Fig. 1. Mechanism of a graphene-based tuneable focal length.

a Illustration of applying the ETF-USSL in a display. The USSL enables multifocusing, allowing implementation of glassless 3D and multiview displays, and the ETF characteristics enable a variable viewing angle. b Illustration of focusing through the graphene arc ribbon pattern. Graphene’s conical band structure and photon absorption transition with a shift of the Fermi level (E_F) from the Dirac point due to a DC voltage bias: c the optical absorption of graphene increases owing to the occurrence of interband transitions, resulting from the excitation of electrons by optical photons (ħω₂), where the Fermi level is close to the Dirac point, resulting in decreased transmittance. d The Fermi level drops to below the transition threshold; because there are no electrons available for transition, the transmittance of the graphene increases. e The Fermi level rises above the transition threshold; the absorption is reduced by Pauli blocking of the interband transition, and the transmittance of the graphene increases. f Schematic of the tuneable focal length when a DC voltage bias is applied to graphene in the in-plane direction. In the ribbon made of graphene, the centre area (C) absorbs the light, and the carrier are concentrated in the left side (L) and right side (R) due to the DC bias; thus, the Fermi level is far from the Dirac point, and light is not absorbed and transmitted. Consequently, the change in the nanoribbon width via an external electric field effectively modulates the FZP topology, thereby changing the focal length of the lens