Tuneable strong optical absorption in a graphene-insulator-metal hybrid plasmonic device

An optical device configuration allowing efficient electrical tuning of near total optical absorption in monolayer graphene is reported. This is achieved by combining a two-dimensional gold coated diffraction grating with a transparent spacer and a suspended graphene layer to form a doubly resonant plasmonic structure. Electrical tuneability is achieved with the inclusion of an ionic gel layer which plays the role of the gate dielectric. The underlying grating comprises a 2-dimensional array of inverted pyramids with a triple layer coating consisting of a reflective gold layer and two transparent dielectric spacers, also forming a vertical micro-cavity known as a Salisbury screen. Resonant coupling of plasmons between the gold grating and graphene result in strong enhancement of plasmon excitations in the atomic monolayer. Plasmon excitations can be dynamically switched off by lowering the chemical potential of graphene. Very high absorption values for an atomic monolayer and large tuning range, extremely large electrostatically induced changes in absorption over very small shifts in chemical potential are possible thus allowing for very sharp transitions in the optical behavior of the device. Overall this leads to the possibility of making electrically tunable plasmonic switches and optical memory elements by exploiting slow modes.

, T the temperature, t the hopping parameter (kinetic energy of electrons hopping between atoms), and ω the angular frequency. This formula takes into account the band broadening that occurs in higher energies of the band structure thus extending beyond the Dirac cone approximation. The permittivity of graphene can finally be obtained through the following equation: where 0 5.5    is the background permittivity, [5][6][7][8] and dg the thickness of Graphene.

Ionic gel gate
By using equations = for the carrier density and = ћ √ for the chemical potential (where Vg the gate voltage, C the gate capacitance, and Fermi velocity) the efficiency of the Ionic gel for modulating the Fermi level in Graphene can be estimated and compared to that of conventional dielectrics. Figure s1 compares the modulation efficiency a 20nm thick SiO2 gate dielectric, a 20nm HfO2 gate dielectric, and that of an Ionic gel with a capacitance value of 10.7 μF/cm 2 as obtained from literature 9 (even higher capacitances up to 30 F/cm 2 have been reported on Si wafers with ionic gel gates) 10 . Thin SiO2 dielectrics suffer from high leakage currents thus high K dielectrics like HfO2 are typically used for achieving high capacitance and low voltage operation. The ionic gel is typically functional as a gate capacitance up to 4eV due to the electrochemical window that leads to high leakage currents above a certain threshold. Nevertheless the Ionic gel easily outperforms conventional dielectrics, providing, much higher Fermi level shifts at a very low voltage. This strong modulation efficiency, transparency, and ability to fully modulate isolated or broken Graphene areas over the entire sample area make ionic gel an ideal candidate for a gate material.

Effect of losses on the graphene layer
Intensity of the plasmon absorption peak strongly depends on optical losses in graphene. These losses are mainly characterized by the imaginary part of permittivity, with higher losses corresponding to broader and lower peaks 11 . Graphene demonstrates significant dissipative losses in the Terahertz 12 / and infrared optical frequencies Grap 13 nevertheless recent efforts have demonstrated mobility values in CVD graphene in excess of 350.000 cm 2 V -1 s -1 at low temperatures and above 50.000 cm 2 V -1 s -1 at room temperature 14 . Strong modulation over the carrier concentration of graphene while maintaining high mobility rates is still a very strong challenge for the scientific community. Ionic gel gating is the most effective method for achieving high chemical potentials in the graphene layer but can introduce carrier scattering [15][16][17][18]

Salisbury screen
The Salisbury screen 19 was invented in the 1940s as a selective wavelength anti-reflection radar material. Its original implementation consisted of a metal reflector and a graphite absorber layer separated by a transparent dielectric spacer. Similar to a quarter-wave antireflective coating, reflections at the material interfaces destructively interfere to give zero reflection at a specific incident wavelength. Nearly total absorption is achieved when waves reflected from the back reflector and the surface of the absorptive layer have equal amplitude and a phase difference of 180. In order to achieve strong destructive interference the transparent spacer separating the back reflector from the top absorptive layer must have a thickness: where ds the thickness of the spacer and ns the value of the spacer refractive index, and m is an integer cavity mode number.
Modifying equation 5s to adjust it for a multilayer setup as for the case of our device gives the following conditions for destructive interference in the vertical cavity: If the surface layer is not perfectly absorptive, photons get reflected back from the surface and so become recycled until they eventually get absorbed 20 .

Contribution of the Salisbury screen to the absorption spectra
It can be seen from figure s3 that the absorption due to the Salisbury screen (peak marked by an S and a white dotted) is spectrally wide and quite low in terms of intensity when compared to the gold and graphene plasmon peaks. The absorption from the Salisbury screen is low because of the it can be seen that the Salisbury screen does not actually result in increased absorption in the graphene or gold layers, instead it is an isolated effect that increases the absorption additively but independently from the other absorption features that appear in the spectrum. This is easy to see as the absorption is increased for the overall spectral region and the peaks originating from other physical mechanisms are simply shifted upwards but are not increased in intensity. Only when the graphene plasmon excitation has at least some overlap with the gold plasmon peak, enhanced absorption in the monolayer can be observed.