Fig. 3: Evolution of the PDoS when transitioning through critical-packing topologies.
From: Emergent scattering regimes in disordered metasurfaces near critical packing
All metasurface patterns are generated using a Poisson disc sampling algorithm40 for Si metaatoms with lateral size \({\ell}=100\,{{\rm{nm}}}\) and height of \(145\,{{\rm{nm}}}\). The filling fraction is 0.2. a PDoS maps of even electromagnetic QNMs for increasing overlap rate \(\widetilde{O}\): (i) particulate (\(\widetilde{O}=0\%\)), (ii, iii) critical packing (\(\widetilde{O}=10\%\) and \(27\%\)), and (iv) aggregate (\(\widetilde{O}=49\%\)). The corresponding packing fractions are \(p=0.5\), \(0.2\), \(0.16\) and \(0.1\), respectively. Colour bands above each map represent the averaged QNM excitation coefficients (see “Methods” section), while cyan squares mark the dominant single-metaatom modes—MDz, EDx and EQ. b Representative field maps showing the \(x\)-component of the QNM electric field (see Supplementary Fig. 2.8 for details). The black inset shows the MDz, EDx and EQ QNM fields in the \({xy}\)-plane. c \(\rho -p{{\mathscr{-}}}{\ell}\) phase diagram distinguishing particulate (blue) and aggregate (red) topologies. d Quantitative analysis of the PDoS evolution shown in (a) from fragmented clouds at small \(\widetilde{O}\) values to a unique spanning cloud at \(\Phi \approx 1\). Insets show the largest connected component for each PDoS map.
