Graphene plasmons were predicted to possess ultra-strong field confinement and very low damping at the same time, enabling new classes of devices for deep subwavelength metamaterials, single-photon nonlinearities, extraordinarily strong light-matter interactions and nano-optoelectronic switches. While all of these great prospects require low damping, thus far strong plasmon damping was observed, with both impurity scattering and many-body effects in graphene proposed as possible explanations. With the advent of van der Waals heterostructures, new methods have been developed to integrate graphene with other atomically flat materials. In this letter we exploit near-field microscopy to image propagating plasmons in high quality graphene encapsulated between two films of hexagonal boron nitride (h-BN). We determine dispersion and particularly plasmon damping in real space. We find unprecedented low plasmon damping combined with strong field confinement, and identify the main damping channels as intrinsic thermal phonons in the graphene and dielectric losses in the h-BN. The observation and in-depth understanding of low plasmon damping is the key for the development of graphene nano-photonic and nano-optoelectronic devices.

Highly confined low-loss plasmons in graphene-boron nitride heterostructures

Plasmon polaritons are hybrid excitations of light and mobile electrons that can confine the energy of long-wavelength radiation at the nanoscale. Plasmon polaritons may enable many enigmatic quantum effects, including lasing1, topological protection2,3 and dipole-forbidden absorption4. A necessary condition for realizing such phenomena is a long plasmonic lifetime, which is notoriously difficult to achieve for highly confined modes5. Plasmon polaritons in graphene—hybrids of Dirac quasiparticles and infrared photons—provide a platform for exploring light–matter interaction at the nanoscale6,7. However, plasmonic dissipation in graphene is substantial8 and its fundamental limits remain undetermined. Here we use nanometre-scale infrared imaging to investigate propagating plasmon polaritons in high-mobility encapsulated graphene at cryogenic temperatures. In this regime, the propagation of plasmon polaritons is primarily restricted by the dielectric losses of the encapsulated layers, with a minor contribution from electron–phonon interactions. At liquid-nitrogen temperatures, the intrinsic plasmonic propagation length can exceed 10 micrometres, or 50 plasmonic wavelengths, thus setting a record for highly confined and tunable polariton modes. Our nanoscale imaging results reveal the physics of plasmonic dissipation and will be instrumental in mitigating such losses in heterostructure engineering applications.The fundamental limits to plasmon damping in graphene are determined using nanoscale infrared imaging at cryogenic temperatures, and plasmon polaritons are observed to propagate over 10 micrometres in high-mobility encapsulated graphene.

Fundamental Limits to graphene plasmonics

Polaritons in anisotropic materials result in exotic optical features, which can provide opportunities to control light at the nanoscale1-10. So far these polaritons have been limited to two classes: bulk polaritons, which propagate inside a material, and surface polaritons, which decay exponentially away from an interface. Here we report a near-field observation of ghost phonon polaritons, which propagate with in-plane hyperbolic dispersion on the surface of a polar uniaxial crystal and, at the same time, exhibit oblique wavefronts in the bulk. Ghost polaritons are an atypical non-uniform surface wave solution of Maxwell's equations, arising at the surface of uniaxial materials in which the optic axis is slanted with respect to the interface. They exhibit an unusual bi-state nature, being both propagating (phase-progressing) and evanescent (decaying) within the crystal bulk, in contrast to conventional surface waves that are purely evanescent away from the interface. Our real-space near-field imaging experiments reveal long-distance (over 20 micrometres), ray-like propagation of deeply subwavelength ghost polaritons across the surface, verifying long-range, directional and diffraction-less polariton propagation. At the same time, we show that control of the out-of-plane angle of the optic axis enables hyperbolic-to-elliptic topological transitions at fixed frequency, providing a route to tailor the band diagram topology of surface polariton waves. Our results demonstrate a polaritonic wave phenomenon with unique opportunities to tailor nanoscale light in natural anisotropic crystals.

Ghost hyperbolic surface polaritons in bulk anisotropic crystals.

Self-assembled multi-layered hexagonal-like MWCNTs/MnF2/CoO nanocomposite with enhanced electromagnetic wave absorption

Second harmonic generation from an antiferromagnetic film in one-dimensional photonic crystals

We present a detailed study on the tunable propagation derived from the coupled surface plasmon–phonon polaritons (SPPPs) with the effective medium theory (EMT) in graphene-hBN metamaterials (MMs). Four reststrahlen bands (RBs) are observed, two of which mainly come from the hBN and the others originate from the effect of the graphene. The RBs frequency windows can be adjusted by the chemical potential and the filling ratio. An epsilon-near-zero-and-pole( e NZP )hyperbolic metamaterial (HMM) is detected at the precise frequency, chemical potential and filling ratio where the HMM undergoes a completely inversion of anisotropy. We derive the relative dispersion relation and demonstrate that the propagation of SPPP modes can be regulated by modifying the chemical potential. In addition, the tunability of the graphene-hBN MMs also can be improved by changing the thicknesses of the hBN and the number of graphene sheets. The energy-flux density in the graphene-hBN MM seriously deviates from its wave vector and can be localized at a certain depth. Besides, the ghost SPPP modes with the oscillation-attenuation character are observed at some special conditions through checking the distribution of electric fields. The attenuation total reflection (ATR) measurement is established to examine these SPPP modes. The numerical results show that the observation of each SPPP modes requires different conditions dictated by material parameters and the polarization direction of the incident light.

Tunable propagation of surface plasmon-phonon polaritons in graphene-hBN metamaterials

Two Dyakonov-like polaritons (DLPs) were found in the hexagonal boron nitride (hBN). DLP-I lies in the lower reststrahlen band (RB-I) where the hBN is a hyperbolic material, but DLP-II exists in a narrower frequency region where the hBN is an elliptical material, adjacent to the higher reststrahlen band (RB-II). After uniformly considering the DLP electromagnetic fields on the two sides of the hBN surface, we found that the two DLPs are highly confined in the hBN, and even are completely confined in a certain wave-vector. And also, the Poynting vector of either DLP in the hBN seriously deviates from its wave vector and the directional difference outside and inside the hBN dramatically changes with the distance from the surface. The above extraordinary results can support some potential applications in the mid-infrared range, such as high-efficient energy conduction, strictly manipulating infrared-ray direction and infrared-filtering as well as continuous light-splittingfrom micro-meter to nano-meter dimensions.

Complete confinement and extraordinary propagation of Dyakonov-like polaritons in hBN

We investigated Goos-Hanchen (GH) and Imbert-Fedorov (IF) shifts on a uniaxial hyperbolic crystal, where a circularly-polarized beam was incident on the crystal from the free space. The GH- and IF-shifts were analytically obtained and numerically calculated for the hexagonal boron nitride. Our results demonstrate that the GH- and IF-shift spectra are complicated and completely different in and out the hyperbolic frequency-bands (the reststrahlen bands in the infrared region). At the critical or Brewster angle, concisely analytical expressions of GH-shift was found, which explicitly state the optical-loss dependence of GH-shift at these special angles. We found the GH-shifts are very large at the critical and Brewster angles. It is very necessary to know these effects since hyperbolic materials are usually applied in the nano- and micro-optics or technology fields.

Goos-Hänchen and Imbert-Fedorov shifts on hyperbolic crystals.

Three Dyakonov-like polaritons (DLPs) exist at the interface between a hyperbolic material (HM) and a covering medium (CM). Each DLP is a hybridized-polarization surface polariton composed of two evanescent waves on both sides of the interface. We investigated their spin and angular momentum. We analytically found that any DLP carries two spins producing mutually orthogonal spin angular-momentum (SAM) components. The spins and angular-momentum have different features on both sides of the interface, and further differences among the three DLPs are very obvious. For the interface structure formed by hexagonal boron nitride (hBN) and air, the SAM mainly distributes in the air for DLP-I, the SAM is approximately transverse to the propagating direction for DLP-II, and it is surprisingly large in the hBN for DLP-III and can reach several ten times that in the usual situation. There is the spin-k locking for every DLP, but the spin-k locking is different for different DLPs. These properties do not exist for traditional surface polaritons or ordinary evanescent waves. The above unique results can support some potential applications in the fields of nano- and micro-photonics, optoelectronics and mechanics, as well as relevant technologies.

Sheng Zhou

Papers

Second harmonic generation from an antiferromagnetic film in one-dimensional photonic crystals

Tunable propagation of surface plasmon-phonon polaritons in graphene-hBN metamaterials

Complete confinement and extraordinary propagation of Dyakonov-like polaritons in hBN

Goos-Hänchen and Imbert-Fedorov shifts on hyperbolic crystals.

Unusual spin and angular momentum of Dyakonov waves at the hyperbolic-material surface