Superlattice Plasmons in Hierarchical Au Nanoparticle Arrays

Transcription

1 SUPPLEMENTAL INFORMATION Superlattice Plasmons in Hierarchical Au Nanoparticle Arrays Danqing Wang 1, Ankun Yang 2, Alexander J. Hryn 2, George C. Schatz 1,3 and Teri W. Odom 1,2,3 1 Graduate Program in Applied Physics 2 Department of Materials Science and Engineering 3 Department of Chemistry, Northwestern University, Evanston, Illinois, 60208, USA Dispersion Property of Immersion Oil... S2 Parameters that Influence Superlattice Plasmon Properties... S3 Dipolar Distribution of 1D NP Patches... S5 Local Field Enhancement of Superlattice Plasmons... S6 Near-field Distribution of 1D NP Patches... S7 Near-field Distribution of 2D Hierarchical NP Arrays... S9 Linear Optical Property Measurements... S10 S1

2 Dispersion Property of Immersion Oil Compared to simulation, a red-shift of the superlattice plasmon wavelength was observed in experiment, which can be attributed in part to the dispersion of the immersion oil used for indexmatching. Figure S1a depicts the dispersion property of the immersion oil (Cargille Labs) between 400 nm and 1000 nm, showing that the refractive index shifted from (at nm) to (at 900 nm). We included this dispersion property of the background material in simulations of 2D hierarchical NP arrays with NP diameter d = 160 nm, patch side length l = 6 µm and patch periodicity A 0 = 9 µm. The shorter-wavelength superlattice plasmons SL shifted from 944 nm to nm and the longer-wavelength SL shifted from nm to 976 nm (Fig. Figure S1. (a) Dispersion property of immersion oil used in experiments. (b) Shift of transmission spectrum of hierarchical arrays with and without incorporating the dispersion property of the immersion oil in finite-difference time-domain (FDTD) simulations. S1b). S2

3 Parameters that Influence Superlattice Plasmon Properties Based on FDTD simulations, we showed how NP diameter d, patch periodicity A 0 and patch side length l influenced the resonance wavelength and intensity of superlattice plasmons. With increasing d, the NP LSPs red-shifted, so the coupling with the high-order Bragg modes became stronger in the long-wavelength region. Figure S2a depicts the red-shifting of superlattice plasmons and the increased resonance intensity for longer-wavelength modes as d increased from 60 nm to 160 nm. For infinite-like superlattice plasmons, the resonance wavelength shifted from 912 nm to 944 nm. The superlattice plasmon resonance wavelength also varied if we varied patch periodicity A 0 and kept NP periodicity a 0 and patch side length l fixed. For 2D hierarchical NP arrays with a 0 = 600 nm and l = 6 µm, the longer-wavelength modes blue-shifted as A 0 increased from 8.4 µm to 12 µm (Fig. S2b) since the high-order Bragg modes blue-shifted. In contrast, the infinite-like superlattice plasmons maintained the same resonance position, which was determined by NP periodicity a 0. Figure S2c depicts that the lattice plasmon resonances became narrower as the number of NPs within a single patch increased from to The patch side length l determined the number of NPs in a single NPs patch; hence, it influenced the resonance linewidths of singlepatch lattice plasmons. As the resonance envelope of single-patch lattice got narrowed, the resonance intensity of different superlattice plasmons evolved accordingly. For 2D hierarchical NP arrays with increasing l, the infinite-like superlattice plasmon resonances increased in intensity while longer-wavelength resonances decreased in intensity (Fig. S2d). The number of dominant superlattice plasmon modes also evolved from multiple to one. S3

4 Figure S2. The simulated transmission spectra of 2D hierarchical Au NP arrays with NP periodicity a 0 = 600 nm and (a) increasing NP diameter d from 60 nm to 160 nm and constant patch side length l = 6 µm and patch periodicity A 0 = 9 µm (b) increasing patch periodicity A 0 from 8.4 µm to 12 µm and constant patch side length l = 6 µm and NP diameter d = 160 nm (c) single-patch lattice plasmons with increasing NPs within single patch from to and NP diameter d = 160 nm. (d) increasing patch side length l from 3.6 µm to 7.2 µm and constant patch periodicity A 0 = 9 µm and NP diameter d = 160 nm. S4

5 Dipolar Distribution of 1D NP Patches Figure S3 illustrates the electric field and charge distributions of superlattice plasmons in 1D NP arrays. With the incident light polarized along x or y, the electric field and charge distribution were also along x or y, which indicated that the dipolar oscillations of NPs agreed with the polarization condition of incident light. Figure S3. The near-field electric field and charge distributions of superlattice plasmons in NP line arrays within simulation scale of 1.2 µm 9 µm, with A 0 = 9 µm, l = 6 µm and d = 160 nm. (a) Incident light polarized along x. (b) Incident light was polarized along y. In simulations, the amplitude of the incident plane wave was set as 1 V/m. The plotted real part of E x had units of V/m. S5

6 Local Field Enhancement of Superlattice Plasmons We compared the electric field intensity ( E 2 ) at the LSP resonance LSP of single NP, lattice plasmon resonance L of single patch (10 10 NPs), and superlattice plasmon resonances λ 15 SL and 14 λ SL in hierarchical arrays. Compared to LSP, single-patch lattice plasmons L had 10-fold local 15 field peak enhancement, while superlattice plasmons had 15-fold and 40-fold enhancement at λ SL Figure S4. Local field enhancement at (a) LSP in single NP, (b) L in single patch ( NPs), (c) λ SL in hierarchical arrays and (d) λ SL in hierarchical arrays with incident light polarized along x direction. In simulations, the amplitude of incident plane wave was set as 1 V/m. The plotted field intensity E 2 had units of (V/m) 2. and λ 14 SL respectively. S6

7 Near-field Distribution of 1D NP Patches We performed calculations of the electric field distribution at superlattice plasmon resonances λ SL and λ SL in 1D patches at different polarization angles. For the shorter-wavelength λ 15 SL, the in-phase oscillation condition between NPs was kept at all polarization angles in both E x and E y field (Fig. S5). In contrast, the longer-wavelength λ 14 SL showed single-period phase oscillations at non-zero polarization angles in both E x and E y field. Examples at = 30 and 90 in Figs. S7b-c are consistent with 2D patch arrays, where λ 15 SL shared in-phase oscillations, and λ 14 SL showed single-period phase oscillations between NPs (Fig. 4b). For 1D NP patches, there was no difference for λ 15 SL at different for resonance wavelength, intensity, or NP in-phase oscillations. Notably, NPs exhibited dipolar oscillations along x at = 0, and the electric field had a dominant E x component. Therefore, at λ 15 SL, NPs showed dipolar distributions in E x field and quadrupole distributions in E y field, which is in agreement with = 90, where NPs showed dipolar distributions in E y and quadrupole distributions in E x at both λ 15 SL and λ 14 SL. At = 30, NPs had dipolar oscillations along and where the electric field had a larger E x component compared to E y. Thus, NPs showed stronger dipolar distributions in E x at λ 15 SL. In contrast, at λ 14 SL, NPs showed a dipolar distribution in E y since the resonance came from NPs oscillating as dipoles along y. S7

8 Figure S5. Local field enhancement in 1D NP arrays (a) Distribution of E x and E y with 15 polarization angle = 0. (b) Distribution of E x and E y with polarization angle = 90 at λ SL (upper images) and λ 14 SL (lower images). (c) Distribution of E x and E y with polarization angle = 30 at λ SL (upper images) and λ SL (lower images). In simulations, the amplitude of incident plane wave was set as 1 V/m. The plotted E x or E y field had units of V/m. S8

9 Near-field Distribution of 2D Hierarchical NP Arrays Figure S6 depicts near-field electric field distributions of infinite-like superlattice plasmons for 2D hierarchical NP arrays with different patch side length l and patch periodicity A 0. NPs all oscillated in phase with each other at the infinite-like resonances of 20 = 920 nm (a 0 = 600 nm and A 0 = 12 µm), 40 = 920 nm (a 0 = 600 nm and A 0 = 24 µm) and 60 = 916 nm (a 0 = 600 nm and Figure S6. The near-field electric field distributions of infinite-like superlattice plasmons for 2D hierarchical NP arrays with (a) patch side length l = 6 µm and patch periodicity A 0 = 12 µm within plotted scale of 1.2 µm 12 µm (b) patch side length l = 18 µm and patch periodicity A 0 = 24 µm within plotted scale of 1.2 µm 24 µm (c) patch side length l = 18 µm and patch periodicity A 0 = 36 µm within plotted scale of 1.2 µm 36 µm. In simulations, the amplitude of the incident plane wave (polarized along x) was set as 1 V/m. The plotted real part of E x had units of V/m. A 0 = 36 µm). S9

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11 Linear Optical Property Measurements Figure S7 shows the scheme used to measure the linear optical properties of hierarchical arrays. The samples were illuminated by collimated white light from a halogen lamp (100 W) with spot size around 2 mm. A linear polarizer was used for the measurements of 1D NP patches with various incident light polarization angle. The transmitted light was collected by a CCD detector placed at the backside of the sample stage and was processed by a Princeton Instruments Figure S7. The scheme of spectrometer used for linear optical property measurements. Acton SP2500 spectrometer. S11