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

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,1,5it 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, itsimplifies the model and reducesthe 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 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 TiO2particle 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.

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.

References:

1M. Natrella, O. Mitrofanov, R. Mueckstein, C. Graham, C.C. Renaud, and A.J. Seeds, Opt. Express 20, 16023 (2012)

2K. Berdel, J. G. Rivas, P. H. Bolivar, P. de Maagt, and H. Kurz, IEEE Trans. Microwave Theory Tech. 53, 1266 (2005)

3H. Němec, C. Kadlec, F. Kadlec, P. Kužel, R. Yahiaoui, U.-C. Chung, C. Elissalde, M. Maglione, and P. Mounaix, Appl. Phys. Lett. 100, 061117 (2012)

4W. G. Spitzer, R. C. Miller D. A. Kleinmanand 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 Milli. Terahz. Waves32, 1031 (2011)

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