Magnetic and Electric Hotspots with Silicon Nanodimers

Transcription

1 Magnetic and Electric Hotspots with Silicon Nanodimers Reuben M. Bakker 1*, Dmitry Permyakov 2, Ye Feng Yu 1, Dmitry Markovich 2, Ramón Paniagua- Domínguez 1, Leonard Gonzaga 1, Anton Samusev 2, Yuri Kivshar 2,3, Boris Luk yanchuk 1, Arseniy I. Kuznetsov 1 1 Data Storage Institute, A*STAR, 5 Engineering Drive 1, , Singapore 2 ITMO University, St. Petersburg, , Russia 3 Nonlinear Physics Centre, Australian National University ACT 0200, Australia * Reuben_Bakker@dsi.a-star.edu.sg Arseniy_K@dsi.a-star.edu.sg 1

2 Supporting Information Six additional figures are provided as supporting information. Figure S1 shows the scattering cross section and multipole decomposition of an equivalent dimer to that of Figure 2 but in air and of a silicon sphere dimer in air. Figure S2 shows the scattering spectrum and mode decomposition for dimers with a gap of 60 nm and 120 nm, which is equivalent to Figure 2 (a, d, g). Figure S3 shows the electric and magnetic field enhancement of the silicon dimer as a function of gap and wavelength. Figures S4, S5 and S6 show a full comparison of experimental NSOM field maps with simulated NSOM field maps plus the X-, Y- and Z- field components of the electric and magnetic fields around the particles for the cases of the 30 nm, 60 nm and 120 nm dimer gaps. This material is available free of charge via the Internet at 2

3 Figure S1. Scattering Cross Section (black solid line) and multipole decomposition in Cartesian (color solid lines) and spherical (color symbols) basis. (a,b) For a silicon dimer equivalent to that of Figure 2 in the main text but in the absence of substrate. (c,d) For a silicon dimer of spheres with radius 75 nm in air. In the Cartesian basis, multipoles are calculated through volume integration of the polarization current inside the particles while in the spherical basis the scattered field is projected into the vector spherical harmonics basis. The Cartesian total electric dipole (ed_total, red curve) accounts for the contributions to scattering from the Cartesian dipole moment and the toroidal dipole moment (and mutual interaction) and coincides with the spherical electric dipole contribution (a 11, red circles). The total magnetic dipole (md_total, blue curve) accounts for the contribution from the Cartesian magnetic dipole corrected with the mean- 3

4 square radius of the magnetic moment and coincides with the spherical magnetic dipole contribution (b 11, blue circles). Cartesian electric (eq, orange curve) and magnetic (mq, purple curve) quadrupole contributions were not corrected with their mean-square radii nor with higher order toroidal moments as they are negligibly small, and coincide with the spherical electric (a 12, orange circles) and magnetic (b 12, purple circles) quadrupole contributions. The isolated toroidal dipole contribution (td, green-dashed curve) is also shown for illustrative purposes. This moment is generated by non-zero circulation of the magnetic dipoles induced in the particles that point in the same direction but are not fully parallel, as readily observed in the electric near-field distribution in the XZ plane in Figure 2f. The Z- component of the magnetic dipole at each particle is induced by interaction with the magnetic field associated to the electric dipole of the neighboring particle. Importantly, these features are inherent to the silicon dimer configuration and not due to the shape of the disks or the presence of the substrate as it can be seen from comparison of this figure with Figure 2. The only, minor, difference between the dimers simulated with and without the substrate is the two small bumps observed in Figure 2 for X- polarized light in the total electric dipole contribution which is easily understood in terms of proximal and distal modes induced by the substrate. 4

5 Figure S2. Scattering Cross section and decomposition of modes for the 60nm and 120nm gap silicon dimers. (a) 60nm gap, X-polarized light. (b) 60nm gap, Y-polarized light. (c) 120nm gap, X-polarized light. (d) 120nm gap Y-polarized light. 5

6 Figure S3. Simulation results for (a) Electric Field (X-polarized incident light) and (b) Magnetic Field (Y-polarized incident light) enhancement as a function of gap and wavelength for the silicon nanodimer. The X-axis scans wavelength and the Y-axis scans the gap. The Electric field hot spot demonstrates a broad spectral width as it is related to the interplay of the electric dipole and magnetic dipole modes. The Magnetic field hotspot redshifts with decreasing gap. The feature seen at short wavelengths is due to a quadrupole mode. The simulations have been carried out for a set of gaps designated by the grey dashed lines with a 10nm step in wavelength. The data in between is interpolated. 6

7 Figure S4. Experimental near-field plots compared with simulation results for the case of the 30 nm gap. (a) NSOM mappings for X-polarized light, (b) Simulated NSOM signal picked up by a probe with 110 nm aperture placed 30 nm above the dimer. (c) Simulations of Electric (E) and Magnetic (H) field amplitudes in XY plane 30 nm above the dimer; separated into X-, Y- and Z- components for X-polarized light, (d)-(f) same as (a)-(c) but for Y-polarized incident light. 7

8 Figure S5. Experimental near-field plots compared with simulation results for the case of the 60 nm gap. (a) NSOM mappings for X-polarized light, (b) Simulated NSOM signal picked up by a probe with 110 nm aperture placed 30 nm above the dimer. (c) Simulations of Electric (E) and Magnetic (H) field amplitudes in XY plane 30 nm above the dimer; separated into X-, Y- and Z- components for X-polarized light, (d)-(f) same as (a)-(c) but for Y-polarized incident light. 8

9 Figure S6. Experimental near-field plots compared with simulation results for the case of the 120 nm gap. (a) NSOM mappings for X-polarized light, (b) Simulated NSOM signal picked up by a probe with 110 nm aperture placed 30 nm above the dimer. (c) Simulations of Electric (E) and Magnetic (H) field amplitudes in XY plane 30 nm above the dimer; separated into X-, Y- and Z-components for X-polarized light, (d)-(f) same as (a)-(c) but for Y-polarized incident light. 9