Terahertz imaging of sub-wavelength particles with Zenneck surface
waves - Supplementary material
M. Navarro-Cía1,2,3,4,a, M. Natrella4, F. Dominec5, J.C. Delagnes6, P. Kužel5,b, P.
Mounaix6,c, C. Graham4, C.C. Renaud4, A.J. Seeds4, and O. Mitrofanov4,d
1Optical
and Semiconductor Devices Group, Department of Electrical and Electronic Engineering, Imperial College
London, London SW7 2BT, UK
2Centre
for Plasmonics and Metamaterials, Imperial College London, London SW7 2AZ, UK
3Centre
for Terahertz Science and Engineering, Imperial College London, London SW7 2AZ, UK
4Department
of Electronic & Electrical Engineering, University College London, London, Torrington Place, WC1E
7JE, UK
5Institute
of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21 Prague 8, Czech Republic
6LOMA,
Bordeaux 1 University, CNRS UMR 4798, 351 cours de la Libération, 33405 Talence, France
a
Electronic mail: m.navarro@imperial.ac.uk
Electronic mail: kuzelp@fzu.cz
c
Electronic mail: p.mounaix@loma.u-bordeaux1.fr
d
Electronic mail: o.mitrofanov@ucl.ac.uk
b
1
Experimental system: surface wave excitation through a THz waveguide:
The sample is illuminated by THz beam from the substrate side. To maintain the beam position with
respect to the bow-tie during the raster scans, we use a cylindrical THz waveguide. Although the
waveguide introduces modal and chromatic dispersion, it preserves the illumination conditions (amplitude
and phase). To map the field distribution, the sample with the waveguide is scanned with respect to the
stationary near-field detector. The waveguide dispersion does not affect the spectroscopic analysis as only
the relative amplitude and phase changes are relevant. We note that scanning the sample only results in
changes of the surface wave excitation during the scan, and therefore, does not produce the true image of
the field distribution on the bow-tie.
Numerical modelling details:
We model the experiment with the TiO2 sphere using the finite-integration-method-based CST
Microwave StudioTM and its transient solver akin to our previous work.1 The dimensions of the substrate,
the bow-tie and the TiO2 particle are determined from the optical microscope images (top left inset of Fig.
4) and used in the calculations. The substrate (GaAs) is modelled as a loss-free dielectric with r = 12.94
and dimensions of 1120 m × 1305 m × 150 m. Gold is modelled by an electrical conductivity Au =
4.561 × 107 S/m and thickness 0.3 m. The TiO2 particle is modelled as a perfect sphere of radius r = 15
m and r = 94 + 2.35i (tan  = 0.025).2,3 Dispersion of the dielectric permittivity is not considered to
alleviate computation effort.4 The detector is modelled as an infinite gold plane placed at 31.5 m away
from the bow-tie. According to our previous findings,1,5 it is sufficient to neglect the presence of the small
aperture in the metallic screen because the aperture itself produces negligible effect on the field
distribution of the bow-tie. At the same time, it simplifies the model and reduces the computation time.
To compare the numerical and experimental results, the dEz/dx field distribution at 0.5 m away from the
gold plane (31 m away from the bow-tie and 1 m above the TiO2 sphere) is calculated and displayed in
Fig. 4. To reduce computation effort, the interdigitated fingers at the centre of the bow-tie and the glue
visible on the left lower quadrant of the substrate are not modelled, and the waveguide is modelled as a
perfect metallic cylindrical waveguide of only 500 m in length. The total number of mesh cells is of the
order of 200,000,000.
Time-domain spectroscopy analysis:
In Fig. S1(a) the experimental waveforms (left-hand side) and the corresponding spectra (right-hand side)
detected at the particle position (x,y) = (xp,yp) and 25 m above and below this position, i.e. (xp,yp±25), are
presented. These positions are shown for clarity in the right most color map in Fig. S1(c), which
represents the experimental near-field image at t = 3.6 ps for z = 31 m. From this set of results it is
evident that the strength of the field depends on the position of detection. The largest amplitude in the
waveform and spectrum is obtained at the particle position; green lines in Fig. S1. This effect can be
explained by the field concentration by the dielectric particle. The elaborate spectra observed in the
experiment, however, prevent us from extracting a clear spectral response of the TiO2 particle. The
interaction of the particle with the Z-TSWs is complex because they are excited at all bow-tie edges.
Higher-order waveguide modes arriving at later times are also likely to affect the spectra. Also, the
spectral resolution impedes us to resolve fine spectral features. All this may be well masking any feature
induced intrinsically by the TiO2 particle, e.g. the fundamental Mie resonances. Therefore, it is evident
that the spectral analysis is rather challenging for this particular configuration. Hence, for spectroscopy
2
applications, a configuration where these effects are reduced, e.g. a tapered strip proposed at the end in
the manuscript, is preferable.
The evolution of the near-field image as a function of the sample-detector distance is shown in Fig. S1(c).
The particle presence is only clearly visible when the detector is almost touching the TiO2 particle since
the field decays rapidly from the TiO2 particle interface as a result of the induced bound mode, i.e. Mie
resonance. Notice that the circular cross section of particle is not only better resolved, but also the
amplitude of the detected field is larger as the sample-detector distance is decreased. This underlines the
exceptionally local effect that the TiO2 particle has in an imaging setup utilising surface waves.
(a)
1.0
(b)
0.9
0.8
0.8
Amplitude (a.u.)
0.7
Amplitude (a.u.)
1.0
0.6
0.5
0.4
0.3
0.2
0.1
0.6
x (m)
0.4
-450
3.5
0.2
0.0
-0.1
-0.2
0
2
4
6
8
10
12
14
16
18
20
0.0
0.0
22
-20
-30
-30
-40
-40
-50
-60
-70
-80
y (m)
-20
y (m)
y (m)
(c)
-50
-60
-150
0
150
300
450
3.0
0.5
)sp( yaled emiT
Time (ps)
-300
2.5
1.0
1.5
2.0
3.760E-04
3.610E-04
3.459E-04
3.309E-04
3.008E-04
1 3.158E-04
2.858E-04
2.707E-04
2.0
-20
2.557E-04
2.406E-04
2.256E-04
2.106E-04
1.955E-04
1.805E-04
1.654E-04
1.504E-04
1.354E-04
1.203E-04
1.053E-04
9.024E-05
7.520E-05
6.016E-05
4.512E-05
3.008E-05
1.504E-05
0.000
-1.504E-05
-3.008E-05
-4.512E-05
-6.016E-05
-7.520E-05
-9.024E-05
-1.053E-04
-1.203E-04
-1.354E-04
-1.504E-04
-1.654E-04
-1.805E-04
-1.955E-04
-2.106E-04
-2.256E-04
-2.406E-04
-2.557E-04
-2.707E-04
-2.858E-04
-3.008E-04
-3.158E-04
-3.309E-04
-3.610E-04
-1 -3.459E-04
-3.760E-04
-30
1.5
-40
1.0
-50
-60
0.5
-70
-70
-80
0.0
-80
2.5
Frequency (THz)
-150 -140 -130 -120 -110 -100 -90
-150 -140 -130 -120 -110 -100 -90
-150 -140 -130 -120 -110 -100 -90
x (m)
x (m)
x (m)
FIG. S1. (Color online) Field amplitude as a function of time (a) and frequency (b) at the positions
indicated by the crosses on the right-most color map in (c). (c) Experimental xy-map for, from left to
right, z = 33, 32, and 31 m, at t = 3.6 ps.
3
References:
1
M. Natrella, O. Mitrofanov, R. Mueckstein, C. Graham, C.C. Renaud, and A.J. Seeds, Opt. Express 20,
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2
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Mounaix, Appl. Phys. Lett. 100, 061117 (2012)
3
4
W. G. Spitzer, R. C. Miller D. A. Kleinman and L. E. Howarth, Phys. Rev. 126, 1710 (1962)
5
R. Mueckstein, C. Graham, C.C. Renaud, A.J. Seeds, J.A. Harrington, and O. Mitrofanov, J. Infrared
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4