Hyperbolic phonon polaritons in hexagonal boron nitride (hBN) were shown in 2015 to act as a subdiffractional 'hyper-focusing lens' and multi-mode waveguide when launched by metallic disks under an hBN crystal, with focal spots of ∼λ/33\sim\lambda/33 and a low loss factor γ∼0.03\gamma\sim0.03. The originating work identified a set of linked open experimental targets: focal spots at the predicted ∼λ/102\sim\lambda/10^{2} scale via much thinner launchers, controlled experiments and dispersion mapping across both hBN stop-bands, quantification of practical confinement limits in device geometries, and integration of launchers, waveguides, resonators and couplers into nanopolaritonic circuits with predictable performance. A decade of follow-up work has closed the source-availability part (Type-I lower-band imaging and focusing were demonstrated within months) and built many circuit elements, but as of 2025 focused, spatially confined polariton waves remain elusive in isotropic hBN — the best reported in-plane confinement is ∼λ/70\sim\lambda/70 — and no integrated hBN nanopolaritonic circuit exists. The surviving open core is the λ/102\lambda/10^{2}-scale focal-spot demonstration in isotropic hBN and the integration of hBN polaritonic components into a functional circuit.

Background

A uniaxial crystal whose dielectric permittivities along the optic axis (εz\varepsilon_z) and in the basal plane (εt\varepsilon_t) have opposite signs is called an indefinite or hyperbolic medium: the isofrequency surface of its allowed electromagnetic modes is a hyperboloid rather than a sphere, so wavevectors of arbitrarily large magnitude (and thus deeply subwavelength wavelengths) are supported. Hexagonal boron nitride (hBN), a layered van der Waals insulator, is a natural hyperbolic material in two mid-infrared Reststrahlen ('stop-') bands — spectral intervals where one principal permittivity is negative because of a lattice phonon resonance: the upper band ω≈1,370\omega\approx1{,}370–1,610 cm−11{,}610\ \mathrm{cm}^{-1} (type II, εt<0\varepsilon_t<0, εz>0\varepsilon_z>0) and the lower band ω≈746\omega\approx746–819 cm−1819\ \mathrm{cm}^{-1} (type I, signs reversed). In these bands, light couples to optical phonons to form hyperbolic phonon polaritons (HPhPs), collective modes that propagate as directional 'polaritonic rays' inside the crystal with a propagation angle set by the frequency-dependent permittivity ratio, and that are confined to volumes orders of magnitude smaller than the free-space wavelength λ\lambda. Because far-field photons cannot supply the huge momentum mismatch, HPhPs are launched in experiments by the sharp metallic tip of a scattering-type scanning near-field optical microscope (s-SNOM, an atomic-force microscope whose tip scatters infrared light and thereby both excites and detects nanoscale fields), or by lithographically patterned metallic structures.

Dai et al. (Nat. Commun. 6, 6963, 2015) demonstrated that Au disks (diameters 200–1,000 nm, thickness ∼50 nm\sim50\ \mathrm{nm}) sandwiched between an hBN crystal of thickness d∼100d\sim100–1,060 nm1{,}060\ \mathrm{nm} and a SiO2_2 substrate act as polariton launchers whose edge-emitted polaritonic rays converge at the top surface into concentric 'hot rings' that, at suitable disk-to-thickness ratios, shrink to a single focal spot of diameter ∼λ/33\sim\lambda/33. Modal analysis of the standing-wave patterns near launchers and sample edges established that a thin hBN slab is a multi-mode HPhP waveguide with loss factor γ∼0.03\gamma\sim0.03 (γ\gamma being the polariton damping relative to its frequency), and the authors argued that in a natural hyperbolic material the ultimate upper momentum cutoff — hence the ultimate spatial resolution — is set by interatomic spacing rather than by the period of an artificial metamaterial, in contrast to lossy metal/dielectric hyperbolic metamaterial stacks. In their discussion the authors identified the forward-looking challenges that define this problem: (i) the focal-spot size was limited by the finite ∼50 nm\sim50\ \mathrm{nm} thickness of the Au launchers, and analytic modeling (Supplementary Note 1) predicted that launchers as thin as ∼20 nm\sim20\ \mathrm{nm} should yield focal spots as small as ∼λ/102\sim\lambda/10^{2}, comparable to the spatial resolution of the nano-infrared apparatus itself; (ii) controlled dispersion-mapping experiments in the lower (type I) stop-band were constrained because no monochromatic laser sources were available there, so complete high-resolution mapping across both stop-bands required broader or tunable mid-infrared sources; (iii) the practical limits to spatial confinement and mode engineering in device geometries — fabrication tolerances, launcher design, integration into complex circuits — remained to be quantified; and (iv) combining focusing elements, waveguides, resonators and couplers into integrated 'nanopolaritonic circuits' was outlined as a promising but undemonstrated direction. These four strands share one objective: converting the demonstrated single-element physics of hBN hyperbolic polaritons into a deterministic mid-infrared nanophotonic technology.

Problem Statement

Starting from the 2015 demonstration that a metallic disk under a hexagonal boron nitride (hBN) crystal launches hyperbolic phonon polaritons that focus to ∼λ/33\sim\lambda/33 spots and that an hBN slab acts as a low-loss (γ∼0.03\gamma\sim0.03) multi-mode polariton waveguide, establish hBN hyperbolic polaritons as a deterministic mid-infrared nanophotonic technology. Concretely, with the four requested results linked by this single objective: (1) experimentally realize the predicted focal spots of order λ/102\lambda/10^{2} in the launcher-focusing geometry (focal-spot full-width at half-maximum ≤λ/102\le \lambda/10^{2}, demonstrably below the ∼λ/70\sim\lambda/70 best reported to date) and verify the launcher-thickness-limited scaling of the focal-spot size; (2) complete high-resolution, controlled dispersion-mapping and launcher experiments across both hBN stop-bands (the type II upper band 1,3701{,}370–1,610 cm−11{,}610\ \mathrm{cm}^{-1} and the type I lower band 746746–819 cm−1819\ \mathrm{cm}^{-1}), which requires suitable tunable or broadband monochromatic mid-infrared sources — a strand largely delivered by companion 2015 work and later electron-energy-loss spectroscopy, so the surviving emphasis is on controlled launcher-based experiments rather than source availability; (3) quantify the practical limits of spatial confinement and mode engineering of hBN hyperbolic polaritons in device geometries, including fabrication tolerances, launcher design, and the ultimate momentum cutoff expected from interatomic spacing; and (4) integrate the individual elements — launchers, waveguides, resonators and couplers — into a functioning hBN nanopolaritonic circuit whose performance is predictable from design — that is, an a-priori model of the circuit, specified independently of the measurements, that predicts the measured device response (e.g. transmission or a resonance) to a stated tolerance. The objective is the ∼λ/102\sim\lambda/10^{2}-scale focal-spot demonstration (1) together with the integrated nanopolaritonic circuit (4); parts (2) and (3) are supporting scientific subgoals. The demonstrations of (1) and (4) involve quantitative near-field characterization (s-SNOM imaging of the focal spots and modal patterns) and modeling that predicts the measured response.

References

  1. S. Dai, Q. Ma, T. Andersen, A. S. McLeod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, D. N. Basov, 'Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material', Nature Communications 6, 6963 (2015). DOI: 10.1038/ncomms7963, https://doi.org/10.1038/ncomms7963
  2. P. Li, M. Lewin, A. V. Kretinin, J. D. Caldwell, K. S. Novoselov, T. Taniguchi, K. Watanabe, F. Gaussmann, T. Taubner, 'Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing', Nature Communications 6, 7507 (2015). DOI: 10.1038/ncomms8507, https://doi.org/10.1038/ncomms8507
  3. J. Duan, R. Chen, J. Li, K. Jin, Z. Sun, J. Chen, 'Launching Phonon Polaritons by Natural Boron Nitride Wrinkles with Modifiable Dispersion by Dielectric Environments', Advanced Materials 29, 1702494 (2017). DOI: 10.1002/adma.201702494, https://doi.org/10.1002/adma.201702494
  4. P. Li, I. Dolado, F. J. Alfaro-Mozaz, F. Casanova, L. E. Hueso, S. Liu, J. H. Edgar, A. Y. Nikitin, S. Vélez, R. Hillenbrand, 'Infrared hyperbolic metasurface based on nanostructured van der Waals materials', Science 359, 892 (2018). DOI: 10.1126/science.aaq1704, https://doi.org/10.1126/science.aaq1704
  5. S. Dai, W. Fang, N. Rivera, Y. Stehle, B.-Y. Jiang, J. Shen, R. Y. Tay, C. J. Ciccarino, Q. Ma, D. Rodan-Legrain, P. Jarillo-Herrero, E. H. T. Teo, M. M. Fogler, P. Narang, J. Kong, D. N. Basov, 'Phonon Polaritons in Monolayers of Hexagonal Boron Nitride', Advanced Materials 31, 1806603 (2019). DOI: 10.1002/adma.201806603, https://doi.org/10.1002/adma.201806603
  6. J. D. Caldwell, I. Aharonovich, G. Cassabois, J. H. Edgar, B. Gil, D. N. Basov, 'Photonics with hexagonal boron nitride', Nature Reviews Materials 4, 552 (2019). DOI: 10.1038/s41578-019-0124-1, https://doi.org/10.1038/s41578-019-0124-1
  7. K. Chaudhary, M. Tamagnone, X. Yin, C. M. Spägele, S. L. Oscurato, J. Li, C. Persch, R. Li, N. A. Rubin, L. A. Jauregui, K. Watanabe, T. Taniguchi, P. Kim, M. Wuttig, J. H. Edgar, A. Ambrosio, F. Capasso, 'Polariton nanophotonics using phase-change materials', Nature Communications 10, 4487 (2019). DOI: 10.1038/s41467-019-12439-4, https://doi.org/10.1038/s41467-019-12439-4
  8. I. Dolado, F. J. Alfaro-Mozaz, P. Li, E. Nikulina, A. Bylinkin, S. Liu, J. H. Edgar, F. Casanova, L. E. Hueso, P. Alonso-González, S. Vélez, A. Y. Nikitin, R. Hillenbrand, 'Nanoscale Guiding of Infrared Light with Hyperbolic Volume and Surface Polaritons in van der Waals Material Ribbons', Advanced Materials 32, 1906530 (2020). DOI: 10.1002/adma.1906530, https://doi.org/10.1002/adma.1906530
  9. I.-H. Lee, M. He, X. Zhang, Y. Luo, S. Liu, J. H. Edgar, K. Wang, P. Avouris, T. Low, J. D. Caldwell, S.-H. Oh, 'Image polaritons in boron nitride for extreme polariton confinement with low losses', Nature Communications 11, 3649 (2020). DOI: 10.1038/s41467-020-17424-w, https://doi.org/10.1038/s41467-020-17424-w
  10. N. Li, X. Guo, X. Yang, R. Qi, T. Qiao, Y. Li, R. Shi, Y. Li, K. Liu, Z. Xu, L. Liu, F. J. García de Abajo, Q. Dai, E.-G. Wang, P. Gao, 'Direct observation of highly confined phonon polaritons in suspended monolayer hexagonal boron nitride', Nature Materials 20, 43 (2020). DOI: 10.1038/s41563-020-0763-z, https://doi.org/10.1038/s41563-020-0763-z
  11. B. Qiang, G. Yuan, M. Zhao, H. Liu, Q. J. Wang, Q. Wang, 'Far-field controllable excitation of phonon polariton via nanostructure engineering', Optics Express 28, 39156 (2020). DOI: 10.1364/OE.410253, https://doi.org/10.1364/OE.410253
  12. B. Borodin, S. Lepeshov, K. Watanabe, T. Taniguchi, P. Stepanov, 'Launching Focused and Spatially Confined Phonon-Polaritons in Hexagonal Boron Nitride', arXiv:2501.01319 (2025). arXiv ID: 2501.01319, https://arxiv.org/abs/2501.01319
  13. L. Jäckering, A. Moos, L. Conrads, Y. Li, A. Rothstein, D. Malik, K. Watanabe, T. Taniguchi, M. Wuttig, C. Stampfer, T. Taubner, 'Tailoring hBN's Phonon Polaritons with the Plasmonic Phase-Change Material In3SbTe2', arXiv:2504.18418 (2025). arXiv ID: 2504.18418, https://arxiv.org/abs/2504.18418