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Natural hyperbolic materials with dielectric permittivities of opposite signs along different principal axes can confine long-wavelength electromagnetic waves down to the nanoscale, well below the diffraction limit. Confined electromagnetic waves coupled to phonons in hyperbolic dielectrics including hexagonal boron nitride (hBN) and α-MoO3 are referred to as hyperbolic phonon polaritons (HPPs). HPP dissipation at ambient conditions is substantial, and its fundamental limits remain unexplored. Here, we exploit cryogenic nanoinfrared imaging to investigate propagating HPPs in isotopically pure hBN and naturally abundant α-MoO3 crystals. Close to liquid-nitrogen temperatures, losses for HPPs in isotopic hBN drop significantly, resulting in propagation lengths in excess of 8 μm, with lifetimes exceeding 5 ps, thereby surpassing prior reports on such highly confined polaritonic modes. Our nanoscale, temperature-dependent imaging reveals the relevance of acoustic phonons in HPP damping and will be instrumental in mitigating such losses for miniaturized mid-infrared technologies operating at liquid-nitrogen temperatures., Research at Columbia is supported by Vannevar Bush Faculty Fellowship ONR-VB: N00014-19-1-2630. We thank A. Sternbach and S. Zhang for helpful discussions. Exfoliation and transfer of hBN onto desired substrates and electron beam lithography of gold disks were performed by J.T.M. and supported by the National Science Foundation (DMR1904793). Additional structure fabrication was supported by the Center on Precision-Assembled Quantum Materials, funded through the U.S. National Science Foundation (NSF) Materials Research Science and Engineering Centers (award no. DMR-2011738). Initial simulations and experimental design from Vanderbilt were provided by J.D.C. in collaboration with the Columbia team (D.N.B. and G.N.) and was supported by the Office of Naval Research (N00014-18-1-2107). The hBN phonon band structure calculation was performed by R.C. and L.A. and supported by the Spanish MINECO/FEDER grant (MAT2015-71035- R). Cryogenics nano-optics experiments at Columbia were solely supported as part of Programmable Quantum Materials, an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award no. DE-SC0019443. D.N.B is the Gordon and Betty Moore Foundation’s EPiQS Initiative Investigator no. 9455.

Semiclassical quantization rules and numerical calculations are applied to study polariton modes of materials whose permittivity tensor has principal values of opposite sign (so-called hyperbolic materials). The spectra of volume- and surface-confined polaritons are computed for spheroidal nanogranules of hexagonal boron nitride, a natural hyperbolic crystal. The field distribution created by polaritons excited by an external dipole source is predicted to exhibit ray-like patterns due to classical periodic orbits. Near-field infrared imaging and Purcell-factor measurements are suggested to test these predictions., Comment: Changes made to improve presentation and update references. Main text: 6 pages, 6 figures. Supplementary: 12 pages, 6 figures