Optical second harmonic generation (SHG) from nanostructured graphene has been studied in the framework of classical electromagnetism using a surface integral equation method. Single disks and dimers are considered, demonstrating that the nonlinear conversion is enhanced when a localized surface plasmon resonance is excited at either the fundamental or second harmonic frequency. The proposed approach, beyond the electric dipole approximation used in the quantum description, reveals that SHG from graphene nanostructures with centrosymmetric shapes is possible when retardation effects and the excitation of high plasmonic modes at the second harmonic frequency are taken into account. Several SHG effects similar to those arising in metallic nanostructures, such as the silencing of the nonlinear emission and the design of double resonant nanostructures, are also reported. Finally, it is shown that the SHG from graphene disk dimers is very sensitive to a relative vertical displacement of the disks, opening new possibilities for the design of nonlinear plasmonic nanorulers.
Insertion of 2D materials in optical systems modifies their electrodynamical response. In particular, the Brewster angle undergoes an up-shift if a substrate is covered with a conducting 2D material. This work theoretically and experimentally investigates this effect related to the 2D induced current at the interface. The shift is predicted for all conducting 2D materials and tunability with respect to the Fermi level of graphene is evidenced. Analytical approximations for high and low 2D conductivities are proposed and avoid cumbersome numerical analysis of experimental data. Experimental demonstration using spectroscopic ellipsometry has been performed in UV to NIR range on mono-, bi-and trilayer graphene samples. The non-contact measurement of this modified Brewster angle allows to deduce the optical conductivity of 2D materials. Applications to telecommunication technologies can be considered thanks to the tunability of the shift at 1.55 µm.
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