Fig. 2: FWM dependence on the AuNP aspect ratio and orientation.

High-magnification TEM images of selected nanoparticles (numbered as in Fig. 1c) were fitted with an elliptical shape (shown in yellow). AuNP 15 is not captured by the TEM overview in Fig. 1c and is shown in SI Fig. S2 and Fig. S7. The corresponding major and minor axis and the orientation angle γ were obtained (see also sketch). The ratio of the cross- to co-circularly polarised FWM components in amplitude (\(A_{{{{\mathrm{FWM}}}}}^ - /A_{{{{\mathrm{FWM}}}}}^ +\)) and phase \(\left( {{{{\mathrm{{\Phi}}}}}_{{{{\mathrm{FWM}}}}}^ - - {{{\mathrm{{\Phi}}}}}_{{{{\mathrm{FWM}}}}}^ + } \right)\) is shown versus the in-plane elliptical aspect ratio and orientation angle. Vertical error bars represent the single-pixel shot noise in the FWM measurements. Single-sided horizontal bars were obtained by fitting the TEM images with a variable contrast threshold (see text). For \(A_{{{{\mathrm{FWM}}}}}^ - /A_{{{{\mathrm{FWM}}}}}^ +\), red (blue) lines are calculated dependences assuming a prolate (oblate) ellipsoid with axis a > b = c (a < b = c) aligned along the x, y, z directions respectively. Dotted lines assume that the NP a and c axis are tilted by 45 degrees in the x, z plane, having a projected axis in the x direction as derived in Section S3.i