SUPPLEMENTARY INFORMATION. Plasmonic black gold by adiabatic nanofocusing and absorption of. light in ultra-sharp convex grooves

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1 SUPPLEMENTARY INFORMATION Plasmonic black gold by adiabatic nanofocusing and absorption of light in ultra-sharp convex grooves Thomas Søndergaard 1, Sergey M. Novikov 2, Tobias Holmgaard 1, René L. Eriksen 2, Jonas Beermann 2, Zhanghua Han 2, Kjeld Pedersen 1 and Sergey I. Bozhevolnyi 2* 1 Department of Physics and Nanotechnology, Aalborg University, Skjernvej 4A, DK-9220 Aalborg Øst, Denmark 2 Institute of Technology and Innovation (ITI), University of Southern Denmark, Niels Bohrs Allé 1, DK-5230 Odense M, Denmark * To whom correspondence should be addressed seib@iti.sdu.dk 1

2 Supplementary Figure S1: Limits imposed by the adiabatic condition. a, Simplified schematic of the considered configuration, representing ultra-sharp (δ = 0) convex grooves made of cylindrical segments of radius R without flat tops and rounding (a = r = α = 0). Other parameters are then related as follows: H = (RΛ Λ 2 ) 0.5, assuming that R > Λ/2. b, The wavelength dependence of the curvature radius R min normalized by the wavelength λ corresponding to the adiabatic parameter γ = 1, so that the adiabatic condition for grooves in air can be written as follows: ( ) R Rmin λ /4 π ε'. Gold dielectric constants are taken from ref. 24. Taking into account that Λ λ << R, results in the simplified expression: H (RΛ) 0.5, implying that even very shallow grooves can be employed provided that the array period is sufficiently small. 2

3 Supplementary Figure S2: Electric field magnitude distributions within grooves. Calculated magnitude of the total electric field normalized with the magnitude of the p- polarized (along the y-direction) incident field in the groove geometry (Fig. 1a) with the parameters a = r = 10 nm, H = 500 nm, Λ = 250 nm, α = 0 and δ = 0.3 nm, for the angle of light incidence θ = 0 and the wavelength λ = 682 nm, represented in a, logarithmic scale, and b, linear scale for the close-up of groove bottom, including a cross section of the field magnitude through the center of the groove. c and d are the same as a and b except that the wavelength is 842 nm. 3

4 Supplementary Figure S3: Influence of groove parameters on reflectivity spectra. Calculated reflectivity spectra of the p-polarized (along the y-axis) light a, for different widths δ at the groove bottom of 500-nm-deep grooves, and for different depths H of grooves with different widths δ at the groove bottom: b, δ = 0.3 nm and c, δ = 1 nm in the groove geometry (Fig. 1a) with the parameters a = r = 10 nm, α = 0 and for the angle of light incidence θ = 0. 4

5 Supplementary Figure S4: Influence of the angle of light incidence on the reflectivity spectra. Calculated reflectivity spectra of the p-polarized (along the y-axis) light for different angles of light incidence θ in the groove geometry (Fig. 1a) with the parameters a = r = 10 nm, H = 500 nm, Λ = 250 nm, α = 0 and δ = 0.3 nm. 5

6 Supplementary Figure S5: Visual appearance of grooves arrays with different depths. SEM images of cross sections (top row) and optical microscope images for p-polarized (along the y-axis) and s-polarized (along the x-axis) incident light (middle and bottom rows, respectively) obtained with 250-nm-period arrays of ultra-sharp grooves of different depths H = a, 50, b, 150, c, 250, d, 350 and e, 450 nm, demonstrating the effect of gradual blackening of nanostructured areas of gold via colour modifications highlighting the importance of groove depth on the GSP damping: shallow grooves require considerably sharper grooves (with smaller minimum gap widths δ) to reduce the influence of GSP reflection from the groove bottom (Fig. S3) and exhibit therefore resonance behaviour, colouring the white light reflection. Similar images were also obtained for 350-nm-period groove arrays. 6

7 Supplementary Figure S6: Influence of the groove depth and period on the reflectivity spectra. Normalized (with respect to the reflection by a flat gold surface) reflection spectra obtained with a microscope objective (N.A. = 0.9) for a, c, 250- and b, d, 350-nm-period arrays of ultra-sharp grooves of different widths for a, b, s- and c, d, p-polarization of incident light, exhibiting very similar responses for relatively shallow grooves with the same depth (50, 150, and 250 nm) and demonstrating thereby that the light absorption takes place separately inside individual grooves (as was implicitly assumed in our qualitative considerations). d, reflection spectra obtained for three different objectives with N.A. = 0.4, 0.75, and 0.9 are shown for comparison, demonstrating that, while the reflection at short wavelength is typically larger for larger numerical apertures (i.e., for larger incident angles) as expected (see Supplementary Fig. S4), the influence is not dramatic, most probably due to only a partial filling of the objective aperture with incident light. Similar influence of different objectives used for the reflection characterization was also observed with the 250-nm-period groove array (not shown). 7

8 Supplementary Figure S7: Influence of gold re-deposition during fabrication on the reflectivity spectra. SEM images taken from orthogonal viewing directions for 2D arrays with the periods a, Λ 1 = 250 nm and b, Λ 2 = 350 nm, demonstrating the asymmetry in the fabricated arrays due to the re-deposition issue. c, Normalized (with respect to the reflection by a flat gold surface) reflection spectra obtained with a microscope objective (N.A. = 0.9) for the 2D groove arrays shown in a and b, demonstrating that the suppression of reflection is more efficient for the polarization directions (along the y-axis) being perpendicular to deeper grooves (along the x-axis) that were the last ones to be FIB milled. Note a remarkably low (< 5%) level of normalized reflection obtained with the 250-nm-pariod array for the y-polarized light, indicating the potential of our approach for reaching extremely low reflectivity levels. 8