Broadband transparency in terahertz free-standing anapole metasurface

The electromagnetic response of subwavelength entities can be significantly enhanced by the Mie-type morphology-dependent resonances. Two- or three-dimensional arrays of such entities with a subwavelength period embedded in an appropriate matrix are commonly referred to as metasurfaces and metamaterials. The entities can be viewed as “artificial” atoms (metaatoms), whose electromagnetic properties can be customized by tailoring the subwavelength structural geometrical features.^1,2 Exploring a subtle balance of these morphological features and the electromagnetic response of conventional metals, dielectrics, and semiconductors allows one to design metamaterials exhibiting exotic electromagnetic properties not found in nature. These include negative refraction, cloaking, and absolute transparency that open up a plethora of new opportunities for applications ranging from telecommunications to microscopy.^1–5 

Design of a metamaterial fully transparent in a wide frequency range is a challenging task, because it implies vanishing radiation scattered by individual metaatoms in the far-field zone even though it may be nonzero in the near-field zone. In terms of multipole expansion of the scattered field,^6–9 the reflection will be suppressed if the dipole moment generated in metaatoms by the incident electromagnetic wave is zero. However, in practice, full suppression of the metasurface reflectivity is hardly achievable due to the presence of a substrate that embeds metaatoms. In addition, a finite conductivity of materials used in the fabrication of metasurfaces leads to dissipative losses that also complicate achieving full transparency.^10–15 It is worth noting that these losses can be significantly reduced in all-dielectric metaatoms, which are capable of achieving a strong enhancement of the electromagnetic field in a vicinity of the metaatom.¹⁶ 

One can observe from Eq. (1) that the electric dipole contribution to $En$ can be nullified by the toroidal moment if $p=−iωc2T$⁠. At such a condition, which is referred to as the anapole resonance, electric dipole radiation in the far zone is suppressed, i.e., in the dipole approximation, the metasurface does not reflect the incident electromagnetic wave. By taking into account that $|T|∝jl2$ and $|p|∝j/ω$⁠, where $l$ is the characteristic size of the metaatom, one can conclude that anapole resonance can be achieved if the size of the metaatom is comparable with the wavelength of the incident wave. This implies that spatial dispersion plays an important role in the electromagnetic response. One may notice that the anapole resonance condition only indirectly (via the current density $j$⁠) depends on the angle of incidence, i.e., one may expect that it should hold in the wide range of the incidence angles.

It is worth noting, however, that at the anapole resonance, contributions of $m$⁠, $Q̂e,$ and $Q̂m$ to the $En$ in Eq. (1) may be significant, which prevents the nullifying of the scattered field in the far zone. This issue has been resolved to some extent in the framework of the compound anapole concept.¹⁸ Specifically, if the metaatoms are constructed out of several elements with proper size, shape, and mutual arrangement it is possible to simultaneously nullify several multipole moments in Eq. (1) (e.g., $p$ or $Q̂e$⁠) at a specific frequency. Such a condition is referred to as the compound anapole resonance,¹⁸ which can be seen as destructive interference of multipole moments of metaatom's elements. For example, if the metaatom consists of a disk and a ring with an electric dipole moment $pdisk$ and $pring$⁠, respectively, at the compound anapole resonance $pdisk= −pring$⁠, i.e., the metaatom's dipole moment vanishes, $p=pdisk+pring=0$⁠, and the dipole contribution to $En$ in Eq. (1) is zero. If the frequencies of the anapole and compound anapole resonances are close enough the broadband transparency can be developed due to suppression of the scattering in the far zone.

In this Letter, we demonstrate that the coexistence of the compound anapole and anapole resonances enables broadband transparency of the metasurface composed of free-standing metaatoms comprising concentric disks and rings (see Fig. 1). To demonstrate this experimentally, we fabricated a metasurface with a unit cell comprising a disk with a radius of 95 μm and a ring with an inner and outer radii of 170 and 250 μm, respectively, (see Fig. 1 metaatom top view). These metaatoms possessing a thickness of about 60 μm were connected by 30 μm wide bridges to arrange them into a square lattice with a period of 630 μm. In the experiment, we measured the transmittance and reflectance spectra of the fabricated metasurface by the terahertz TDS system in the frequency range of 0.2–1.0 THz. The experimental results correspond well with the numerical simulations, which predicted almost 70% transmittance between 500 and 700 GHz frequencies. In this transparency region, the coexisting anapole and compound anapole resonances considerably suppress multipole moments of the metaatoms for a wide range of incident angles and orthogonal polarizations of incident wave.

The metasurface was fabricated out of 100 μm thick double-side polished silicon wafer possessing an electrical p-type resistivity of about 10 Ohm/cm. First, a 100 nm thick Cr layer was sputtered onto the wafer, followed by spin coating with a positive AR-P 6200 resist (Allresist GmbH). The coated wafer was exposed using the Raith EBPG 5000+ ESHR electron beam lithographer and developed. The Cr layer was etched through the obtained resist mask using the Oxford Instruments Plasmalab 100 reactive ion etcher (RIE) with inductively coupled plasma (ICP). After that the silicon was etched to 70 μm depth with Oxford Instruments Plasmalab 80 ICP-RIE, and the sidewalls of created pattern in silicon were protected by sputtering a 100 nm thick Cr layer. Then the wafer was flipped over and the remaining non-patterned layer with a thickness of about 40 μm was etched uniformly in ICP-RIE to develop a pattern of the free-standing metasurface. Finally, by removing the fluorocarbon residues and chromium protective layer with oxygen plasma and wet etching techniques, we reached a 60 μm total thickness of the metaatoms (see Fig. 1).

Transmittance and reflectance spectra of the metasurface were measured with a commercial terahertz TDS system (TeraVil T-SPEC 800) in the frequency range of 0.2–1.0 THz. In transmission geometry, we measured the terahertz pulses transmitted through the air (reference) and the metasurface (sample) using an aperture of 4.0 mm diameter, the size of which is sufficient to irradiate a sufficient number of metaatoms (5 × 5 array) to neglect the boundary effects.¹⁹ In reflection geometry, the terahertz pulses reflected from a gold mirror (reference) and the metasurface (sample) were recorded at normal incidence. The amplitudes of the Fourier harmonics were obtained by fast Fourier transform (FFT) of the sample and reference terahertz pulse traces. The squared ratio of these Fourier harmonic amplitudes determined the transmittance and reflectance spectra of the metasurface. More details about measurement setup and data analysis can be found elsewhere.^20,21

Figures 2(a) and 2(b) show transmittance and reflectance spectra, respectively, of the fabricated metasurface in the frequency range of 0.4–0.8 THz at normal incidence for the electric field polarized along the x and y axes. The solid lines present the spectra simulated in the COMSOL Multiphysics environment, while the circles show the experimental data. The THz permittivity of the silicon wafers used in our experiment was measured in the spectral range 0.1–3.5 THz in Ref. 22. These data were used for COMSOL Multiphysics modeling.

The simulated and measured transmittances [see Fig. 2(a)] are as high as 70% and are almost frequency-independent between 0.5 and 0.7 THz. Since the observed variation of the transmittance in the transparency window does not exceed 30%, the anisotropy induced by intra-metaatom bridges is relatively low. Figure 2(b) shows that in the transparency window, calculated and measured reflectance values do not exceed 20%. The numerical simulation predicts a pronounced dip in the reflectance spectrum for both polarizations at the frequency of 0.55 THz, which, however, was not well reproduced in the experiment.

To gain qualitative understanding of the origin of the transparency window, we evaluate the contributions of individual multipoles to the scattered radiation and consider the frequency dependence of the radiation power scattered by the metaatom. Figure 3 shows power spectra of the radiation scattered by the electric and magnetic dipoles, electric and magnetic quadrupoles, and toroidal moment, which are introduced in Eq. (1). Since toroidal and electric dipole moments produce identical radiation patterns in the far zone, we also calculated power generated by the combined source $TED=p+iωc2T$⁠. It is worth noting that interference between $p$ and $T$ may either be constructive or destructive. The latter corresponds to the anapole resonance, which manifests itself as a dip in the TED emission spectrum. One can observe from Figs. 3(a) and 3(b) that there exist two anapole resonances situated at the frequencies of 0.52 and 0.625 THz, where a suppression of the scattering and, correspondingly, an increase in the transmittance is expected. In addition, in the frequency range of 0.54–0.56 THz, the powers produced by all multipole moments but magnetic dipole are minima, i.e., this frequency range corresponds to the compound anapole resonance. The coexistence of two anapole resonances and a compound anapole resonance in a relatively narrow spectrum region essentially suppresses the scattering of the metaatoms that results in the transparency window spanning from 0.5 to 0.7 THz. Figures 3(a) and 3(b) show that the magnetic dipole dominates in scattering in this frequency range. Our numerical simulation showed that silicon conductivity is responsible for about 30% reduction of the transmittance within the transparency window.

Although the intra-metaatom bridges do not influence the primary multipoles or the overall response of the metamaterial, they introduce asymmetry affecting higher-order multipoles in the metamaterial response. Specifically, the contribution of the magnetic quadrupole moment to the emission in Fig. 3(a) becomes comparable with that of magnetic dipole moment. We believe that this is manifestation of so-called trapped^23,24 magnetic quadrupole mode, which emerges at the incident wave polarized perpendicular to the interatom bridge [E_x in Fig. 3(a)]. When the polarization of the incident wave rotates by 90°, this mode experiences leakage because the magnetic field penetrates the intra-metaatom bridges. However, when the structure is irradiated with the y-polarized wave, the magnetic field penetrates intra-metaatom bridges and this trapped mode experiences leakage leading to an increase in the magnetic quadrupole emission.

To study the effect of the anapole and compound resonances on the reflectance further, we compared the reflectance spectra of a gold mirror with and without our metasurface. Results are shown in Fig. 4(a). One can see that placing the metasurface on top of the gold mirror leaves reflectance in the transparency window virtually unchanged for x- and y-polarized incident light, i.e., the presence of the metasurface is hardly noticeable. On the contrary, outside the transparency window, the metasurface strongly suppresses the terahertz wave reflected from the mirror. Figure 4(b) demonstrates that the reflectance spectrum of empty aperture remained order of magnitude below than that of metasurface in all experiments.

Finally, we investigated the dependence of the terahertz transmittance on the angle of incidence for different polarizations of the incident wave. The results are shown in Fig. 5. One can observe that within the transparency window of 0.5–0.7 THz the transmittance shows a pronounced frequency dependence at oblique incidence and may become as low as 10% when the metasurface is rotated by 45° for both polarizations of the incident wave. The obtained weak dependence of the transmittance on the angle of incidence in the red part of the transparency window may indicate that anapole resonance at 0.52 THz dominates the metasurface response. However, in the vicinity of the compound anapole resonance at 0.55 THz and anapole resonance at 0.625 THz we observe pronounced transmission dependences on the incident angle. This may be caused by the mutual coupling effects between inter-metaatom bridge, disk, and ring at these frequencies that require further investigation.¹⁹ It is worth noting that altering the angle of incidence and/or polarization of the incoming light may drastically change the electromagnetic field in the near zone; however, this hardly affects the suppression of the field in the far zone at the anapole resonance.

In conclusion, we developed the compound anapole metasurface consisting of concentric disks and rings arranged in a square lattice. The proposed design allowed us to achieve the compound anapole regime, in which the scattered radiation in the far field is drastically suppressed and provides enhanced transparency in the range of 0.5–0.7 THz independently of the angle of incidence and of the polarization of incident light. The results of the terahertz time-domain spectroscopy measurements correspond well to the predictions of the first-principle numerical simulations in the COMSOL environment. The compound anapole metasurface has significant potential for suppressing background noise and improving the resolution in the terahertz imaging systems or designing low-loss filters and antennas.

This work was supported by the Research Council of Finland via Flagship Programme Photonics Research and Innovation decision #320166 (PREIN), grant decision #343393 (TETRAMETER), and the Horizon 2020 RISE projects #101007896 (CHARTIST) and #823878 (TERASSE). The Vilnius group was supported by the EU H2020 programme ITN-MCS project TERAOPTICS under the grant agreement No. 956857 and EU Next Generation Grant under Measure No. #10-038-T-0010.