Suboptimal Coding Metasurfaces for Terahertz Diffuse Scattering

Coding metasurfaces, composed of only two types of elements arranged according to a binary code, are attracting a steadily increasing interest in many application scenarios. In this study, we apply this concept to attain diffuse scattering at THz frequencies. Building up on previously derived theoretical results, we carry out a suboptimal metasurface design based on a simple, deterministic and computationally inexpensive algorithm that can be applied to arbitrarily large structures. For experimental validation, we fabricate and characterize three prototypes working at 1 THz, which, in accordance with numerical predictions, exhibit significant reductions of the radar cross-section, with reasonably good frequency and angular stability. Besides the radar-signature control, our results may also find potentially interesting applications to diffusive imaging, computational imaging, and (scaled to optical wavelengths) photovoltaics.

shows the coding sequences pertaining to the three designs, from which the 2-D binary codings are obtained via dyadic products. Figure S1 shows the resulting layouts. As mentioned in the main text, the 5 P -and 5 Q -type sequences consist of 32 bits, and the corresponding patterns (Figs. S1b and S1c, respectively) are globally aperiodic. Note that the first halves of these sequences coincide, whereas the second halves are flipped. Conversely, the 2 P -type sequence is only four-element long, and the corresponding 2-D pattern is a periodic replication of this basic coding (see Fig. S1a) so as to obtain the same size as the other two.  Figure S1. (a), (b), (c) 2-D patterns pertaining to the GRS 2 P -, 5 P -and 5 Q -type designs, respectively. The codings are generated via dyadic products of the sequences in Table 1. Figure S2 illustrates the schematics of the two setups utilized for the experimental characterization of the metasurfaces (backscattering and angular-scan measurements).

Details on Measurement Setup
A rendering of the customized THz time-domain spectrometer (TERA 15, MENLO Systems GmbH, Germany) is shown in Fig. S3a. The system is driven by a femtosecond fiber laser (operating at 1560 nm) with a fiber-coupled output with optical power < 100 mW, pulse length < 90 fs, and bandwidth ~3.5 THz. The setup employs fiber-coupled photoconductive antenna (PCA) modules (TERA 15 TX/RX FC) both for signal emission and detection. Best values for the antenna performance are: spectral range > 4 THz, dynamic range > 75 dB, and frequency resolution < 1.2 GHz.
Plano-convex, aspherical, polymethylpentene (TPX) lenses are used to collimate the broadband THz radiation onto both the metasurface and the unpatterned gold plated substrate used as a reference. The beam waist, measured via a standard edge technique, is found to be ~11 mm in diameter at 1 THz. A fiber-coupled opto-mechanical light path is utilized for the optical delay. For backscattering measurements (see the discussion below), a high transmittance single-pass silicon THz beam-splitter placed at 45° angle is utilized. The target holder and the beam-splitter are placed on kinematic mounts connected to a micro-scaled rotation stage to adjust the tilts. Accurate target positioning is maintained by a computer-controlled x-y stage. Since the spot size of the THz beam is slightly larger than the metasurface dimensions ( 9.6 9.6 × mm 2 ), a "wet masking" method is utilized to avoid any signal interference from the environment. Basically, the ends of the sample under test are covered with highly absorbing stripes (wet anti-dust cloths) in order to suppress any unwanted specular reflections from the surrounding unpatterned gold; these latter would be dominant at the specific incident angles (0, 10° or 20°) by comparison with the signal scattered by the metasurface. Oblique-incidence and angular scan. The pink-shaded area represents an angular region that is not accessible by the receiver (blind zone).
As mentioned in the main text, two different setups are utilized. Figure S3b shows a rendering of the setup for backscattering measurements (also schematized in Fig. S2a). In this configuration, the THz signal emitted by the first PCA impinges directly onto the target at normal incidence after passing through the silicon beam-splitter, and the backscattered signal is collected along the orthogonal direction. Figure S3c shows instead the rendering of the setup for angular measurements (also schematized in Fig.   S2b). In this case, the THz beam impinges on the target with a fixed angle (  software. It is worth highlighting that, although the working bandwidth of the system is 0.2-3.5 THz, our observations are focused on the frequency region 0.8-1.6 THz where the response of the two basic unit-cells is close to the desired 180° out-of-phase condition (cf. Fig. 2a).

Results for GRS Q 5 -type Design
Figures S4-S6 illustrate the results pertaining to the GRS 5 Q -type design. Overall, the experimental results are comparable with those observed for the 5 P -type design (cf. Figs. 3b,5,6c,6d). It is worth stressing that the theoretical predictions for the 5 Q -type design are rather extreme, as the specular reflection should be exactly zero at those frequencies where the reflection coefficients of the two elements are out of phase. As it can be observed from Fig. 2a, this condition is numerically met at the design frequency of 1 THz and also at a higher frequency around 1.3 THz. Accordingly, the numerically predicted RCS ratio attains two nulls at those frequencies (see Fig. S4), and exhibits generally smaller values than the 5 P -type design (cf. Fig. 3b) over most of the observed frequency region. On the other hand, the measured backscattering is not very different from the 5 P -type case, with a visible dip at the design frequency. The discrepancies with the numerical simulations at higher frequencies can be attributed to the various approximations in the model, as well as fabrication tolerances and uncertainty in the constitutive parameters of the dielectric layer. Moreover, we estimate that reductions in the RCS ratio >40 dB are likely beyond the experimental sensitivity of our current measurement setup. Nevertheless, we remark that RCS reductions ~20 dB are maintained over a sizable bandwidth.
From Fig. S5, we observe a rather flat angular response, uniformly across the observed frequency region, once again devoid of Bragg-type peaks. In fact, unlike the 5 P -type case (cf. Fig. 5b), the measured angle/frequency map in Fig. S5b does not show any visible residual of trivial Bragg modes.
Also remarkable is the good agreement between simulations and measurements in the angular response at the design frequency of 1 THz (Fig. S5d).
Finally, Fig. S6 shows the results for oblique incidence. Also in this case, the experimental responses are in line with those observed in the 5 P -type case (cf. Figs. 6c and 6d), with the RCS generally exhibiting a reduction ≥ 20 dB. Once again, the perceived deterioration of the agreement with the simulations is attributable to the various approximations and inaccuracies in our modeling (e.g., unmodeled finite-size and coupling effects) which, as already mentioned in the main text, become more prominent at oblique incidence.  Fig. S2a), as a function of frequency, for the GRS 5 Q -type design. The coding sequence and corresponding layout are explicitly given in Table S1 and Fig. S1. θ =° and 1 f = THz, respectively, comparing measurements (blue-solid) and simulations (red-dashed). The magentacross markers in panel (c) indicate the water-vapor absorption peaks. The pink-shaded area in panel (d) indicates a 20° angular region that is not accessible by the detector (blind region, cf. Fig. S2b). Also shown (blue-circle marker) is the backscattering measurement sample (extracted from Fig. S4).