Hyperbolic Plasmons and Topological Transitions Over Uniaxial Metasurfaces

We explore the unusual electromagnetic response of ultrathin anisotropic $\sigma$-near-zero uniaxial metasurfaces, demonstrating extreme topological transitions—from closed elliptical to open hyperbolic—for surface plasmon propagation, associated with a dramatic tailoring of the local density of states. The proposed metasurfaces may be implemented using nanostructured graphene monolayers and open unprecedented venues for extreme light confinement and unusual propagation and guidance, combined with large tunability via electric bias.

Figure 1

SPP excitation along homogeneous uniaxial metasurfaces by a $z$-oriented dipole emitter (represented by a black arrow) located at a distance $d=10\mathrm{nm}$ above the surface. The 2D plots show the $E_z$ field component of propagating SPPs. The insets present the corresponding isofrequency contour. (a) Isotropic metasurface ${\sigma }_{\mathrm{xx}}={\sigma }_{\mathrm{yy}}=0.08+i0.1\mathrm{mS}$. (b) Extremely anisotropic $\sigma$-near-zero metasurface, ${\sigma }_{\mathrm{xx}}=0.08+i10\mathrm{mS}$, ${\sigma }_{\mathrm{yy}}=0.08-i0.1\mathrm{mS}$. (c) Hyperbolic metasurface, ${\sigma }_{\mathrm{xx}}=0.08-i0.1\mathrm{mS}$, ${\sigma }_{\mathrm{yy}}=0.08+i0.1\mathrm{mS}$. (d) Hyperbolic metasurface, ${\sigma }_{\mathrm{xx}}=0.08+i0.1\mathrm{mS}$, ${\sigma }_{\mathrm{yy}}=0.08-i0.1\mathrm{mS}$. Operation frequency is 10 THz.

Figure 2

Practical implementation of different metasurface topologies using an array of graphene strips. (a) Effective conductivity tensor of the uniaxial metasurface versus the strips width ($W$) for a fixed period $L=50\mathrm{nm}$. Graphene chemical potential is ${\mu }_c=0.4\mathrm{eV}$. The inset shows a schematic of the proposed hyperbolic metasurface. Results have been computed with Eq. (4) (solid line) and are validated using a mode-matching approach (markers) [40]. (b) Field confinement of surface plasmons supported by the metasurface versus their angle of propagation with respect to the $x$ axis. (c)–(e) Average power flow of SPPs excited on the structure (periodicity $L=50\mathrm{nm}$) by a $z$-oriented dipole located at 50 nm above the structure. The emitter is placed at the center bottom of the panels. (c) $W=10\mathrm{nm}$ and graphene chemical potential ${\mu }_c=0.5\mathrm{eV}$. (d)–(e) $W=25\mathrm{nm}$ and graphene chemical potential is set to (d) ${\mu }_c=0.1\mathrm{eV}$ and (e) ${\mu }_c=0.3\mathrm{eV}$. Operation frequency is 10 THz.

Figure 3

Topological transitions in metasurfaces. (a) SER in logarithm scale of a $z$-oriented dipole located at $d=5\mathrm{nm}$ above a lossless uniaxial metasurface. The conductivity components of the structure are simultaneously varied in order to fully explore the SER in all topologies, including elliptic (first and third quadrants) and hyperbolic (second and forth quadrants) cases. The inset details the transition among all topologies. (b) Lossless elliptic isofrequency contours, ranging from the isotropic case ($\mathrm{Im}[{\sigma }_{\mathrm{xx}}]=\mathrm{Im}[{\sigma }_{\mathrm{yy}}]=2.5\mathrm{mS}$, black solid line) to the extremely anisotropic $\sigma$-near-zero case ($\mathrm{Im}[{\sigma }_{\mathrm{xx}}]=2.5$, $\mathrm{Im}[{\sigma }_{\mathrm{yy}}]=0.005\mathrm{mS}$, red solid line). (c) Lossless hyperbolic isofrequency contours, ranging from the isotropic case ($\mathrm{Im}[{\sigma }_{\mathrm{xx}}]=-2.5$, $\mathrm{Im}[{\sigma }_{\mathrm{yy}}]=2.5\mathrm{mS}$, black solid line) to the extremely anisotropic $\sigma$-near-zero case ($\mathrm{Im}[{\sigma }_{\mathrm{xx}}]=-2.5$, $\mathrm{Im}[{\sigma }_{\mathrm{yy}}]=0.1\mathrm{mS}$, red solid line). Operation frequency is 10 THz.

Figure 4

SER of a $z$-oriented dipole located above a lossless uniaxial metasurface. The 2D plot shows the Purcell enhancement in logarithmic scale versus (i) the distance of the dipole from the metasurface, and (ii) different ${\sigma }_{\mathrm{yy}}$ values, considering a fix ${\sigma }_{\mathrm{xx}}=i0.2\mathrm{mS}$ conductivity component. Operation frequency is 10 THz.