Symmetry Breaking in Oligomer Surface Plasmon Lattice Resonances

Transcription

1 Supporting Information Symmetry Breaking in Oligomer Surface Plasmon Lattice Resonances Marco Esposito 1, Francesco Todisco 2, Said Bakhti 3, Adriana Passaseo* 1, Iolena Tarantini 4, Massimo Cuscunà 1, Nathalie Destouches 3 and Vittorianna Tasco* 1 1 CNR NANOTEC-Nanotechnology Institute, Campus Ecotekne, via Monteroni, IT Lecce, Italy 2 Center for Nano Optics, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark 3 Univ. Lyon, UJM Saint Etienne, CNRS, Institut d'optique Graduate School, Laboratoire Hubert Curien UMR 5516, F 42023, SAINT-ETIENNE, France 4 University of Salento, Department of Mathematics and Physics Ennio De Giorgi, Via Arnesano, Lecce Italy * corresponding authors

2 Supporting Figure 1 Figure S1 Extinction cross section of a) single nanodisk and b) dimer calculated by commercial software. The extinction cross section for a single Al nanodisk with diameter D=100nm is shown in a). It exhibits a LSPR peaked at 550nm. The extinction cross section for a single dimer of nanodisks with the same diameter and spacing of 20 nm is displayed in b), as calculated for incident polarization along the dimer axis. In this case the resonance is redshifted and broadened, with a main peak at 700nm. The oligomer cross section shown in figure 1 b in the main text can be approximated to a combination of these two resonances.

3 Supporting Figure 2 Figure S2 2D colour palette driven by size and periodicity. a) FDTD simulations of normal incidence X- polarized transmission spectra from the tetramer array as a function of single disk diameter (D); lattice periodicities have been kept at the design values of Px=450nm and Py=340nm. b) Corresponding calculated CIE colour chart displaying the colours achievable by the diameter modulation considered in a). c) Calculated transmission spectra from the tetramer array as a function of lattice periodicity (Px); the single disk diameter has been kept at the design value of 100nm. d) Calculated CIE colour chart displaying the colours achievable by the periodicity modulation considered in c). Thick green lines in a) and c) refer to the resonant (zero detuning) condition between LSPR and DO. In c) and d) the arrow indicates increase of D and Px, respectively. At a first level, in the proposed system, the resonant overlap between the LSPR and the DO modes can be obtained varying D, thus enabling a tuning of the perceived colour at normal incidence X-polarized transmission, as calculated in Figure S2a. Here, a clear asymmetric peak-valley lineshape arises, whose central wavelength, efficiency (in terms of lowest transmission level), spectral linewidth and magnitude of peak/valley ratio, strongly depend on this design parameter. In particular, the best balance of transmitted colour full width at half maximum and contrast (in terms of peak-valley transmission ratio) is achieved when the two modes resonantly overlap (thick green curve in Figure S3a). The related colour gamut, shown in the CIE color chart (Figure S2b), spans from pastel to vibrant colours as the spectral overlap between the LSPR and DO modes is maximized by the geometrical variation of D. Similar results can be achieved by keeping D constant and changing P x (figures S2c).

4 Supporting Figure 3 Figure S3 Calculated transmission maps (for X-polarization) of arrayed oligomers as a function of diameter, while keeping Px=450nm and Py=340nm (A), and as a function of Px while keeping D=100nm and Py=340nm(B). Figure S3A reports calculated transmission maps of the arrayed oligomers for a wide set of diameter sizes from 80 nm to 150 nm. Figure S3B shows calculated transmission maps as a function of P x parameter, ranging from 240 nm to 440 nm. Both maps have been calculated considering X-polarized incident condition.

5 Supporting Figure 4 Figure S4 Nanopixel engineering(left side) by analysis of the DO wavelength position as shown in the simulated colour maps (right side). The in-plane diffraction orders orientation is shown with respect to the oligomer lattice. The nanopixel has a rectangular layout with periodicity P x and P y. We used equation (1) in the main text to engineer the fabricated lattice periodicities in order to set the dispersions of some diffractive orders for normal incidence condition(i.e., k x =k y =0) in the visible spectral range The directions of the considered diffractive orders coincide with the main reference axes of the lattice: the (±1,0)DOs are aligned along the X- axis; the (0,±1)DOs are aligned along the Y-axis; the (±1,±1) DOs are aligned along the nanopixel rectangle diagonals. In particular, by setting P x =450nm and P y =340nm and considering the array embedded within an homogeneous medium with n=1.515(refractive index matching oil): - the (0,±1) DO was set at a wavelength of 515nm(Green Transmission Window-GTW); - the (±1,0) DO was set at a wavelength of 680nm(Red Transmission Window-RTW); - the (±1,±1) DO was set at a wavelength of 415 nm(blue Transmission Window-BTW).

6 Supporting Figure 5 a b Figure S5 Measured transmission maps of fabricated array samples as a function of displacement parameter (S, from 0 to 140 nm)) and for the two incident polarizations (a, X-polarization, and b, Y-polarization). Data from figure 2 are displayed in figure S5 as transmission maps to better visualize the formation of upper and lower SLPR branches (SLPR-1 and SLPR-2), positioned around the GTW. For X-polarization, the decrease of energy gap between these two modes by increasing the satellite displacement S is also evident from the map (a).

7 Supporting Figure 6 Figure S6 Measured (a) and numerically simulated (b) transmitted spectra of the array as a function of S for X-polarization. Measured (c) and numerically simulated (d) transmitted spectra of the array as a function of S for Y-polarization.

8 Supporting Figure 7 Figure S7 Far field (left) simulations of scattering intensity distribution when the cluster is excited at the BTW (Y-polarization), as a function of S; near field behaviour (right) of the structure at three significant S values (0, 70nm, 140nm) and correspondingly calculated polar plot.

9 Supporting Figure 8 Figure S8 Electric field distribution maps calculated at excitation wavelengths corresponding to different lattice regimes: at the DO wavelengths(gtw, RTW and BTW), and at SLPR-1 position. The maps are displayed for the three most representative displacement positions.

10 Figure S8 shows the calculated electric field distribution in the oligomer plane, for different lattice regimes and at three representative displacement positions, i.e., S=0, S=70nm and S=140nm. X-polarization GTW: at S=0 the maximum magnitude is located in the space between oligomers and a standing wave pattern is generated by two counter-propagating lattice modes. The S increment induces a spatial detuning between the LSPR and (0,+1) DO. This results in a localized electric field mainly at the nanodisk edges due to the plasmonic character of the mode. By further increasing S, the plasmonic component is reduced and the standing wave pattern is shifted because of the change of the unit cell. SLPR-1: at S=0, where a weak dip is observed in transmission spectrum (figure 2b in the main text), the electric field distribution has a well-balanced photonic/plasmonic character. By increasing S, the plasmonic localization becomes more prominent because of the formation of the broad transmission valley (figure 2b in the main text), where also SLPR-2 converges. Upon further S increase, up to 140 nm, the oligomer scattering and, consequently, the field distribution align to the (-1,+1) DO direction, following the trend evidenced by single structure scattering (figure 3d in the main text). BTW: for S=0, a standing wave pattern distribution is evident for the electric field associated to the weakly excited DO, with a lower intensity as compared to (0,±1) DO excitation (the corresponding peak in transmission is accordingly less pronounced). By increasing S, the delocalized field pattern rotates and at S=140nm it aligns to the (+1,+1) DO direction. Y-polarization RTW: the electric field distribution is only photonic, independently on S. The standing wave pattern is oriented along the Y-axis for S=0, then rotates following the oligomer axis rotation and, at the maximum displacement, it aligns to (1,1)DO direction.

11 Supporting Figure 9 Figure S9 Measured Fourier images of the arrays as a function of displacement S and at excitation wavelength of SLPR-1 for X-polarization(top panel) and of RTW for Y-polarization(bottom panel). In the Fourier space, the SLPR-1(under X-polarization) is initially well coupled with the (0, ±1) DO (for S=0), in agreement with the relative minimum detected in transmission measurements (upper branch in figure 2b). In the intermediate position (S=70nm) this hybrid mode has a weaker dispersion around the diffractive mode, while for the final position, a new coupling with (0, ±1) and (±1, ±1) DOs occurs, induced by the plasmon scattering rotation. Excitation at RTW, with Y-polarization, leads to a Fourier image not dependent on S parameter, and thus on structure symmetry changes. The images can be always fitted with (±1,0) DO and, as S increases also with (±1,±1)DO.