators, CNT plasmons retain their excellent intrinsic properties, significantly lowering\noptical scattering losses, and maintaining low intrinsic dissipation, thus preserving optical state\ncoherence [Nano Lett. 2021, 21, 8707−8714] [Nature, 2020, 582(7810): 46-49].\nTo support this conclusion, we collected frequency-dependent near-field signal intensity data with\nthe background subtracted, from a specific point (denoted by a blue dot in Fig. R3a) on the closed-\nloop CNT-array ring on hBN. The results (see Fig. R3b), which exhibit a strong fit to a standard\nresonance peak curve, confirm the presence of a whispering-gallery mode. From this fitting, we\nextracted the quality factor (Q) as follows: 𝑄 =\n𝜔𝑐\n=\n1600.16 𝑐𝑚−1\n=67.63 , where 𝜔 is the\n∆𝜔 23.66 𝑐𝑚−1 𝑐\nresonance frequency and ∆𝜔 is the full width at half maximum (FWHM) of the resonance peak.\nHowever, we acknowledge that some expressions in our manuscript are not rigorous enough and\nrequire further refinement. For example, we have revised “lossless ring-shaped interfaces” to\n“low-loss ring-shaped interfaces”, and “The high compression ratio not only preserves quantum\nstate coherence” to “The high compression ratio and quality factor not only preserve optical\nstate coherence”.\nFigure R2. Extraction of the quality factor of plasmons in CNT array. a, The near-field profile along the axial\ndirection of CNT array at the frequency of 1111 cm-1 and the corresponding fitting curve. b, The near-field profile\nalong the axial direction of CNT array at the frequency of 1639 cm-1 and the corresponding fitting curve.\nFigure R3. Extraction of the quality factor of the whispery-gallery mode polaritons in closed-loop CNT array/hBN.\na, A typical infrared nano-imaging of polaritons in the CNT-array/hBN. b, Frequency-dependent near-field signal\nintensity at a certain point on the closed-loop CNT-array ring on hBN. The position where the experimental data\nwere extracted from is denoted by a blue dot in (a).\nd. The term “characteristic dimensions and performance” in the manuscript refers to the mode\nvolume ratio 𝑉/𝑉 , which is approximately one order of magnitude lower than that of the\n𝑝 0\nnanocavity reported in reference 38 [Nat. Mater. 22, 838–843 (2023)]. This estimation method\nfollows the approach used in previous literatures [Science 360, 291-295 (2018)] [Science 368, 1219-\n1223 (2020)], where the polariton wavelength 𝜆 =𝜆 /16.5 is used. Given our CNT nanocavity’s\n𝑝 0\nthickness is on the atomic scale, roughly 4 nm, we obtain 𝑉/𝑉 =2.3×10−6, which is less than\n𝑝 0\nthe value of 10−5 reported in reference 38 [Nat. Mater. 22, 838–843 (2023)].\ne. We have conducted numerical simulations of the polariton whispering-gallery mode and\nincorporated these results into Fig.4 of the revised manuscript (see Fig. R4). Our simulation method\ninvolved placing an electric dipole above the resonant ring to mimic the AFM tip to excite the\npolaritons, and collecting the 𝐸 component below the dipole. The mapping of dipole scanning\nz\npositions yielded results that correlate well with our experimental findings.\nFigure R4. The revised version of Figure 4 of the manuscript. a, Schematic of infrared nano-imaging of whispering-\ngallery polaritonic mode in the CNT-array/hBN by using s-SNOM. b, AFM topography image of a closed-loop CNT\narray ring on hBN. Infrared nano-imaging experiment (c) and corresponding numerical simulations (d) of polaritons\nin the CNT-array/hBN at different frequencies, respectively. e, The Near-field line profiles along the sections marked\nby the dashed line in (b).\nResponse to Reviewer #2\nThis manuscript presents an approach to modulate the dispersion of hyperbolic Luttinger-liquid\nplasmon polaritons (HLLPPs) in carbon nanotube (CNT) arrays through coupling with phonon\npolaritons (PhPs) in hexagonal boron nitride (h-BN). The authors demonstrate a frequency-\ncontrolled topological transition from hyperbolic to elliptic polariton wavefronts and report the\nobservation of a whispering-gallery confined plasmonic mode in the coupled CNT/h-BN\nheterostructure. The study addresses a topic of clear relevance to the fields of nanophotonics and\npolaritonics, potentially contributing to the development of tunable hybrid polaritonic systems.\nHowever, in my opinion, this manuscript in its current form requires major revisions to become\nacceptable for publication in Nature Communications.\nFirst, the novelty and physical interpretation need to be clarified, several claims must be\nquantitatively supported, and the results should be better addressed considering previous works.\nIn addition, several figures and methodological descriptions require improved clarity. Addressing\nthese issues would significantly enhance the scientific quality and overall impact of the manuscript.\nPlease, find detailed comments below.\nOur reply: We appreciate the reviewer’s recognition of our work and the valuable suggestions for\nenhancing the manuscript. Below, we address each question and comment and question in detail.\n1. The authors should carefully revise the manuscript to ensure consistent and precise use of\npolaritonic terminology. Terms such as “plasmon polaritons”, “hybrid polaritons”, and “phonon\npolaritons” appear to be used interchangeably, which can lead to conceptual ambiguity. Each\npolariton type should be clearly defined and used consistently according to its physical origin and\ndistinctive characteristics.\nOur reply: We appreciate the reviewer’s insightful suggestions regarding the use of polaritonic\nterminology.\nIn response, we have revised some terms throughout the manuscript. In particular, we have revised\nthe manuscript title from “Configurable plasmon polaritons in carbon nanotube array/hBN\nheterostructures” to “Frequency-dependent topological polaritons in carbon nanotube array/hBN\nheterostructures” for greater clarity.\nTo clarify terminology within the manuscript: “plasmon polaritons” refers to the polaritons\ngenerated from the interaction between charges in CNT arrays and incident photons, while\n“phonon polaritons” denote the interactions between phonons in hBN and photons. The term\n“hybrid polaritons” describes the coupled modes resulting from plasmon and phonon polariton\ninteractions. Specifically, in regions outside the Reststrahlen band 2 of hBN, only plasmon\npolaritons propagate in the CNT-array/hBN system. However, within the Reststrahlen band, CNT\narrays plasmon polaritons are classified as hybrid polaritons due to their coupling with phonon\npolaritons in hBN.\nTo eliminate ambiguity, we have made these definitions consistent throughout the revised\nmanuscript.\n2. In Supplementary Information Note 4, the authors state: “The dispersion relations are similar to\nFig. 3e, indicating reliable and accurate results.” This appears instead to refer to Figure 2e. The\nauthors should verify the accuracy of all internal references (figures, tables, and text sections)\nthroughout the manuscript.\nOur reply: We thank the reviewer for his/her careful review, and for pointing out our mistake.\nThe typo has been corrected, as shown below.\n“Here, we calculated the frequency-momentum dispersion relations of hybrid plasmons using the\nfinite element simulation method (COMSOL), as shown in Supplementary Figure 3. The dispersion\nrelations are similar to Fig.2e, indicating reliable and accurate results.”\n3. In the Introduction, the authors compare plasmon polaritons in CNTs with phonon polaritons in\nmaterials such as h-BN and α-MoO . They mention that plasmon polaritons exhibit superior\n3\nproperties, including low loss and broad spectral range. This claim should be quantitatively\nsupported with comparative metrics such as propagation length, lifetime, and confinement, or\notherwise tempered. Moreover, phonon polariton systems, though spectrally limited to the\nReststrahlen bands, are typically characterized by longer lifetimes and reduced losses compared to\nplasmonic systems due to their distinct scattering mechanisms. I would recommend the authors to\nreference prior reports on controlled polariton propagation in phonon-polariton systems (Nano Lett.\n2020, 20, 5301–5308; Nano Lett. 2020, 20, 5323–5329; Nat Commun 2024, 15, 9042).\nOur reply: We appreciate the reviewer’s valuable comments regarding the comparative analysis of\nplasmon polaritons in CNTs and phonon polaritons in materials like h-BN and α-MoO .\n3\nIn our manuscript, we attribute the low loss of CNT plasmons to the suppression of electron\nbackscattering in their one-dimensional structure, allowing Luttinger-liquid plasmons to achieve\nhigh quality factors of up to 20 (Nat. Photon., 9, 515 [2015]). This quality factor is generally superior\nto that of plasmons observed on other low-dimensional surfaces, such as graphene. However, we\nacknowledge that CNT plasmons do not possess this advantage when compared to phonon\npolaritons.\nTo enhance clarity and precision, we have revised the introduction with the following statement:\n“ Plasmon polaritons, particularly in one-dimensional carbon nanotubes (CNTs), exhibit\nexceptional properties, including deep subwavelength confinement and a broad spectral range.”\nFurthermore, we have incorporated the references suggested by the reviewer (Nano Lett. 2020,\n20, 5301–5308; Nano Lett. 2020, 20, 5323–5329; Nat Commun 2024, 15, 9042) as citations in the\nrevised manuscript.\n4. The authors report a topological transition of hybrid polaritons from hyperbolic to elliptic\nwavefronts. Such transitions have been extensively investigated in recent literature, as they can\nlead to the emergence of the so-called canalized propagation regime. It would be expected that\nthis system also exhibits polariton canalization at the precise topological transition frequency\n(Optica 2025, 12, 343-349; Nano Lett. 2025, 25, 6, 2203–2209). The authors should discuss whether\nsuch canalized regime is expected in the topological transition observed in the CNT array/h-BN\nsystem. Also, the qualitative explanation of the hyperbolic-to-elliptic transition based on the sign\nchange of hBN’s in-plane permittivity is reasonable and consistent with established polaritonic\nbehavior. However, the authors show only two discrete frequency cases. A continuous evolution of\nisofrequency contours across the transition region would more convincingly demonstrate the\nclaimed topological change.\nOur reply: We appreciate the reviewer’s constructive suggestions regarding the topological\ntransition of hybrid polaritons.\nThe small width of our as-grown CNT arrays (only several hundred nanometers) makes it\nexperimentally challenging to accurately determine the excitation frequency for polariton\ncanalization. To address this, we have supplemented our experimental findings with analytical\ncalculations, as shown in Fig. R5. The results, illustrated in the figure below, show that the polariton\niso-frequency contours transition from elliptic to hyperbolic as the excitation frequency increases.\nThis analysis indicates that a canalization state emerges around the frequency of 1605 cm⁻¹.\nFurthermore, we have incorporated the Fig. R5 as part of the revised Supplementary Information\nand added the references suggested by the reviewer (Optica 2025, 12, 343-349; Nano Lett. 2025,\n25, 6, 2203–2209) as citations in the revised manuscript.\nFigure R5. The continuous evolution of iso-frequency contours across the transition region. The excitation\nfrequencies are 1585cm-1 (a), 1595cm-1 (b), 1600cm-1(c), 1605 cm-1 (d) and 1610cm-1 (e), respectively.\n5. The authors describe the observed phenomena as resulting from “strong coupling” between CNT\nplasmons and h-BN phonon polaritons yet no quantitative coupling parameters (e.g., mode\nsplitting, coupling rate, or linewidth analysis) are provided. This statement should be substantiated\nwith a detailed discussion of the mode splitting visible in the dispersion (Fig. 2e). For completeness,\nI recommend including the individual dispersions of the CNT array and of h-BN (plots shown in the\nSupplementary Information), alongside their coupled dispersion, to help the reader clearly visualize\nthe hybridization effect.\nOur reply: We thank the reviewer for the valuable suggestions regarding the coupling parameters\nof the observed phenomena.\nTo quantitatively address the mode splitting of hybrid polaritons in the CNT array/hBN system,\nwe employed a method similar to that used in previous literature [Nat. Mater. (2025).\nhttps://doi.org/10.1038/s41563-025-02412-6]. The mode splitting of hybrid polaritons in the CNT\narray/hBN can be expressed as:\n1\n𝜔 = √𝜔2 +𝜔2 +4𝑔2±√(𝜔2 +𝜔2 +4𝑔2)2−4𝜔2 𝜔2\n± 𝑠𝑝𝑝 𝑝ℎ𝑝 𝑠𝑝𝑝 𝑝ℎ𝑝 𝑠𝑝𝑝 𝑝ℎ𝑝\n√2\nwhere, g is the coupling strength, 𝜔 and 𝜔 represent the bare modes of CNT array\n𝑠𝑝𝑝 𝑝ℎ𝑝\nplasmons and hBN phonon polaritons, respectively.\nThen, we extracted 𝜔 =1357 𝑐𝑚−1 and 𝑔 = ∆𝜔 =319.2 𝑐𝑚−1 from the calculated\n𝑐\n2\ndispersion relations, where the 𝜔 represents the frequency where bare modes cross. Therefore,\n𝑐\ng\nthe normalized coupling strength is calculated as =3.45>1 , where Γ =\n𝑝ℎ𝑝\n(Γ𝑝ℎ𝑝+Γ𝑠𝑝𝑝)/2\n10 𝑐𝑚−1 and Γ =174.79 𝑐𝑚−1 represent the loss rates of hBN phonon polaritons and CNT\n𝑠𝑝𝑝\narray plasmons, respectively. This result substantiates that the hybrid mode between CNT array\nplasmons and hBN phonon polaritons can be classified as strong coupling. [Nat. Rev. Phys. 1, 19–\n40 (2019)]\nFollowing the referee’s suggestion, we have included a comparative plot of the dispersions for the\nindividual carbon nanotube array plasmons, individual hBN phonon polaritons, and their hybrid\nmode, as shown in Figure R6 below. This figure is now part of the Supplementary Information.\nFigure R6. Calculated dispersion relation of the individual carbon nanotube array plasmons, individual hBN\nphonon polaritons, and their hybrid modes. a, The dispersion relation of the individual carbon nanotube array\nplasmons. b, The dispersion relation of the individual hBN phonon polaritons. c, The dispersion relation of the\nhybrid mode. The calculated dispersion is visualized using a false-color map of the imaginary part of the reflection\ncoefficient r .\np\n6. In Figure 1b, the notation “x4” is unclear. Please define this multiplier explicitly. The authors\nshould also indicate on this panel the excitation frequencies corresponding to the simulated\ndistributions shown in panels c and d.\nOur reply: We appreciate the reviewer’s careful review and valuable feedback.\nTo enhance clarity, we have added the following note to the caption of Figure 1b:\n“The ‘x4’ label means that the in-plane permittivity of hBN has been multiplied by four so that the\ndielectric functions of both hBN and CNTs can be displayed together on the same y-axis.”\nAdditionally, we have indicated the excitation frequencies in Figure 1b that correspond to the\nsimulated distributions shown in Figures 1c and 1d of the revised manuscript.\n7. In Figure 1, all panels should include scale bars. If the same scale applies to multiple panels,\nthis should be clearly stated in the caption. Panels c and d should include a shared colorbar indicating\nthe plotted quantity (Re(Ez)), and panels e and f should include a grayscale colorbar for the\ncorresponding magnitude. Please, see, for example, (Nanophotonics 2024, 13, 4761–4770). The use\nof the term “measured” in the caption is misleading, as Figure 1 presents simulated data. Please\nreplace it with a term such as “calculated” or “simulated”.\nOur reply: We appreciate the reviewer’s careful and precise feedback.\nIn the revised Figure 1, we have included scale bars in all panels. If the same scale applies to\nmultiple panels, this has been clearly stated in the caption. Additionally, we have added a shared\ncolor bar for panels c and d, indicating the plotted quantity Re(E), and a grayscale color bar for\nz\npanels e and f to represent the corresponding magnitude.\nFurthermore, we have replaced the term “measured” with “simulated” in the caption to accurately\nreflect the nature of the data presented. Besides, we have incorporated the references suggested\nby the reviewer (Nanophotonics 2024, 13, 4761–4770) as citations in the revised manuscript.\n8. In Figure 2e, the authors should explain the discrepancy observed near 1400 cm-1 in the\nexperimental data points (high-order mode). Additionally, it would strengthen the analysis to\ninclude error bars in the experimental estimations (blue dots) and overlay the analytical dispersion\n(for example, with a dashed line) on the colorplot derived from the transfer-matrix model for\ncomparison.\nOur reply: We appreciate the reviewer’s important suggestions regarding Figure 2e.\nThe observed discrepancy near 1400 cm-1 between the experimental data points and the calculated\ndispersion relation can be attributed to measurement uncertainties. Specifically, in the frequency\nregion of plasmon-phonon polariton coupling, our experimental signal reflects a superposition of\nthe fundamental and second-order polariton modes. Due to an insufficient number of\nmeasurement periods caused by the sample size, the extracted wavelength values may not align\nperfectly with theoretical calculations.\nIn the revised manuscript, we have incorporated the following analysis:\n“The discrepancy between the experimental data and the calculated dispersion in the Reststrahlen\nband arises because our measurement captures a superposition of the fundamental and second-\norder modes of the hybrid polariton.”\nIn response, we measured the polariton wavelength again and quantified the reading uncertainty,\nwith the results plotted in Fig. R7a. As can be seen, the reading error in extracting wave vectors\nfrom the experimental data is negligible, rendering error bars virtually invisible on the plot;\ntherefore, they have been omitted. We attribute the observed discrepancy in the Reststrahlen\nband to the experimental indistinguishability between the fundamental and higher-order modes.\nTherefore, to ensure optimal visual presentation and avoid readability issues, we have chosen not\nto include error bars in the experimental dispersion relation. Similar treatment has been employed\nin many previously reported studies on the coupling of hBN polaritons and graphene plasmons,\nas depicted in Fig. R8. [Nature Nanotech. 10, 682–686 (2015)] [Nature Mater. 14, 421–425 (2015)].\nFigure R7. Experimental dispersion relation including error bars. a, Experimental dispersion relation of hybrid\npolaritons in the CNT-array/hBN, with error bars included. B, Comparison of calculated and experimental dispersion\nrelations taken from the Fig.2e of the manuscript.\nFigure R8. Experimental dispersion relation of hybrid polaritons in graphene/hBN heterostructure.\nCorresponding simulation results are also provided as the background in previous literatures. (a) is taken from\nFig. 2c of the paper Dai et al. [Nature Nanotech. 10, 682–686 (2015)]. (b) is taken from Fig. 2d of the paper Woessner\net al. [Nature Mater. 14, 421–425 (2015)].\n9. In the experimental measurement panels (Figure 2c, Figure 3a, Figure 4c, Supplementary Figures\n4a,b, and Supplementary Figure 6a), the authors should add a colorbar and clearly specify which\nexperimentally extracted quantity is plotted in each case (amplitude, phase). Was the signal\ndemodulated at higher harmonics? If so, up to which harmonic order?\nOur reply: We appreciate the reviewer’s careful review and valuable suggestions.\nIn the revised manuscript, we have added color bars and provided textual descriptions of the\nextracted physical quantities for each experimental measurement panel (Figure 2c, Figure 3a,\nFigure 4c, Supplementary Figures 4a and 4b, and Supplementary Figure 6a). The extracted quantity\nrepresents the magnitude of the electric field, corresponding to the third order near-field signal.\n10. In Figure 3a,b, the authors present an experimental-simulation comparison. First, as previously\nnoted, the authors should indicate which experimentally obtained magnitude is plotted in Figure\n3a. Second, please, ensure that the aspect ratios of the experimental and simulated subpanels are\nidentical for a fair visual comparison. Third, I assume that in Figure 3b the authors plot the\nsimulated Re(Ez) … if so, this should be explicitly stated. The authors should note that the only\nphysically meaningful magnitude comparable to Re(Ez) is the real part of the near-field signal,\nRe(σ_n). If the experiment cannot independently and simultaneously extract s_n and ϕ_n, the only\nvalid comparison with simulations would be between |Ez| and s_n. Finally, this experiment-\nsimulation correspondence could be made clearer by comparing field profiles. Since the dispersion\nis already shown in Figure 2e, the authors could overlay the experimental data points on the\nisofrequency contour (IFC) plots in Figure 3c,d as another direct comparison.\nOur reply: We thank the reviewer for his/her significant comments and insightful suggestions.\nThe physical quantity depicted in Fig. 3a is the near-field intensity, while Fig. 3b shows 𝑅𝑒(𝐸 ).\nz\nThis information has been labeled in the revised manuscript. The experimentally observed pattern\narises from the interference between the incident field 𝐸 and the polariton field 𝐸 , i.e. 𝐸 =\nin 𝑝 𝑧\n𝐸 +𝐸 , as depicted in Figs. R9 a,b [eLight 3, 14 (2023)]. The polariton field forms an interference\nin 𝑝\npattern from its tip-excited and reflected components. Hence, the resulting fringes correspond to\nthe phase information of 𝑅𝑒(𝐸 ) . In contrast, the amplitude map, |𝐸 | , which lacks such\nz 𝑧\ninterference, does not match the experimental observations. Similar comparison methods have\nbeen employed in many previously reported studies [Nat. Nanotechnol. 17, 940–946\n(2022)][Nature 582, 209–213 (2020)][Nature 596, 362–366 (2021)][eLight 3, 14 (2023)]. A\ncomparison is commonly made between the simulated 𝑅𝑒(𝐸 ) and the near-field amplitude, as\nz\npresented in Figure R9.\nOtherwise, the Fourier transform of our imaging data, limited by the sample's small size, is\ncurrently of insufficient quality for overlaying onto the iso-frequency contours in Figures 3c, d.\nFigure R9. Experimental launching of polaritons and corresponding simulations in previous literatures. a, b,\nSchematic of the near-field polariton-launching experiment (a) and experimental near-field amplitude |𝐸 +𝐸 |\nin 𝑝\nand |𝐸 | (b), which are taken from Fig. 3 of the paper Hu et al. [eLight 3, 14 (2023)]. c, d, Experimentally measured\np\nnear-field images (c) of polaritons and the corresponding numerically simulated near-field distributions (Re(Ez)) (d),\nwhich are taken from Fig. 2 of the paper Zheng et al. [Science advances, 2019, 5(5): eaav8690]. e, f, Experimentally\nmeasured near-field images (e) of polaritons and the corresponding numerically simulated near-field distributions\n(Re(Ez)) (f), which are taken from Fig. 3 of the paper Hu et al. [Nat. Nanotechnol. 17, 940–946 (2022)]\n11. The authors state: “In this study, we focus exclusively on the analysis of polaritons at frequencies\naround the type-II band.” To strengthen this discussion, they should include numerical simulations\nshowing the spatial distributions of Re(Ez) across three distinct regions: i) the frequency range\nwhere CNT plasmons does not intersect with h-BN phonon polaritons; ii) the frequency range where\nCNT plasmons intersect with h-BN type I RB phonon polaritons; and iii) the frequency range where\nCNT plasmons intersect with h-BN type II RB phonon polaritons. What do the authors expect to\nobserve in s-SNOM nano-imaging for type I RB frequencies in this system?\nOur reply: We appreciate the reviewer’s helpful comments and insightful suggestions.\nThe reviewer correctly highlights the significance of examining hBN's two Reststrahlen bands.\nWhile we considered both type I and type II hyperbolic phonon polaritons (HPPs) in our theoretical\nanalysis, our experimental measurements were limited to type II HPPs. This limitation is due to the\nunavailability of continuous-wave laser sources operating in the 760–820 cm-1 range, which\ncorresponds to type I HPPs. Furthermore, the anisotropic nature of hBN causes the out-of-plane\nmode (type I HPPs) to be significantly weaker than the in-plane mode (type II HPPs). Consequently,\nour experimental study primarily focused on the type II Reststrahlen band, which is also the most\nexamined frequency range in hBN phonon polariton research.\nTo address the reviewer’s request, we performed finite-element simulations using COMSOL to\nsimulate the hybrid polariton mode in the type I HPPs of hBN, and the corresponding results are\npresented in Figure R10. It is noted that due to the emergence of well-defined hyperbolic phonon\npolaritons in hBN, the hyperbolic plasmons of the carbon nanotube array have also evolved into\nelliptical wavefront shapes.\nFigure R10. Numerical simulations of the hybrid polariton mode in the type I HPPs of hBN. The numerical\nsimulated spatial distribution of the polariton field Re(E) measured above the CNT-array/hBN at frequencies\nz\n770cm-1 (a) and 775cm-1 (b), respectively.\n12. Are the authors able to grow or transfer the CNT array onto different substrates (e.g. BaF or\n2\nSiO ) and perform nano-imaging measurements there? I believe it would be highly beneficial for\n2\nthe manuscript to show a direct experimental and numerical comparison between the coupled\nsystem (CNT arrays/h-BN) and its individual constituents (CNT array on one side, h-BN on the other)\nincluding dispersion plots, Re(Ez) simulations, and s-SNOM measurements.\nOur reply: We thank the reviewer for his/her important suggestions.\nWe have tried to transfer the CNT array onto different substrate, such as SiO ; however, current dry\n2\ntransfer techniques disrupt the ordered, densely packed alignment of the nanotube array during\nthe process.\nAccording to the reviewer's suggestion, we have calculated the dispersion relation of the individual\nCNT array (without hBN) and included it in the Supplementary Information. Unfortunately, as the\nCNT array cannot be effectively transferred to a freestanding condition, we are currently unable to\nobtain experimental data for the dispersion of the isolated CNT array at this time.\n13. Regarding the sample fabrication process, the authors could clarify whether CNT arrays could\nbe integrated with other 2D van der Waals materials such as graphene, α-MoO or α-V O .\n3 2 5\nOur reply: We thank the reviewer for his/her constructive suggestions regarding sample\nfabrication.\nIn our experiments, we have also attempted to integrate the CNT array with other two-dimensional\nmaterials (graphene, α-MoO , or α-V O ) through stacking. As mentioned above, current transfer\n3 2 5\ntechniques tend to disrupt the structure of the CNT array during the process. However, we can\ntransfer other two-dimensional materials successfully onto the CNT array, which is part of our\nfuture research plan.\n14. The coupling strength and dispersion modification in plasmon–phonon systems are known to\ndepend sensitively on the hBN thickness. The authors mention using a 55 nm-thick flake “to reduce\nphonon intensity,” but no data or criteria are shown to justify this choice or demonstrate systematic\nthickness dependence. I believe that presenting simulations or experiments across several hBN\nthicknesses would greatly strengthen the coupling interpretation.\nOur reply: We appreciate the reviewer’s insightful suggestions regarding the dependence of\ncoupling strength and dispersion on hBN thickness.\nIndeed, the intensity and wavelength of phonon polaritons in hBN are thickness-dependent, as\nreported in previous literature [Science 343, 1125-1129 (2014)]. As indicated in Fig. R11, thicker\nhBN leads to larger phonon polariton amplitude and longer polariton wavelength. In Fig. R12 below,\nwe simulate the coupling between polaritons in hBN flakes of varying thicknesses and CNT array\nplasmons at a frequency of 1538 cm⁻¹. When the hBN flake is too thin, the resulting phonon\npolaritons exhibit an extremely small amplitude and a very short wavelength. This prevents\neffective coupling with plasmons in the CNT array, and the wavefront maintains its hyperbolic\ncharacter. A transition to an elliptical wavefront occurs only when the hBN thickness is sufficient.\nOn the other hand, since hBN serves as a substrate material, its phonon response acts as a\nbackground signal. To prevent this phonon response from overwhelming the CNT array plasmon\nsignal, we cannot use excessively thick hBN. Besides, as mentioned before, the wavelength of\nphonon polaritons in hBN is proportional to its thickness. Due to the size constraints of our CNT\narray sample, overly thick hBN flakes produce hybrid polaritons with a wavelength that exceeds\nthe CNT array dimensions, thereby preventing the visualization of interference fringes. To achieve\ncoupling visualization between phonon polaritons and plasmons, their wavelengths need to be\ncomparable.\nTaking all factors into consideration, we selected hBN with a thickness of several tens of\nnanometers. The 55 nm thickness is not necessarily optimal; rather, it represents a suitable choice\nthat balances these conditions.\nFigure R11. The evolution of the phonon polariton amplitude and wavelength with the thickness of hBN crystals.\nThese figures are taken from Fig. 3 of the paper Dai et al. [Science 343, 1125-1129 (2014)]\nFigure R12. The hBN thickness dependence of the hybrid polaritons. a-f, The numerical simulated spatial\ndistribution of the polariton field Re(Ez) measured above the CNT-array/hBN at the frequency of 1538cm-1 for hBN\nthickness of 5, 20, 50, 80, 100, and 150 nm, respectively.\n15. As pointed out in previous comments, the comparison between experiment and simulation\nthroughout the work is mostly qualitative (“good agreement”). The authors should provide\nquantitative comparisons to substantiate the agreement. Also, regarding the experimental results,\nseveral statements refer to “low loss” “long lifetime”, and “high-quality factor” without quantitative\nsupport. Extracted propagation lengths or damping constants from s-SNOM data would be\nwelcome and allow comparison with other polaritonic materials.\nOur reply: We appreciate the reviewer’s valuable suggestions regarding quantitative comparisons\nand the characterization of the experimental results.\nFor the comparison between experiment and simulation, a key quantifiable parameter is the\nwavelength. We provide a comprehensive comparison of wavelengths between experiment,\ncalculations, and numerical simulations in Fig. 2e and Supplementary Figure 3.\nAs for the quality factor, we analyzed it using the definitions 𝑄 =𝑅𝑒(𝑞)/𝐼𝑚(𝑞), and fitted the\nexperimental near-field profile with the formula below:\n1 −2𝑥\n𝐼 =|𝜂 +𝜂 𝑒 𝑎 𝑒𝑖(2𝑞𝑥+𝜙𝑅)|\n𝑠 𝑅\n√2𝑥\nwhere 𝜂 is the scattering rate of incident light back into the detector, 𝜂 is the reflectivity of\n𝑠 𝑅\nHPs at the edge, 𝑞 is the plasmon wavevector, a is the decay length, and 𝜙 is the reflection\n𝑅\nphase. This formula is derived from previous literature. [Adv. Funct. Mater. 2019, 29, 1904662.]\nWe selected the experimental data at frequencies of 1111 cm-1 and 1639 cm-1 for fitting, and the\nresults are shown in Fig. R13 below. It should be noted that the quality factor of the CNT array\nplasmons can reach as high as 21, and the compression factor is 21.57. The hyperbolic plasmons\nin our CNT array demonstrate a quality factor comparable to the widely studied systems of MoOCl\n2\nhyperbolic plasmons and α-MoO₃ hyperbolic polaritons [Science387,786-791(2025)] [Nature 562,\n557–562 (2018)]. More importantly, our closed-loop CNT-array ring supports polaritons with a\nsignificantly enhanced quality factor of 67.63, as discussed in the subsequent question. This\nperformance justifies our use of the term \"low-loss\" to characterize the system.\nFigure R13. Extraction of the quality factor of plasmons in CNT array. a, The near-field profile along the axial\ndirection of CNT array at the frequency of 1111 cm-1 and the corresponding fitting curve. b, The near-field profile\nalong the axial direction of CNT array at the frequency of 1639 cm-1 and the corresponding fitting curve.\n16. The interpretation of the observed near-field patterns in Figure 4 as whispering-gallery modes\nremains highly speculative. The near-field images presented in Figure 4 and the Supplementary\nInformation are consistent with frequency-dependent interference effects, but they do not\nconstitute conclusive evidence of resonant mode confinement. To substantiate the claim of\nwhispering-gallery plasmonic modes, the authors should (i) perform full-wave electromagnetic\nsimulations of the circular CNT-array/hBN structure to visualize the modal field distributions and\nconfirm the existence of azimuthally confined resonances; (ii) provide frequency-dependent\nspectral data from s-SNOM amplitude or phase measurements to identify discrete resonance peaks;\nand (iii) estimate the corresponding quality factors (Q) to demonstrate true cavity behavior.\nAdditionally, a systematic comparison across rings of different diameters would enable verification\nof the expected quantized angular momentum dependence (mode number scaling with\ncircumference). Without such quantitative analysis and modeling, the evidence remains insufficient\nto support the claim of an “on-chip whispering-gallery nanocavity” and the observed oscillations\ncould alternatively arise from simple standing-wave interference in the hybrid polariton field.\nOur reply: We appreciate the reviewer’s significant suggestions and have addressed each comment\npoint by point, as outlined below.\n(i) We have performed numerical simulations of polariton whispering gallery modes (WGMs) and\nincorporated the results into Figure 4 of the revised manuscript, specifically shown as Figure R14.\nNotably, the simulation results are in excellent agreement with the experimental observations,\nconfirming that the signals observed in the experiment indeed originate from WGMs. Regarding\nthe mode field distribution: the CNT arrays we fabricated exhibit an almost ideal circular geometry,\nenabling the polaritons to propagate along the circumference in a WGM-like manner. Due to the\nabsence of reflective boundaries that would generate noticeable interference patterns, it is\nchallenging to directly obtain a clear angular mode field distribution in the experiment.\nConsequently, when the atomic force microscope (AFM) probe is positioned along a ring of the\nsame diameter, the conditions for near-field excitation and signal collection remain unchanged.\nThis results in a nearly uniform infrared intensity within the same-diameter ring in nano-infrared\nimaging. The same principle applies to rings with different diameters. In the corresponding\nnumerical simulations, this scenario is modeled by scanning the position of an electric dipole to\nemulate the tip‑scanning process, while simultaneously recording the electric field E component\nz\ndirectly beneath the dipole.\n(ii)-(iii) We have collected the frequency-dependent near-field signal intensity, with the background\nsubtracted at a certain point (denoted by a blue dot in Fig. R15a) on the closed-loop CNT-array ring\non hBN, and the results are plotted in Figure R15b. The data are well fitted by a standard resonance\npeak curve, confirming that the observed signal corresponds to a whispering-gallery mode. From\nthis fitting, the quality factor (Q) is extracted as follows: 𝑄 =\n𝜔𝑐\n=\n1600.16 𝑐𝑚−1\n=67.63, where\n∆𝜔 23.66 𝑐𝑚−1\n𝜔 is the resonance frequency and ∆𝜔 is the full width at half maximum (FWHM) of the\n𝑐\nresonance peak.\nFigure R14 The revised version of Figure 4 of the manuscript. a, Schematic of infrared nano-imaging of whispering-\ngallery polaritonic mode in the CNT-array/hBN by using s-SNOM. b, AFM topography image of a closed-loop CNT\narray ring on hBN. c, d, Infrared nano-imaging and corresponding numerical simulations of polaritons in the CNT-\narray/hBN at different frequencies, respectively. d, The Near-field line profiles along the sections marked by the\ndashed line in (b).\nFigure R15 Extraction of the quality factor of the whispery-gallery mode polaritons in closed-loop CNT array/hBN.\na, A typical infrared nano-imaging of polaritons in the CNT-array/hBN. b, Frequency-dependent near-field signal\nintensity at a certain point on the closed-loop CNT-array ring on hBN. The position where the experimental data\nwere extracted from is denoted by a blue dot in (a).\n17. The Discussion section includes numerous overstatements (“approached physical limits”,\n“unprecedented capabilities”, “lays a solid foundation”). These claims should be revised or\nsupported by quantitative metrics.\nOur reply: We appreciate the reviewer's valuable suggestions.\nIn response, we have removed all the aforementioned overstatements and made comprehensive\nrevisions to the manuscript. The specific changes are as follows:\na. Revised “This on-chip natural whispering-gallery nanocavity structure has approached the\nphysical limits, with its diameter reduced to about a hundred nanometers” to “This on-chip\nnatural whispering-gallery nanocavity structure features a diameter reduced to approximately\none hundred nanometers”.\nb. Revised “showcasing unprecedented capabilities for on-chip manipulation of whispering-\ngallery optical fields” to “exhibiting capabilities for on-chip manipulation of whispering-\ngallery optical fields”.\nc. Revised “laying a solid foundation for the realization of integrated optoelectronic systems”\nto “providing a new pathway for achieving integrated optoelectronic systems”.\nResponse to Reviewer #3\nThe manuscript reports configurable plasmon–polaritons arising from the coupling between\nhyperbolic plasmons and phonon polaritons in CNT array/hBN heterostructures. Infrared (IR) nano-\nimaging is performed as a function of excitation laser energy, which reveals multiple branches of\ncoupled phonon plasmon modes. Topological transition of a hyperbolic isofrequency contour to an\nelliptical one is observed using IR nano-imaging and from numerical calculations. Plasmonic\nwhispering-gallery modes are presented in closed-loop CNT array ring on a hBN substrate. Due to\nthe lack of novelty and impact of the work, and multiple significant claims with insufficient evidence\nand premature data analysis, the reviewer does not recommend the publication of this manuscript\nin Nature Communications.\nOur reply: We appreciate the reviewer’s evaluation of our work and the valuable feedback\nprovided. Below, we address each question and comment raised by the reviewer one by one.\nComment 1: First and foremost, the main concern of the manuscript is the lack of novelty.\nHyperbolic polaritons have been demonstrated numerous times in other vdW materials, with\ncanonical examples including phonon polaritons hBN and a-MoO3 as the authors have referenced\nas well as in nanopatterned hBN [Science 359, 892 (2018)]. Hyperbolic plasmons have also been\ndemonstrated in multiple other vdW materials, including in ZrSiSe at infrared frequencies [Sci Adv\n8, add6169 (2022)] and in MoOCl2 at visible frequencies [Science 387, 786 (2025)]. The properties\nclaimed by the authors (deep subwavelength confinement, broad spectral range, etc) are generic\nto these known (plasmonic) hyperbolic systems. Furthermore, the coupling-induced topological\ntransition of polaritons has been repeatedly demonstrated in other vdW materials platforms,\nincluding in twisted a-MoO3 [Nature Mater 19, 1307 (2020); Nature 582, 209 (2020)] or in\ngraphene/a-MoO3 [Nature Nanotech 17, 940 (2022); Nature Commun 13, 3719 (2022)].\nTherefore, the reviewer does not find that the work provides a sufficient conceptual advance to\nwarrant publication in Nature Communications.\nOur reply: We sincerely thank the reviewers for their thorough and systematic review of work in\nthis field.\nWe fully agree that the concept of \"hyperbolic polaritons and coupling-induced topological\ntransitions\" has been extensively studied in van der Waals materials. Therefore, the core\ninnovation of this work does not lie in merely reproducing this phenomenon, but rather in the\nconstruction and validation of a novel platform with fundamentally different properties and unique\nadvantages for manipulation: by utilizing directly grown, ultra-clean CNT arrays as a natural\nhyperbolic polariton substrate, we have achieved broadband, low-loss, and directly imageable in-\nplane hyperbolic plasmons, as well as tunable topological transitions through hybridization with\nhBN phonon polaritons. The distinctiveness of this platform is demonstrated in the following four\nkey aspects:\n(1) Broadband In-Plane Hyperbolic Plasmons vs. Narrowband Phonon Hyperbolic Polaritons\nThe hBN, α-MoO₃, and other systems mentioned by the reviewers primarily rely on phonon\npolaritons, whose hyperbolic response is constrained by the Reststrahlen band, resulting in\ninherently narrow bandwidths. In contrast, our work leverages the effective medium anisotropy of\nCNT arrays, where the hyperbolic behavior originates from the Luttinger-liquid plasmon properties\nof CNTs. This enables high Q-factors and nearly linear dispersion over an exceptionally broad\nspectral range (e.g., 6–11 μm). Our platform fundamentally differs from conventional narrowband\nphonon systems in terms of bandwidth, loss levels, and mode controllability.\n(2) In-Plane Wavefront Visualization and Manipulation vs. Out-of-Plane Propagation Limitations\nUnlike the out-of-plane propagation or vertically quantized modes commonly observed in systems\nsuch as ZrSiSe, our CNT array platform supports in-plane hyperbolic plasmons. This allows for direct\nimaging and observation of isofrequency profiles and energy flow directions, overcoming the\ngeometric constraints of vertical propagation in atomically thin layers. Consequently, it enables\npractical, on-demand manipulation of in-plane momentum propagation and wavefront shapes,\noffering a new level of control.\n(3) Ultra-Clean Direct Growth vs. Nanofabrication or Twisting Engineering\nWhile nanopatterning techniques (e.g., etching) can induce hyperbolicity, they often introduce\nedge roughness and defect scattering, which degrade performance. In contrast, our platform\nemploys directly grown, crystal-scale CNT arrays with atomically smooth surfaces and minimal\nimpurity scattering. This \"ultra-clean\" approach eliminates the need for complex nanofabrication\nor twisting engineering, thereby directly reducing polariton transmission losses and significantly\nenhancing experimental reproducibility.\n(4) Universal Coupling Platform vs. Strict Frequency Matching\nRegarding coupling-induced topological transitions, our work goes beyond merely replicating\nexisting concepts (e.g., twisted α-MoO₃) by extending them to a broadband hyperbolic plasmonic\nplatform. The broadband hyperbolic response of CNT arrays significantly relaxes the frequency-\nmatching requirements for coupled systems, functioning as a universal \"coupling platform\" that\nallows greater design flexibility for hybridization with various polariton modes (e.g., phonons,\nplasmons) without the stringent material and frequency constraints of narrowband systems.\nIn conclusion, the innovation of this work lies in the establishment of an ultra-clean, low-loss,\nbroadband, and directly imageable in-plane hyperbolic plasmon platform. This provides a scalable\nand practical pathway for polariton manipulation and topological transitions without relying on\ncomplex fabrication techniques. Our work represents a substantial advancement in the\ndevelopment of polariton-based devices and tunable nanophotonics, far beyond merely\nreproducing known phenomena in new materials.\nFurthermore, we have incorporated the references suggested by the reviewer (Science 359, 892\n(2018); Sci Adv 8, add6169 (2022); Science 387, 786 (2025); Nature Mater 19, 1307 (2020); Nature\n582, 209 (2020); Nature Nanotech 17, 940 (2022); Nature Commun 13, 3719 (2022)) as citations in\nthe revised manuscript.\nComment 2: Another significant concern is that the manuscript repeatedly makes claims that are\nnot substantiated by sufficient experimental evidence or logical derivation, which compromises the\nscientific integrity of the manuscript.\n2-i: The claim of “configurability” based on simple frequency dependence is misleading. This is\na basic material property of CNT array/hBN device, but not an externally tunable feature that\n“configurability” typically implies. The authors’ method of labelling “configurability” can\nbe applied to most all vdW polaritonic materials. For example, phonon polaritons in hBN exist only\nwithin the Reststrahlen band. In this case, hBN phonon polaritons would also be “configurable”\nas one can switch phonon polaritons on and off simply by tuning frequency.\nOur reply: We thank the reviewer for his/her insightful comments\nTo prevent misunderstanding, we have revised all mentions of \"configurable polaritons\" in the text\nto \"frequency-dependent topological polaritons,\" and changed the title to \" Frequency-dependent\ntopological polaritons in carbon nanotube array/hBN heterostructures\". The polaritons reported\nin this work exhibit distinct topological characteristics (hyperbolic or elliptical) depending on\nfrequency, which better captures the fundamental nature of this system.\nWe demonstrated the unique capability of our polaritons to tune their wavefront shape and\nwavelength simply by adjusting the excitation frequency across a wide spectral range, an\nunprecedented feature that distinguishes our system from other conventional ones. Our approach\noffers an ultra-clean, efficient, and versatile solution for on-demand polariton manipulation,\ncompletely eliminating the need for complicated twist-angle engineering in van der Waals\nheterostructures or complex micro/nanofabrication of electrodes for electrostatic gating.\nTherefore, this inherent advantage of our system enables direct optical control without physical\nmodifications or additional fabrication steps.\n2-ii: The authors claim to be the “first” to demonstrate, “a whispering-gallery plasmonic mode\nconfined in closed-loop CNT array on hBN.” However, this claim of novelty is overstated. As the\nauthors' own citations (Ref. 38) confirm, whispering-gallery plasmonic modes have already been\ndemonstrated in other vdW materials, such as graphene. Therefore, the simple extension of this\nwork to a CNT array does not seem to be a significant conceptual advance, and the manuscript fails\nto convey the importance of this observation in CNT arrays.\nOur reply: We thank the reviewer for his/her constructive suggestions.\nWe refer to being the \"first\" to demonstrate a whispering-gallery plasmonic mode confined in CNT\narrays. Due to the extremely small diameter of CNTs, typically around 1 nm, it is experimentally\ndifficult to observe whispering gallery modes within their cross-sections (such as the polariton\nwhispering gallery modes observed in BN nanotubes [Nat. Nanotechnol. 18, 529–534 (2023)]).\nTherefore, forming CNTs into nano-rings is essential to achieve this phenomenon. We are the first\nto assemble CNTs into close-loop nano-rings, and have observed a plasmonic whispering gallery\nmode with a very high quality-factor (as described in the following Fig. R18) and excellent\ncoherence.\nTo prevent any misunderstanding, we have removed the word \"first\" from the revised manuscript.\n2-iii: In addition, the authors’ claim of a whispering-gallery plasmonic mode itself is not convincing.\nPlasmonic whispering gallery modes are those that travel around a circumference of the cavity.\nBased on the main dataset shown in Fig. 4c, the reviewer does not see any clear signatures of\nplasmonic wave travel around the circular, donut shaped structure, forming a whispering-gallery\nmode. IR nano-imaging shown in Fig. 4c seems rather a result of tip-launched (or cavity edge\nlaunched) plasmons interacting with the entire cavity structure, forming a cavity-like nano-IR\nresponse, but not necessarily a whispering-gallery mode specific to the chiral motion of polaritons\naround the loop. More rigorous analysis needs to be performed to support their claim of\nwhispering-gallery modes.\nOur reply: We appreciate the reviewer’s valuable feedback regarding the interpretation of the\nobserved phenomena as whispering-gallery plasmonic modes.\nThe polaritons we observe are excited by an AFM tip and propagate along the axial direction of\ncarbon nanotubes, completing a full loop before being detected again by the tip. Since our ring-\nshaped CNT array is highly centrosymmetric and perfectly circular, when the tip is positioned above\na path at the same radius, the excitation of polaritons is identical, and the detected signals are also\nidentical. This is manifested as completely identical infrared signals along the same radial path in\nthe final near-field imaging.\nHowever, paths at different radii display varying brightness—either brighter or darker—\ncorresponding to the constructive or destructive interference of the polaritons. Notably, this\nbrightness contrast changes with the excitation frequency, which we attribute to the presence of\nthe whispering-gallery mode of polaritons.\nTo further support our claim that these are indeed whispering-gallery modes propagating along\nthe axial direction of the CNT array—as opposed to radial propagation modes— we have selected\na larger closed-loop CNT array ring for analysis. The results, presented in Fig. R16, illustrate that\nthe path length for polaritons to complete one loop (i.e., the circumference of the circle) is\nsignificantly longer, far exceeding the propagation distance of the polaritons. As a result, no\nconstructive or destructive interferences are observed in this configuration.\nFigure R16. The evolution of the hybrid polaritons in a larger closed-loop CNT array ring on hBN with the\nexcitation frequency, displaying nearly no interference. a, AFM topography image of a closed-loop CNT array ring\non hBN. b-h, Infrared nano-imaging of plasmons in the CNT-array/hBN at different frequencies.\n2-iv: The authors claim that “the synergy of the low-loss characteristics of the Luttinger liquid\nelectronic state, uniform chirality, and near-atomic-level smooth, lossless ring-shaped interfaces\nenables efficient optical field confinement and the formation of strong optical resonances,” is\nhighly speculative and lacks quantitative support. The manuscript provides no metrics to define,\nmeasure, and quantify the efficient optical field confinement and strong optical resonances.\nFurthermore, the authors do not demonstrate how their data supports the existence of or the\nconnection to the low-loss Luttinger liquid, uniform chirality, or lossless interfaces. These claims are\nconcerning because they are presented without any supporting evidence. At the very least, the\nauthors should provide a quantitative comparison of the polariton quality factors in their straight\nand circular structures.\nOur reply: We thank the reviewer for his/her comments.\nThe plasmonic properties of carbon nanotubes have been reported to exhibit high spatial\nconfinement capability and high quality factors in previous literatures. [Nature Photon. 9, 515-519\n(2015)]\nWe performed a quantitative analysis of the Q factors of polaritons in the CNT array/hBN system,\nusing the definitions of the quality factor 𝑄 =𝑅𝑒(𝑞)/𝐼𝑚(𝑞) and the compression factor 𝑁 =\n𝑅𝑒(𝑞)/𝑘 , and fit the experimental near-field profile with the formula below:\n0\n1 −2𝑥\n𝐼 =|𝜂 +𝜂 𝑒 𝑎 𝑒𝑖(2𝑞𝑥+𝜙𝑅)|\n𝑠 𝑅\n√2𝑥\nwhere 𝜂 is the scattering rate of incident light back into the detector, 𝜂 is the reflectivity of\n𝑠 𝑅\nHPs at the edge, 𝑞 is the plasmon wavevector, a is the decay length, and 𝜙 is the reflection\n𝑅\nphase. This formula is derived from the previous literature [Adv. Funct. Mater. 2019, 29, 1904662].\nWe selected experimental data at frequencies of 1111 cm-1 and 1639 cm-1 for fitting, and the\nresults are shown in Fig. R17 below. It can be observed that the Q factors of the polaritons in the CNT\narray/hBN exceed 20, with a wavelength compression ratio reaching 21.\nAdditionally, we collected the near-field signal intensity with the background subtracted, at a\ncertain point (denoted by a blue dot in Fig. R18a) on the closed-loop CNT-array ring at different\nexcitation frequencies and the results are plotted in the Fig. R18b. The data are well fitted by a\nstandard resonance peak curve. From this fitting, the quality factor (Q factor) is extracted as follows:\n𝑄 =\n𝜔𝑐\n=\n1600.16 𝑐𝑚−1\n=67.63, where 𝜔 is the resonance frequency and ∆𝜔 is the full width\n∆𝜔 23.66 𝑐𝑚−1 𝑐\nat half maximum (FWHM) of the resonance peak.\nThese results demonstrate the advantage of achieving both a relatively strong spatial confinement\nand a high Q factor compared to other two-dimensional metallic plasmonic systems. Typically,\nstrong spatial confinement can only be achieved at the expense of a low Q factor due to the\nabsorption loss of metals. For instance, a two-dimensional surface plasmon at a silver/air interface\nhas a quality factor of ∼16 with λ /λ = 1.16 at 400 nm, but Q worsens to ∼2.27 when λ /λ\np 0 p 0\nincreases to 1.51 at 350 nm. [Nature Photon. 9, 515-519 (2015)] However, due to the different\nscattering mechanisms between plasmons and phonon polaritons, the Q factors of our coupled\npolaritons are lower than those of phonon polaritons in systems like hBN, which is inherently\nattributed to electron-electron scattering in plasmons.\nIn summary, compared to two-dimensional metallic plasmons, the polaritons we report exhibit\nadvantages in wavefront tunability and higher Q factors. In contrast to hyperbolic phonon\npolaritons in materials such as α-MoO₃, our coupled polaritons offer advantages in broadband\nresponse and wavefront tunability.\nFigure R17. Extraction of the quality factor of plasmons in CNT array. a, The near-field profile along the axial\ndirection of CNT array at the frequency of 1111 cm-1 and the corresponding fitting curve. b, The near-field profile\nalong the axial direction of CNT array at the frequency of 1639 cm-1 and the corresponding fitting curve.\nFigure R18. Extraction of the quality factor of the whispery-gallery mode polaritons in closed-loop CNT array/hBN.\na, A typical infrared nano-imaging of polaritons in the CNT-array/hBN. b, Frequency-dependent near-field", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "Response to Reviewers' Comments (NCOMMS-25-86882)\nWe sincerely thank all the referees for their careful review of our work and for providing insightful\nand constructive comments. Below, please find our detailed point-by-point responses.\nResponse to Reviewer #1\nIn their work, “Configurable plasmon polaritons in carbon nanotube array/hBN heterostructures”,\nY. Xie et al. report on coupled polaritons in heterostructures of carbon nanotubes (CNT) arrays and\nhexagonal boron nitride (hBN). They carefully study a frequency-dependent transition of the\npolaritons from hyperbolic to elliptical propagation and show indications of a whispering-gallery\nplasmonic mode in a closed-loop CNT array structure. I feel their work is particularly interesting as\nit explores polaritons of a relatively new material structure (CNT arrays), which here are hybridized\nwith hBN phonon polaritons.\nOverall, I think the results are interesting, novel, and worth publishing. It appears that most of the\nfindings presented are well-supported by an instructive combination of experimental results,\nnumerical simulations, and comparison with literature. While the final section of the manuscript —\non whispering-gallery modes — presents interesting findings, it does not yet match the quality and\nclarity of the rest of the manuscript and should be revised before publication.\nPlease find below some detailed comments.\nOur reply: We thank the reviewer for his/her appreciation of our work and for the positive\nevaluation. We are also very grateful for the constructive comments provided by the reviewer that\nhave helped us improve the manuscript. Below, we address the questions and comments raised by\nthe reviewer one by one.\n1. The manuscript presents experimental results in a relatively broad spectral range from around\n900 to >1600 cm-1, which requires a tunable or broadband light source. However, the methods\nsection mentions that the results have been obtained with a CO laser at a single wavelength of\n2\n10.6 um. Please add relevant information on the laser used for the experiments.\nOur reply: We thank the reviewer for pointing out our mistake in the Methods section.\nIn addition to the CO laser, we also used a quantum cascade laser (QCL) with a tunable frequency\n2\nranging from 900 cm-1 to 1600 cm-1 in our near-field optical measurement. We have revised the\nMethods section of the manuscript and added the relevant information as follows.\n“For near-field infrared nano-imaging, we employed a custom-built scattering-type scanning near-\nfield optical microscope (s-SNOM) that integrates a tapping-mode atomic force microscope (AFM,\nBruker Innova) with a CO laser and a Daylight Solution quantum cascade laser (QCL). The system\n2\noperates by focusing a mid-infrared laser (900~1650cm-1) beam onto the apex of a conductive AFM\nprobe, generating a highly localized enhanced optical field. This near-field interacts with the sample,\nand the resulting scattered light, which encodes local optical information, is collected in the far field\nusing a mercury cadmium telluride (MCT) detector (KLD-0.1-J1, Kolmar). To suppress background\nscattering, the collected signal is demodulated using a lock-in amplifier (Zurich Instruments HF2LI).\nThis configuration allows for the simultaneous acquisition of high-resolution near-field optical\nimages alongside topography information during measurements.”\n2. As shown in Fig. 1b and described in Supplementary Note 2, the authors simply assume the\nconductivity of air for the radial direction (y-direction) of the CNT permittivity. While they state that\nthis is consistent with previous research on CNT arrays, the authors do not provide specific\nreferences. The permittivity is an essential assumption that should be discussed in more detail. If\nthe permittivity along the y-direction was in fact slightly negative, would this mean that the\nbehavior qualitatively more resembled the well-studied case of graphene and the “topological\ntransition” with frequency may disappear?\nOur reply: We sincerely thank the reviewer for his/her insightful comments and suggestions.\nFor the selection of the radial dielectric constant of carbon nanotube (CNT) arrays, we adopted a\nstrategy that combines referencing parameters from the literature with fitting experimental\nobservations. Theoretically, based on the coupled Luttinger liquid theory, CNT arrays exhibit\ncharge-insulating properties in the radial direction [Phys. Rev. Lett. 86, 676 (2001)], which aligns\nwith our previous studies on the material properties of CNT arrays [Science, 387, 1310 (2025)].\nBased on this, we treated the radial direction as a quasi-air medium (insulating assumption). This\nsimplified approach has been widely adopted in the field of CNT array research [IEEE Trans.\nAntennas Propag. 57 1412(2009)] [Phys. Rev. B 82 155423(2010)] [IEEE Trans. Nanotechnol. 11\n964(2012)]. It has been confirmed that this parameter setting achieves excellent agreement in\nreproducing the CNT hyperbolic experimental phenomena [Chinese Phys. Lett. 42, 090710 (2025)]\nas well as in fitting the topological hybridization experiments in this study, thereby verifying the\nrobustness of the theoretical model.\nRegarding the comment on the possibility that the dielectric constant in the y-direction might be\nslightly negative, we conducted an in-depth analysis. In the mid-infrared range, the response of\nCNT arrays in the radial (y) direction to external fields is extremely weak (the magnitude of the\ndielectric constant is very small), and the dominant characteristic of the system is hyperbolic\nplasmonic behavior. Simulations and corresponding iso-frequency contours (see Fig. R1 below)\nshow that setting the radial dielectric constant to small negative values (e.g., -2) yields results that\nare nearly identical to those obtained with a value of +1. Physically, while a negative dielectric\nconstant supports high-momentum radial modes (manifested as short-period oscillations), these\nmodes are distinct from the characteristics of axial hyperbolic modes and do not significantly affect\nthe propagation behavior of the hyperbolic wavefront.\nIt is important to emphasize that only when the absolute value of the radial dielectric constant\nbecomes sufficiently large does the momentum of the radial mode significantly decrease, leading\nto a topological phase transition from hyperbolic polaritons to elliptical polaritons (as shown in Fig.\nR1f). Only under such extreme conditions would the frequency-dependent topological transition\ndisappear, and the system would exhibit isotropic behavior similar to graphene. Therefore, within\nthe current parameter range, our conclusions remain robust.\nFigure R1. The influence of radial dielectric constant on the topological transition. The numerical simulated spatial\ndistribution of the real part of the polariton field Re(E) (top)measured above the CNT-array/hBN at frequencies of\nz\n1639cm-1 and corresponding iso-frequency contours (bottom) with different radial dielectric constants.\n3. Regarding the whispering-gallery modes, the authors mention “the intensity of the constructive\ninterference peaks also oscillates with changes in frequency, revealing an inverse relationship\nbetween peak spacing and intensity: the smaller the peak spacing, the higher the intensity”.\nHowever, Fig. 4d shows “IR intensity” in arbitrary units. How is “intensity” defined here? I.e., how\ndo the authors make sure that their definition of “intensity” is consistent across different\nfrequencies and a frequency-dependent comparison of “intensity” is useful?\nOur reply: We appreciate the reviewer's insightful comments.\nIn our study, \"intensity\" is defined as the relative difference between the near-field signal—\nspecifically, the magnitude of the electric field perpendicular to the surface (|E|)—at the\nz\ninterference-enhanced peak of CNT-array/hBN polaritons and the background level observed in\nthe pure hBN region. Given that hBN forms a substantial part of the substrate, providing an\noverarching background, we believe this definition of intensity is appropriate. Throughout the\nexperiments, we maintained a consistent intensity of incident light across varying frequencies to\nensure comparability.\nTo enhance clarity, we have refined our statement to:\n“As the two interference peaks move closer together, the interference pattern becomes more\nstrongly constructive.”\n4. While all figures in the main manuscript use false-color maps, none of these includes a color bar.\nIt would be helpful to either include color bars for all false-color maps or at least provide a more\ndetailed description of the displayed quantities in the caption.\nOur reply: We thank the reviewer for his/her kind reminder.\nIn our revised manuscript, we have added color bars to all false-color maps to enhance clarity.\nAdditionally, we have provided more detailed descriptions of the displayed quantities in the figure\ncaptions.\n5. The section on the on the whispering-gallery modes appears to include several claims that are\nnot well supported. Specifically, the following claims should be supported by a quantitative analysis:\na. The authors mention “near-atomic-level smooth, lossless ring-shaped interfaces”. While “lossless”\nis a strong claim, no quantitative analysis of losses is provided.\nb. “The high compression ratio (…) preserves quantum state coherence”. “quantum state coherence”\nappears vague here and it is not clear how this statement is supported by the data.\nc. The authors mention that their structures “showcase the unique benefits of Luttinger liquid\nplasmons”. This should be discussed in more detail. Specifically, how are the benefits “unique”\ncompared to other plasmonic systems?\nd. The authors mention “Compared to traditional low-dimensional plasmonic whispering-gallery\nnanocavities38, its characteristic dimensions and performance have improved by nearly an order\nof magnitude.” They refer to reference 38 here. As the authors claim that the performance has\nincreased by nearly an order of magnitude, this should be quantified by comparing suitable figures\nof merit such as the quality factor. At first glance, the whispering gallery modes shown in Fig. 4 do\nnot appear to have a significantly higher quality compared to the ones shown in reference 38,\nmaking a quantitative comparison important.\ne. It might be helpful to support the experimental findings on the whispering-gallery modes in Fig.\n4 with numerical simulations (e.g., similar to those provided in Fig. 3).\nOur reply: We thank the reviewer for his/her constructive comments. We have addressed each\ncomment and suggestion point by point as outlined below.\na-c: The plasmons in CNTs have been reported to exhibit characteristics of Luttinger liquid\nplasmons, demonstrating excellent properties of high spatial confinement and high quality factors,\nas detailed in previous literature [Nature Photon. 9, 515-519 (2015)]. We have quantitatively\nanalyzed these properties using the quality factor 𝑄 =𝑅𝑒(𝑞)/𝐼𝑚(𝑞) and the compression factor\n𝑁 =𝑅𝑒(𝑞)/𝑘 . Additionally, we fitted the experimental near-field profile with the following\n0\nformula,\n1 −2𝑥\n𝐼 =|𝜂 +𝜂 𝑒 𝑎 𝑒𝑖(2𝑞𝑥+𝜙𝑅)|\n𝑠 𝑅\n√2𝑥\nwhere 𝜂 represents the scattering rate of incident light back into the detector, 𝜂 is the\n𝑠 𝑅\nreflectivity of HPs at the edge, 𝑞 is the plasmon wavevector, a is the decay length, and 𝜙 is the\n𝑅\nreflection phase. This formula is derived from the literature [Adv. Funct. Mater. 2019, 29, 1904662].\nWe selected experimental data at frequencies of 1111 cm-1 and 1639 cm-1 for fitting, as shown in\nFig. R2 below. Notably, the quality factor of the CNT array plasmons reaches up to 21, while the\ncompression factor is 21.57. These results highlight that even structured into whispering-gallery-\nmode oscillators, CNT plasmons retain their excellent intrinsic properties, significantly lowering\noptical scattering losses, and maintaining low intrinsic dissipation, thus preserving optical state\ncoherence [Nano Lett. 2021, 21, 8707−8714] [Nature, 2020, 582(7810): 46-49].\nTo support this conclusion, we collected frequency-dependent near-field signal intensity data with\nthe background subtracted, from a specific point (denoted by a blue dot in Fig. R3a) on the closed-\nloop CNT-array ring on hBN. The results (see Fig. R3b), which exhibit a strong fit to a standard\nresonance peak curve, confirm the presence of a whispering-gallery mode. From this fitting, we\nextracted the quality factor (Q) as follows: 𝑄 =\n𝜔𝑐\n=\n1600.16 𝑐𝑚−1\n=67.63 , where 𝜔 is the\n∆𝜔 23.66 𝑐𝑚−1 𝑐\nresonance frequency and ∆𝜔 is the full width at half maximum (FWHM) of the resonance peak.\nHowever, we acknowledge that some expressions in our manuscript are not rigorous enough and\nrequire further refinement. For example, we have revised “lossless ring-shaped interfaces” to\n“low-loss ring-shaped interfaces”, and “The high compression ratio not only preserves quantum\nstate coherence” to “The high compression ratio and quality factor not only preserve optical\nstate coherence”.\nFigure R2. Extraction of the quality factor of plasmons in CNT array. a, The near-field profile along the axial\ndirection of CNT array at the frequency of 1111 cm-1 and the corresponding fitting curve. b, The near-field profile\nalong the axial direction of CNT array at the frequency of 1639 cm-1 and the corresponding fitting curve.\nFigure R3. Extraction of the quality factor of the whispery-gallery mode polaritons in closed-loop CNT array/hBN.\na, A typical infrared nano-imaging of polaritons in the CNT-array/hBN. b, Frequency-dependent near-field signal\nintensity at a certain point on the closed-loop CNT-array ring on hBN. The position where the experimental data\nwere extracted from is denoted by a blue dot in (a).\nd. The term “characteristic dimensions and performance” in the manuscript refers to the mode\nvolume ratio 𝑉/𝑉 , which is approximately one order of magnitude lower than that of the\n𝑝 0\nnanocavity reported in reference 38 [Nat. Mater. 22, 838–843 (2023)]. This estimation method\nfollows the approach used in previous literatures [Science 360, 291-295 (2018)] [Science 368, 1219-\n1223 (2020)], where the polariton wavelength 𝜆 =𝜆 /16.5 is used. Given our CNT nanocavity’s\n𝑝 0\nthickness is on the atomic scale, roughly 4 nm, we obtain 𝑉/𝑉 =2.3×10−6, which is less than\n𝑝 0\nthe value of 10−5 reported in reference 38 [Nat. Mater. 22, 838–843 (2023)].\ne. We have conducted numerical simulations of the polariton whispering-gallery mode and\nincorporated these results into Fig.4 of the revised manuscript (see Fig. R4). Our simulation method\ninvolved placing an electric dipole above the resonant ring to mimic the AFM tip to excite the\npolaritons, and collecting the 𝐸 component below the dipole. The mapping of dipole scanning\nz\npositions yielded results that correlate well with our experimental findings.\nFigure R4. The revised version of Figure 4 of the manuscript. a, Schematic of infrared nano-imaging of whispering-\ngallery polaritonic mode in the CNT-array/hBN by using s-SNOM. b, AFM topography image of a closed-loop CNT\narray ring on hBN. Infrared nano-imaging experiment (c) and corresponding numerical simulations (d) of polaritons\nin the CNT-array/hBN at different frequencies, respectively. e, The Near-field line profiles along the sections marked\nby the dashed line in (b).\nResponse to Reviewer #2\nThis manuscript presents an approach to modulate the dispersion of hyperbolic Luttinger-liquid\nplasmon polaritons (HLLPPs) in carbon nanotube (CNT) arrays through coupling with phonon\npolaritons (PhPs) in hexagonal boron nitride (h-BN). The authors demonstrate a frequency-\ncontrolled topological transition from hyperbolic to elliptic polariton wavefronts and report the\nobservation of a whispering-gallery confined plasmonic mode in the coupled CNT/h-BN\nheterostructure. The study addresses a topic of clear relevance to the fields of nanophotonics and\npolaritonics, potentially contributing to the development of tunable hybrid polaritonic systems.\nHowever, in my opinion, this manuscript in its current form requires major revisions to become\nacceptable for publication in Nature Communications.\nFirst, the novelty and physical interpretation need to be clarified, several claims must be\nquantitatively supported, and the results should be better addressed considering previous works.\nIn addition, several figures and methodological descriptions require improved clarity. Addressing\nthese issues would significantly enhance the scientific quality and overall impact of the manuscript.\nPlease, find detailed comments below.\nOur reply: We appreciate the reviewer’s recognition of our work and the valuable suggestions for\nenhancing the manuscript. Below, we address each question and comment in detail.\n1. The authors should carefully revise the manuscript to ensure consistent and precise use of\npolaritonic terminology. Terms such as “plasmon polaritons”, “hybrid polaritons”, and “phonon\npolaritons” appear to be used interchangeably, which can lead to conceptual ambiguity. Each\npolariton type should be clearly defined and used consistently according to its physical origin and\ndistinctive characteristics.\nOur reply: We appreciate the reviewer’s insightful suggestions regarding the use of polaritonic\nterminology.\nIn response, we have revised some terms throughout the manuscript. In particular, we have revised\nthe manuscript title from “Configurable plasmon polaritons in carbon nanotube array/hBN\nheterostructures” to “Frequency-dependent topological polaritons in carbon nanotube array/hBN\nheterostructures” for greater clarity.\nTo clarify terminology within the manuscript: “plasmon polaritons” refers to the polaritons\ngenerated from the interaction between charges in CNT arrays and incident photons, while\n“phonon polaritons” denote the interactions between phonons in hBN and photons. The term\n“hybrid polaritons” describes the coupled modes resulting from plasmon and phonon polariton\ninteractions. Specifically, in regions outside the Reststrahlen band 2 of hBN, only plasmon\npolaritons propagate in the CNT-array/hBN system. However, within the Reststrahlen band, CNT\narrays plasmon polaritons are classified as hybrid polaritons due to their coupling with phonon\npolaritons in hBN.\nTo eliminate ambiguity, we have made these definitions consistent throughout the revised\nmanuscript.\n2. In Supplementary Information Note 4, the authors state: “The dispersion relations are similar to\nFig. 3e, indicating reliable and accurate results.” This appears instead to refer to Figure 2e. The\nauthors should verify the accuracy of all internal references (figures, tables, and text sections)\nthroughout the manuscript.\nOur reply: We thank the reviewer for his/her careful review, and for pointing out our mistake.\nThe typo has been corrected, as shown below.\n“Here, we calculated the frequency-momentum dispersion relations of hybrid plasmons using the\nfinite element simulation method (COMSOL), as shown in Supplementary Figure 3. The dispersion\nrelations are similar to Fig.2e, indicating reliable and accurate results.”\n3. In the Introduction, the authors compare plasmon polaritons in CNTs with phonon polaritons in\nmaterials such as h-BN and α-MoO . They mention that plasmon polaritons exhibit superior\n3\nproperties, including low loss and broad spectral range. This claim should be quantitatively\nsupported with comparative metrics such as propagation length, lifetime, and confinement, or\notherwise tempered. Moreover, phonon polariton systems, though spectrally limited to the\nReststrahlen bands, are typically characterized by longer lifetimes and reduced losses compared to\nplasmonic systems due to their distinct scattering mechanisms. I would recommend the authors to\nreference prior reports on controlled polariton propagation in phonon-polariton systems (Nano Lett.\n2020, 20, 5301–5308; Nano Lett. 2020, 20, 5323–5329; Nat Commun 2024, 15, 9042).\nOur reply: We appreciate the reviewer’s valuable comments regarding the comparative analysis of\nplasmon polaritons in CNTs and phonon polaritons in materials like h-BN and α-MoO .\nbackscattering in their one-dimensional structure, allowing Luttinger-liquid plasmons to achieve\nhigh quality factors of up to 20 (Nat. Photon., 9, 515 [2015]). This quality factor is generally superior\nto that of plasmons observed on other low-dimensional surfaces, such as graphene. However, we\nacknowledge that CNT plasmons do not possess this advantage when compared to phonon\npolaritons.\nTo enhance clarity and precision, we have revised the introduction with the following statement:\n“ Plasmon polaritons, particularly in one-dimensional carbon nanotubes (CNTs), exhibit\nexceptional properties, including deep subwavelength confinement and a broad spectral range.”\nFurthermore, we have incorporated the references suggested by the reviewer (Nano Lett. 2020,\n20, 5301–5308; Nano Lett. 2020, 20, 5323–5329; Nat Commun 2024, 15, 9042) as citations in the\nrevised manuscript.\n4. The authors report a topological transition of hybrid polaritons from hyperbolic to elliptic\nwavefronts. Such transitions have been extensively investigated in recent literature, as they can\nlead to the emergence of the so-called canalized propagation regime. It would be expected that\nthis system also exhibits polariton canalization at the precise topological transition frequency\n(Optica 2025, 12, 343-349; Nano Lett. 2025, 25, 6, 2203–2209). The authors should discuss whether\nsuch canalized regime is expected in the topological transition observed in the CNT array/h-BN\nsystem. Also, the qualitative explanation of the hyperbolic-to-elliptic transition based on the sign\nchange of hBN’s in-plane permittivity is reasonable and consistent with established polaritonic\nbehavior. However, the authors show only two discrete frequency cases. A continuous evolution of\nisofrequency contours across the transition region would more convincingly demonstrate the\nclaimed topological change.\nOur reply: We appreciate the reviewer’s constructive suggestions regarding the topological\ntransition of hybrid polaritons.\nThe small width of our as-grown CNT arrays (only several hundred nanometers) makes it\nexperimentally challenging to accurately determine the excitation frequency for polariton\ncanalization. To address this, we have supplemented our experimental findings with analytical\ncalculations, as shown in Fig. R5. The results, illustrated in the figure below, show that the polariton\niso-frequency contours transition from elliptic to hyperbolic as the excitation frequency increases.\nThis analysis indicates that a canalization state emerges around the frequency of 1605 cm⁻¹.\nFurthermore, we have incorporated the Fig. R5 as part of the revised Supplementary Information\nand added the references suggested by the reviewer (Optica 2025, 12, 343-349; Nano Lett. 2025,\n25, 6, 2203–2209) as citations in the revised manuscript.\nFigure R5. The continuous evolution of iso-frequency contours across the transition region. The excitation\nfrequencies are 1585cm-1 (a), 1595cm-1 (b), 1600cm-1(c), 1605 cm-1 (d) and 1610cm-1 (e), respectively.\n5. The authors describe the observed phenomena as resulting from “strong coupling” between CNT\nplasmons and h-BN phonon polaritons yet no quantitative coupling parameters (e.g., mode\nsplitting, coupling rate, or linewidth analysis) are provided. This statement should be substantiated\nwith a detailed discussion of the mode splitting visible in the dispersion (Fig. 2e). For completeness,\nI recommend including the individual dispersions of the CNT array and of h-BN (plots shown in the\nSupplementary Information), alongside their coupled dispersion, to help the reader clearly visualize\nthe hybridization effect.\nOur reply: We thank the reviewer for the valuable suggestions regarding the coupling parameters\nof the observed phenomena.\nTo quantitatively address the mode splitting of hybrid polaritons in the CNT array/hBN system,\nwe employed a method similar to that used in previous literature [Nat. Mater. (2025).\nhttps://doi.org/10.1038/s41563-025-02412-6]. The mode splitting of hybrid polaritons in the CNT\narray/hBN can be expressed as:\n1\n𝜔 = √𝜔2 +𝜔2 +4𝑔2±√(𝜔2 +𝜔2 +4𝑔2)2−4𝜔2 𝜔2\n± 𝑠𝑝𝑝 𝑝ℎ𝑝 𝑠𝑝𝑝 𝑝ℎ𝑝 𝑠𝑝𝑝 𝑝ℎ𝑝\n√2\nwhere, g is the coupling strength, 𝜔 and 𝜔 represent the bare modes of CNT array\n𝑠𝑝𝑝 𝑝ℎ𝑝\nplasmons and hBN phonon polaritons, respectively.\nThen, we extracted 𝜔 =1357 𝑐𝑚−1 and 𝑔 = ∆𝜔 =319.2 𝑐𝑚−1 from the calculated\n𝑐\n2\ndispersion relations, where the 𝜔 represents the frequency where bare modes cross. Therefore,\n𝑐\ng\nthe normalized coupling strength is calculated as =3.45>1 , where Γ =\n𝑝ℎ𝑝\n(Γ𝑝ℎ𝑝+Γ𝑠𝑝𝑝)/2\n10 𝑐𝑚−1 and Γ =174.79 𝑐𝑚−1 represent the loss rates of hBN phonon polaritons and CNT\n𝑠𝑝𝑝\narray plasmons, respectively. This result substantiates that the hybrid mode between CNT array\nplasmons and hBN phonon polaritons can be classified as strong coupling. [Nat. Rev. Phys. 1, 19–\n40 (2019)]\nFollowing the referee’s suggestion, we have included a comparative plot of the dispersions for the\nindividual carbon nanotube array plasmons, individual hBN phonon polaritons, and their hybrid\nmode, as shown in Figure R6 below. This figure is now part of the Supplementary Information.\nFigure R6. Calculated dispersion relation of the individual carbon nanotube array plasmons, individual hBN\nphonon polaritons, and their hybrid modes. a, The dispersion relation of the individual carbon nanotube array\nplasmons. b, The dispersion relation of the individual hBN phonon polaritons. c, The dispersion relation of the\nhybrid mode. The calculated dispersion is visualized using a false-color map of the imaginary part of the reflection\ncoefficient r .\np\n6. In Figure 1b, the notation “x4” is unclear. Please define this multiplier explicitly. The authors\nshould also indicate on this panel the excitation frequencies corresponding to the simulated\ndistributions shown in panels c and d.\nOur reply: We appreciate the reviewer’s careful review and valuable feedback.\nTo enhance clarity, we have added the following note to the caption of Figure 1b:\n“The ‘x4’ label means that the in-plane permittivity of hBN has been multiplied by four so that the\ndielectric functions of both hBN and CNTs can be displayed together on the same y-axis.”\nAdditionally, we have indicated the excitation frequencies in Figure 1b that correspond to the\nsimulated distributions shown in Figures 1c and 1d of the revised manuscript.\n7. In Figure 1, all panels should include scale bars. If the same scale applies to multiple panels, this\nshould be clearly stated in the caption. Panels c and d should include a shared colorbar indicating\nthe plotted quantity (Re(Ez)), and panels e and f should include a grayscale colorbar for the\ncorresponding magnitude. Please, see, for example, (Nanophotonics 2024, 13, 4761–4770). The use\nof the term “measured” in the caption is misleading, as Figure 1 presents simulated data. Please\nreplace it with a term such as “calculated” or “simulated”.\nOur reply: We appreciate the reviewer’s careful and precise feedback.\nIn the revised Figure 1, we have included scale bars in all panels. If the same scale applies to\nmultiple panels, this has been clearly stated in the caption. Additionally, we have added a shared\ncolor bar for panels c and d, indicating the plotted quantity Re(E), and a grayscale color bar for\nz\npanels e and f to represent the corresponding magnitude.\nFurthermore, we have replaced the term “measured” with “simulated” in the caption to accurately\nreflect the nature of the data presented. Besides, we have incorporated the references suggested\nby the reviewer (Nanophotonics 2024, 13, 4761–4770) as citations in the revised manuscript.\n8. In Figure 2e, the authors should explain the discrepancy observed near 1400 cm-1 in the\nexperimental data points (high-order mode). Additionally, it would strengthen the analysis to\ninclude error bars in the experimental estimations (blue dots) and overlay the analytical dispersion\n(for example, with a dashed line) on the colorplot derived from the transfer-matrix model for\ncomparison.\nOur reply: We appreciate the reviewer’s important suggestions regarding Figure 2e.\nThe observed discrepancy near 1400 cm-1 between the experimental data points and the calculated\ndispersion relation can be attributed to measurement uncertainties. Specifically, in the frequency\nregion of plasmon-phonon polariton coupling, our experimental signal reflects a superposition of\nthe fundamental and second-order polariton modes. Due to an insufficient number of\nmeasurement periods caused by the sample size, the extracted wavelength values may not align\nperfectly with theoretical calculations.\nIn the revised manuscript, we have incorporated the following analysis:\n“The discrepancy between the experimental data and the calculated dispersion in the Reststrahlen\nband arises because our measurement captures a superposition of the fundamental and second-\norder modes of the hybrid polariton.”\nIn response, we measured the polariton wavelength again and quantified the reading uncertainty,\nwith the results plotted in Fig. R7a. As can be seen, the reading error in extracting wave vectors\nfrom the experimental data is negligible, rendering error bars virtually invisible on the plot;\ntherefore, they have been omitted. We attribute the observed discrepancy in the Reststrahlen\nband to the experimental indistinguishability between the fundamental and higher-order modes.\nTherefore, to ensure optimal visual presentation and avoid readability issues, we have chosen not\nto include error bars in the experimental dispersion relation. Similar treatment has been employed\nin many previously reported studies on the coupling of hBN polaritons and graphene plasmons, as\ndepicted in Fig. R8. [Nature Nanotech. 10, 682–686 (2015)] [Nature Mater. 14, 421–425 (2015)].\nFigure R7. Experimental dispersion relation including error bars. a, Experimental dispersion relation of hybrid\npolaritons in the CNT-array/hBN, with error bars included. B, Comparison of calculated and experimental dispersion\nrelations taken from the Fig.2e of the manuscript.\nFigure R8. Experimental dispersion relation of hybrid polaritons in graphene/hBN heterostructure.\nCorresponding simulation results are also provided as the background in previous literatures. (a) is taken from\nFig. 2c of the paper Dai et al. [Nature Nanotech. 10, 682–686 (2015)]. (b) is taken from Fig. 2d of the paper Woessner\net al. [Nature Mater. 14, 421–425 (2015)].\n9. In the experimental measurement panels (Figure 2c, Figure 3a, Figure 4c, Supplementary Figures\n4a,b, and Supplementary Figure 6a), the authors should add a colorbar and clearly specify which\nexperimentally extracted quantity is plotted in each case (amplitude, phase). Was the signal\ndemodulated at higher harmonics? If so, up to which harmonic order?\nOur reply: We appreciate the reviewer’s careful review and valuable suggestions.\nIn the revised manuscript, we have added color bars and provided textual descriptions of the\nextracted physical quantities for each experimental measurement panel (Figure 2c, Figure 3a,\nFigure 4c, Supplementary Figures 4a and 4b, and Supplementary Figure 6a). The extracted quantity\nrepresents the magnitude of the electric field, corresponding to the third order near-field signal.\n10. In Figure 3a,b, the authors present an experimental-simulation comparison. First, as previously\nnoted, the authors should indicate which experimentally obtained magnitude is plotted in Figure\n3a. Second, please, ensure that the aspect ratios of the experimental and simulated subpanels are\nidentical for a fair visual comparison. Third, I assume that in Figure 3b the authors plot the\nsimulated Re(Ez) … if so, this should be explicitly stated. The authors should note that the only\nphysically meaningful magnitude comparable to Re(Ez) is the real part of the near-field signal,\nRe(σ_n). If the experiment cannot independently and simultaneously extract s_n and ϕ_n, the only\nvalid comparison with simulations would be between |Ez| and s_n. Finally, this experiment-\nsimulation correspondence could be made clearer by comparing field profiles. Since the dispersion\nis already shown in Figure 2e, the authors could overlay the experimental data points on the\nisofrequency contour (IFC) plots in Figure 3c,d as another direct comparison.\nOur reply: We thank the reviewer for his/her significant comments and insightful suggestions.\nThe physical quantity depicted in Fig. 3a is the near-field intensity, while Fig. 3b shows 𝑅𝑒(𝐸 ).\nz\nThis information has been labeled in the revised manuscript. The experimentally observed pattern\narises from the interference between the incident field 𝐸 and the polariton field 𝐸 , i.e. 𝐸 =\nin 𝑝 𝑧\n𝐸 +𝐸 , as depicted in Figs. R9 a,b [eLight 3, 14 (2023)]. The polariton field forms an interference\nin 𝑝\npattern from its tip-excited and reflected components. Hence, the resulting fringes correspond to\nthe phase information of 𝑅𝑒(𝐸 ) . In contrast, the amplitude map, |𝐸 | , which lacks such\nz 𝑧\ninterference, does not match the experimental observations. Similar comparison methods have\nbeen employed in many previously reported studies [Nat. Nanotechnol. 17, 940–946\n(2022)][Nature 582, 209–213 (2020)][Nature 596, 362–366 (2021)][eLight 3, 14 (2023)]. A\ncomparison is commonly made between the simulated 𝑅𝑒(𝐸 ) and the near-field amplitude, as\nz\npresented in Figure R9.\nOtherwise, the Fourier transform of our imaging data, limited by the sample's small size, is\ncurrently of insufficient quality for overlaying onto the iso-frequency contours in Figures 3c, d.\nFigure R9. Experimental launching of polaritons and corresponding simulations in previous literatures. a, b,\nSchematic of the near-field polariton-launching experiment (a) and experimental near-field amplitude |𝐸 +𝐸 |\nin 𝑝\nand |𝐸 | (b), which are taken from Fig. 3 of the paper Hu et al. [eLight 3, 14 (2023)]. c, d, Experimentally measured\np\nnear-field images (c) of polaritons and the corresponding numerically simulated near-field distributions (Re(Ez)) (d),\nwhich are taken from Fig. 2 of the paper Zheng et al. [Science advances, 2019, 5(5): eaav8690]. e, f, Experimentally\nmeasured near-field images (e) of polaritons and the corresponding numerically simulated near-field distributions\n(Re(Ez)) (f), which are taken from Fig. 3 of the paper Hu et al. [Nat. Nanotechnol. 17, 940–946 (2022)]\n11. The authors state: “In this study, we focus exclusively on the analysis of polaritons at frequencies\naround the type-II band.” To strengthen this discussion, they should include numerical simulations\nshowing the spatial distributions of Re(Ez) across three distinct regions: i) the frequency range\nwhere CNT plasmons does not intersect with h-BN phonon polaritons; ii) the frequency range where\nCNT plasmons intersect with h-BN type I RB phonon polaritons; and iii) the frequency range where\nCNT plasmons intersect with h-BN type II RB phonon polaritons. What do the authors expect to\nobserve in s-SNOM nano-imaging for type I RB frequencies in this system?\nOur reply: We appreciate the reviewer’s helpful comments and insightful suggestions.\nThe reviewer correctly highlights the significance of examining hBN's two Reststrahlen bands.\nWhile we considered both type I and type II hyperbolic phonon polaritons (HPPs) in our theoretical\nanalysis, our experimental measurements were limited to type II HPPs. This limitation is due to the\nunavailability of continuous-wave laser sources operating in the 760–820 cm-1 range, which\ncorresponds to type I HPPs. Furthermore, the anisotropic nature of hBN causes the out-of-plane\nmode (type I HPPs) to be significantly weaker than the in-plane mode (type II HPPs). Consequently,\nour experimental study primarily focused on the type II Reststrahlen band, which is also the most\nexamined frequency range in hBN phonon polariton research.\nTo address the reviewer’s request, we performed finite-element simulations using COMSOL to\nsimulate the hybrid polariton mode in the type I HPPs of hBN, and the corresponding results are\npresented in Figure R10. It is noted that due to the emergence of well-defined hyperbolic phonon\npolaritons in hBN, the hyperbolic plasmons of the carbon nanotube array have also evolved into\nelliptical wavefront shapes.\nFigure R10. Numerical simulations of the hybrid polariton mode in the type I HPPs of hBN. The numerical\nsimulated spatial distribution of the polariton field Re(E) measured above the CNT-array/hBN at frequencies\nz\n770cm-1 (a) and 775cm-1 (b), respectively.\n12. Are the authors able to grow or transfer the CNT array onto different substrates (e.g. BaF or\n2\nthe manuscript to show a direct experimental and numerical comparison between the coupled\nsystem (CNT arrays/h-BN) and its individual constituents (CNT array on one side, h-BN on the other)\nincluding dispersion plots, Re(Ez) simulations, and s-SNOM measurements.\nOur reply: We thank the reviewer for his/her important suggestions.\nWe have tried to transfer the CNT array onto different substrate, such as SiO ; however, current dry\n2\ntransfer techniques disrupt the ordered, densely packed alignment of the nanotube array during\nthe process.\nAccording to the reviewer's suggestion, we have calculated the dispersion relation of the individual\nCNT array (without hBN) and included it in the Supplementary Information. Unfortunately, as the\nCNT array cannot be effectively transferred to a freestanding condition, we are currently unable to\nobtain experimental data for the dispersion of the isolated CNT array at this time.\n13. Regarding the sample fabrication process, the authors could clarify whether CNT arrays could\nbe integrated with other 2D van der Waals materials such as graphene, α-MoO or α-V O .\n3 2 5\nOur reply: We thank the reviewer for his/her constructive suggestions regarding sample\nfabrication.\nIn our experiments, we have also attempted to integrate the CNT array with other two-dimensional\nmaterials (graphene, α-MoO , or α-V O ) through stacking. As mentioned above, current transfer\n3 2 5\ntechniques tend to disrupt the structure of the CNT array during the process. However, we can\ntransfer other two-dimensional materials successfully onto the CNT array, which is part of our\nfuture research plan.\n14. The coupling strength and dispersion modification in plasmon–phonon systems are known to\ndepend sensitively on the hBN thickness. The authors mention using a 55 nm-thick flake “to reduce\nphonon intensity,” but no data or criteria are shown to justify this choice or demonstrate systematic\nthickness dependence. I believe that presenting simulations or experiments across several hBN\nthicknesses would greatly strengthen the coupling interpretation.\nOur reply: We appreciate the reviewer’s insightful suggestions regarding the dependence of\ncoupling strength and dispersion on hBN thickness.\nIndeed, the intensity and wavelength of phonon polaritons in hBN are thickness-dependent, as\nreported in previous literature [Science 343, 1125-1129 (2014)]. As indicated in Fig. R11, thicker\nhBN leads to larger phonon polariton amplitude and longer polariton wavelength. In Fig. R12 below,\nwe simulate the coupling between polaritons in hBN flakes of varying thicknesses and CNT array\nplasmons at a frequency of 1538 cm⁻¹. When the hBN flake is too thin, the resulting phonon\npolaritons exhibit an extremely small amplitude and a very short wavelength. This prevents\neffective coupling with plasmons in the CNT array, and the wavefront maintains its hyperbolic\ncharacter. A transition to an elliptical wavefront occurs only when the hBN thickness is sufficient.\nOn the other hand, since hBN serves as a substrate material, its phonon response acts as a\nbackground signal. To prevent this phonon response from overwhelming the CNT array plasmon\nsignal, we cannot use excessively thick hBN. Besides, as mentioned before, the wavelength of\nphonon polaritons in hBN is proportional to its thickness. Due to the size constraints of our CNT\narray sample, overly thick hBN flakes produce hybrid polaritons with a wavelength that exceeds\nthe CNT array dimensions, thereby preventing the visualization of interference fringes. To achieve\ncoupling visualization between phonon polaritons and plasmons, their wavelengths need to be\ncomparable.\nTaking all factors into consideration, we selected hBN with a thickness of several tens of\nnanometers. The 55 nm thickness is not necessarily optimal; rather, it represents a suitable choice\nthat balances these conditions.\nFigure R11. The evolution of the phonon polariton amplitude and wavelength with the thickness of hBN crystals.\nThese figures are taken from Fig. 3 of the paper Dai et al. [Science 343, 1125-1129 (2014)]\nFigure R12. The hBN thickness dependence of the hybrid polaritons. a-f, The numerical simulated spatial\ndistribution of the polariton field Re(Ez) measured above the CNT-array/hBN at the frequency of 1538cm-1 for hBN\nthickness of 5, 20, 50, 80, 100, and 150 nm, respectively.\n15. As pointed out in previous comments, the comparison between experiment and simulation\nthroughout the work is mostly qualitative (“good agreement”). The authors should provide\nquantitative comparisons to substantiate the agreement. Also, regarding the experimental results,\nseveral statements refer to “low loss” “long lifetime”, and “high-quality factor” without quantitative\nsupport. Extracted propagation lengths or damping constants from s-SNOM data would be\nwelcome and allow comparison with other polaritonic materials.\nOur reply: We appreciate the reviewer’s valuable suggestions regarding quantitative comparisons\nand the characterization of the experimental results.\nFor the comparison between experiment and simulation, a key quantifiable parameter is the\nwavelength. We provide a comprehensive comparison of wavelengths between experiment,\ncalculations, and numerical simulations in Fig. 2e and Supplementary Figure 3.\nAs for the quality factor, we analyzed it using the definitions 𝑄 =𝑅𝑒(𝑞)/𝐼𝑚(𝑞), and fitted the\nexperimental near-field profile with the formula below:\n1 −2𝑥\n𝐼 =|𝜂 +𝜂 𝑒 𝑎 𝑒𝑖(2𝑞𝑥+𝜙𝑅)|\n𝑠 𝑅\n√2𝑥\nwhere 𝜂 is the scattering rate of incident light back into the detector, 𝜂 is the reflectivity of\n𝑠 𝑅\nHPs at the edge, 𝑞 is the plasmon wavevector, a is the decay length, and 𝜙 is the reflection\n𝑅\nphase. This formula is derived from previous literature. [Adv. Funct. Mater. 2019, 29, 1904662.]\nWe selected the experimental data at frequencies of 1111 cm-1 and 1639 cm-1 for fitting, and the\nresults are shown in Fig. R13 below. It should be noted that the quality factor of the CNT array\nplasmons can reach as high as 21, and the compression factor is 21.57. The hyperbolic plasmons\nin our CNT array demonstrate a quality factor comparable to the widely studied systems of MoOCl\n2\nhyperbolic plasmons and α-MoO₃ hyperbolic polaritons [Science387,786-791(2025)] [Nature 562,\n557–562 (2018)]. More importantly, our closed-loop CNT-array ring supports polaritons with a\nsignificantly enhanced quality factor of 67.63, as discussed in the subsequent question. This\nperformance justifies our use of the term \"low-loss\" to characterize the system.\nFigure R13. Extraction of the quality factor of plasmons in CNT array. a, The near-field profile along the axial\ndirection of CNT array at the frequency of 1111 cm-1 and the corresponding fitting curve. b, The near-field profile\nalong the axial direction of CNT array at the frequency of 1639 cm-1 and the corresponding fitting curve.\n16. The interpretation of the observed near-field patterns in Figure 4 as whispering-gallery modes\nremains highly speculative. The near-field images presented in Figure 4 and the Supplementary\nInformation are consistent with frequency-dependent interference effects, but they do not\nconstitute conclusive evidence of resonant mode confinement. To substantiate the claim of\nwhispering-gallery plasmonic modes, the authors should (i) perform full-wave electromagnetic\nsimulations of the circular CNT-array/hBN structure to visualize the modal field distributions and\nconfirm the existence of azimuthally confined resonances; (ii) provide frequency-dependent\nspectral data from s-SNOM amplitude or phase measurements to identify discrete resonance peaks;\nand (iii) estimate the corresponding quality factors (Q) to demonstrate true cavity behavior.\nAdditionally, a systematic comparison across rings of different diameters would enable verification\nof the expected quantized angular momentum dependence (mode number scaling with\ncircumference). Without such quantitative analysis and modeling, the evidence remains insufficient\nto support the claim of an “on-chip whispering-gallery nanocavity” and the observed oscillations\ncould alternatively arise from simple standing-wave interference in the hybrid polariton field.\nOur reply: We appreciate the reviewer’s significant suggestions and have addressed each comment\npoint by point, as outlined below.\n(i) We have performed numerical simulations of polariton whispering gallery modes (WGMs) and\nincorporated the results into Figure 4 of the revised manuscript, specifically shown as Figure R14.\nNotably, the simulation results are in excellent agreement with the experimental observations,\nconfirming that the signals observed in the experiment indeed originate from WGMs. Regarding\nthe mode field distribution: the CNT arrays we fabricated exhibit an almost ideal circular geometry,\nenabling the polaritons to propagate along the circumference in a WGM-like manner. Due to the\nabsence of reflective boundaries that would generate noticeable interference patterns, it is\nchallenging to directly obtain a clear angular mode field distribution in the experiment.\nConsequently, when the atomic force microscope (AFM) probe is positioned along a ring of the\nsame diameter, the conditions for near-field excitation and signal collection remain unchanged.\nThis results in a nearly uniform infrared intensity within the same-diameter ring in nano-infrared\nimaging. The same principle applies to rings with different diameters. In the corresponding\nnumerical simulations, this scenario is modeled by scanning the position of an electric dipole to\nemulate the tip‑scanning process, while simultaneously recording the electric field E component\nz\ndirectly beneath the dipole.\n(ii)-(iii) We have collected the frequency-dependent near-field signal intensity, with the background\nsubtracted at a certain point (denoted by a blue dot in Fig. R15a) on the closed-loop CNT-array ring\non hBN, and the results are plotted in Figure R15b. The data are well fitted by a standard resonance\npeak curve, confirming that the observed signal corresponds to a whispering-gallery mode. From\nthis fitting, the quality factor (Q) is extracted as follows: 𝑄 =\n𝜔𝑐\n=\n1600.16 𝑐𝑚−1\n=67.63, where\n∆𝜔 23.66 𝑐𝑚−1\n𝜔 is the resonance frequency and ∆𝜔 is the full width at half maximum (FWHM) of the\n𝑐\nresonance peak.\nFigure R14 The revised version of Figure 4 of the manuscript. a, Schematic of infrared nano-imaging of whispering-\ngallery polaritonic mode in the CNT-array/hBN by using s-SNOM. b, AFM topography image of a closed-loop CNT\narray ring on hBN. c, d, Infrared nano-imaging and corresponding numerical simulations of polaritons in the CNT-\narray/hBN at different frequencies, respectively. d, The Near-field line profiles along the sections marked by the\ndashed line in (b).\nFigure R15 Extraction of the quality factor of the whispery-gallery mode polaritons in closed-loop CNT array/hBN.\na, A typical infrared nano-imaging of polaritons in the CNT-array/hBN. b, Frequency-dependent near-field signal\nintensity at a certain point on the closed-loop CNT-array ring on hBN. The position where the experimental data\nwere extracted from is denoted by a blue dot in (a).\n17. The Discussion section includes numerous overstatements (“approached physical limits”,\n“unprecedented capabilities”, “lays a solid foundation”). These claims should be revised or\nsupported by quantitative metrics.\nOur reply: We appreciate the reviewer's valuable suggestions.\nIn response, we have removed all the aforementioned overstatements and made comprehensive\nrevisions to the manuscript. The specific changes are as follows:\na. Revised “This on-chip natural whispering-gallery nanocavity structure has approached the\nphysical limits, with its diameter reduced to about a hundred nanometers” to “This on-chip\nnatural whispering-gallery nanocavity structure features a diameter reduced to approximately\none hundred nanometers”.\nb. Revised “showcasing unprecedented capabilities for on-chip manipulation of whispering-\ngallery optical fields” to “exhibiting capabilities for on-chip manipulation of whispering-\ngallery optical fields”.\nc. Revised “laying a solid foundation for the realization of integrated optoelectronic systems”\nto “providing a new pathway for achieving integrated optoelectronic systems”.\nResponse to Reviewer #3\nThe manuscript reports configurable plasmon–polaritons arising from the coupling between\nhyperbolic plasmons and phonon polaritons in CNT array/hBN heterostructures. Infrared (IR) nano-\nimaging is performed as a function of excitation laser energy, which reveals multiple branches of\ncoupled phonon plasmon modes. Topological transition of a hyperbolic isofrequency contour to an\nelliptical one is observed using IR nano-imaging and from numerical calculations. Plasmonic\nwhispering-gallery modes are presented in closed-loop CNT array ring on a hBN substrate. Due to\nthe lack of novelty and impact of the work, and multiple significant claims with insufficient evidence\nand premature data analysis, the reviewer does not recommend the publication of this manuscript\nin Nature Communications.\nOur reply: We appreciate the reviewer’s evaluation of our work and the valuable feedback\nprovided. Below, we address each question and comment raised by the reviewer one by one.\nComment 1: First and foremost, the main concern of the manuscript is the lack of novelty.\nHyperbolic polaritons have been demonstrated numerous times in other vdW materials, with\ncanonical examples including phonon polaritons hBN and a-MoO3 as the authors have referenced\nas well as in nanopatterned hBN [Science 359, 892 (2018)]. Hyperbolic plasmons have also been\ndemonstrated in multiple other vdW materials, including in ZrSiSe at infrared frequencies [Sci Adv\n8, add6169 (2022)] and in MoOCl2 at visible frequencies [Science 387, 786 (2025)]. The properties\nclaimed by the authors (deep subwavelength confinement, broad spectral range, etc) are generic\nto these known (plasmonic) hyperbolic systems. Furthermore, the coupling-induced topological\ntransition of polaritons has been repeatedly demonstrated in other vdW materials platforms,\nincluding in twisted a-MoO3 [Nature Mater 19, 1307 (2020); Nature 582, 209 (2020)] or in\ngraphene/a-MoO3 [Nature Nanotech 17, 940 (2022); Nature Commun 13, 3719 (2022)].\nTherefore, the reviewer does not find that the work provides a sufficient conceptual advance to\nwarrant publication in Nature Communications.\nOur reply: We sincerely thank the reviewers for their thorough and systematic review of work in\nthis field.\nWe fully agree that the concept of \"hyperbolic polaritons and coupling-induced topological\ntransitions\" has been extensively studied in van der Waals materials. Therefore, the core\ninnovation of this work does not lie in merely reproducing this phenomenon, but rather in the\nconstruction and validation of a novel platform with fundamentally different properties and unique\nadvantages for manipulation: by utilizing directly grown, ultra-clean CNT arrays as a natural\nhyperbolic polariton substrate, we have achieved broadband, low-loss, and directly imageable in-\nplane hyperbolic plasmons, as well as tunable topological transitions through hybridization with\nhBN phonon polaritons. The distinctiveness of this platform is demonstrated in the following four\nkey aspects:\n(1) Broadband In-Plane Hyperbolic Plasmons vs. Narrowband Phonon Hyperbolic Polaritons\nThe hBN, α-MoO₃, and other systems mentioned by the reviewers primarily rely on phonon\npolaritons, whose hyperbolic response is constrained by the Reststrahlen band, resulting in\ninherently narrow bandwidths. In contrast, our work leverages the effective medium anisotropy of\nCNT arrays, where the hyperbolic behavior originates from the Luttinger-liquid plasmon properties\nof CNTs. This enables high Q-factors and nearly linear dispersion over an exceptionally broad\nspectral range (e.g., 6–11 μm). Our platform fundamentally differs from conventional narrowband\nphonon systems in terms of bandwidth, loss levels, and mode controllability.\n(2) In-Plane Wavefront Visualization and Manipulation vs. Out-of-Plane Propagation Limitations\nUnlike the out-of-plane propagation or vertically quantized modes commonly observed in systems\nsuch as ZrSiSe, our CNT array platform supports in-plane hyperbolic plasmons. This allows for direct\nimaging and observation of isofrequency profiles and energy flow directions, overcoming the\ngeometric constraints of vertical propagation in atomically thin layers. Consequently, it enables\npractical, on-demand manipulation of in-plane momentum propagation and wavefront shapes,\noffering a new level of control.\n(3) Ultra-Clean Direct Growth vs. Nanofabrication or Twisting Engineering\nWhile nanopatterning techniques (e.g., etching) can induce hyperbolicity, they often introduce\nedge roughness and defect scattering, which degrade performance. In contrast, our platform\nemploys directly grown, crystal-scale CNT arrays with atomically smooth surfaces and minimal\nimpurity scattering. This \"ultra-clean\" approach eliminates the need for complex nanofabrication\nor twisting engineering, thereby directly reducing polariton transmission losses and significantly\nenhancing experimental reproducibility.\n(4) Universal Coupling Platform vs. Strict Frequency Matching\nRegarding coupling-induced topological transitions, our work goes beyond merely replicating\nexisting concepts (e.g., twisted α-MoO₃) by extending them to a broadband hyperbolic plasmonic\nplatform. The broadband hyperbolic response of CNT arrays significantly relaxes the frequency-\nmatching requirements for coupled systems, functioning as a universal \"coupling platform\" that\nallows greater design flexibility for hybridization with various polariton modes (e.g., phonons,\nplasmons) without the stringent material and frequency constraints of narrowband systems.\nIn conclusion, the innovation of this work lies in the establishment of an ultra-clean, low-loss,\nbroadband, and directly imageable in-plane hyperbolic plasmon platform. This provides a scalable\nand practical pathway for polariton manipulation and topological transitions without relying on\ncomplex fabrication techniques. Our work represents a substantial advancement in the\ndevelopment of polariton-based devices and tunable nanophotonics, far beyond merely\nreproducing known phenomena in new materials.\nFurthermore, we have incorporated the references suggested by the reviewer (Science 359, 892\n(2018); Sci Adv 8, add6169 (2022); Science 387, 786 (2025); Nature Mater 19, 1307 (2020); Nature\n582, 209 (2020); Nature Nanotech 17, 940 (2022); Nature Commun 13, 3719 (2022)) as citations in\nthe revised manuscript.\nComment 2: Another significant concern is that the manuscript repeatedly makes claims that are\nnot substantiated by sufficient experimental evidence or logical derivation, which compromises the\nscientific integrity of the manuscript.\n2-i: The claim of “configurability” based on simple frequency dependence is misleading. This is\na basic material property of CNT array/hBN device, but not an externally tunable feature that\n“configurability” typically implies. The authors’ method of labelling “configurability” can\nbe applied to most all vdW polaritonic materials. For example, phonon polaritons in hBN exist only\nwithin the Reststrahlen band. In this case, hBN phonon polaritons would also be “configurable”\nas one can switch phonon polaritons on and off simply by tuning frequency.\nOur reply: We thank the reviewer for his/her insightful comments\nTo prevent misunderstanding, we have revised all mentions of \"configurable polaritons\" in the text\nto \"frequency-dependent topological polaritons,\" and changed the title to \" Frequency-dependent\ntopological polaritons in carbon nanotube array/hBN heterostructures\". The polaritons reported\nin this work exhibit distinct topological characteristics (hyperbolic or elliptical) depending on\nfrequency, which better captures the fundamental nature of this system.\nWe demonstrated the unique capability of our polaritons to tune their wavefront shape and\nwavelength simply by adjusting the excitation frequency across a wide spectral range, an\nunprecedented feature that distinguishes our system from other conventional ones. Our approach\noffers an ultra-clean, efficient, and versatile solution for on-demand polariton manipulation,\ncompletely eliminating the need for complicated twist-angle engineering in van der Waals\nheterostructures or complex micro/nanofabrication of electrodes for electrostatic gating.\nTherefore, this inherent advantage of our system enables direct optical control without physical\nmodifications or additional fabrication steps.\n2-ii: The authors claim to be the “first” to demonstrate, “a whispering-gallery plasmonic mode\nconfined in closed-loop CNT array on hBN.” However, this claim of novelty is overstated. As the\nauthors' own citations (Ref. 38) confirm, whispering-gallery plasmonic modes have already been\ndemonstrated in other vdW materials, such as graphene. Therefore, the simple extension of this\nwork to a CNT array does not seem to be a significant conceptual advance, and the manuscript fails\nto convey the importance of this observation in CNT arrays.\nOur reply: We thank the reviewer for his/her constructive suggestions.\nWe refer to being the \"first\" to demonstrate a whispering-gallery plasmonic mode confined in CNT\narrays. Due to the extremely small diameter of CNTs, typically around 1 nm, it is experimentally\ndifficult to observe whispering gallery modes within their cross-sections (such as the polariton\nwhispering gallery modes observed in BN nanotubes [Nat. Nanotechnol. 18, 529–534 (2023)]).\nTherefore, forming CNTs into nano-rings is essential to achieve this phenomenon. We are the first\nto assemble CNTs into close-loop nano-rings, and have observed a plasmonic whispering gallery\nmode with a very high quality-factor (as described in the following Fig. R18) and excellent\ncoherence.\nTo prevent any misunderstanding, we have removed the word \"first\" from the revised manuscript.\n2-iii: In addition, the authors’ claim of a whispering-gallery plasmonic mode itself is not convincing.\nPlasmonic whispering gallery modes are those that travel around a circumference of the cavity.\nBased on the main dataset shown in Fig. 4c, the reviewer does not see any clear signatures of\nplasmonic wave travel around the circular, donut shaped structure, forming a whispering-gallery\nmode. IR nano-imaging shown in Fig. 4c seems rather a result of tip-launched (or cavity edge\nlaunched) plasmons interacting with the entire cavity structure, forming a cavity-like nano-IR\nresponse, but not necessarily a whispering-gallery mode specific to the chiral motion of polaritons\naround the loop. More rigorous analysis needs to be performed to support their claim of\nwhispering-gallery modes.\nOur reply: We appreciate the reviewer’s valuable feedback regarding the interpretation of the\nobserved phenomena as whispering-gallery plasmonic modes.\nThe polaritons we observe are excited by an AFM tip and propagate along the axial direction of\ncarbon nanotubes, completing a full loop before being detected again by the tip. Since our ring-\nshaped CNT array is highly centrosymmetric and perfectly circular, when the tip is positioned above\na path at the same radius, the excitation of polaritons is identical, and the detected signals are also\nidentical. This is manifested as completely identical infrared signals along the same radial path in\nthe final near-field imaging.\nHowever, paths at different radii display varying brightness—either brighter or darker—\ncorresponding to the constructive or destructive interference of the polaritons. Notably, this\nbrightness contrast changes with the excitation frequency, which we attribute to the presence of\nthe whispering-gallery mode of polaritons.\nTo further support our claim that these are indeed whispering-gallery modes propagating along\nthe axial direction of the CNT array—as opposed to radial propagation modes— we have selected\na larger closed-loop CNT array ring for analysis. The results, presented in Fig. R16, illustrate that\nthe path length for polaritons to complete one loop (i.e., the circumference of the circle) is\nsignificantly longer, far exceeding the propagation distance of the polaritons. As a result, no\nconstructive or destructive interferences are observed in this configuration.\nFigure R16. The evolution of the hybrid polaritons in a larger closed-loop CNT array ring on hBN with the\nexcitation frequency, displaying nearly no interference. a, AFM topography image of a closed-loop CNT array ring\non hBN. b-h, Infrared nano-imaging of plasmons in the CNT-array/hBN at different frequencies.\n2-iv: The authors claim that “the synergy of the low-loss characteristics of the Luttinger liquid\nelectronic state, uniform chirality, and near-atomic-level smooth, lossless ring-shaped interfaces\nenables efficient optical field confinement and the formation of strong optical resonances,” is\nhighly speculative and lacks quantitative support. The manuscript provides no metrics to define,\nmeasure, and quantify the efficient optical field confinement and strong optical resonances.\nFurthermore, the authors do not demonstrate how their data supports the existence of or the\nconnection to the low-loss Luttinger liquid, uniform chirality, or lossless interfaces. These claims are\nconcerning because they are presented without any supporting evidence. At the very least, the\nauthors should provide a quantitative comparison of the polariton quality factors in their straight\nand circular structures.\nOur reply: We thank the reviewer for his/her comments.\nThe plasmonic properties of carbon nanotubes have been reported to exhibit high spatial\nconfinement capability and high quality factors in previous literatures. [Nature Photon. 9, 515-519\n(2015)]\nWe performed a quantitative analysis of the Q factors of polaritons in the CNT array/hBN system,\nusing the definitions of the quality factor 𝑄 =𝑅𝑒(𝑞)/𝐼𝑚(𝑞) and the compression factor 𝑁 =\n𝑅𝑒(𝑞)/𝑘 , and fit the experimental near-field profile with the formula below:\n0\n1 −2𝑥\n𝐼 =|𝜂 +𝜂 𝑒 𝑎 𝑒𝑖(2𝑞𝑥+𝜙𝑅)|\n𝑠 𝑅\n√2𝑥\nwhere 𝜂 is the scattering rate of incident light back into the detector, 𝜂 is the reflectivity of\n𝑠 𝑅\nHPs at the edge, 𝑞 is the plasmon wavevector, a is the decay length, and 𝜙 is the reflection\n𝑅\nphase. This formula is derived from the previous literature [Adv. Funct. Mater. 2019, 29, 1904662].\nWe selected experimental data at frequencies of 1111 cm-1 and 1639 cm-1 for fitting, and the\nresults are shown in Fig. R17 below. It should be noted that the Q factors of the polaritons in the CNT\narray/hBN exceed 20, with a wavelength compression ratio reaching 21.\nAdditionally, we collected the near-field signal intensity with the background subtracted, at a\ncertain point (denoted by a blue dot in Fig. R18a) on the closed-loop CNT-array ring at different\nexcitation frequencies and the results are plotted in the Fig. R18b. The data are well fitted by a\nstandard resonance peak curve. From this fitting, the quality factor (Q factor) is extracted as follows:\n𝑄 =\n𝜔𝑐\n=\n1600.16 𝑐𝑚−1\n=67.63, where 𝜔 is the resonance frequency and ∆𝜔 is the full width\n∆𝜔 23.66 𝑐𝑚−1 𝑐\nat half maximum (FWHM) of the resonance peak.\nThese results demonstrate the advantage of achieving both a relatively strong spatial confinement\nand a high Q factor compared to other two-dimensional metallic plasmonic systems. Typically,\nstrong spatial confinement can only be achieved at the expense of a low Q factor due to the\nabsorption loss of metals. For instance, a two-dimensional surface plasmon at a silver/air interface\nhas a quality factor of ∼16 with λ /λ = 1.16 at 400 nm, but Q worsens to ∼2.27 when λ /λ\np 0 p 0\nincreases to 1.51 at 350 nm. [Nature Photon. 9, 515-519 (2015)] However, due to the different\nscattering mechanisms between plasmons and phonon polaritons, the Q factors of our coupled\npolaritons are lower than those of phonon polaritons in systems like hBN, which is inherently\nattributed to electron-electron scattering in plasmons.\nIn summary, compared to two-dimensional metallic plasmons, the polaritons we report exhibit\nadvantages in wavefront tunability and higher Q factors. In contrast to hyperbolic phonon\npolaritons in materials such as α-MoO₃, our coupled polaritons offer advantages in broadband\nresponse and wavefront tunability.\nFigure R17. Extraction of the quality factor of plasmons in CNT array. a, The near-field profile along the axial\ndirection of CNT array at the frequency of 1111 cm-1 and the corresponding fitting curve. b, The near-field profile\nalong the axial direction of CNT array at the frequency of 1639 cm-1 and the corresponding fitting curve.\nFigure R18. Extraction of the quality factor of the whispery-gallery mode polaritons in closed-loop CNT array/hBN.\na, A typical infrared nano-imaging of polaritons in the CNT-array/hBN. b, Frequency-dependent near-field signal\nintensity at a certain point on the closed-loop CNT-array ring on hBN. The position where the experimental data\nwere extracted from is denoted by a blue dot in (a).\n2-iv: The authors also make a direct comparison of their whispering gallery modes with that in Ref.\n38, stating that “characteristic dimensions and performance have improved by nearly an order of\nmagnitude” in their materials with “high compression ratio.” However, this comparison to Ref.\n38 is misleading. Dimensions may be smaller than the ones shown in Ref. 38, but it is unclear how\nthe performance is improved. The authors’ claim that their compression ratio is higher, but this\nis not supported quantitatively. The compression ratio (or perhaps the effective mode volume) of\npolaritons does not have one-to-one correspondence with the physical dimension of the cavity.\nWhile physical dimensions can be smaller, effective mode volume can be larger. One needs to\nperform a rigorous quantitative analysis to make a case for such a claim. Without a quantitative\nanalysis, the authors’ claim is unsubstantiated.\nOur reply: We thank the reviewer for his/her significant comments.\nThe term “characteristic dimensions and performance” in the manuscript refers specifically to our\nmode volume ratio 𝑉/𝑉 , which we estimate to be one order of magnitude lower than that of the\n𝑝 0\nnanocavity reported in Reference 38 [Nat. Mater. 22, 838–843 (2023)]. This estimation method\nfollows the approach in previous literatures [Science 360, 291-295 (2018)] [Science 368, 1219-1223\n(2020)], where the polariton wavelength 𝜆 =𝜆 /16.5 is used. Given that the thickness of our\n𝑝 0\nnanocavity is on the atomic scale—approximately 4 nm—we obtain 𝑉/𝑉 =2.3×10−6 . This\n𝑝 0\nvalue is nearly an order of magnitude smaller than the previously reported value of 10−5 in\nReference 38 [Nat. Mater. 22, 838–843 (2023)].\nOther minor comments: -hBN phonon polaritons are also hyperbolic. Can the authors comments on\nif the hyperbolicity of phonon polaritons play any role in the coupling and topological transition of\nhyperbolic plasmons in CNT array/hBN system? -The authors selected an hBN flake with a thickness\nof 55 nm to demonstrate the polaritonic coupling. Why does this particular thickness allow the\nintensity of the hBN phonon-polaritons to match that of the CNT plasmons? Do the authors have\nany data or calculations to justify that 55 nm is the optimal thickness?\nOur reply: We appreciate the reviewer’s interesting suggestions.\nAs previously noted, although hBN supports out-of-plane hyperbolic phonon polaritons, these do\nnot directly govern the coupling and topological transitions of in-plane hyperbolic plasmons in the\nCNT array/hBN system. Specifically, within Reststrahlen band 2, hBN exhibits in-plane isotropy and\nout-of-plane hyperbolic anisotropy. Due to finite thickness effects, the out-of-plane hyperbolic\ndispersion of hBN is quantized, which in turn modulates the size of the in-plane circular\nisofrequency contours. Consequently, it is not the out-of-plane hyperbolic dispersion itself that\ndirectly participates in the hybrid coupling within the CNT array/hBN heterostructure; rather, it is\nthe in-plane isofrequency contours—tuned by the hBN thickness—that determine the\nmomentum-matching conditions with CNT plasmons.\nWe chose this specific thickness of hBN because previous studies have shown that the strength\nand wavelength of hBN phonon polariton depends on thickness [Science 343, 1125-1129 (2014)].\nAs indicated in Fig. R19, the thicker hBN leads to the larger polariton amplitude and larger polariton\nwavelength. Numerical simulations for the coupling between polaritons in hBN of varying flake\nthicknesses and CNT array plasmons are shown in Fig. R20. If the hBN flake is too thin (for example,\n5 nm thick), the hybrid polaritons maintain the hyperbolic character due to the extremely small\namplitude and a very short wavelength of hBN phonon polaritons. A transition to an elliptical\nwavefront occurs only when the hBN thickness is sufficient.\nRegarding excessively thick hBN flakes, several shortcomings emerge. First, since hBN functions as\na substrate, its phonon response serves as a background signal. Overly thick hBN will mask the\nplasmon signal from the CNT array. Additionally, as previously noted, the wavelength of phonon\npolaritons in hBN scales with its thickness. Given the finite size of our CNT array sample, overly\nthick hBN flakes generate hybrid polaritons with wavelengths that exceed the spatial dimensions\nof the array, precluding the observation of interference fringes. To enable clear visualization of the\ncoupling between phonon polaritons and plasmons, their wavelengths must be comparable.\nTaking all factors into consideration, we selected an appropriately thin hBN flake with a thickness\nof several tens of nanometers—suitable for our purpose, though not necessarily the optimal\nchoice.\nFigure R19. The evolution of the phonon polariton amplitude and wavelength with the thickness of hBN crystals.\nThese figures are taken from Fig. 3 of the paper Dai et al. [Science 343, 1125-1129 (2014)]\nFigure R20. The hBN thickness dependence of the hybrid polaritons. a-f, The numerical simulated spatial\ndistribution of the polariton field Re(Ez) measured above the CNT-array/hBN at the frequency of 1538cm-1 for hBN\nthickness of 5, 20, 50, 80, 100, and 150 nm, respectively.\nResponse to Reviewer #4\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part\nof the Nature Communications initiative to facilitate training in peer review and to provide\nappropriate recognition for Early Career Researchers who co-review manuscripts.\nOur reply: We thank the referee for letting us know about his/her involvement in the Nature\nCommunications initiative. It's commendable to see efforts towards training in peer review and\nrecognizing the contributions of Early Career Researchers. The referee’s commitment to this\ninitiative is valuable for the research community.\nResponse to Reviewers' Comments (NCOMMS-25-86882A)\nWe sincerely thank all reviewers for their careful evaluation of our work and for their insightful and\nconstructive feedback. Below are our detailed point-by-point responses.\nResponse to Reviewer #1:\nThe authors addressed my comments and could resolve most issues. While the revision has\nimproved and strengthened the manuscript and the manuscript contains novel and interesting\nresults worth publishing, some inaccuracies remain. Particularly, the comments related to the\nwhispering-gallery modes (previous comment 5) have not fully been resolved.\nPlease find some detailed comments below.\nOur reply: We sincerely thank the reviewer for their positive evaluation and constructive feedback,\nwhich have significantly contributed to strengthening the manuscript. We acknowledge that some\nconcerns remain, particularly regarding the whispering-gallery modes. Below we address each of\nthe reviewer's questions and comments point by point.\n1. The abstract now mentions “configurable plasmon frequency-dependent topological polaritons”.\nI assume this does not indicate any topological protection but simply the transition between the\nopen and closed-loop shape of the IFC, is this correct? If so, this could be clarified.\nOur reply: We thank the reviewer for his/her insightful comments and suggestions.\nThe term “topological polaritons” in our manuscript indeed refers to the topological transition of\nthe iso-frequency contours shape, rather than topological protection. This concept have been\nextensively studied and reported in the field of nanophotonics, as documented in the following\nreferences: [Nature 582, 209–213 (2020)][Nat. Nanotechnol. 17, 940–946 (2022)][Nat. Mater.\n19, 1307–1311 (2020)][Nat. Commun. 13, 3719 (2022)]. To clarify this point, we have added the\nfollowing explanation:\n“Here, with a homemade scattering-type scanning near-field optical microscope (s-SNOM), we\nexperimentally demonstrate nanoscale frequency-dependent topological polaritons—specifically,\nthe topological transition of polariton iso-frequency contours between open and closed-loop\nshapes, in CNT-array/hBN heterostructures.’’\n2. The authors now mention “as the two interference peaks move closer together, the interference\npattern becomes more strongly constructive”. The authors could further clarify how\n“constructiveness” can be quantified/seen from Fig. 4c.\nOur reply: We thank the reviewer for his/her insightful comments.\nTo clarify the concept of \"constructiveness\", we extracted the near-field intensity profile (reflecting\nthe magnitude of the E component) from Fig. 4c and plotted it in Fig. 4e. The relationship between\nz\nthe peak-to-peak distance and the peak height in the profile curve of Fig. 4e is shown in the Fig.\nR1. It can be observed that a smaller peak-to-peak distance corresponds to a higher resonance\npeak, indicating a more strongly constructive interference pattern.\nFigure R1. The relationship between the peak-to-peak distance and the peak height of the constructive\ninterference peak. These data were extracted from the Fig.4e of the manuscript.\n3. Regarding the whispering-gallery modes, the added comparison with the numerical simulations\nis helpful. However, some comments are still not sufficiently clear. In their response and revised\nsupplementary information, the authors mention “The results (see Supplementary Fig. 9b), which\nexhibit a strong fit to a standard resonance peak curve, confirm the presence of a whispering-\ngallery mode.” It is not clear to me why “a strong fit to a standard resonance peak curve” should\nindicate whispering-gallery mode polaritons. Rather a “standard” resonance peak curve should\nhave various possible explanations, with whispering-gallery mode polaritons being only one of\nmany. As such, the authors should clarify which parts of the results confirm the presence of a\nwhispering-gallery mode.\nOur reply: We thank the reviewer for his/her constructive comments.\nA standard resonance peak curve indicates the presence of polariton interference resonance within\nthe array, which we attribute to the whispering‑gallery mode of polaritons. To better explain the\nwhispering gallery mode, we performed further numerical simulations. The results are shown in\nthe Fig. R2.\nIn these simulations, we maintained the radial width of the CNT array consistent with that of the\nexperimental sample while appropriately increasing the axial length to observe more periods. To\nintuitively visualize the phase information of the polaritons, we placed an electric dipole above the\narray to excite the polaritons and extracted the Re(E) component from above the array.\nz\nThe simulation results clearly demonstrate the characteristics of whispering gallery modes of the\npolaritons. As the incident frequency increases, the polariton wavelength decreases, and the\nnumber of interference nodes in the standing wave increases.\nMoreover, these simulation results align with our experimentally observed tip-excite-and-tip-\nprobe conditions, confirming that constructive interference manifests in circular patterns with\nvarying perimeters, consistent with the behavior expected from whispering-gallery modes.\nFigure R2. The evolution of whispering-gallery mode of polaritons in CNT-array/hBN at different frequencies. The\nexcitation frequencies are 1563cm-1 (a), 1575cm-1 (b), 1595cm-1(c), 1600 cm-1 (d) and 1634cm-1 (e), respectively.\nThe blue dot in (a) represents the electric dipole for exciting the polaritons. The dashing black circles represents\nthe boundary of the CNT array loop.\n4. The claims on the whispering-gallery modes should generally be weakened, e.g., using weaker\nwording, or additional discussion should be included in the manuscript and/or supplementary\ninformation. For example, parts of the response to the different reviewers’ comments might be\nincluded in the manuscript/SI instead of in the rebuttal letter only, e.g., Fig. R16 and corresponding\ndiscussion.\nOur reply: We thank the reviewer for his/her constructive suggestions.\nWe have already incorporated Fig.R3 (Fig. R16 of the last rebuttal letter) into the revised\nSupplementary Information, and have added the following description in the revised SI.\n“To further support our claim that these are indeed whispering-gallery modes propagating along\nthe axial direction of the CNT array—instead of radial propagation modes— we have selected a\nlarger closed-loop CNT array ring for analysis. The results, presented in Supplementary Fig. 10,\nillustrate that the path length for polaritons to complete one loop (i.e., the circumference of the\ncircle) is significantly longer, far exceeding the propagation distance of the polaritons. As a result,\nno constructive or destructive interferences are observed in this configuration.”\nFigure R3. The evolution of the hybrid polaritons in a larger closed-loop CNT array ring on hBN with the\nexcitation frequency, displaying nearly no interference. a, AFM topography image of a closed-loop CNT array ring\non hBN. b-h, Infrared nano-imaging of plasmons in the CNT-array/hBN at different frequencies.\n5. Finally, the authors still state that “Compared to traditional low-dimensional polaritonic\nwhispering-gallery nanocavities, its characteristic dimensions and performance have improved by\nnearly an order of magnitude.” In their rebuttal, the authors indicate that the claimed\nimprovements mainly refer to the critical dimensions. However, the wording in the authors’\nmanuscript still indicates a broader “performance” improvement by “nearly an order of magnitude”.\nThe authors should either clarify, in the manuscript, that the improvement solely refers to the mode\nvolume (or even just to the physical dimension), or they should detail which other performance\nimprovements they refer to compared to previous work.\nOur reply: We thank the reviewer for his/her significant suggestions.\nThe reviewer is correct that the improvement solely refers to the mode volume. To clarify the\ncomparison, we have revised the statement as follows,\n“Compared to traditional low-dimensional polaritonic whispering-gallery nanocavities, its\ncharacteristic dimensions have improved by nearly an order of magnitude. Its mode volume is as\nsmall as on the order of 10-6.”\nResponse to Reviewer #2:\nThe authors have adequately addressed my comments. I recommend publication in its present form.\nOur reply: We sincerely thank the reviewer for his/her appreciation of our work and\nrecommendation for the publication of our manuscript.\nResponse to Reviewer #3:\nThe authors have made a significant improvement of the manuscript and clearly addressed most\nof my previous comments. Before the acceptance of the manuscript, I just a have a few minor points\nthat need to be clarified and would further strengthen the manuscript.\nOur reply: We sincerely thank the reviewer for his/her appreciation of our work and for the\npositive evaluation.\n1) Q-factor of 60 derived from the frequency dependent measurements of a cavity is exceptionally\nhigh. Can the authors explain why such a high Q-factor is possible? This three-fold enhancement\ncompared to Q-factors of 20 in straight devices derived by the authors is counterintuitive. Either\nthe specific method of extracting Q-factor of 60 is inaccurate or there is an unknown procedure\nthat enhances the Q-factor in a closed-loop CNT array versus a straight CNT array. This point should\nbe clarified.\nOur reply: We thank the reviewer for his/her careful review and insightful comments.\nThe Q-factor of 20 was obtained by fitting the data from straight CNT array devices under\nexcitations at 1111 cm⁻¹ and 1639 cm⁻¹. Both frequencies lie outside the Reststrahlen band of hBN,\nmeaning no coupling with hBN phonon polaritons. This value reflects the intrinsic Q-factor of the\nCNT array plasmons.\nIn contrast, the Q-factor of 60 was derived from the resonant peak's center frequency near 1600\ncm⁻¹, which falls within the Reststrahlen band of hBN. Therefore, this value represents the Q-factor\nof the hybrid polaritons resulting from the coupling between the CNT array plasmons and hBN\nphonon polaritons. The intrinsically high Q-factor of hBN phonon polaritons (which experience zero\nelectronic loss) contributes to the enhanced Q-factor observed in the hybrid system.\nFurthermore, polaritons propagating within a nanocavity can exhibit further enhanced Q-factors.\nPrevious literature has reported the Q-factor of hBN phonon polaritons in optical microcavities\nreaching values as high as 100~400 [Nat. Commun. 8, 15624 (2017)] [Nat. Mater. 23, 499–505\n(2024)].\nThese factors collectively explain the observed enhancement of the Q-factor from 20 in straight\ndevices to 60 in closed-loop CNT arrays.\n2) Whispering gallery mode, WGM, scenario is still not fully clear based on the data itself. Could the\nauthors potentially show a more direct visualization of the WGM, e.g., by placing a gold launcher\nat one location of the (larger) closed-loop array to visualize the propagating/circulating WGM?\nAnother simple point to check is whether the WGM wavelength between 1563-1593 cm-1 in a\nresonance condition. Can the authors compare the round-trip distance around the cavity with\nrespect to the mode wavelength, and confirm if the resonance condition matches the experimental\nobservations?\nOur reply: We appreciate the reviewer’s insightful comments and helpful suggestions.\nUnfortunately, fabricating a gold launcher directly on the CNT array would introduce polymeric\nresidues and contaminants that are nearly impossible to completely eliminate. Given the small size\nof the sample, these contaminations would significantly increase the loss of polaritons and severely\ncompromise the acquisition of near-field optical signals. As a result, this approach is experimentally\nunfeasible.\nTo address the reviewer’s question, we conducted additional numerical simulations, the results of\nwhich are presented in Figure R4. To align with the experimental conditions, we set the radial width\nof the CNT array equal to that of the experimental sample while intentionally extending the axial\nlength to observe more oscillation periods. For clearer visualization of the polariton phase\ndistribution, we positioned an electric dipole (indicated by the blue dot in Figure R4a) above the\narray to excite the polaritons and extracted the Re(Ez) component directly above the array.\nThe simulations clearly reveal the characteristics of whispering-gallery modes of the polaritons; as\nthe incident frequency increases, the polariton wavelength decreases, resulting in more\ninterference nodes within the standing wave pattern.\nFigure R4. The evolution of whispering-gallery mode of polaritons in CNT-array/hBN at different frequencies. The\nexcitation frequencies are 1563cm-1 (a), 1575cm-1 (b), 1595cm-1(c), 1600 cm-1 (d) and 1634cm-1 (e), respectively.\nThe blue dot in (a) represents the electric dipole for exciting the polaritons. The dashing black circles represents\nthe boundary of the CNT array loop.\nFurthermore, the direct fabrication of gold launchers without residual contamination on CNT arrays\nposes significant challenges, preventing the extraction of polariton phase information from\nexperiments or the precise determination of their wavelengths for comparison. According to the\npolariton dispersion relation, the theoretical wavelength range is between 600 and 1000 nm,\nroughly matching the circumference of a single ring in the CNT array.\nAdditionally, previous studies have shown that when the cavity size is reduced to approximately\n~𝜆 , polariton modes are dominated by standing waves confined along the cavity circumference\n𝑝\n[Nat. Mater. 22, 838–843 (2023)]. However, the quantitative conditions for low-order standing\nwave resonances remain challenging to analyze at this cavity size [Nat. Commun. 8, 15624 (2017)].\nIn conclusion, it remains uncertain whether the resonance conditions are strictly satisfied.\nTherefore, we propose that CNT arrays support standing wave interference induced by whispering-\ngallery modes, which may manifest as either constructive or destructive interference. However,\nthe specific resonance mode cannot yet be definitively identified from the available experimental\ndata.\nResponse to Reviewer #4:\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part\nof the Nature Communications initiative to facilitate training in peer review and to provide\nappropriate recognition for Early Career Researchers who co-review manuscripts.\nOur reply: We thank the reviewer for his/her appreciation of our work and for the positive\nevaluation.\nResponse to Reviewers' Comments (NCOMMS-25-86882B)\nWe sincerely thank all reviewers for their careful evaluation of our work and for their insightful and\nconstructive feedback. Below are our detailed point-by-point responses.\nResponse to Reviewer #1:\nThe authors addressed all my comments, and the manuscript appears publishable without further\nrevision.\nOur reply: We sincerely thank the reviewer for his/her appreciation of our work and\nrecommendation for the publication of our manuscript.\nResponse to Reviewer #3:\nWhile the reviewer agrees that hybridization with hBN phonon polaritons can enhance Q-factor,\nthe authors need to show quantitative evidence of Q-factor enhancement up to 60. Since high\nquality factor WGM is one of the central claims of the paper, emphasized both in abstract and main\ntext, these points need to be clarified and the derivation and analysis of Q-factor needs to be more\nrigorously presented.\nBesides, based on the additional simulations provided by the authors (Figure R2), the peak in their\nspectral evolution of near-field signal in a fixed on position within WGM cavity appears to be related\nto a geometric effect. Near field amplitude under the tip results from tip-launched polaritons under\nthe tip interfering with those making a round-trip across the circumference of cavity. Changing\nfrequency changes WGM wavelength, which shifts the phase of round-trip polaritons with respect\nto those launched under the tip. When frequency is continuously swept, this continuous increase in\nthe relative phase shift will lead to destructive and to constructive and back to destructive\ninterference, which looks like a peak in spectra. Q-factor derived from the FWHM of the standard\nfitting to this peak then does not (accurately) reflect the loss of WGM. Can the authors clarify this\npoint?\nOur reply: We appreciate the reviewer’s insightful comments and helpful suggestions.\nFirst, we wish to clarify the core novelty of our manuscript lies in the discovery of frequency-\ndependent topological polaritons arising from the coupling between hyperbolic plasmons and\nphonon polaritons in CNT-array/hBN heterostructures. In particular, we achieved a controllable\ntopological transition of the polariton wavefront from hyperbolic to elliptical. The whispering-\ngallery mode (WGM) presented here serves as a natural extension and an in-depth investigation of\nthis hybrid polariton mode, providing quantitative evidence of its low-loss characteristics and\nenhanced coherence\nWe agree with the reviewer’s physical interpretation that the resonance peak of the WGM\nobserved in our fixed-position near-field measurement may arise from the interference between\nthe tip-launched field and the field that has completed one round trip along the cavity\ncircumference. Consequently, the linewidth of such a peak should not be directly and exclusively\ninterpreted as the intrinsic material loss.\nIn response, we wish to offer the following clarification:\n1. The \"Geometric Effect\" is the Essence of Cavity Resonance:\nThe \"geometric effect\", i.e., the round-trip phase-matching condition requiring an integer multiple\nof 2𝜋 along the circumference, is precisely the fundamental physical mechanism underlying all\noptical microcavities, including whispering-gallery mode cavities and Fabry-Perot resonators. In\nthis context, the resonance linewidth is governed by two factors: (a) the intrinsic propagation loss\nof the polaritons (including attenuation, radiation, and boundary scattering) and (b) the phase\naccumulation in the closed-loop geometry.\n2. The Linewidth is a Valid Proxy for Loss:\nIn such interference-based resonant cavities, the contrast and sharpness of the resonance peak are\ninherently limited by the intrinsic propagation loss of the polaritons within the cavity.\nIf the propagation loss is high (short propagation length), the signal returning after one or multiple\nround trips is too weak to interfere significantly, resulting in a broad, low-contrast spectral fringe\n(corresponding to a low Q-factor). Conversely, if the propagation loss is extremely low, as achieved\nhere through hybridization with low-loss hBN phonon polaritons, the polaritons survive for\nmultiple round trips, enabling sharp constructive interference and a narrow spectral linewidth\n(corresponding to a high Q-factor).\nTherefore, fitting the resonance peak to extract ∆𝜔 and calculating 𝑄 =\n𝜔𝑐\nis a standard and\n∆𝜔\nrigorous approach in nanophotonics and cavity physics to assess the effective Q-factor of a\nresonant mode. The extracted value of Q≈60 from our fitting indeed reflects the intrinsically low-\nloss nature and enhanced coherence of the closed-loop CNT/hBN hybrid polariton WGM resonance.\nRevision in Supplementary Information:\nTo prevent over-interpretation, we have added the relevant section to explicitly define this value\nas the \"effective Q-factor\":\n“We now explicitly describe the extracted value as the effective Q-factor under our specific near-\nfield excitation and detection conditions, rather than the intrinsic material Q. We clarify that the\nlinewidth is determined by both the round-trip attenuation and the phase-matching. Therefore, the\nQ-factor extracted from the FWHM provides an upper-bound estimate of the lifetime of the\ncirculating hybrid polariton mode.”\nResponse to Reviewer #4:\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part\nof the Nature Communications initiative to facilitate training in peer review and to provide\nappropriate recognition for Early Career Researchers who co-review manuscripts.\nOur reply: We thank the referee for letting us know about his/her involvement in the Nature\nCommunications initiative. It's commendable to see efforts towards training in peer review and\nrecognizing the contributions of Early Career Researchers. The referee’s commitment to this\ninitiative is valuable for the research community."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors addressed my comments and could resolve most issues. While the revision has improved and strengthened the manuscript and the manuscript contains novel and interesting results worth publishing, some inaccuracies remain.\nParticularly, the comments related to the whispering-gallery modes (previous comment 5) have not fully been resolved.\nPlease find some detailed comments below:\n1. The abstract now mentions “configurable plasmon frequency-dependent topological polaritons”. I assume this does not indicate any topological protection but simply the transition between the open and closed-loop shape of the IFC, is this correct? If so, this could be clarified.\n2. The authors now mention “as the two interference peaks move closer together, the interference pattern becomes more strongly constructive”. The authors could further clarify how “constructiveness” can be quantified/seen from Fig. 4c.\n3. Regarding the whispering-gallery modes, the added comparison with the numerical simulations is helpful. However, some comments are still not sufficiently clear. In their response and revised supplementary information, the authors mention “The results (see Supplementary Fig. 9b), which exhibit a strong fit to a standard resonance peak curve, confirm the presence of a whispering-gallery mode.” It is not clear to me why “a strong fit to a standard resonance peak curve” should indicate whispering-gallery mode polaritons. Rather a “standard” resonance peak curve should have various possible explanations, with whispering-gallery mode polaritons being only one of many. As such, the authors should clarify which parts of the results confirm the presence of a whispering-gallery mode.\n4. The claims on the whispering-gallery modes should generally be weakened, e.g., using weaker wording, or additional discussion should be included in the manuscript and/or supplementary information. For example, parts of the response to the different reviewers’ comments might be included in the manuscript/SI instead of in the rebuttal letter only, e.g., Fig. R16 and corresponding discussion.\n5. Finally, the authors still state that “Compared to traditional low-dimensional polaritonic whispering-gallery nanocavities, its characteristic dimensions and performance have improved by nearly an order of magnitude.” In their rebuttal, the authors indicate that the claimed improvements mainly refer to the critical dimensions. However, the wording in the authors’ manuscript still indicates a broader “performance” improvement by “nearly an order of magnitude”. The authors should either clarify, in the manuscript, that the improvement solely refers to the mode volume (or even just to the physical dimension), or they should detail which other performance improvements they refer to compared to previous work.", "reviewer_2": "The authors have adequately addressed my comments. I recommend publication in its present form.", "reviewer_3": "The authors have made a significant improvement of the manuscript and clearly addressed most of my previous comments.\nBefore the acceptance of the manuscript, I just a have a few minor points that need to be clarified and would further strengthen the manuscript.\n1) Q-factor of 60 derived from the frequency dependent measurements of a cavity is exceptionally high. Can the authors explain why such a high Q-factor is possible? This three-fold enhancement compared to Q-factors of 20 in straight devices derived by the authors is counterintuitive. Either the specific method of extracting Q-factor of 60 is inaccurate or there is an unknown procedure that enhances the Q-factor in a closed-loop CNT array versus a straight CNT array. This point should be clarified.\n2) Whispering gallery mode, WGM, scenario is still not fully clear based on the data itself. Could the authors potentially show a more direct visualization of the WGM, e.g., by placing a gold launcher at one location of the (larger) closed-loop array to visualize the propagating/circulating WGM? Another simple point to check is whether the WGM wavelength between 1563-1593 cm-1 in a resonance condition. Can the authors compare the round-trip distance around the cavity with respect to the mode wavelength, and confirm if the resonance condition matches the experimental observations?", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "Response to Reviewers' Comments (NCOMMS-25-86882A)\nWe sincerely thank all reviewers for their careful evaluation of our work and for their insightful and\nconstructive feedback. Below are our detailed point-by-point responses.\nResponse to Reviewer #1:\nThe authors addressed my comments and could resolve most issues. While the revision has\nimproved and strengthened the manuscript and the manuscript contains novel and interesting\nresults worth publishing, some inaccuracies remain. Particularly, the comments related to the\nwhispering-gallery modes (previous comment 5) have not fully been resolved.\nPlease find some detailed comments below.\nOur reply: We sincerely thank the reviewer for their positive evaluation and constructive feedback,\nwhich have significantly contributed to strengthening the manuscript. We acknowledge that some\nconcerns remain, particularly regarding the whispering-gallery modes. Below we address each of\nthe reviewer's questions and comments point by point.\n1. The abstract now mentions “configurable plasmon frequency-dependent topological polaritons”.\nI assume this does not indicate any topological protection but simply the transition between the\nopen and closed-loop shape of the IFC, is this correct? If so, this could be clarified.\nOur reply: We thank the reviewer for his/her insightful comments and suggestions.\nThe term “topological polaritons” in our manuscript indeed refers to the topological transition of\nthe iso-frequency contours shape, rather than topological protection. This concept have been\nextensively studied and reported in the field of nanophotonics, as documented in the following\nreferences: [Nature 582, 209–213 (2020)][Nat. Nanotechnol. 17, 940–946 (2022)][Nat. Mater.\n19, 1307–1311 (2020)][Nat. Commun. 13, 3719 (2022)]. To clarify this point, we have added the\nfollowing explanation:\n“Here, with a homemade scattering-type scanning near-field optical microscope (s-SNOM), we\nexperimentally demonstrate nanoscale frequency-dependent topological polaritons—specifically,\nthe topological transition of polariton iso-frequency contours between open and closed-loop\nshapes, in CNT-array/hBN heterostructures.’’\n2. The authors now mention “as the two interference peaks move closer together, the interference\npattern becomes more strongly constructive”. The authors could further clarify how\n“constructiveness” can be quantified/seen from Fig. 4c.\nOur reply: We thank the reviewer for his/her insightful comments.\nTo clarify the concept of \"constructiveness\", we extracted the near-field intensity profile (reflecting\nthe magnitude of the E component) from Fig. 4c and plotted it in Fig. 4e. The relationship between\nz\nthe peak-to-peak distance and the peak height in the profile curve of Fig. 4e is shown in the Fig.\nR1. It can be observed that a smaller peak-to-peak distance corresponds to a higher resonance\npeak, indicating a more strongly constructive interference pattern.\nFigure R1. The relationship between the peak-to-peak distance and the peak height of the constructive\ninterference peak. These data were extracted from the Fig.4e of the manuscript.\n3. Regarding the whispering-gallery modes, the added comparison with the numerical simulations\nis helpful. However, some comments are still not sufficiently clear. In their response and revised\nsupplementary information, the authors mention “The results (see Supplementary Fig. 9b), which\nexhibit a strong fit to a standard resonance peak curve, confirm the presence of a whispering-\ngallery mode.” It is not clear to me why “a strong fit to a standard resonance peak curve” should\nindicate whispering-gallery mode polaritons. Rather a “standard” resonance peak curve should\nhave various possible explanations, with whispering-gallery mode polaritons being only one of\nmany. As such, the authors should clarify which parts of the results confirm the presence of a\nwhispering-gallery mode.\nOur reply: We thank the reviewer for his/her constructive comments.\nA standard resonance peak curve indicates the presence of polariton interference resonance within\nthe array, which we attribute to the whispering‑gallery mode of polaritons. To better explain the\nwhispering gallery mode, we performed further numerical simulations. The results are shown in\nthe Fig. R2.\nIn these simulations, we maintained the radial width of the CNT array consistent with that of the\nexperimental sample while appropriately increasing the axial length to observe more periods. To\nintuitively visualize the phase information of the polaritons, we placed an electric dipole above the\narray to excite the polaritons and extracted the Re(E) component from above the array.\nz\nThe simulation results clearly demonstrate the characteristics of whispering gallery modes of the\npolaritons. As the incident frequency increases, the polariton wavelength decreases, and the\nnumber of interference nodes in the standing wave increases.\nMoreover, these simulation results align with our experimentally observed tip-excite-and-tip-\nprobe conditions, confirming that constructive interference manifests in circular patterns with\nvarying perimeters, consistent with the behavior expected from whispering-gallery modes.\nFigure R2. The evolution of whispering-gallery mode of polaritons in CNT-array/hBN at different frequencies. The\nexcitation frequencies are 1563cm-1 (a), 1575cm-1 (b), 1595cm-1(c), 1600 cm-1 (d) and 1634cm-1 (e), respectively.\nThe blue dot in (a) represents the electric dipole for exciting the polaritons. The dashing black circles represents\nthe boundary of the CNT array loop.\n4. The claims on the whispering-gallery modes should generally be weakened, e.g., using weaker\nwording, or additional discussion should be included in the manuscript and/or supplementary\ninformation. For example, parts of the response to the different reviewers’ comments might be\nincluded in the manuscript/SI instead of in the rebuttal letter only, e.g., Fig. R16 and corresponding\ndiscussion.\nOur reply: We thank the reviewer for his/her constructive suggestions.\nWe have already incorporated Fig.R3 (Fig. R16 of the last rebuttal letter) into the revised\nSupplementary Information, and have added the following description in the revised SI.\n“To further support our claim that these are indeed whispering-gallery modes propagating along\nthe axial direction of the CNT array—instead of radial propagation modes— we have selected a\nlarger closed-loop CNT array ring for analysis. The results, presented in Supplementary Fig. 10,\nillustrate that the path length for polaritons to complete one loop (i.e., the circumference of the\ncircle) is significantly longer, far exceeding the propagation distance of the polaritons. As a result,\nno constructive or destructive interferences are observed in this configuration.”\nFigure R3. The evolution of the hybrid polaritons in a larger closed-loop CNT array ring on hBN with the\nexcitation frequency, displaying nearly no interference. a, AFM topography image of a closed-loop CNT array ring\non hBN. b-h, Infrared nano-imaging of plasmons in the CNT-array/hBN at different frequencies.\n5. Finally, the authors still state that “Compared to traditional low-dimensional polaritonic\nwhispering-gallery nanocavities, its characteristic dimensions and performance have improved by\nnearly an order of magnitude.” In their rebuttal, the authors indicate that the claimed\nimprovements mainly refer to the critical dimensions. However, the wording in the authors’\nmanuscript still indicates a broader “performance” improvement by “nearly an order of magnitude”.\nThe authors should either clarify, in the manuscript, that the improvement solely refers to the mode\nvolume (or even just to the physical dimension), or they should detail which other performance\nimprovements they refer to compared to previous work.\nOur reply: We thank the reviewer for his/her significant suggestions.\nThe reviewer is correct that the improvement solely refers to the mode volume. To clarify the\ncomparison, we have revised the statement as follows,\n“Compared to traditional low-dimensional polaritonic whispering-gallery nanocavities, its\ncharacteristic dimensions have improved by nearly an order of magnitude. Its mode volume is as\nsmall as on the order of 10-6.”\nResponse to Reviewer #2:\nThe authors have adequately addressed my comments. I recommend publication in its present form.\nOur reply: We sincerely thank the reviewer for his/her appreciation of our work and\nrecommendation for the publication of our manuscript.\nResponse to Reviewer #3:\nThe authors have made a significant improvement of the manuscript and clearly addressed most\nof my previous comments. Before the acceptance of the manuscript, I just a have a few minor points\nthat need to be clarified and would further strengthen the manuscript.\nOur reply: We sincerely thank the reviewer for his/her appreciation of our work and for the\npositive evaluation.\n1) Q-factor of 60 derived from the frequency dependent measurements of a cavity is exceptionally\nhigh. Can the authors explain why such a high Q-factor is possible? This three-fold enhancement\ncompared to Q-factors of 20 in straight devices derived by the authors is counterintuitive. Either\nthe specific method of extracting Q-factor of 60 is inaccurate or there is an unknown procedure\nthat enhances the Q-factor in a closed-loop CNT array versus a straight CNT array. This point should\nbe clarified.\nOur reply: We thank the reviewer for his/her careful review and insightful comments.\nThe Q-factor of 20 was obtained by fitting the data from straight CNT array devices under\nexcitations at 1111 cm⁻¹ and 1639 cm⁻¹. Both frequencies lie outside the Reststrahlen band of hBN,\nmeaning no coupling with hBN phonon polaritons. This value reflects the intrinsic Q-factor of the\nCNT array plasmons.\nIn contrast, the Q-factor of 60 was derived from the resonant peak's center frequency near 1600\ncm⁻¹, which falls within the Reststrahlen band of hBN. Therefore, this value represents the Q-factor\nof the hybrid polaritons resulting from the coupling between the CNT array plasmons and hBN\nphonon polaritons. The intrinsically high Q-factor of hBN phonon polaritons (which experience zero\nelectronic loss) contributes to the enhanced Q-factor observed in the hybrid system.\nFurthermore, polaritons propagating within a nanocavity can exhibit further enhanced Q-factors.\nPrevious literature has reported the Q-factor of hBN phonon polaritons in optical microcavities\nreaching values as high as 100~400 [Nat. Commun. 8, 15624 (2017)] [Nat. Mater. 23, 499–505\n(2024)].\nThese factors collectively explain the observed enhancement of the Q-factor from 20 in straight\ndevices to 60 in closed-loop CNT arrays.\n2) Whispering gallery mode, WGM, scenario is still not fully clear based on the data itself. Could the\nauthors potentially show a more direct visualization of the WGM, e.g., by placing a gold launcher\nat one location of the (larger) closed-loop array to visualize the propagating/circulating WGM?\nAnother simple point to check is whether the WGM wavelength between 1563-1593 cm-1 in a\nresonance condition. Can the authors compare the round-trip distance around the cavity with\nrespect to the mode wavelength, and confirm if the resonance condition matches the experimental\nobservations?\nOur reply: We appreciate the reviewer’s insightful comments and helpful suggestions.\nUnfortunately, fabricating a gold launcher directly on the CNT array would introduce polymeric\nresidues and contaminants that are nearly impossible to completely eliminate. Given the small size\nof the sample, these contaminations would significantly increase the loss of polaritons and severely\ncompromise the acquisition of near-field optical signals. As a result, this approach is experimentally\nunfeasible.\nTo address the reviewer’s question, we conducted additional numerical simulations, the results of\nwhich are presented in Figure R4. To align with the experimental conditions, we set the radial width\nof the CNT array equal to that of the experimental sample while intentionally extending the axial\nlength to observe more oscillation periods. For clearer visualization of the polariton phase\ndistribution, we positioned an electric dipole (indicated by the blue dot in Figure R4a) above the\narray to excite the polaritons and extracted the Re(Ez) component directly above the array.\nThe simulations clearly reveal the characteristics of whispering-gallery modes of the polaritons; as\nthe incident frequency increases, the polariton wavelength decreases, resulting in more\ninterference nodes within the standing wave pattern.\nFigure R4. The evolution of whispering-gallery mode of polaritons in CNT-array/hBN at different frequencies. The\nexcitation frequencies are 1563cm-1 (a), 1575cm-1 (b), 1595cm-1(c), 1600 cm-1 (d) and 1634cm-1 (e), respectively.\nThe blue dot in (a) represents the electric dipole for exciting the polaritons. The dashing black circles represents\nthe boundary of the CNT array loop.\nFurthermore, the direct fabrication of gold launchers without residual contamination on CNT arrays\nposes significant challenges, preventing the extraction of polariton phase information from\nexperiments or the precise determination of their wavelengths for comparison. According to the\npolariton dispersion relation, the theoretical wavelength range is between 600 and 1000 nm,\nroughly matching the circumference of a single ring in the CNT array.\nAdditionally, previous studies have shown that when the cavity size is reduced to approximately\n~𝜆 , polariton modes are dominated by standing waves confined along the cavity circumference\n𝑝\n[Nat. Mater. 22, 838–843 (2023)]. However, the quantitative conditions for low-order standing\nwave resonances remain challenging to analyze at this cavity size [Nat. Commun. 8, 15624 (2017)].\nIn conclusion, it remains uncertain whether the resonance conditions are strictly satisfied.\nTherefore, we propose that CNT arrays support standing wave interference induced by whispering-\ngallery modes, which may manifest as either constructive or destructive interference. However,\nthe specific resonance mode cannot yet be definitively identified from the available experimental\ndata.\nResponse to Reviewer #4:\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part\nof the Nature Communications initiative to facilitate training in peer review and to provide\nappropriate recognition for Early Career Researchers who co-review manuscripts.\nOur reply: We thank the reviewer for his/her appreciation of our work and for the positive\nevaluation."}, {"round": 3, "reviewer_comments": {"reviewer_1": "The authors addressed all my comments, and the manuscript appears publishable without further revision.", "reviewer_3": "While the reviewer agrees that hybridization with hBN phonon polaritons can enhance Q-factor, the authors need to show quantitative evidence of Q-factor enhancement up to 60. Since high quality factor WGM is one of the central claims of the paper, emphasized both in abstract and main text, these points need to be clarified and the derivation and analysis of Q-factor needs to be more rigorously presented.\nBesides, based on the additional simulations provided by the authors (Figure R2), the peak in their spectral evolution of near-field signal in a fixed on position within WGM cavity appears to be related to a geometric effect. Near field amplitude under the tip results from tip-launched polaritons under the tip interfering with those making a round-trip across the circumference of cavity. Changing frequency changes WGM wavelength, which shifts the phase of round-trip polaritons with respect to those launched under the tip. When frequency is continuously swept, this continuous increase in the relative phase shift will lead to destructive and to constructive and back to destructive interference, which looks like a peak in spectra. Q-factor derived from the FWHM of the standard fitting to this peak then does not (accurately) reflect the loss of WGM. Can the authors clarify this point?", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "Response to Reviewers' Comments (NCOMMS-25-86882B)\nWe sincerely thank all reviewers for their careful evaluation of our work and for their insightful and\nconstructive feedback. Below are our detailed point-by-point responses.\nResponse to Reviewer #1:\nThe authors addressed all my comments, and the manuscript appears publishable without further\nrevision.\nOur reply: We sincerely thank the reviewer for his/her appreciation of our work and\nrecommendation for the publication of our manuscript.\nResponse to Reviewer #3:\nWhile the reviewer agrees that hybridization with hBN phonon polaritons can enhance Q-factor,\nthe authors need to show quantitative evidence of Q-factor enhancement up to 60. Since high\nquality factor WGM is one of the central claims of the paper, emphasized both in abstract and main\ntext, these points need to be clarified and the derivation and analysis of Q-factor needs to be more\nrigorously presented.\nBesides, based on the additional simulations provided by the authors (Figure R2), the peak in their\nspectral evolution of near-field signal in a fixed on position within WGM cavity appears to be related\nto a geometric effect. Near field amplitude under the tip results from tip-launched polaritons under\nthe tip interfering with those making a round-trip across the circumference of cavity. Changing\nfrequency changes WGM wavelength, which shifts the phase of round-trip polaritons with respect\nto those launched under the tip. When frequency is continuously swept, this continuous increase in\nthe relative phase shift will lead to destructive and to constructive and back to destructive\ninterference, which looks like a peak in spectra. Q-factor derived from the FWHM of the standard\nfitting to this peak then does not (accurately) reflect the loss of WGM. Can the authors clarify this\npoint?\nOur reply: We appreciate the reviewer’s insightful comments and helpful suggestions.\nFirst, we wish to clarify the core novelty of our manuscript lies in the discovery of frequency-\ndependent topological polaritons arising from the coupling between hyperbolic plasmons and\nphonon polaritons in CNT-array/hBN heterostructures. In particular, we achieved a controllable\ntopological transition of the polariton wavefront from hyperbolic to elliptical. The whispering-\ngallery mode (WGM) presented here serves as a natural extension and an in-depth investigation of\nthis hybrid polariton mode, providing quantitative evidence of its low-loss characteristics and\nenhanced coherence\nWe agree with the reviewer’s physical interpretation that the resonance peak of the WGM\nobserved in our fixed-position near-field measurement may arise from the interference between\nthe tip-launched field and the field that has completed one round trip along the cavity\ncircumference. Consequently, the linewidth of such a peak should not be directly and exclusively\ninterpreted as the intrinsic material loss.\nIn response, we wish to offer the following clarification:\n1. The \"Geometric Effect\" is the Essence of Cavity Resonance:\nThe \"geometric effect\", i.e., the round-trip phase-matching condition requiring an integer multiple\nof 2𝜋 along the circumference, is precisely the fundamental physical mechanism underlying all\noptical microcavities, including whispering-gallery mode cavities and Fabry-Perot resonators. In\nthis context, the resonance linewidth is governed by two factors: (a) the intrinsic propagation loss\nof the polaritons (including attenuation, radiation, and boundary scattering) and (b) the phase\naccumulation in the closed-loop geometry.\n2. The Linewidth is a Valid Proxy for Loss:\nIn such interference-based resonant cavities, the contrast and sharpness of the resonance peak are\ninherently limited by the intrinsic propagation loss of the polaritons within the cavity.\nIf the propagation loss is high (short propagation length), the signal returning after one or multiple\nround trips is too weak to interfere significantly, resulting in a broad, low-contrast spectral fringe\n(corresponding to a low Q-factor). Conversely, if the propagation loss is extremely low, as achieved\nhere through hybridization with low-loss hBN phonon polaritons, the polaritons survive for\nmultiple round trips, enabling sharp constructive interference and a narrow spectral linewidth\n(corresponding to a high Q-factor).\nTherefore, fitting the resonance peak to extract ∆𝜔 and calculating 𝑄 =\n𝜔𝑐\nis a standard and\n∆𝜔\nrigorous approach in nanophotonics and cavity physics to assess the effective Q-factor of a\nresonant mode. The extracted value of Q≈60 from our fitting indeed reflects the intrinsically low-\nloss nature and enhanced coherence of the closed-loop CNT/hBN hybrid polariton WGM resonance.\nRevision in Supplementary Information:\nTo prevent over-interpretation, we have added the relevant section to explicitly define this value\nas the \"effective Q-factor\":\n“We now explicitly describe the extracted value as the effective Q-factor under our specific near-\nfield excitation and detection conditions, rather than the intrinsic material Q. We clarify that the\nlinewidth is determined by both the round-trip attenuation and the phase-matching. Therefore, the\nQ-factor extracted from the FWHM provides an upper-bound estimate of the lifetime of the\ncirculating hybrid polariton mode.”\nResponse to Reviewer #4:\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part\nof the Nature Communications initiative to facilitate training in peer review and to provide\nappropriate recognition for Early Career Researchers who co-review manuscripts.\nOur reply: We thank the referee for letting us know about his/her involvement in the Nature\nCommunications initiative. It's commendable to see efforts towards training in peer review and\nrecognizing the contributions of Early Career Researchers. The referee’s commitment to this\ninitiative is valuable for the research community."}, {"round": 4, "reviewer_comments": {"reviewer_3": "The authors have replied to all the questions I raised. Manuscript can be accepted in the revised form.", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": ""}]

Decision letter