van der Waals heterostructures assembled from atomically thin crystalline layers of diverse two-dimensional solids are emerging as a new paradigm in the physics of materials. We use infrared (IR) nano-imaging to study the properties of surface phonon polaritons in a representative van der Waals crystal, hexagonal boron nitride (hBN). We launched, detected and imaged the polaritonic waves in real space and altered their wavelength by varying the number of crystal layers in our specimens. The measured dispersion of polaritonic waves was shown to be governed by the crystal thickness according to a scaling law that persists down to a few atomic layers. Our results are likely to hold true in other polar van der Waals crystals and may lead to their new functionalities.Main Text: Layered van der Waals (vdW) crystals consist of individual atomic planes weakly coupled by vdW interaction, similar to graphene monolayers in bulk graphite (1-3). These materials can harbor superconductivity (2) and ferromagnetism (4) with high transition temperatures, emit light (5-6) and exhibit topologically protected surface states (7), among many other effects (8). An ambitious practical goal (9) is to exploit atomic planes of van der Waals

Conventional optical components are limited to size scales much larger than the wavelength of light, as changes to the amplitude, phase and polarization of the electromagnetic fields are accrued gradually along an optical path. However, advances in nanophotonics have produced ultrathin, so-called 'flat' optical components that beget abrupt changes in these properties over distances significantly shorter than the free-space wavelength. Although high optical losses still plague many approaches, phonon polariton (PhP) materials have demonstrated long lifetimes for sub-diffractional modes in comparison to plasmon-polariton-based nanophotonics. We experimentally observe a threefold improvement in polariton lifetime through isotopic enrichment of hexagonal boron nitride (hBN). Commensurate increases in the polariton propagation length are demonstrated via direct imaging of polaritonic standing waves by means of infrared nano-optics. Our results provide the foundation for a materials-growth-directed approach aimed at realizing the loss control necessary for the development of PhP-based nanophotonic devices.

Uniaxial materials whose axial and tangential permittivities have opposite signs are referred to as indefinite or hyperbolic media. In such materials, light propagation is unusual leading to novel and often non-intuitive optical phenomena. Here we report infrared nano-imaging experiments demonstrating that crystals of hexagonal boron nitride, a natural mid-infrared hyperbolic material, can act as a ‘hyper-focusing lens' and as a multi-mode waveguide. The lensing is manifested by subdiffractional focusing of phonon–polaritons launched by metallic disks underneath the hexagonal boron nitride crystal. The waveguiding is revealed through the modal analysis of the periodic patterns observed around such launchers and near the sample edges. Our work opens new opportunities for anisotropic layered insulators in infrared nanophotonics complementing and potentially surpassing concurrent artificial hyperbolic materials with lower losses and higher optical localization.

Hexagonal boron nitride (h-BN) is a natural hyperbolic material, in which the dielectric constants are the same in the basal plane (ε(t) ≡ ε(x) = ε(y)) but have opposite signs (ε(t)ε(z) < 0) in the normal plane (ε(z)). Owing to this property, finite-thickness slabs of h-BN act as multimode waveguides for the propagation of hyperbolic phonon polaritons--collective modes that originate from the coupling between photons and electric dipoles in phonons. However, control of these hyperbolic phonon polaritons modes has remained challenging, mostly because their electrodynamic properties are dictated by the crystal lattice of h-BN. Here we show, by direct nano-infrared imaging, that these hyperbolic polaritons can be effectively modulated in a van der Waals heterostructure composed of monolayer graphene on h-BN. Tunability originates from the hybridization of surface plasmon polaritons in graphene with hyperbolic phonon polaritons in h-BN, so that the eigenmodes of the graphene/h-BN heterostructure are hyperbolic plasmon-phonon polaritons. The hyperbolic plasmon-phonon polaritons in graphene/h-BN suffer little from ohmic losses, making their propagation length 1.5-2.0 times greater than that of hyperbolic phonon polaritons in h-BN. The hyperbolic plasmon-phonon polaritons possess the combined virtues of surface plasmon polaritons in graphene and hyperbolic phonon polaritons in h-BN. Therefore, graphene/h-BN can be classified as an electromagnetic metamaterial as the resulting properties of these devices are not present in its constituent elements alone.

Graphene1 , a two-dimensional honeycomb lattice of carbon atoms, is of great interest in (opto)electronics 2,3 and plasmonics 4-11 and can be obtained by means of diverse fabrication techniques, among which chemical vapor deposition (CVD) is one of the most promising for technological applications 12 . The electronic and mechanical properties of CVD-grown graphene depend in large part on the characteristics of the grain boundaries [13][14][15][16][17][18][19] . However, the physical properties of these grain boundaries remain challenging to characterize directly and conveniently [15][16][17][18][19][20][21][22][23] . Here, we show that it is possible to visualize and investigate the grain boundaries in CVD-grown graphene using an infrared nano-imaging technique. We harness surface plasmons that are reflected and scattered by the graphene grain boundaries, thus causing plasmon interference. By recording and analyzing the interference patterns, we can map grain boundaries for a large area CVD-grown graphene film and probe the electronic properties of individual grain boundaries. Quantitative analysis reveals that grain boundaries form electronic barriers that obstruct both electrical transport and plasmon propagation. The effective width of these barriers (~10-20 nm) depends on the electronic screening and it is on the order of the Fermi wavelength of graphene. These results uncover a microscopic mechanism that is responsible for the low electron mobility observed in CVD-grown graphene, and suggest the possibility of using electronic barriers to realize tunable plasmon reflectors and phase retarders in future graphene-based plasmonic circuits.Our imaging technique, which we refer to as "scanning plasmon interferometery", is implemented in a setting of an antenna-based infrared (IR) nanoscope [6][7][8] . A schematic diagram of the scanning plasmon interferometry technique is shown in Fig. 1a. Infrared light focused on a metalized tip of an atomic force microscope (AFM) generates a strong localized field around the sharp tip apex, analogous to a "lightning-rod" effect 24 . This concentrated electric field launches circular SPs around the tip (pink circles in Fig. 1a).The process is controlled by two experimental parameters: the wavelength of light  IR and the curvature radius of the tip R. In order to efficiently launch SPs on our highly doped graphene films, we chose IR light with  IR close to 10 m and AFM tips with R ≈ 25 nm (Methods). The experimental observable of the scanning plasmon interferometry is the scattering amplitude s that is collected simultaneously with AFM topography.