The spectral characteristics of localized surface plasmons (LSPs) depend strongly on the geometry of the metal nanostructure sustaining them.1, 2 This fact makes the tuning of their light-harvesting and focusing abilities across the whole visible and infra-red regimes possible. Lately, the tailoring of the spectral width of LSP resonances through design has attracted much attention due to its many potential applications in technological areas as diverse as sensing, imaging and photovoltaics.3, 4 The excitation of Fano-like resonances in composite nanoparticles has been shown to be useful for controlling their optical properties within an extremely narrow frequency window.5 In contrast, transformation optics (TO) has recently been proposed as a route to transfer the broad bandwidth behavior of plasmonic waveguides to nanoantennas using geometric singularities.6, 7
Whereas sharp LSP resonances have been reported experimentally in different configurations,8, 9 the realization of broadband plasmonic antennas implementing TO recipes remains a challenge. Although efforts have been made to reduce the exceedingly acute geometric features required for these nanostructures,10 theoretical designs are still largely beyond current nanofabrication capabilities. In this communication, a simple strategy is followed to circumvent this obstacle. By replacing the usual plasmonic materials (noble metals such as gold or silver) with a semiconductor, indium antimonide (InSb), the wavelength of operation for the device shifts from the optical (λ ∼ 102-103 nm) to the THz (λ ∼ 102-103 μm) regime.11, 12 Taking advantage of this length scaling (which greatly eases the device fabrication) we report the THz broadband response of InSb microstructures devised using TO ideas.
The use of LSPs in the THz regime offers the potential to overcome the restriction posed by the diffraction limit and the relatively long wavelength, and allow its application towards deep sub-wavelength sensing. The strong field confinement permitted by plasmonics, combined with the broadband response provided by TO design may be of great importance for a number of applications. For example, many large biomolecules have a broad dielectric response in the THz range rather than narrowband resonances.13 A broadband LSP based sensor would allow for the detection of biomolecules and other substances in low concentrations with high sensitivity. From a fundamental perspective, the transfer of TO designs to the THz domain presents several advantageous side effects. The fact that spatial dispersion in semiconductors at THz frequencies is similar to that of metals in the optical regime14 could be exploited to probe nonlocal effects in plasmonic phenomena15 with high accuracy. Another advantage is that the plasmonic properties of semiconductors can be controlled by varying the free carrier density through photoexcitation, thermal means or direct injection of carriers. This allows for the response of semiconductor plasmonic devices to be dynamically tuned, creating new device possibilities.
The structure we investigate consists of two just-touching, deeply sub-wavelength InSb disks, which have a surface plasmon frequency in the terahertz range (∼0.8 THz). This geometry has previously been theoretically shown to exhibit a broadband behavior in the visible range;16 however, a conclusive experimental realization is still lacking.17 In this work, we demonstrate experimentally and numerically the spectral broadening that occurs in a periodic array of InSb disk dimers due to plasmonic interactions between the two disks forming each pair.
The disks are fabricated from a 1.3 μm thick layer of InSb grown using molecular beam epitaxy (MBE) on a 0.46 mm thick semi-insulating gallium arsenide (GaAs) substrate. They have a D = 20 μm diameter and are patterned through electron beam lithography. The plasma etching process achieved a sidewall angle of approximately 73° leading to a ‘V’ shaped gap between the disks, with the contact occurring at the bottom of the gap as depicted in Figure 1(a). In order to measure the overlap between the two disks, we introduce the parameter δ, defined in Figure 1(a).
To facilitate measurement, the touching dimers are arranged in a square array with a pitch of 50 μm, as shown in Figure 1(b). Importantly, the array pitch is small enough to prevent the emergence of diffraction effects within the spectral window under study (the so-called metamaterial regime). Three touching dimer array samples, covering the beam spot diameter size of approximately 3 mm, were made with increasing proportion of overlap δ [see Figure 1(c–e)]. Sample 1 is designed so that the disks are just touching (δ ∼ 0.05 μm), while samples 2 and 3 overlap by approximately δ ∼ 0.1 μm and δ ∼ 0.4 μm, respectively. Note that these δ values are nominal as imperfections in the fabrication process led to a variation of the amount of disk overlap across the sample array as revealed by SEM imaging. The small amount of overlap and angled sidewalls ensured that a sub-micrometer gap existed between the disks at their top surface in all three samples.
Extinction spectra for the three touching dimer arrays were measured by placing them at the focal point of a Gaussian beam produced by a THz time-domain spectrometer (Teraview TPS Spectra 3000). We analyze the electromagnetic response of the samples within a spectral window ranging from 0.1 to 1.6 THz. Since the beam spot size is substantially larger than the dimensions of a single pair of disks, a single transmission measurement probes several hundred to several thousand dimers, depending on the frequency. We assume that the dimers' absorption cross-section (ACS) is approximately equal to their extinction spectra as their sub-wavelength size ensures an extremely low scattering efficiency.18
In order to fully understand our experimental results, we performed full-wave electromagnetic simulations using the finite element method (FEM). We calculated the absorption cross-section of infinite arrays of touching dimers with geometric parameters taken from the SEM images in Figure 1(c–e). We modeled the InSb permittivity through the usual Drude-like formula ϵln Sb(ω) = ϵ∞[1 − ω2P/(ω2 + iωγ)]. The Drude parameters were obtained by fitting the transmission spectrum for a 1 μm thick InSb layer on top of a 0.46 mm GaAs substrate, having ϵ∞ = 15.68, ωp = 1.52 × 1013 rad/s, and γ = 1.79 × 1012 rad/s. The complex permittivity of the GaAs substrate ϵGaAs was taken from published data.19
Figure 2(a) shows the measured extinction spectra for sample 1 as a function of incident polarization angle. By investigating the polarization sensitivity, we gain insight into the plasmonic coupling taking place between the disks forming the dimers. This electromagnetic interaction is predicted to lead to the emergence of distinct plasmonic modes, resulting in the effective broadening of the THz response of the structure. When the incident electric field polarization is transverse to the dimer's axis (ϕ = 0°), a single strong absorption peak is observed at 0.75 THz. This absorption maximum corresponds to a transverse dipole-dipole (D-D) mode, which is located at the same position as the dipolar resonance supported by an array of single disks [see Figure 3(a)]. Figure 2(d) shows the electric field amplitude |E| and charge distribution for this plasmonic mode calculated numerically. Note that these panels resemble the field and charge distribution for the dipolar plasmonic modes sustained by two isolated InSb disks. Thus, we can conclude that, under transverse polarization illumination, the interaction between the two disks is extremely weak, and the dimer response is very similar to that of isolated disks.
As the electric field vector is rotated through ϕ = 45° to ϕ = 90°, we observe the resonance at 0.75 THz being modified from a transverse D-D mode to a longitudinal D-D mode [see Figure 2(b)]. The wavelength of this resonance remains relatively unchanged since we are operating in the quasi-static regime where retardation effects are negligible, which makes the plasmonic mode wavelength independent of the size of the supporting structure. Importantly, contrary to the transverse mode, the electromagnetic interaction between the two disks at resonance is now very strong. This is demonstrated by the electric field distribution in Figure 2(b). Note that the |E| profile for the longitudinal D-D mode is completely different from the dipole resonance for isolated disks and shows strong field enhancement (∼270) and localization near the point where the disks touch.
The change in polarization also leads to the emergence of a new lower frequency absorption maxima (∼0.4 THz), which originates from the excitation of a single dipole (D) mode parallel to the dimer's axis. This mode is only possible because the overlap between the disks allows for electric conduction between the disks and the charge neutrality of each disk can be broken. For this reason, this longitudinal D mode has recently been termed the charge transfer plasmon mode in the context of close touching metallic nanoparticles.20–23
Importantly, Figure 2(a) demonstrates that, as predicted theoretically,6, 16 the effect of the D mode is to effectively broaden the ACS, leading to greater absorption at lower frequencies. Figure 2(c) shows that, similarly to the longitudinal D-D mode, this resonance yields a strong (∼130 fold) field enhancement in the narrow gap separating the two disks, above the contact point. This sub-micrometer field localization is caused by charge pile-up in the vicinity of the gap. Note that it takes place within the broad frequency window that spans both the longitudinal D and D-D plasmonic modes supported by the dimer, which makes it very promising for sensing applications.
The enhancement of the electric field amplitude around the circumference of one of the disks is shown in Figure 2(e) for the three different modes. It can be seen that the field is strongly enhanced for the longitudinal D and D-D modes only over a small angular range close to the touching point (θ = 180°). In contrast, the transverse D-D mode produces a small enhancement (∼6 fold) over a broad angular range around θ = 90°. This demonstrates that the plasmonic interaction between the dimers plays a key role in the performance of the field enhancement of the device. The relatively smooth character of the electric fields in Figure 2(e) (note that they present a few oscillations along the disks perimeter) demonstrates that the plasmonic response of the fabricated dimers is governed by large wavevector (k ∼ 1/2D) field components. This indicates that non-local effects (spatial dispersion) have little impact on their optical properties, and ensures the validity of the local description.
We next investigate the effect of increasing the conductive overlap of the disks. Figure 3(a) plots the experimental extinction spectra for a periodic array (50 μm pitch) of single disks and the three touching dimer samples 1, 2 and 3 under longitudinal polarization (ϕ = 90°) illumination. It can be clearly seen that the overlapping disks exhibit substantial absorption broadening with respect to the single disk case. Following the theoretical TO approach in Ref. , a lower frequency cut-off for the ACS, ωc, can be introduced, which is largely determined by the resonant frequency of the longitudinal D-mode. It can be observed that ωc shifts to higher frequencies with increasing δ, reducing the absorption broadening. From the experimental spectra in Figure 3(a), we can extract cut-off frequencies of 0.31, 0.33 and 0.38 THz for disk samples 1, 2 and 3, respectively. The blue-shift of ωc with increasing overlap can be interpreted as a result of the smoothing of the dimer geometry. Theoretical calculations in Ref.  predict that as the overlap between the disks is enlarged, the response of the touching dimer will approach that of a single disk. Evidence for this trend can be seen in the experimental results in Figure 3(a), which show the D mode shifting towards the D-D resonance for touching dimers with increasing δ.
Let us remark that size effects are negligible in our samples, as the dimers are much smaller than the incoming wavelength (quasi-static limit). Therefore, the spectral broadening in Figure 3(a) cannot be linked to radiation losses, but to the geometric dependence of the plasmon coupling between the disks. On the other hand, the loss of the broadening effect with δ is accompanied by the strengthening of the lower frequency D-mode, as the charge transfer channel between the disks is enhanced.
Figure 3(b) renders the calculated ACS for the three experimental samples. The numerical results are in good agreement with the measured spectra, except for the absorption peaks being more pronounced in the simulations. This effect can be linked to the variability of the dimers' geometry across the experimental arrays, which leads to the effective smoothing and broadening of the experimental spectra.
Figure 3(b) also shows a slight blue-shifting of the D-D mode with increasing overlap. This effect is not observed in the experiments, which seems to indicate that it is related to the sharp geometry of the V-shaped junction between the disks in our numerical modeling (note that the junction geometry varies slightly from one dimer to the other in the experimental arrays). In our model, the reduction of δ increases the Coulomb attraction between charges of opposite sign across the dimer's gap [see Figure 2(b)]. This charge interaction depends strongly on the gap geometry, which explains why the mode sensitivity is lost in our experimental spectra. In order to test this hypothesis, we have used the theoretical approach in Ref.  to calculate the ACS of infinitely long overlapping InSb cylinders (D = 20 μm). In this case, the structure is illuminated from the side transverse to the dimers' axis with the wave polarized along the axis. Figure 3(c) renders the spectra for isolated, free-standing dimers of infinite length with different δ: 0.1 μm (blue), 0.2 μm (green), and 0.5 μm (magenta). For reference, the cross-section for a single infinitely long cylinder is also shown. The position of the various absorption maxima is strongly blue shifted with respect to the experimental results (∼1 THz) since the substrate is not included in the 2D simulation and a constant GaAs background is assumed instead. Despite of this, the theoretical profiles greatly resemble the measured ones. They not only describe the blue-shift of ωc with larger overlap, but also reproduce the robustness of the D-D mode frequency against variations in δ. This demonstrates that the blue-shift predicted by the simulations for this resonance originates from the sensitivity of the electromagnetic fields to the acute geometry of the overlapping region in our numerical modeling.
To conclude, the electromagnetic properties of InSb touching disks in the THz regime were studied both experimentally and numerically. The structures were realized by making use of the plasmonic response of InSb in the THz range, proving that semiconductors are an extremely useful vehicle for testing plasmonic devices whose fabrication requirements are overly onerous in the optical regime. We showed that, for the samples fabricated, the touching disk geometry displays a broadband absorption response consistent with the theoretical predictions of transformation optics for gold nanostructures at visible frequencies. Simulations demonstrated that InSb touching dimers display strong field enhancement and sub-wavelength confinement in the gap between the disks over a broad THz range. We expect that the efficient broadband THz harvesting properties of touching InSb disks will find applications in technological areas such as spectroscopy, biosensing, and security.