Slabs formed by wire medium metamaterials are capable of transmitting evanescent waves over several wavelengths, and enable perfect imaging of field patterns with deeply subwavelength features over such long distances. To date, perfect imaging has been limited to narrow frequency windows defined by the Fabry–Perot (FP) resonance condition. Away from such resonances, backreflections within the slab result in the excitation of surface waves supported by the wire medium. This leads to image distortions, thus severely limiting the use of wire media for broadband subwavelength imaging. Here, we propose and demonstrate that this limitation can be overcome by using ultrashort electromagnetic pulses as the field source, allowing separation of the initial pulse from subsequent backreflections, which cannot be achieved using continuous-wave sources. Using a terahertz (THz) near-field microscope based on a time-domain approach, we demonstrate ultrabroadband transmission of distortion-free images over the entire frequency band of the source (0.1–1.75 THz). Such performance requires the slabs to be sufficiently long; the limits of this approach are also demonstrated by imaging a resonant mode with high -factor through a short slab. Our results pave the way for the implementation of wire media in broadband imaging applications based on short electromagnetic pulses, such as THz pulse imaging or optical imaging with ultrashort laser pulses.
© 2016 Optical Society of America
Wire media (WM) consisting of subwavelength periodic arrays of metal wires embedded in a dielectric host represent an important group of uniaxial metamaterials. Such WM possess remarkable properties due to their extreme optical anisotropy and strong spatial dispersion [1,2]. The study of WM has a long history; however, most of their important and useful properties have been revealed and understood only recently . A particularly interesting feature is their ability to operate as a superresolving lens supporting the propagation of evanescent spatial harmonics, which carry subwavelength information. In ordinary isotropic materials, such evanescent waves are exponentially decaying from their source, leading to the diffraction limit, and limiting the resolution of conventional imaging systems. At the interface of a WM, however, evanescent waves in free space can be transformed into propagating transverse electromagnetic waves, enabling the transport of a given field distribution through such a material with no loss of resolution [4,5].
A metal wire array with subwavelength diameter and pitch, directed along the axis, is well-approximated as an effective medium with permittivity tensor
It is worth noting that, in the THz frequency regime and for subwavelength wire spacing, for all spatial frequencies, so that . Therefore, the dispersion relation of all transverse spatial frequencies reduces to . Hence, the isofrequency contour is flat and all extraordinary waves propagate with the speed of light in the host in the direction of the wires. The frequency range in which this effect occurs is referred to as the “canalization” regime . In this regime, images can in principle propagate without distortion and without being subject to the diffraction limit.
In a previous experiment we have demonstrated the superior image transmission properties of a WM by imaging a subwavelength-sized structure (a double aperture) through up to several-millimeters long WM with a spatial resolution of at terahertz (THz) frequencies . For this purpose the sample was illuminated with TEM-polarized THz pulses, which were linearly polarized in the transverse () direction. The component of the transmitted field was then mapped using a THz near-field microscope [8,9]. Our experiments revealed an effect that severely deteriorates the imaging capability of such a hyperlens. Since the light is scattered at the edges of the apertures, only the vectorial part scattered in the direction is polarized, while the vectorial part that is scattered in the direction is polarized. In the case of -polarized incident light, ordinary waves are excited in the WM and diffract as in an isotropic medium of permittivity . Thus, the images of the apertures, while preserved in the direction, can be dramatically stretched in the direction. This limit is inherent when measuring transversely polarized fields; in fact, -polarized fields—i.e., the polarization perpendicular to the source plane and parallel to the wires of the hyperlens—are transmitted without any distortions, since they consist exclusively of extraordinary waves. Therefore, perfect image transmission through the wire medium can be achieved by filtering out all ordinary waves, as we will demonstrate in this paper.
Since the wire medium has to be placed in close vicinity to the source in order to detect the evanescent waves, its presence may strongly distort the source field. It is accepted that tuning the length of the wire medium to the FP resonance condition is crucial for obtaining distortion-free images , since otherwise backreflections perturb the image formation at the source plane, amplifying the evanescent modes supported by the WM, and severely distorting the image [11–13]. As we will demonstrate by our THz time-domain measurements, in the case of experiments with pulsed light sources, obeying the FP condition is not necessarily required, since reflected pulses are usually well-separated from the main pulse and the pulses are typically short enough to prohibit the formation of resonant slab modes.
Here, we overcome both these limits. We measure -polarized fields transmitted in THz WM for the first time, to the best of our knowledge, and additionally show that using pulsed sources allows us to remove detrimental backreflections through simple postprocessing. In combination, these results yield perfect ultrabroadband THz imaging.
2. EXPERIMENTAL DETAILS
THz WM of different lengths have been fabricated by a fiber-drawing technique described elsewhere [14–16]. The WM are composed of 453 hexagonally arranged indium wires of nominally 10 μm diameter, and 50 μm pitch, and have lengths of 1.36 and 6.76 mm (Fig. 1). The wires are embedded in a 1-mm-diameter Zeonex host (). To demonstrate the transport of -polarized field distributions through the WM, we used two different metallic sample structures that produce strong -polarized field patterns close to their surface after excitation by an incident transverse electromagnetic field: a plasmonic lens and a complementary split-ring resonator (CSRR). The electric near-field distributions are mapped by a THz near-field microscope, which is capable of resolving field patterns with subwavelength spatial resolution [9,17]. Briefly, a femtosecond (fs)-laser beam is focused through a 1 mm thick ZnTe crystal cut along the (100) crystal axis. This allows for the detection of the component of the THz electric field by inducing a polarization rotation of the fs laser in the detection crystal. The laser pulses are backreflected from the HR-coated front side of the crystal, and the induced polarization rotation is measured by balanced photodetection. By raster-scanning the electro-optical crystal together with the laser, the spatial distribution of the electric near-field close to either the structures or the WM can be mapped.
The two metallic samples used in our study are shown in Fig. 2. A plasmonic lens, consisting of a metal disk of 350 μm diameter surrounded by a 90 μm wide annular gap has been fabricated by etching the circular gap through a 500 nm thick aluminum layer that was deposited on a 300 μm thick quartz wafer [Fig. 2(a)]. The underlying concept of such a plasmonic lens is based on the excitation of surface plasmon polaritons (SPPs) in the outer region of the concentric structure. The SPPs propagate toward the center of the disk, where they are focused . For THz radiation with correspondingly small wave vectors, the SPP propagation constant is close to the wave vector of freely propagating light, and, therefore, SPPs acquire the nature of Sommerfeld–Zenneck surface waves . If -polarized light is normally incident from the bottom side of the annular slit, the light is diffractively coupled into SPPs, which counterpropagate toward the center of the disk. Due to the opposite polarization of the incident electric field with respect to the metal edges of the disk, SPPs launched on both sides have opposite phase when propagating toward the center. As a consequence they interfere destructively exactly in the disk center, leading to an electric field node (). As a result of the cylindrical symmetry of the structure, interference leads to the dominant electric field component of the SPPs being proportional to the first-order Bessel function as20].
As another source for a -polarized complex field pattern we use a CSRR [Fig. 2(b)], a highly resonant structure that has previously also been investigated by THz near-field microscopy . CSRR structures were fabricated by laser cutting an array of square slit patterns into a thin copper foil. When illuminating the array of CSRRs by linearly polarized THz radiation, with polarization perpendicular to the complementary gaps, two dominant transmission maxima are observed, which can be assigned to the excitation of eigenmodes forming a dipole-like and quadrupole-like field pattern on the surface of the CSRR. The dominant field distributions of these near-field patterns are polarized perpendicular to the surface. At higher frequencies, even more complicated modes, which are only weakly radiating but can also be resolved by THz near-field microscopy, are formed on the surface.
As a reference, we initially mapped the near-field patterns in the vicinity of the two sample structures without WM. Subsequently, we scanned the transmitted field distributions on the image plane of the WM with 1.36 and 6.76 mm length, placed directly on top of the sample structures. Additionally, we performed full wave simulations of the fields close to the structures, as well as after transmission through the WM by using the time-domain solver of CST Microwave Studio .
3. TRANSMITTING LONGITUDINALLY POLARIZED FIELDS
A. Plasmonic Lens
Figure 3 shows experimental THz near-field images of the out-of-plane field distribution () on top of the plasmonic lens at two selected frequencies, 0.5 and 1.75 THz. Note that field maps are plotted normalized to the field maxima. As expected from Eq. (3), the field distribution directly above the plasmonic lens forms an antisymmetric two-lobe pattern with a node along the axis. With increasing frequency, additional maxima appear.
After this initial reference measurement, the 1.36 mm long WM was placed on top of the plasmonic lens and the out-of-plane field distribution was mapped on the image plane of the WM (WM exit). The results are presented in Fig. 4. In spite of image transport over distances of at 0.5 THz and at 1.75 THz, the field distribution is reproduced without significant loss in image quality, showing the same features as the reference image of the original structure. The full width at half-maximum (FWHM) of the two main lobes in the center of the disk are of the order of 20%–30% of the wavelength at 0.5 THz, demonstrating the diffraction-free transmission of subwavelength scaled details.
Figure 5 shows the results for the 6.76 mm WM. The field pattern is again reconstructed with very high fidelity after transmission through the WM. At 1.75 THz, the image is transmitted over a distance of 60 wavelengths without significant distortions or loss of subwavelength details.
The THz time-domain approach provides imaging data over a broad frequency range (0.1–1.75 THz) by Fourier transforming the time-dependent signals. Figure 6 shows line scans along a line through the center of the plasmonic lens as sketched in Fig. 6(a) of the frequency-dependent intensity profiles measured [Fig. 6(b)] without WM, with the 1.36 mm long WM [Fig. 6(c)], and with the 6.76 mm long WM [Fig. 6(d)]. Note that, for better representation, each scan along the axis has been normalized to the field maximum at the respective frequency. The dashed horizontal lines indicate the extent of the metal structure.
Generally, the field profiles with and without the WM are similar. Up to approximately 250 GHz, no field maxima are able to form on the central disk since the wavelength is larger than the disk diameter. In the spectral window ranging from 250 GHz up to 1.5 THz, the two-lobe pattern of the first-order Bessel mode is formed on the disk. At a frequency of approximately 1.5 THz, the next order Bessel mode emerges, having enough space to spread on the structure. Interestingly, we find that, for the long WM, the emergence of the second-order Bessel mode occurs very abruptly and already at a slightly lower frequency. This may be due to slightly different distances between the WM and the plasmonic lens in each case, resulting in a different local refractive index, leading to a different cut-off frequency for the formation of the higher order Bessel mode. Furthermore, above 1.3 THz the signal through the WM strongly diminishes, mainly due to increased absorption in the host material, in particular for the long WM, although the structure of the field intensity remains visible due to the normalized representation. Further studies are required to fully clarify this difference in imaging performance; however, high-quality images can still be discerned from the field distribution for the longer sample, as shown in Fig. 5 at 1.75 THz. Note that the field minima at 0.56 and 0.75 THz observed in all spectra are due to the absorption of water vapor in the beam path . While all the general features in the frequency-dependent field profiles on top of the plasmonic lens in Fig. 6(b) are preserved after transmission through the WM, in the case of the short WM in Fig. 6(c), periodic oscillations markedly modulate the intensity profile. The modulations disappear again in the measurement with the long WM [Fig. 6(d)].
The image transmission and reconstruction properties of a wire medium have been intensively studied in the past decade. In this regard, it has been demonstrated that tuning the length of the wire medium to the FP resonance condition is crucial for obtaining distortion-free images , since otherwise backreflections perturb the image formation at the source plane, as well as the resonant amplification of the evanescent waves away from the FP resonance supported by the wire medium, which may severely distort the image [11,12]. For WM of length , the FP condition is given by , where is an integer and is the speed of light.
While much of the theoretical and experimental work so far has been performed in the frequency domain that corresponds to cw measurements, we are recording field pulses in the time domain. In this case no standing waves inside the wire medium are able to form. Instead, after a certain time, reflected pulses that propagate back and forth inside the wire medium are measured. Such trailing pulses in time-domain measurements that occur after a time cause periodic oscillations on the spectrum with a periodicity given by . The reflected pulses inside the WM are separated by , resulting in spectral oscillations with a periodicity corresponding to the FP frequency, leading to the spectral behavior observed in Fig. 6(c).
The effect of the reflected pulses on the image quality is demonstrated by simulations, whose results are shown in Fig. 7. In this case we simulated the near field of a plasmonic lens without WM [Figs. 7(a) and 7(b)] and the field distribution after transmission through the 1.36 mm long WM [Figs. 7(c) and 7(h)]. In the simulation, a semicycle THz pulse polarized along the axis () was incident from the back side of the plasmonic lens, and the longitudinal field component was sampled on the front side of the lens, as well as at the image plane of the WM.
Simulated electric field transients obtained at the indicated lateral position of an image are shown in Fig. 7 (left column). The right column shows a cross section of the entire simulated frequency-dependent intensity profile along the axis through the center of a field image (see Fig. 6). In case of the plasmonic lens without WM [Figs. 7(a) and 7(b)], the steady state energy criterion that defines the width of the temporal window of the time-dependent simulation is reached within approximately 15 ps. As a result, the entire information on the field distribution is contained in a single pulse, as shown in Fig. 7(a). Figure 7(b) shows the frequency-dependent intensity profile sampled 100 μm above the plasmonic lens. Figures 7(c) and 7(d) show the corresponding field transient and intensity profile after transmission through the 1.36 mm long WM until the steady-state energy criterion was met. In this case the simulation covers a much larger temporal window (0–140 ps) because the pulse is reflected several times inside the WM. The transients and corresponding intensity profile were sampled 100 μm above the end facet of the WM. The reflections induce characteristic image distortions, manifesting as periodic oscillation in the frequency-dependent intensity profile. These features appear periodically every 75 GHz, corresponding to the FP frequency of the 1.36 mm long WM. To investigate the effect of the reflected pulse, we applied a window function to the transient, which suppresses the reflections. Figures 7(e) and 7(f) show the transient and corresponding intensity profile, taking the first reflected pulse into account and suppressing the rest of the internal reflections. In this case, the intensity profile is very similar to the profile obtained when all internal reflections are taken into account. The amplitude of the periodically occurring image distortions slightly decreases, but their spectral positions do not change as expected. This clearly indicates that already one internal reflection of the pulse severely distorts the image. Finally, we applied a window function that suppressed all internal reflections, leaving only the main pulse [Figs. 7(g) and 7(h)]. A smooth, unperturbed intensity profile is obtained that is nearly identical to the near-field distribution on top of the plasmonic lens, demonstrating perfect image transmission through the WM. In essence, the internal etalon reflections of the WM modulate the frequency-dependent field profile at the FP frequency, and nearly unperturbed images can be obtained if only the main pulse is used as input for the Fourier transformation.
Experimentally such a separation of main pulse and reflections is only possible in experiments with short light pulses (e.g., short laser pulses or THz pulses) and cannot be achieved in cw measurements. The simulated effect can be reproduced in our experiments, as demonstrated in Fig. 8, where the intensity profiles measured at the end of the 1.36 mm long WM are shown. In the top row, only the main pulse has been taken into account by imposing a window function on the transients, effectively suppressing the reflected pulse [Figs. 8(a) and 8(b)]. In the bottom row, we have taken also the first reflected pulse into account [Figs. 8(c) and 8(d)] by increasing the temporal width of the window function. As in the simulation, the reflected pulse causes periodic distortions in the frequency-dependent intensity profile with a periodicity of approximately 75 GHz. Due to the limited frequency resolution of our experiment of 20 GHz, the effect is not as pronounced as in the simulation, but is still clearly visible. When no windowing function is applied to the data, clear unperturbed images are obtained only for frequencies where the length of the WM fulfils the FP condition as defined earlier. By windowing the transients such that backreflections are suppressed, undistorted images are obtained over the entire frequency band covered by the experiment.
It is important to note that reducing the temporal width of the windowing function effectively reduces the frequency resolution of the experiment, which is given by . Hence, the length of the WM has to be chosen long enough so that the internal reflection of the pulse is outside the time window required to achieve the desired frequency resolution (finesse). Note that the results obtained for the 6.76 mm long WM satisfy this criterion for the frequency resolution of our experiment of . Therefore, the first internal reflection is beyond the time scan in the experiment, and the intensity profile of the component of the electric field distribution shows no periodic distortions [Fig. 6(d)].
B. Complementary Split-Ring Resonator
In the case of transmitting field distributions of high- resonant structures, which support resonances leading to strong resonant oscillations of the electromagnetic field that decay relatively slowly, a sufficient length of the WM is important. Otherwise, the correspondingly short time window (for masking the backreflection) would result in a low spectral resolution, and the narrow resonances cannot be resolved. This leads to blurred field images associated with the loss of image details at frequencies that do not satisfy the FP condition . Here, we demonstrate this effect on the example of the near-field produced by the CSRR shown in Fig. 2(b). The transmission spectrum of an array of CSRRs (periodicity ) exhibits two narrow transmission maxima at 75 and 225 GHz, representing the structure’s first- and third-fundamental resonances (here referred to as and , respectively) of the CSRR . In Fig. 9 we map the field intensity and the distribution of the real part of the electric field () in the direct vicinity of the plasmonic lens at the eigenmodes (middle row), and at the higher order eigenmode (lower row). The distance of our detection crystal from the sample was estimated to be about 125 μm, which has been deduced from a comparison of the measured field patterns with field distributions simulated at various distances from the sample surface.
Figures 10 and 11 show the corresponding field distributions measured in the image plane of the 1.36 and the 6.76 mm long WM, respectively. For all measurements, the polarization of the incident THz pulses was as indicated.
For both resonance frequencies of the CSRR, the characteristic field patterns are well reproduced on the image plane of both WM. Interestingly, the field distribution measured with the short WM shows even more fine details than the original field distribution measured directly above the structure (without WM). For example, at 225 GHz the sign reversal of the electric field on the right-hand side of the CSRR is more clearly visible in Fig. 10 than in Fig. 9. Simulations show that this particular feature can be observed only at distances of less than 50 μm from the surface of the sample, indicating that the WM allows sampling of near fields even closer to the surface than the THz near-field detector itself, which demonstrates the application of these THz WM as high-performance “near-field endoscopes” capable of picking up near fields in ultimate vicinity of a sample. Note that, with the long WM, the image quality decreases slightly, showing less detail due to increased transmission loss. Nevertheless, all relevant details of the field pattern are still observed, demonstrating that even the complex field distributions of resonant structures can be transported through our WM.
Whereas the field distribution of the fundamental resonance at 75 GHz imaged through the 1.36 mm long WM in Fig. 10 shows no image distortions, an image slightly above that frequency exhibits additional unwanted features originating from the etalon effect. This is shown in Fig. 12, where we plot the field patterns measured at 75 and 87 GHz. Since the WM satisfies the FP condition for 75 GHz, no noticeable image distortions occur for that particular frequency. However, at 87 GHz, the internal backreflections lead to artifacts that blur the entire field image. By applying a window function to suppress the reflected pulse, we are able to eliminate these artifacts. However, in this case the image of the field distribution loses important features [Fig. 12(b)] since fine details on the resonance itself are also suppressed. In addition, the inherent frequency resolution is decreased such that the images at both frequencies are no longer distinguishable [Figs. 12(b) and 12(d)]. Hence, for resonant structures featuring resonances with large -factors, sufficiently long WM need to be deployed to produce unperturbed field distributions at the image plane of the WM over a broad bandwidth. Note that in this case, however, WM with low transmission losses have to be used, so that the image quality is not compromised by the inherent losses.
In summary, we have investigated the image transmission capabilities of a WM consisting of periodically arranged subwavelength metal wires forming a hyperbolic metamaterial at THz frequencies. We experimentally demonstrate that such WM are capable of transporting longitudinally polarized electric fields over long distances of several wavelengths without significant image distortions, using the near-field profiles of a plasmonic lens and CSRR as a proof-of-concept. The field distributions are perfectly reconstructed on the image plane of the WM.
We have elucidated the impact of internal reflections within the WM on the image quality; such reflections may cause severe artifacts, unless the WM length is tuned to the frequencies obeying the FP condition. We have shown that such a criterion is not required in time-domain measurements using short light pulses, if the main pulse can be temporally separated from subsequent internal reflections, resulting in broadband operation with a single WM length. We have also shown that sufficiently large WM lengths are required if highly resonant structures are imaged so that all fine details of the field patterns of the resonant modes can be fully resolved. Our work has important implications for implementing WM in THz pulse imaging, as well as generally in various forms of optical imaging based on short (e.g., picosecond or femtosecond) laser pulses.
Australian Research Council (ARC) (DP120103942); German Research Foundation (DFG) (WA 2641/7).
1. D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003). [CrossRef]
2. T. G. Mackay, A. Lakhtakia, and R. A. Depine, “Uniaxial dielectric media with hyperbolic dispersion relations,” Microwave Opt. Technol. Lett. 48, 363–367 (2006). [CrossRef]
3. C. R. Simovski, P. A. Belov, A. V. Atrashchenko, and Y. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mater. 24, 4229–4248 (2012). [CrossRef]
4. P. A. Belov, Y. Zhao, S. Tse, P. Ikonen, M. G. Silveirinha, C. R. Simovski, S. Tretyakov, Y. Hao, and C. Parini, “Transmission of images with subwavelength resolution to distances of several wavelengths in the microwave range,” Phys. Rev. B 77, 193108 (2008). [CrossRef]
5. P. A. Belov, G. K. Palikaras, Y. Zhao, A. Rahman, C. R. Simovski, Y. Hao, and C. Parini, “Experimental demonstration of multiwire endoscopes capable of manipulating near-fields with subwavelength resolution,” Appl. Phys. Lett. 97, 191905 (2010). [CrossRef]
6. P. A. Belov, C. R. Simovski, and P. Ikonen, “Canalization of subwavelength images by electromagnetic crystals,” Phys. Rev. B 71, 193105 (2005). [CrossRef]
7. A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 4, 2706 (2013). [CrossRef]
8. A. Bitzer, H. Merbold, A. Thoman, T. Feurer, H. Helm, and M. Walther, “Terahertz near-field imaging of electric and magnetic resonances of a planar metamaterial,” Opt. Express 17, 3826–3834 (2009). [CrossRef]
9. A. Bitzer, A. Ortner, and M. Walther, “Terahertz near-field microscopy with subwavelength spatial resolution based on photoconductive antennas,” Appl. Opt. 49, E1–E6 (2010). [CrossRef]
10. P. A. Belov and M. G. Silveirinha, “Resolution of subwavelength transmission devices formed by a wire medium,” Phys. Rev. E 73, 056607 (2006). [CrossRef]
11. A. Rahman, P. A. Belov, M. G. Silveirinha, C. R. Simovski, Y. Hao, and C. Parini, “The importance of Fabry–Perot resonance and the role of shielding in subwavelength imaging performance of multiwire endoscopes,” Appl. Phys. Lett. 94, 031104 (2009). [CrossRef]
12. A. Tuniz, D. Ireland, L. Poladian, A. Argyros, C. M. de Sterke, and B. T. Kuhlmey, “Imaging performance of finite uniaxial metamaterials with large anisotropy,” Opt. Lett. 39, 3286–3289 (2014). [CrossRef]
13. A. Tuniz and B. Kuhlmey, “Two-dimensional imaging in hyperbolic media-the role of field components and ordinary waves,” Sci. Rep. 5, 17690 (2015). [CrossRef]
14. A. F. Abouraddy, M. Bayindir, G. Benoit, S. D. Hart, K. Kuriki, N. Orf, O. Shapira, F. Sorin, B. Temelkuran, and Y. Fink, “Towards multimaterial multifunctional fibres that see, hear, sense and communicate,” Nat. Mater. 6, 336–347 (2007). [CrossRef]
15. A. Tuniz, B. T. Kuhlmey, R. Lwin, A. Wang, J. Anthony, R. Leonhardt, and S. C. Fleming, “Drawn metamaterials with plasmonic response at terahertz frequencies,” Appl. Phys. Lett. 96, 191101 (2010). [CrossRef]
16. A. Tuniz, R. Lwin, A. Argyros, S. C. Fleming, and B. T. Kuhlmey, “Fabricating metamaterials using the fiber drawing method,” J. Visualized Exp. 68, 4299 (2012). [CrossRef]
17. A. Bitzer, A. Ortner, H. Merbold, T. Feurer, and M. Walther, “Terahertz near-field microscopy of complementary planar metamaterials: Babinet’s principle,” Opt. Express 19, 2537–2545 (2011). [CrossRef]
18. S. Waselikowski, C. Fischer, J. Wallauer, and M. Walther, “Optimal plasmonic focusing on a metal disc under radially polarized terahertz illumination,” New J. Phys. 15, 075005 (2013). [CrossRef]
19. G. Goubau, “Surface waves and their application to transmission lines,” J. Appl. Phys. 21, 1119–1128 (1950). [CrossRef]
20. G. M. Lerman, A. Yanai, and U. Levy, “Demonstration of nanofocusing by the use of plasmonic lens illuminated with radially polarized light,” Nano Lett. 9, 2139–2143 (2009). [CrossRef]
21. CST Gesellschaft für Computersimulationstechnik, Bad Nauheimer Str. 19, 64289 Darmstadt, Germany, CST Microwave Studio.
22. M. van Exter, C. Fattinger, and D. Grischkowsky, “Terahertz time-domain spectroscopy of water vapor,” Opt. Lett. 14, 1128–1130 (1989). [CrossRef]