Figure 4

Calculated full band diagram and density of optical states of the nanostructure covered with air and water. (a) Band diagram of the nanostructure of Fig. 1a when the structure is covered with air. The blue curve shows the light line of air. The 2D Brillouin zone used in the calculation of the band diagram is shown in the inset. (b) Same as (a) except that the SLG is covered with water. The blue curve shows the light line of water. Placing water on the SLG pushes the light-line to lower frequencies, freeing up more radiative optical states at 581 nm (516 THz) and 620 nm (484 THz) for G and 2D Raman emission wavelengths of the SLG (shown with dotted lines). (c) Calculated averaged LDOS enhancement with respect to the DOS of a dipole emitter in free space when air (black) and water droplets (red) are placed on top of the graphene on the nanohole array. Average LDOS enhancement for a glass substrate is also shown (blue). The average was taken over the surface of the graphene in one unit cell of the nanohole array and also over all polarizations of the dipole emitter (See Supplementary Information). Placing water droplets on the SLG increases the LDOS at the Raman emission frequencies of the SLG. Inset shows the average enhancement in spontaneous emission rate. At the G and 2D Raman emission peaks of the SLG the averaged LDOS on the surface of the nanostructure covered with air and water, is increased ~2 and ~3 times, respectively, compared to the averaged LDOS on the surface of a glass substrate. Band diagram and density of states calculations are performed using 3D FDTD.