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Negative refraction of highly squeezed polaritons is a fundamental building block for nanophotonics, since it can enable many unique applications, such as deep-subwavelength imaging. However, the phenomenon of all-angle negative refraction of highly squeezed polaritons, such as graphene plasmons with their wavelength squeezed by a factor over 100 compared to free-space photons, was reported to work only within a narrow bandwidth (<1 THz). Demonstrating this phenomenon within a broad frequency range remains a challenge that is highly sought after due to its importance for the manipulation of light at the extreme nanoscale. Here we show the broadband all-angle negative refraction of highly squeezed hyperbolic polaritons in 2D materials in the infrared regime, by utilizing the naturally hyperbolic 2D materials or the hyperbolic metasurfaces based on nanostructured 2D materials (e.g., graphene). The working bandwidth can vary from several tens of THz to over a hundred of THz by tuning the chemical potential of 2D materials.

Realizing negative refraction of highly squeezed polaritons, especially that supported by two-dimensional (2D) materials [

Here we predict the phenomenon of broadband all-angle negative refraction of highly squeezed

We note that there are other types of negative refraction studied in the platform of 2D materials, including the negative refraction of electrons [

To highlight the underlying physics, we begin with the dispersion of hyperbolic polaritons supported by a uniaxial metasurface. The metasurface, such as that in the left region of Figure

^{2}V^{−1}s^{−1}, a pitch of

Importantly, for the highly squeezed hybrid polaritons (i.e.,

Figure ^{2}V^{−1}s^{−1} [_{2}) and air, respectively.

For the emergence of refraction phenomenon, the graphene metasurface in the right region in Figure ^{0} shown in Figure

Figure

Figure

Figure

To numerically validate the all-angle negative refraction of hyperbolic polaritons in a broad bandwidth, Figure

To further extend the bandwidth of all-angle negative refraction of highly squeezed polaritons, one may adopt the naturally anisotropic 2D materials to support tunable hyperbolic polaritons, such as those described in [

As a concrete example, Figure

In conclusion, we have revealed a viable way to realize the all-angle negative refraction of highly squeezed polariton in a broadband infrared regime, by utilizing hyperbolic metasurfaces based on 2D materials or naturally anisotropic 2D materials. Due to the combined advantages of highly directional propagation, active tunability, low loss, and ultrahigh confinement provided by hyperbolic polaritons in 2D materials, the broad class of 2D materials can provide a versatile platform for the manipulation of light-matter interaction at the extreme nanoscale and for the design of highly compact nanodevices and circuits.

The finite element simulation is implemented via the frequency domain simulation in the commercial software of COMSOL Multiphysics. To enable the high calculation accuracy, the 2D material is modeled as a surface, where an anisotropic surface conductivity is used to fulfill the conditions for discontinuities in the electromagnetic fields. The meshing resolution in the plane of 2D material is 5 nm. For Figures

All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors.

The authors declare that they have no conflicts of interest.

Xiao Lin conceived the research. Jing Jiang performed the main calculation. Xiao Lin and Baile Zhang contributed insight and discussion on the results. Jing Jiang, Xiao Lin, and Baile Zhang wrote the paper. Xiao Lin and Baile Zhang supervised the project. Jing Jiang and Xiao Lin contributed equally to this work.

The authors thank Y. Yang, I. Kaminer and M. Soljačić for useful discussions. This work was sponsored by the Singapore Ministry of Education (Grant nos. MOE2015-T2-1-070, MOE2016-T3-1-006, and Tier 1 RG174/16 (S)).

Section S1: Dispersion of hybrid polaritons supported by anisotropic metasurfaces. Section S2: All-angle negative refraction of hyperbolic graphene plasmons. Section S3: Loss influence on the bandwidth having

^{3}nanoribbons: Width-independent band gap and strain-tunable electronic properties