Supplementary Information for “Directional
plasmonic scattering from metal nanoparticles in
thin-film environments”
A. W. Powell*, N. Hjerrild, A. A. R. Watt, H. E. Assender, and J. M. Smith
Department of Materials, University of Oxford, Parks Road, Oxford, OX1 3PH,
United Kingdom
*alexander.powell@materials.ox.ac.uk
NP’s and NW’s were measured in a JEOL 840F scanning electron microscope (SEM), both to
observe the particle shapes and dispersion on the substrate, and to calculate the size
dispersion of the particles. Fig. S1 displays some typical examples of particles, dispersed on
a silicon substrate.
Figure S1: SEM images of a) NP’s obtained from Sigma Aldrich and b),c) NW’s produced in-house, spin
coated onto an Si substrate.
The homebuilt dark-field, Fourier microscope used to image the scattering patterns is shown
below in Fig. S2. The fact that this setup can measure scattering without needing to use any
kind of fluorescence makes accurate detection of particles and visualisation of scattering
patterns a far more convenient process. This has been achieved without use of Total Internal
Reflection (TIR) measurements also, which means that we are only limited by the NA of the
objective and the rod mirror diameter, not the critical angle for the substrate. This allows for
a greater angular range and also more choice in the material interfaces at which we can
choose to observe our particles. Through measuring the extent of the Fourier space that can
be observed with this setup, it was determined that the objective actually has a working NA
of 1.23 ± 0.01.
Figure S2: The dark-field Fourier microscope used to obtain images, highlighting the processes around the rod
mirror.
Figure S3 shows the Fourier space scattering patterns for NW’s on a), a bare coverslip and c),
when overcoated with 185 ± 5 nm PTFE AF, with incident illumination polarised
perpendicular to the NW axis. In Fig. S3c a slight asymmetry is observable, as well as some
disagreement in the intensity of the side lobes. This is most likely due to the area of the glass
substrate containing the NW not being exactly square with the objective. The presence of
organic precursor still present around the NW, might also cause slight discrepancies by
altering the dielectric surroundings of the NW.
Figure S3: Experimental Fourier space images and line traces of scattering from 115 nm diameter NW's on the
surface of a glass coverslip with incident radiation polarised perpendicular to the wire axis. (a) and (c) show
results for a wire on bare glass, (b) and (d) for a NW overcoated in 185 ± 5 nm PFTE AF. The line trace plots also
show results from FDTD simulations.
Sersic et al.1 modelled nanowires as a set of equivalent point dipoles arranged in a line the
same length as the wire to obtain a theoretical value for the radiation pattern. The dipoles
representing each volume element were excited in phase, with equal incident amplitude and
equal polarisation, dictated by the incoming radiation. The slight phase difference from
these dipoles in the far field leads to an interference effect, which is represented by
multiplying the dipole radiation pattern by a form factor dictated by the wire dimensions.
Figure S3: Traces taken across the Fourier patterns from NW’s shown in Fig. 3 parrallel to the axis of
the wire (perpendicular to the line in Fourier space). Experimental results (blue) are fitted to a sinc 2
function (orange) to find the length of the wire. This can be compared with values observed on the
webcam (inset) to test the theory.
It can therefore be demonstrated that the radiation pattern in the far field, E(k∥) from a wire
aligned along the y-axis can be approximated to:
𝑓𝑎𝑟
𝑦
𝑬(𝒌∥ ) ∝ 𝑬𝑑𝑖𝑝 (𝒌∥ )sinc(𝑘∥ 𝐿)
(1)
𝑓𝑎𝑟
Where 𝑬𝑑𝑖𝑝 is the far-field radiation pattern from a single dipole, and L is the length of the
wire. Thus a trace of the scattering intensity along the axis of the wire should produce a sinc2
pattern, which can be fitted to experimental results to determine the length of the wire. This
is shown in Fig. S3: the model has been fitted to the experimental trace using the Ezyfit
toolbox for MatLab and shows good agreement with experiment for a NW of 6.9 μm length.
The inset to Fig. S3 shows a webcam image of the NW, which, when magnifications from the
microscope components are taken into account gives a wire length of 6.4 ± 0.5 μm, which is
in agreement with the model.
The discreet dipole model proposed is therefore seen to be sufficiently accurate for the
purposes of this research and is a convenient way to understand the scattering traces seen in
figures 3 and 4 in the main body. This process has been repeated for all the NW’s used in the
investigation.
1.
I. Sersic, C. Tuambilangana and A. F. Koenderink, N. J. Phys., 13, 083019, (2011)