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.
Giovanni Sartorello, Guixin Li, Shumei Chen, Luke H. Nicholls, King Fai Li, Thomas Zentgraf, Shuang Zhang, and Anatoly V. Zayats, "Spin and geometric phase control four-wave mixing from metasurfaces (Conference Presentation)," Proc. SPIE 10671, Metamaterials XI, 1067107 (Presented at SPIE Photonics Europe: April 23, 2018; Published: 23 May 2018); https://doi.org/10.1117/12.2306817.5788795294001.
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