Fig. 2: Experimental observation of nonlinear scattering.

a–c Excitation intensity-dependent scattering for \(w = 100\,{\mathrm{nm}},170\,{\mathrm{nm}},190\,{\mathrm{nm}}\), observed using a dark-field laser-scanning microscope at λ = 561 nm. In the main frames, red lines and colored dots indicate linear scattering intensity (S_e, extrapolated from low-intensity excitation, see Supplementary Figs. 4 and 5) and measured scattering intensity (whose deviation from S_e is ΔS), respectively. An unexpectedly large nonlinearity is manifested through the significant deviation from linear intensity dependence. The color of the dots represents nonlinear deviation ratio (NDR), i.e., percentage of ΔS/S_e. The insets correspond to PSFs at low and high intensities (lateral distance: 4 μm). d NDR versus different sizes of nanoblocks at a 6 mW μm⁻² excitation intensity. The dotted line marks 100%, which means no nonlinear response. The blue, red, and green rectangles highlight the regions of large NDR. The insets present the corresponding PSF profiles at low excitation (red curves) and high excitation (blue curves) intensities, where the large nonlinearity is again manifested by the large deviation of blue profiles from Gaussian distribution. e The PSF recovery during repetitive switching between low-intensity (1.3 mW μm⁻²) and high-intensity (6 mW μm⁻²) excitations, demonstrating reversible and repeatable nonlinear responses (see Supplementary Fig. 6 for other nanoblocks). f Experimental NDR map of the whole array. The diagonal dashed line marks the nanoblocks for analysis in Fig. 1d and Fig. 2. The horizontal dashed line marks non-diagonal nanoblocks that are compared to simulation in Supplementary Fig. 7.