We study the polarisation and geometry dependence of four-wave mixing (FWM) on nanocross arrays. The arrays are composed of gold meta-atoms fabricated via EBL and lift-off on a glass substrate coated with a 15 nm ITO film. The individual nanocrosses are C4-symmetric, 360 nm by 360 nm, with 80 nm wide arms. The array period is 550 nm.
FWM is generated by two-colour illumination. The two input wavelengths are 1028 nm (wavelength 1) and 1310 nm (wavelength 2), and we look for the degenerate FWM signal at 846 nm (2*frequency 1 - frequency 2). Using all combinations of handedness for circularly polarised inputs, we verify the theoretical selection rules for FWM on systems of this type. They are LLL-L, RRR-R, LRR-L, and RLL-R, where the first letter is the handedness of beam 2, the following two are the handedness of beam 1, and the last letter is the handedness of the output FWM.
We measure several metasurfaces. In each, the two nanocrosses in a unit cell are rotated towards each other by an angle theta, which is varied 0 to 45 degrees in 7.5 degree increments. With co-polarised inputs (LLL and RRR) the FWM signal is the same from all metasurfaces. With cross-polarised inputs (LRR and RLL) it follows cos^2(4*theta). This behaviour, which is predicted theoretically, is due to the nonlinear Pancharatnam-Berry geometric phase of the FWM from the rotated nanocrosses.
We further support our results with numerical simulations, which match the experimental behaviour for all metasurfaces and show the angle-dependent phase of the nonlinear polarisations on the meta-atoms.
We report the generation of spin controlled OAM of light in harmonic generations by using ultrathin photonic metasurfaces. The spin manipulation of OAM mode of harmonic waves is experimentally verified by using second harmonic generation (SHG) from gold meta-atom with three-fold rotational symmetry. By introducing nonlinear phase singularity into the metasurface devices, we successfully generate and measure the topological charges of spin-controlled OAM mode of SHG through an on-chip metasurface interferometer. The nonlinear photonic metasurface proposed in this work not only opens new avenues for manipulating the OAM of nonlinear optical signals, but also benefits the understanding of the nonlinear spin-orbit interaction of light in nanoscale devices.