Maximal Anderson localization and suppression of surface plasmons in two-dimensional random Au networks (2024)

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  Figure 1

  Transmission electron microscopy image of an exemplary 2D Au network.

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  Figure 2

  (a)Experimental setup. (b)2D slice of the 3D dataset [$\mathrm{\Gamma }(x,y,\omega )$] at $\hslash \omega =0.6\mathrm{eV}$. The color scale corresponds to the spatially resolved loss probability; the gray arrows illustrate propagators of the surface plasmons eventually interfering constructively at random hot spots. (c)Spectrally resolved loss probability at a specific scan positioyn.

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  Figure 3

  (a) As-recorded and absorption-corrected loss probability map at 1.62 eV. (b) EELS spectra from different scanning regions indicated by the solid (overall image) and dashed blue rectangle (upper right corner) in the bottom image of (a). (c) High-angle annular dark-field (HAADF) image of EELS scanning region (a), and corresponding absorption-corrected loss probability maps at different energies (the contours of the metal web are highlighted for better visibility). The intensity scaling of the absorption-corrected loss probability maps is individual to compensate for the effect of decreasing loss probability with increasing energy for better visibility of the hotspots.

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  Figure 4

  (a)Optical transmission of a macroscopic web (mm in size, coverage $\approx 0.4$) compared to the spatially averaged loss probability ${\overline{\mathrm{\Gamma }}}_{\text{n}}^{\text{exp}}\left(\omega \right)$ as well as the simulated loss probability ${\overline{\mathrm{\Gamma }}}^{\text{sim}}\left(\omega \right)={\mathcal{N}}_{\text{res}}\left(\omega \right)\left|\overline{\mathit{P}}\left(\omega \right)\right|$. (b)Azimuthally averaged autocorrelation $R(r,\omega )$ of resonant LSP modes at 0.8eV energy loss. The width of the blue shaded area indicates the FWHM $\xi$ of the central peak (correlation length). (c)Spectral dependence of the inverse participation number $1/p\left(\omega \right)$ and correlation length $1/\xi \left(\omega \right)$. (d)Spectral dependence of the number of resonant eigenmodes, ${\mathcal{N}}_{\text{res}}\left(\omega \right)$, of the simulated system of coupled electric dipoles. The simulated data were averaged over an ensemble of 10 disorder configurations in all cases.

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  Figure 5

  Spatial distribution of the induced dipole moments of selected resonant eigenmodes of the simulated system of coupled dipoles at different energies. The number of dipoles participating to a resonant mode (participation number) decreases with increasing energy, revealing stronger localization with higher energy.

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  Figure 6

  Comparison of the mean dipole moment, in-plane (${\overline{P}}_{\perp }$) and perpendicular to the nano-oblates (${\overline{P}}_z$).

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  Figure 7

  Simulated inverse participation number for different coverages (red and blue curves) and material (orange curve). The green and black graphs correspond to simulations of the quasistatic case (neglecting retardation effects) and loss-free (no dielectric damping) material, both for gold and coverage of 0.4.

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  Figure 8

  Effect of diagonal (NP geometry variation only) and off-diagonal (position randomization only) disorder on the inverse participation ratio. Only randomizing the positions did not yield resonant modes according to the resonance criterion, which is indicated by a dashed line.

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