{"id":295901,"date":"2025-11-20T17:40:20","date_gmt":"2025-11-20T17:40:20","guid":{"rendered":"https:\/\/www.newsbeep.com\/ca\/295901\/"},"modified":"2025-11-20T17:40:20","modified_gmt":"2025-11-20T17:40:20","slug":"observation-of-hyperbolic-intersubband-polaritons-in-native-dielectric-doped-van-der-waals-semiconductor-quantum-wells","status":"publish","type":"post","link":"https:\/\/www.newsbeep.com\/ca\/295901\/","title":{"rendered":"Observation of hyperbolic intersubband polaritons in native-dielectric-doped van der Waals semiconductor quantum wells"},"content":{"rendered":"<p>Intersubband transition and native-dielectric-doping<\/p>\n<p>The intersubband transition energies in the WSe2 QWs can be approximated with an infinite square well potential with well width L\u2009=\u2009Nd, where N is number of layers and d is the monolayer thickness (Fig.\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#Fig1\" rel=\"nofollow noopener\" target=\"_blank\">1a<\/a>). The dispersion near the band edge at the \u0393 point can be obtained from<\/p>\n<p>$${E}_{\\Gamma }\\left({k}_{z},{\\boldsymbol{k}}\\right)\\approx -\\frac{{\\hslash }^{2}{k}_{z}^{2}}{2{m}_{v,z}}-\\frac{{\\hslash }^{2}{k}^{2}}{2{m}_{v,{xy}}}(1+\\zeta {k}_{z}^{2})$$<\/p>\n<p>\n                    (1)\n                <\/p>\n<p>where \\({m}_{v,z}\\) and \\({m}_{v,{xy}}\\) are the out-of-plane and in-plane effective masses, \u03b6 is the nonlinearity parameter and \\({k}_{z}\\approx \\frac{\\pi n}{d(N+2v)}\\)<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 22\" title=\"Ruiz-Tijerina, D. A., Danovich, M., Yelgel, C., Z&#xF3;lyomi, V. &amp; Fal&#x2019;ko, V. I. Hybrid k&#xB7;p tight-binding model for subbands and infrared intersubband optics in few-layer films of transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2. Phys. Rev. B 98, 035411 (2018).\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#ref-CR22\" id=\"ref-link-section-d56712268e1238\" rel=\"nofollow noopener\" target=\"_blank\">22<\/a>. The intersubband transition energies can be expressed as<\/p>\n<p>$$\\left|{E}_{1}-{E}_{2}\\right|=\\frac{3{\\pi }^{2}{\\hslash }^{2}}{{2{m}_{v,z}d}^{2}{\\left(N+2v\\right)}^{2}}$$<\/p>\n<p>\n                    (2)\n                <\/p>\n<p>and<\/p>\n<p>$$\\left|{E}_{2}-{E}_{3}\\right|=\\frac{5{\\pi }^{2}{\\hslash }^{2}}{{2{m}_{v,z}d}^{2}{\\left(N+2v\\right)}^{2}}$$<\/p>\n<p>\n                    (3)\n                <\/p>\n<p>We compare the intersubband transition energies calculated with this modified infinite square well model with density function theory (DFT) and find a good agreement with experimental values<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 21\" title=\"Zhang, Y. et al. Electronic structure, surface doping, and optical response in epitaxial WSe2 thin films. Nano Lett. 16, 2485&#x2013;2491 (2016).\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#ref-CR21\" id=\"ref-link-section-d56712268e1542\" rel=\"nofollow noopener\" target=\"_blank\">21<\/a> (Fig.\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#Fig1\" rel=\"nofollow noopener\" target=\"_blank\">1b<\/a>). The intersubband transition energies in multilayer WSe2 can be tuned from 636\u2009meV to 39\u2009meV by control of the number of layers. To engineer optical access to the intersubband states in the mid-infrared energy range, typical of a QCL source, we specifically choose a platform of a five-layer (5\u2009L) 2H-WSe2 homostructure to create a highly doped vdW multi-QW with accessible, partially occupied subbands. Figure\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#Fig1\" rel=\"nofollow noopener\" target=\"_blank\">1c<\/a> illustrates the fabrication process of WOx-doped WSe2 multilayers. In our method, the electronic band structure is, in essence, adjusted through the self-limiting oxidation of the top WSe2 layer. We subject a dry-transferred WSe2 flake to a UV-Ozone treatment, designed to convert the top layer into a TMO layer which has a high work function, while maintaining the atomic integrity of the underlying layers (see Methods and Supplementary Note\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">1<\/a>). The significant work function difference between WO\u2093 and WSe2 induces a surface charge transfer<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 32\" title=\"Kim, Y. S. et al. Atomic&#x2013;layer&#x2013;confined multiple quantum wells enabled by monolithic bandgap engineering of transition metal dichalcogenides. Sci. Adv. 7, eabd7921 (2021).\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#ref-CR32\" id=\"ref-link-section-d56712268e1571\" rel=\"nofollow noopener\" target=\"_blank\">32<\/a>, promoting strong hole doping in the WSe2 layers. The hole density in these p-doped WSe2 multilayers is measured under ambient conditions using standard four-probe measurements (Supplementary Note\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">2<\/a>). We find a hole density of p\u2009=\u20090.93\u2009\u00d7\u20091013\u2009cm\u22122 at VGS\u2009=\u20090\u2009V, aligning with prior reports of doping in the 1013\u2009cm\u22122 range<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 29\" title=\"Choi, M. S. et al. High carrier mobility in graphene doped using a monolayer of tungsten oxyselenide. Nat. Electron. 4, 731&#x2013;739 (2021).\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#ref-CR29\" id=\"ref-link-section-d56712268e1602\" rel=\"nofollow noopener\" target=\"_blank\">29<\/a>. By applying a back gate voltage, VGS, to the heavily doped Si substrate separated by the 300\u2009nm silicon oxide layer, we can further increase this density to p\u2009=\u20091.11\u2009\u00d7\u20091013\u2009cm\u22122 at VGS\u2009=\u2009\u221225 V. The doping level achieved through the TMO layer process surpasses most electrostatic gating methods using solid dielectrics by an order of magnitude. Electrostatic approaches generally yield densities in the 1011 to 1012\u2009cm\u22122 range<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 33\" title=\"Amet, F. et al. Composite fermions and broken symmetries in graphene. Nat. Commun. 6, 5838 (2015).\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#ref-CR33\" id=\"ref-link-section-d56712268e1628\" rel=\"nofollow noopener\" target=\"_blank\">33<\/a>.<\/p>\n<p>Fig. 1: Intersubband transition in WSe2 and WOx heterostructure.<a class=\"c-article-section__figure-link\" data-test=\"img-link\" data-track=\"click\" data-track-label=\"image\" data-track-action=\"view figure\" href=\"https:\/\/www.nature.com\/articles\/s41467-025-65196-y\/figures\/1\" rel=\"nofollow noopener\" target=\"_blank\"><img decoding=\"async\" aria-describedby=\"Fig1\" src=\"https:\/\/www.newsbeep.com\/ca\/wp-content\/uploads\/2025\/11\/41467_2025_65196_Fig1_HTML.png\" alt=\"figure 1\" loading=\"lazy\" width=\"685\" height=\"493\"\/><\/a><\/p>\n<p>a Schematic illustration of subbands in the van der Waals (vdW) material quantum wells with different thickness defined by the number of layers N. Black dashed lines illustrate the subband energy positions. b Theoretical calculation of the intersubband transition energy of the first and second subband as a function of N for holes in the valence band using density function theory (DFT) (green circles) and modified infinite quantum well model, respectively. Red shaded area indicates the energy coverage of our mid-infrared laser. c Schematics of the doping process. Ultraviolet-ozone oxidation transforms the topmost layer of the 5L-WSe2 into transition metal oxides (TMOs) resulting in WOx\/4L-WSe2. The oxidation process effectively doped the underneath WSe2 layers. DFT calculated band structure for WOx\/4L-WSe2 heterostructure showing contribution from 4L-WSe2 in green (d) and top WOx layer in blue (e). Red dashed lines indicate the Fermi energy EF. Red solid arrows indicated the optical transition. f Illustration of charge transfer between WOx and WSe2 as the result of the work-function mismatch. EC is conduction band edge and EV is valence band edge;Excitation light with out-of-plane polarization can excite the charge carriers from the lower state to the upper excited state if excitation photon energy Eph is in resonant with the E23 intersubband transition energy. g Nano Fourier transform infrared spectrum of the WOx\/4L-WSe2 near-field amplitude s(\u03c9) and phase \u03c6(\u03c9). h Phase contrast between the sample and substrate as a function of gate voltage Vg.<\/p>\n<p>We calculated the expected electronic band structure modification from the top WOx layer onto the WSe2 layers underneath, using density functional theory (DFT) incorporating spin-orbit coupling effects (Supplementary Note\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">2<\/a>). Figure\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#Fig1\" rel=\"nofollow noopener\" target=\"_blank\">1d, e<\/a> presents the band structure of WOx\/4L-WSe2 heterostructure calculated using this approach. These calculations elucidate the splitting of the highest valence band into multiple subbands at the \u0393 point in the Brillouin zone, corresponding to the interlayer coupling. Upon p-doping, free holes partially occupy these subbands from the subband base to the Fermi energy (EF), transitions can occur within the |k|\u2009\u2264\u2009kF range between a subband and a higher unoccupied subband. This is manifested as an absorption peak. To investigate the influence from the WOx layer, selenium atoms in the topmost layer were substituted with oxygen, and the ionic positions subsequently re-optimized. As depicted in Fig.\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#Fig1\" rel=\"nofollow noopener\" target=\"_blank\">1d, e<\/a>, this modification of the electronic states results in an altered band structure at the \u0393 point, displaying distinct subband splitting at mid-IR energies. Our calculation suggests that when the top layer (L5) is oxidized, the symmetry is broken and the top valence subband comes almost exclusively from the L5. The 2nd valence subband then comes mostly from L4 and L3 while the 3rd valence subband from L2. In order to maximize the coupling of light to intersubband transitions, it is desirable to populate holes in the second subbands in a few-layer WSe2, which requires carrier density more than ~1013\u2009cm\u22122 and has been challenging to reach by electrostatic gating alone. In contrast, using the TMO layer we can easily generate the sufficient carrier density with EF positioned within the valence band. As illustrated in Fig.\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#Fig1\" rel=\"nofollow noopener\" target=\"_blank\">1f<\/a>, when the heterostructure is excited by photon with the out-of-plane polarization whose energy is resonant with the transition energy between the subbands, an intersubband transition between the second and third subbands can be observed.<\/p>\n<p>Near-field imaging of the intersubband polaritons<\/p>\n<p>An s-SNOM equipped with a broadband pulsed laser is utilized to carry out the nano-Fourier-transform infrared spectroscopy (nano-FTIR). The infrared excitation laser beam is focused on the metallized tip of the atomic force microscope (AFM), generating an enhanced optical field that interacts with the heterostructure sample beneath. With that configuration, we are able to characterize the intersubband transitions in WOx\/4L-WSe2 at near-field with out-of-plane excitation polarization. The scattered light from the tip is collected, and the near-field amplitude and phase are recorded from the sample flake. This data is calibrated against a gold substrate to eliminate any instrumental responses. The near-field results provide insights into the sample\u2019s complex permittivity, optical conductivity, and its absorption characteristics under the excitation energy Eph (Fig.\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#Fig1\" rel=\"nofollow noopener\" target=\"_blank\">1g<\/a>). Notably, while the dielectric response of WSe2 remains featureless from 120\u2009meV to 160\u2009meV<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 34\" title=\"Ruta, F. L., Sternbach, A. J., Dieng, A. B., McLeod, A. S. &amp; Basov, D. N. Quantitative nanoinfrared spectroscopy of anisotropic van der Waals materials. Nano Lett. 20, 7933&#x2013;7940 (2020).\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#ref-CR34\" id=\"ref-link-section-d56712268e1831\" rel=\"nofollow noopener\" target=\"_blank\">34<\/a>, WOx\/4L-WSe2 heterostructure exhibits a distinct absorption peak, clearly indicative of the predicted intersubband transition. To avoid interference from SiO2 phonons, typically prominent around 140\u2009meV, an Au\/Si substrate without an SiO2 layer was utilized. We further explore the nano-FTIR result by fitting the data with modulated scattered field where tip-sample interaction and complex permittivity described as Lorentz model are taken into consideration (Supplementary Note\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">4<\/a>). We then demonstrate intersubband absorption control by analyzing the phase contrast between the sample and the substrate \u03c6sample-\u03c6sub while changing the carrier density using a gate bias. The interferometric detection of the near-field optical response can decouple the amplitude and phase components from the scattered field as Escat \u221d Sei\u03c6 Ein, where S is the relative amplitude and \u03c6 is the phase shift<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 35\" title=\"Cvitkovic, A., Ocelic, N. &amp; Hillenbrand, R. Analytical model for quantitative prediction of material contrasts in scattering-type near-field optical microscopy. Opt. Express 15, 8550 (2007).\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#ref-CR35\" id=\"ref-link-section-d56712268e1880\" rel=\"nofollow noopener\" target=\"_blank\">35<\/a>. Hence, the relative phase shift is a measurement of absorption at the near-field. As shown in Fig.\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#Fig1\" rel=\"nofollow noopener\" target=\"_blank\">1h<\/a>, we can clearly see that the absorption decreases when we inject electron into the sample to decrease the hole carrier density. (Note the electrostatic bias cannot tune the carrier density to the charge neutrality point due to the high doping level from the charge transfer of the WOx).<\/p>\n<p>According to the nano-FTIR spectrum, the \\({\\varepsilon }_{{imag}}\\) should exhibit strong resonant-like features along the out-of-plane crystal direction, implying the anisotropic dielectric permittivity should satisfy \\({\\varepsilon }_{{real},i}\\times {\\varepsilon }_{{real},j\\ne i} &lt; 0\\), since the real and imaginary parts of the dielectric function are connected through the Kramers\u2013Kroing relation<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 36\" title=\"Wang, H. et al. Planar hyperbolic polaritons in 2D van der Waals materials. Nat. Commun. 15, 69 (2024).\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#ref-CR36\" id=\"ref-link-section-d56712268e2003\" rel=\"nofollow noopener\" target=\"_blank\">36<\/a>. Due to the different value of the effective masses and dielectric screening in the in-plane and out-of-plane directions, the highly doped WOx\/4L-WSe2 heterostructure exhibits strong anisotropy in the frequency range (Fig.\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#Fig2\" rel=\"nofollow noopener\" target=\"_blank\">2a<\/a>). The heterostructure behaves like a dielectric in-plane, where \\({\\varepsilon }^{x,y} &gt; 0\\). For the out-of-plane direction, the heterostructure behaves like metal under the high carrier density conditions, showing a strong intersubband absorption with \\({\\varepsilon }^{z} &lt; 0\\) at the mid-IR frequency. We note that this phenomenon is fundamentally different from recently demonstrated bound carrier excitation in bulk WSe2 near the interband optical transition energy<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 37\" title=\"Sternbach, A. J. et al. Programmable hyperbolic polaritons in van der Waals semiconductors. Science 371, 617&#x2013;620 (2021).\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#ref-CR37\" id=\"ref-link-section-d56712268e2089\" rel=\"nofollow noopener\" target=\"_blank\">37<\/a>. In the bulk WSe2 crystal, the subbands remain degenerate, and hyperbolic behavior emerges only under non-equilibrium conditions, in contrast to the ISPs studied here.<\/p>\n<p>Fig. 2: Nano-imaging of intersubband transition and hyperbolic plasmon polariton in WOx\/4L-WSe2.<a class=\"c-article-section__figure-link\" data-test=\"img-link\" data-track=\"click\" data-track-label=\"image\" data-track-action=\"view figure\" href=\"https:\/\/www.nature.com\/articles\/s41467-025-65196-y\/figures\/2\" rel=\"nofollow noopener\" target=\"_blank\"><img decoding=\"async\" aria-describedby=\"Fig2\" src=\"https:\/\/www.newsbeep.com\/ca\/wp-content\/uploads\/2025\/11\/41467_2025_65196_Fig2_HTML.png\" alt=\"figure 2\" loading=\"lazy\" width=\"685\" height=\"400\"\/><\/a><\/p>\n<p>a Permittivity of the WSe2 (dashed lines) and with high carrier density under charge transfer (solid lines). Inset: the isofrequency surface modified from ellipse to a hyperboloid in the red-shaded region. Images of near-field scattering amplitude s(\u03c9) for WOx\/4L-WSe2 with excitation energy Eph\u2009=\u2009144\u2009meV (b) and Eph\u2009=\u2009149\u2009meV (c). The layer thickness is d\u2009~\u20094.5\u2009nm. Scale bar: 500\u2009nm. d Line traces of the interference pattern from the edge-reflected plasmon polariton taken from the near-field scattering amplitude image as illustrated in (b) and (c) (white dashed lines). Black dashed line marks the edge of the sample and red dashed line marks the peak position. e Dispersion of the intersubband polariton (ISP) in WOx\/4L-WSe2. Color plot is calculated using the Fresnel reflection coefficients Im(rp). Yellow squares are experimental data. The error bars are determined from the fitting uncertainties of the fringe periodicities. f The extracted real part of momentum q as a function of carrier density n for WOx\/4L-WSe2. The red solid line is the fit to the data using the relation \\(q\\approx 1\/n\\). The error bars are determined from the fitting uncertainties of the fringe periodicities. g Images of near-field scattering amplitude s(\u03c9) for WOx\/3L-WSe2 and WOx\/5L-WSe2 with excitation energies Eph\u2009=\u2009270\u2009meV and Eph\u2009=\u200998\u2009meV, respectively. Scale bar: 250\u2009nm.<\/p>\n<p>To effectively couple intersubband transitions to free-space photons and excite ISPs in the WSe2 quantum wells, we employed s-SNOM with both a continuous-wave QCL and a pulsed optical parametric oscillator laser to sweep across the transition energies. This configuration introduces an out-of-plane light component that drives the intersubband transitions within the heterostructure, thereby giving rise to ISPs. In order to reveal the ISP propagation in the heterostructure, we now investigate the polariton dispersive dynamics interferometrically using the real-space near-field nano-imaging technique. Figure\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#Fig2\" rel=\"nofollow noopener\" target=\"_blank\">2b, c<\/a> presents data collected at different excitation energies, Eph\u2009=\u2009144\u2009meV and Eph\u2009=\u2009149\u2009meV, respectively. Oscillations of the near-field amplitude s(\u03c9) are observable at the flake edge. These fringes arise from the interference between the tip-launched polariton and the propagated polariton reflected at the sample edge. By examining the cross-sectional profile perpendicular to the sample edge, we can extract the periodicity of the bright-dark fringes, which corresponds to half of the polariton wavelength (\u03bbISP\/2). As the excitation energy increases from 144\u2009meV to 149\u2009meV, the polariton wavelength increases from 317\u2009\u00b1\u200910\u2009nm to 453\u2009\u00b1\u200912\u2009nm (Fig.\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#Fig2\" rel=\"nofollow noopener\" target=\"_blank\">2d<\/a>). The propagation length of the ISP is fitted to be 0.8 \u03bcm (Supplementary Note\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">5<\/a>). The lifetime of the ISP is calculated as \\({\\tau }_{{\\rm{ISP}}}=\\frac{L}{{v}_{g}}=0.4{ps}\\) (Supplementary Note\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">10<\/a>). Using the same method, we systematically extract the polariton wavelengths at various tuned excitation energies from the nano-imaging data. The confinement factor \\({\\lambda }_{0}\/{\\lambda }_{{ISP}}\\) reaches up to 27, comparable to that of plasmon polaritons in graphene and phonon polaritons in h-BN, while still smaller than the acoustic plasmon in graphene<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 38\" title=\"Lee, I.-H., Yoo, D., Avouris, P., Low, T. &amp; Oh, S.-H. Graphene acoustic plasmon resonator for ultrasensitive infrared spectroscopy. Nat. Nanotechnol. 14, 313&#x2013;319 (2019).\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#ref-CR38\" id=\"ref-link-section-d56712268e2395\" rel=\"nofollow noopener\" target=\"_blank\">38<\/a>. We visualize the dispersion relations with a false color mapping of the imaginary part of the reflection coefficients Im (rp), representing the photonic density of states as a function of wave vector \\(q=2\\pi \/{\\lambda }_{{ISP}}\\) (Fig.\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#Fig2\" rel=\"nofollow noopener\" target=\"_blank\">2e<\/a> and Supplementary Note\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">6<\/a>). This inverse relationship between energy and momentum confirms the Type I hyperbolic polariton dispersion, where \\({\\varepsilon }^{z} &lt; 0\\) and \\({\\varepsilon }^{x,y} &gt; 0\\).<\/p>\n<p>As noted, in addition to the charge transfer process via TMO layer, the carrier density can be further tuned. We demonstrate the electrical control of the polaritons by systematically tuning of the intersubband transitions in the valence band via back-gating. Since the charge transfer method between the TMO layer and WSe2 drives a much higher carrier density than that possible via tuning by electrostatic gating, we can vary the carrier density modestly in the p-type doping regime. Figure\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#Fig2\" rel=\"nofollow noopener\" target=\"_blank\">2f<\/a> shows the ISP momentum q as a function of the back-gate voltage Vg at a representative energy Eph\u2009=\u2009144\u2009meV. The magnitude of q is approximately proportional to n\u22121, where higher hole density leads to increased negative permittivity<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 39\" title=\"Ni, G. X. et al. Fundamental limits to graphene plasmonics. Nature 557, 530&#x2013;533 (2018).\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#ref-CR39\" id=\"ref-link-section-d56712268e2559\" rel=\"nofollow noopener\" target=\"_blank\">39<\/a>. The evolution of q with Vg further confirms the hole doping in the WO\u2093\/4L-WSe2 structure and the observed negative dispersion relation (Supplementary Note\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">8<\/a>). Such active tunability is generally absent in the natural hyperbolic materials such as h-BN<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 40\" title=\"Dai, S. et al. Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride. Science 343, 1125&#x2013;1129 (2014).\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#ref-CR40\" id=\"ref-link-section-d56712268e2575\" rel=\"nofollow noopener\" target=\"_blank\">40<\/a> and MoO3<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 41\" title=\"Ma, W. et al. In-plane anisotropic and ultra-low-loss polaritons in a natural van der Waals crystal. Nature 562, 557&#x2013;562 (2018).\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#ref-CR41\" id=\"ref-link-section-d56712268e2580\" rel=\"nofollow noopener\" target=\"_blank\">41<\/a>. The intersubband transition energy can be controlled with the thickness of the vdW layers. We also demonstrated the nano-imaging of the ISP in both WOx\/3L-WSe2 and WOx\/5L-WSe2 heterostructure at excitation wavelength Eph\u2009=\u2009270\u2009meV and Eph\u2009=\u200998\u2009meV, respectively (Fig.\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#Fig2\" rel=\"nofollow noopener\" target=\"_blank\">2g<\/a>). This finding aligns well with the theoretical calculation shown in Fig.\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#Fig1\" rel=\"nofollow noopener\" target=\"_blank\">1b<\/a>.<\/p>\n<p>Measurement of the hyperbolic propagation<\/p>\n<p>We explore the presence of hyperbolic ISP by positioning the WOx\/4L-WSe2 heterostructure on the 50\u2009nm Au disk (Fig.\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#Fig3\" rel=\"nofollow noopener\" target=\"_blank\">3b<\/a>). The conical-shaped rays launched by the edge of the Au disk will reach the top surface of the heterostructure forming bright rings separated by the edge (Fig.\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#Fig3\" rel=\"nofollow noopener\" target=\"_blank\">3a<\/a>). The distance between the bright ring and the electrostatic edge, denoted as \u0394R, is modulated by the isotropic components of the dielectric tensor, with the relationship \\(\\Delta R\/d=\\left|\\tan \\theta \\right|=i\\sqrt{{\\varepsilon }_{{xy}}}\/\\sqrt{{\\varepsilon }_{z}}\\), where d represents the heterostructure\u2019s thickness, and \u03b8 is the angle from the surface normal<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 42\" title=\"Li, P. et al. Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing. Nat. Commun. 6, 7507 (2015).\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#ref-CR42\" id=\"ref-link-section-d56712268e2723\" rel=\"nofollow noopener\" target=\"_blank\">42<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 43\" title=\"Dai, S. et al. Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material. Nat. Commun. 6, 6963 (2015).\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#ref-CR43\" id=\"ref-link-section-d56712268e2726\" rel=\"nofollow noopener\" target=\"_blank\">43<\/a>. Directional propagation of the hyperbolic ISP along the resonance cone is observed at Eph\u2009=\u2009145\u2009meV (Fig.\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#Fig3\" rel=\"nofollow noopener\" target=\"_blank\">3c<\/a>). The line-profiles taken from the s-SNOM amplitude image reveal that the radial distance \u0394R is significantly smaller than that observed in bulk hyperbolic materials, due to the thickness of the heterostructure as thin as d\u2009~\u20094.5\u2009nm (Fig.\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#Fig3\" rel=\"nofollow noopener\" target=\"_blank\">3d<\/a>). We further verify the hot-ring feature for different layer number samples by transferring the heterostructure with different thickness onto the same Au disk. When the excitation energy matches the E23 transition energy of the WOx\/6L-WSe2 at Eph\u2009=\u2009114\u2009meV, we can see only the bottom half lights up (Fig.\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#Fig3\" rel=\"nofollow noopener\" target=\"_blank\">3e<\/a>). When we increase the excitation energy to Eph\u2009=\u2009146\u2009meV, the upper half lights up as the intersubband transition energy increases with the fewer layer numbers (Fig.\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#Fig3\" rel=\"nofollow noopener\" target=\"_blank\">3f<\/a>). The layer-dependent hyperbolicity highlights ISPs as a promising addition to the family of hyperbolic polaritons, complementing other recently demonstrated phenomena such as topological transitions<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 44\" title=\"Hu, H. et al. Doping-driven topological polaritons in graphene\/&#x3B1;-MoO3 heterostructures. Nat. Nanotechnol. 17, 940&#x2013;946 (2022).\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#ref-CR44\" id=\"ref-link-section-d56712268e2771\" rel=\"nofollow noopener\" target=\"_blank\">44<\/a>, negative refraction<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 45\" title=\"Hu, H. et al. Gate-tunable negative refraction of mid-infrared polaritons. Science 379, 558&#x2013;561 (2023).\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#ref-CR45\" id=\"ref-link-section-d56712268e2775\" rel=\"nofollow noopener\" target=\"_blank\">45<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 46\" title=\"Sternbach, A. J. et al. Negative refraction in hyperbolic hetero-bicrystals. Science 379, 555&#x2013;557 (2023).\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#ref-CR46\" id=\"ref-link-section-d56712268e2778\" rel=\"nofollow noopener\" target=\"_blank\">46<\/a>, and low-loss propagation<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 47\" title=\"Ruta, F. L. et al. Good plasmons in a bad metal. Science 387, 786&#x2013;791 (2025).\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#ref-CR47\" id=\"ref-link-section-d56712268e2782\" rel=\"nofollow noopener\" target=\"_blank\">47<\/a>.<\/p>\n<p>Fig. 3: Hyperbolic ISP revealed by nano-imaging on Au nanodisk.<a class=\"c-article-section__figure-link\" data-test=\"img-link\" data-track=\"click\" data-track-label=\"image\" data-track-action=\"view figure\" href=\"https:\/\/www.nature.com\/articles\/s41467-025-65196-y\/figures\/3\" rel=\"nofollow noopener\" target=\"_blank\"><img decoding=\"async\" aria-describedby=\"Fig3\" src=\"https:\/\/www.newsbeep.com\/ca\/wp-content\/uploads\/2025\/11\/41467_2025_65196_Fig3_HTML.png\" alt=\"figure 3\" loading=\"lazy\" width=\"685\" height=\"309\"\/><\/a><\/p>\n<p>a Schematic of hyperbolic polaritons launched at the edge of the Au nanodisk, which travel along conical trajectories and form a bright ring. The distance between the ring and the edge of the Au nanodisk is \u2206R. Topography (b) and near-field scattering amplitude s(\u03c9) image of WOx\/4L-WSe2 plasmonic cavity with diameter D\u2009=\u2009300\u2009nm and excitation energy Eph\u2009=\u2009145\u2009meV (c). Scale bar: 300\u2009nm. d Line profile of the measured near-field amplitude taken at the dashed line in (c). Near-field scattering amplitude s(\u03c9) image of sample on the Au nanodisk that is partially covered by WOx\/4L-WSe2 and WOx\/6L-WSe2 simultaneously and excited with Eph\u2009=\u2009114\u2009meV (e) and Eph\u2009=\u2009146\u2009meV (f), respectively. Red dashed lines indicate the boundary. Scale bar: 150\u2009nm.<\/p>\n<p>Intersubband polaritons in nanoresonators<\/p>\n<p>We further manipulate the hyperbolic ISP by fabricate the WO\u2093\/4L-WSe2 heterostructure into nanoresonators where the polariton modes are confined by the circular boundaries. Figure\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#Fig4\" rel=\"nofollow noopener\" target=\"_blank\">4a<\/a> illustrates the schematic of an s-SNOM measurement conducted on focus ion beam (FIB) patterned WO\u2093\/4L-WSe2 nanoresonators with an underlying gold mirror. By eliminating the need for a polymer mask in the etching process, direct FIB fabrication keeps the heterostructure surface uncontaminated, minimizing the risk of residue deposition or chemical interaction commonly associated with mask-based techniques, thereby preserving the material\u2019s intrinsic properties and optimizing the quality of subsequent device performance. Additionally, a gold mirror is deposited on the substrate to minimize radiative decay into the silicon substrate, thereby resulting in lower loss and longer lifetime (Supplementary Notes <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">9<\/a> and <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">10<\/a>). To explore the relation between the resonant energy and the diameters of the nanoresonators, we patterned disk nanoresonators with diameters ranging from 100\u2009nm to 800\u2009nm. The propagation of the ISP in the nanoresonators can be described by the wave equation \\({\\rho (i\\omega )}^{2}={\\nabla }^{2}\\rho {v}_{p}^{2}(\\omega )\\), where \u03c1 denotes the integrated two-dimensional charge density and vp is the group velocity<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 48\" title=\"Tamagnone, M. et al. Ultra-confined mid-infrared resonant phonon polaritons in van der Waals nanostructures. Sci. Adv. 4, eaat7189 (2018).\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#ref-CR48\" id=\"ref-link-section-d56712268e2991\" rel=\"nofollow noopener\" target=\"_blank\">48<\/a>. For a disk-shaped resonator, the solution of \u03c1 can be expressed in terms of Bessel functions, with the eigenvalues ksn determined by the disk diameter. Consequently, because the ISP can resonate only with resonators of specific sizes at a given excitation photon energy, tuning the Eph enables the systematic mapping of the relationship between disk diameter and the ISP resonant modes (Fig.\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#Fig4\" rel=\"nofollow noopener\" target=\"_blank\">4b<\/a>).<\/p>\n<p>Fig. 4: Intersubband polariton confined in WOx\/4L-WSe2\/Au nanoresonators.<a class=\"c-article-section__figure-link\" data-test=\"img-link\" data-track=\"click\" data-track-label=\"image\" data-track-action=\"view figure\" href=\"https:\/\/www.nature.com\/articles\/s41467-025-65196-y\/figures\/4\" rel=\"nofollow noopener\" target=\"_blank\"><img decoding=\"async\" aria-describedby=\"Fig4\" src=\"https:\/\/www.newsbeep.com\/ca\/wp-content\/uploads\/2025\/11\/41467_2025_65196_Fig4_HTML.png\" alt=\"figure 4\" loading=\"lazy\" width=\"685\" height=\"403\"\/><\/a><\/p>\n<p>a Schematics of WOx\/4L-WSe2\/Au nanoresonators fabricated by focused ion beam on gold substrate. b Near-field scattering amplitude s(\u03c9) images of an array of WOx\/4L-WSe2\/Au nanoresonators with different diameters (100\u2009nm to 800\u2009nm) and different shapes. The images are measured at a series of excitation energies from 139\u2009meV to 161\u2009meV. Scale bar: 1\u2009\u03bcm. c Near-field scattering amplitude s(\u03c9) image of WOx\/4L-WSe2\/Au nanoresonator with diameter D\u2009=\u2009600\u2009nm. The excitation energy is Eph\u2009=\u2009146\u2009meV. Scale bar: 250\u2009nm. d The corresponding Fourier transform image of (c). kx and ky are wavevectors in x and y direction. Scale bar: 40 k0, where k0 is the momentum of light in free space. e Normalized near-field scattering amplitude as a function of diameters of the resonators with excitation energy at Eph\u2009=\u2009151\u2009meV (top panel), Eph\u2009=\u2009144\u2009meV (middle panel) and Eph\u2009=\u2009139\u2009meV (bottom panel). Red arrows help to identify the peak value of s(\u03c9). f Normalized amplitude as a function of excitation energy for the WOx\/4L-WSe2\/Au nanoresonator with diameter D\u2009=\u2009600\u2009nm (green circles). Gray solid line is the Gaussian fitting. g Finite-difference time-domain simulation of the out-of-plane field Ez in WOx\/4L-WSe2\/Au nanoresonator with different excitation energies of Eph\u2009=\u2009144\u2009meV, Eph\u2009=\u2009146\u2009meV, Eph\u2009=\u2009148\u2009meV and Eph\u2009=\u2009151\u2009meV, respectively. The diameter of the nanoresonator is D\u2009=\u2009600\u2009nm.<\/p>\n<p>To quantitatively study the confined mode in the resonators, we analyzed each disk resonator at different excitation energies. The near-field amplitude image of a representative nanoresonator with a diameter of D\u2009=\u2009500\u2009nm is shown in Fig.\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#Fig4\" rel=\"nofollow noopener\" target=\"_blank\">4c<\/a>, where a standing-wave pattern with multiple fringes emerges<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 49\" title=\"Luo, Y. et al. Highly confined hybridized polaritons in scalable van der Waals heterostructure resonators. ACS Nano 18, 17492&#x2013;17499 (2024).\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#ref-CR49\" id=\"ref-link-section-d56712268e3180\" rel=\"nofollow noopener\" target=\"_blank\">49<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 50\" title=\"Sumikura, H. et al. Highly confined and switchable mid-infrared surfacephonon polariton resonances of planar circular cavities with a phase change material. Nano Lett. 19, 2549&#x2013;2554 (2019).\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#ref-CR50\" id=\"ref-link-section-d56712268e3183\" rel=\"nofollow noopener\" target=\"_blank\">50<\/a>. Figure\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#Fig4\" rel=\"nofollow noopener\" target=\"_blank\">4d<\/a> presents the Fourier transform |s(kx, ky)| of the near-field amplitude image from Fig.\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#Fig4\" rel=\"nofollow noopener\" target=\"_blank\">4c<\/a>, revealing the iso-frequency contours for the ISP at 146\u2009meV. The in-plane permittivity of the WO\u2093\/4L-WSe2 heterostructure is isotropic. We then extract the near-field amplitude response from the standing wave in the resonator at different excitation energies (Fig.\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#Fig4\" rel=\"nofollow noopener\" target=\"_blank\">4e<\/a>). The signal was normalized to the background at the surrounding gold surface to compensate for variations in the laser power and optical alignment in each measurement. At Eph\u2009=\u2009139\u2009meV, the near-field amplitude shows a peak D\u2009=\u2009300\u2009nm. The size of the resonator imposes a constraint on the ISP wavelength confined in the resonator. With increasing Eph, disk diameter exhibiting a stronger scattered near-field response also increases due to the longer polariton wavelength, aligning with the hyperbolic dispersion relation observed in the unpatterned heterostructures. We then investigate the field concentration and the resonance behavior of the confined ISP by analyzing a resonator with D\u2009=\u2009600\u2009nm under various excitation energies. Figure\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#Fig4\" rel=\"nofollow noopener\" target=\"_blank\">4f<\/a> shows the near-field optical response as a function of the excitation energy. The signal is normalized to the substrate background to eliminate the influence from the power stability and detection efficiency. We fit the peak with Gaussian function with center energy at 147\u2009meV and FWHM\u2009=\u20093.2\u2009\u00b1\u20090.3\u2009meV. The quality factor is then calculated as Q\u2009=\u2009\u03c9\/FWHM\u2009=\u200945.9, where \u03c9 is the resonant frequency<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 48\" title=\"Tamagnone, M. et al. Ultra-confined mid-infrared resonant phonon polaritons in van der Waals nanostructures. Sci. Adv. 4, eaat7189 (2018).\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#ref-CR48\" id=\"ref-link-section-d56712268e3238\" rel=\"nofollow noopener\" target=\"_blank\">48<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 51\" title=\"Herzig Sheinfux, H. et al. High-quality nanocavities through multimodal confinement of hyperbolic polaritons in hexagonal boron nitride. Nat. Mater. 23, 499&#x2013;505 (2024).\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#ref-CR51\" id=\"ref-link-section-d56712268e3241\" rel=\"nofollow noopener\" target=\"_blank\">51<\/a>.<\/p>\n<p>We finally conducted a numerical simulation for the resonator with same diameter of D\u2009=\u2009600\u2009nm to further explore the polaritons propagation in WO\u2093\/4L-WSe2 nanoresonators. The z-component electric field distribution, mapped at various excitation energies in Fig.\u00a0<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#Fig4\" rel=\"nofollow noopener\" target=\"_blank\">4f<\/a>, shows that as the Eph increases from 144\u2009meV to 148\u2009meV, the distance between the bright maxima widens, following the negative dispersion relation. At an Eph\u2009=\u2009151\u2009meV, the polariton wavelength \u03bbISP\u2009=\u2009478\u2009nm exceeds the nanoresonator\u2019s radius, precluding effective ISP mode confinement. Our FDTD simulations show that the highly confined modes have an effective mode volume V of \\(2\\times {10}^{-6}\/{\\lambda }_{0}^{3}\\), respective to the free space photon wavelength \u03bb0, which quantifies the strong spatial confinement of light in the disk nanoresonators<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 52\" title=\"Srinivasan, K., Borselli, M., Painter, O., Stintz, A. &amp; Krishna, S. Cavity Q, mode volume, and lasing threshold in small diameter AlGaAs microdisks with embedded quantum dots. Opt. Express 14, 1094 (2006).\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#ref-CR52\" id=\"ref-link-section-d56712268e3340\" rel=\"nofollow noopener\" target=\"_blank\">52<\/a>. These observations highlight that the structural refinement of nanoresonators via FIB patterning facilitates enhanced control over polariton modes, resulting in a higher quality factor and improved mode confinement. Importantly, there remains potential to further optimize the cavity design to achieve even greater polariton confinement with a significantly reduced mode volume<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 53\" title=\"Chikkaraddy, R. et al. Single-molecule strong coupling at room temperature in plasmonic nanocavities. Nature 535, 127&#x2013;130 (2016).\" href=\"http:\/\/www.nature.com\/articles\/s41467-025-65196-y#ref-CR53\" id=\"ref-link-section-d56712268e3344\" rel=\"nofollow noopener\" target=\"_blank\">53<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"Intersubband transition and native-dielectric-doping The intersubband transition energies in the WSe2 QWs can be approximated with an infinite&hellip;\n","protected":false},"author":2,"featured_media":295902,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[24],"tags":[49,48,1099,1100,26662,314,25338,66,3675],"class_list":{"0":"post-295901","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-physics","8":"tag-ca","9":"tag-canada","10":"tag-humanities-and-social-sciences","11":"tag-multidisciplinary","12":"tag-nanophotonics-and-plasmonics","13":"tag-physics","14":"tag-polaritons","15":"tag-science","16":"tag-two-dimensional-materials"},"_links":{"self":[{"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/posts\/295901","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/comments?post=295901"}],"version-history":[{"count":0,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/posts\/295901\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/media\/295902"}],"wp:attachment":[{"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/media?parent=295901"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/categories?post=295901"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/tags?post=295901"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}