We have wrapped metallic cylinders with strongly absorbing metamaterials. These resonant structures, which are patterned on flexible substrates, smoothly coat the cylinder and give it an electromagnetic response designed to minimize its radar cross section. We compare the normal-incidence, small-beam reflection coefficient with the measurement of the far-field bistatic radar cross section of the sample, using a quasi-planar THz wave with a beam diameter significantly larger than the sample dimensions. In this geometry we demonstrate a near-400-fold reduction of the radar cross section at the design frequency of 0.87 THz. In addition we discuss the effect of finite sample dimensions and the spatial dependence of the reflection spectrum of the metamaterial.
© 2011 OSA
Fabrication and optical characterization of metamaterial (MM) films designed for terahertz (THz) frequencies is a rapidly advancing research field [1,2] which has enabled the demonstration of device concepts such as frequency-agile components , absorbers [4,5], polarizers [6–10] and sensing devices [11–13]. Optical characterization at THz frequencies of metamaterial surfaces can be carried out in a phase-sensitive manner in reflection and transmission with the aid of THz time-domain spectroscopy techniques . Common to the absolute majority of published results is that the optical characterization is carried out with a sampling beam significantly smaller than the active sample area and thus under the implicit assumption that the metamaterial film effectively is of infinite extent. Hence, edge effects arising from the finite extent of a MM film are neglected.
Recently the concept of perfect absorbing MM surfaces at THz frequencies has emerged [4,14], and it has been demonstrated that such surfaces can be fabricated in the form of thin, flexible membranes which easily can be wrapped around cylindrical objects . These surfaces have demonstrated very high absorptivity and thus very low reflectivity at the resonant design frequency.
Here we use a newly developed setup for determination of broadband THz-frequency bistatic radar cross sections (RCS)  for characterization of flexible, resonantly absorbing MM films wrapped around a cylinder. The RCS is defined as the projected area required for intercepting and isotropically radiating the same amount of power as the target actually radiates toward the receiving antenna [15,16]. We measure the RCS with fixed antenna geometry while rotating the sample at the target position, thereby mimicking a tracking radar system which follows a moving object. To support the interpretation of the RCS measurements we use normal-incidence reflection measurements for the characterization of the local properties of the MM film. While the RCS measurements employ a collimated THz beam significantly larger than the MM-covered cylinder, the normal-incidence reflection measurements employ a tightly focused beam which provides a local probe of the reflectivity across the MM film.
2. Sample properties
The metamaterial absorber is based on the principle of minimal transmission and simultaneously, minimal reflection. Tao et al.  recently designed, fabricated and characterized thin, flexible films of metamaterial-based, resonant, near-unity absorbers which could be wrapped around mm-sized cylinders . We follow closely this design, with a geometry shown in Fig. 1(a) . A 12 µm thick polyimide (PI) layer is covered with a 200 nm thick gold layer, followed by another 12 µm thick layer of PI. On top of this sandwich structure a periodic array of electric split-ring resonators (SRR) consisting of 200 nm thick gold is patterned using photolithography. The SRR side length is 54.5 µm with a capacitor gap of 2 µm, line width of 4 µm, and a lattice period of 75 µm, as illustrated in Fig. 1(a). The only differences between the design shown in Fig. 1(a) and the design in  are in the shape of the capacitive element and minor scaling adjustments in the overall dimensions of the structure.
The resonant electromagnetic response to an electric field applied parallel to the central capacitor is due to the LC resonator formed by the two inductive loops on each side of the central capacitor and a dipolar response of the side conductors . For electric fields polarized perpendicular to the central capacitor leads, a single dipole resonance is expected.
The metamaterial array forms an active area of 20x10 mm, flanked by pads of dimensions 10x10 mm, consisting of the gold layer embedded between the PI layers but without MM structures defined on top. The full sample of dimensions 40x10 mm is wrapped around an aluminum cylinder with circumference 80 mm (radius 12.73 mm) and height 10 mm, thus covering exactly half of the circumference of the cylinder. The MM absorber was attached to the cylinder by double-sided sticky tape. The macroscopic sample geometry is illustrated in Fig. 1(b).
3. Normal-incidence reflection measurements
Normal-incidence reflection spectra were recorded with a reflection-type THz time-domain spectroscopy (THz-TDS) system based on low-temperature-grown GaAs photoconductive emitters and detectors (Menlo Systems) and driven by a femtosecond oscillator (Femtolasers Fusion 300 Pro). The experimental setup is illustrated schematically in Fig. 2(a) . Succinctly, the THz beam is coupled from the emitter onto the sample at normal incidence by a 2-mm thick high-resistivity silicon wafer . The reflected beam is transmitted back through the beamsplitter and directed to the detector. The spot size of the THz probe beam on the sample for this measurement is slightly below 1 mm, measured as the 10-90% rise distance of the reflection signal when scanned over a razor blade edge. The focusing is achieved by a polymer lens with 40 mm focal length. The flexible sample is mounted on a flat aluminum plate during this normal incidence reflection measurement, as opposed to the cylindrical mount used in the bistatic RCS measurements in Sec. 4.
The reflection spectrum recorded at a position close to the center of the active area of the sample is shown in Fig. 2(b), for the two polarizations of the incident THz field parallel (red curve) and perpendicular (black curve) to the central capacitor leads. The LC resonance is seen as a sharp dip in the reflection coefficient, reaching a minimum power reflectivity of −27 dB at 0.89 THz. This corresponds to an absorptivity A = 1-R-T = 0.998, assuming that the transmission T through the 200-nm gold film is insignificant. A second, less pronounced reflectivity-minimum (corresponding to the electric dipole resonance) is seen at 1.9 THz. For the perpendicular polarization the dipole resonance is seen as a relatively broad reflectivity minimum reaching −7.5 dB at 1.35 THz. A weak, secondary reflectivity minimum is observed at 1.6 THz. The reflectivity spectra are each normalized to the reflectivity of the bare aluminum surface on which the sample was mounted.
In Fig. 3(a) we have plotted the positional dependence of the reflectivity spectrum of the sample across its surface along the route indicated in the illustration above the diagram. The LC resonance is clearly visible at 0.89 THz in the region from −7 to 9 mm. Near the edges of the MM array the resonance is blurred and abruptly shifted to a higher frequency of 1.3 THz. While this edge effect is subject to ongoing further investigations we believe that it is a signature of the finite size of the MM array and modified coupling between the MM cells near the edge of the sample area. In addition to this significant modification of the reflection spectrum we observe a slight variation across the active area of the resonance frequency of the order of 0.03 THz around the average resonance frequency of 0.89 THz. This may be due to fabrication tolerances or the subsequent significant handling of the film during repeated attachment and release on various metallic objects.
Figure 3(b) shows the positional dependence of the reflectivity at three relevant frequencies across the sample, namely off resonance (0.42 THz), on the main LC resonance (0.89 THz), and at the resonance appearing at the edges of the active MM area (1.32 THz). The cross sections at these three frequencies reveal a uniform, off-resonance reflectivity (black curve), an on-resonance reflectivity with a broad minimum in the −7 to 7 mm range, and edge effects seen as significant reflectivity reduction at the edges of the active area (near ± 10 mm). The suppressed reflectivity observed further towards the edges of the whole sample (near ± 20 mm) is due to the physical edges of the sample.
4. Radar cross section measurements
The experimental setup for determination of the far-field bistatic radar cross section (RCS) of the sample as a whole is illustrated in Fig. 4 .
The setup is similar to the one described in , and here we give only a brief description of it. Femtosecond laser pulses from a regenerative amplifier (SpectraPhysics Spitfire) are split in two parts for electro-optic generation and sampling of the THz transients. The THz pulses are generated by the tilted pulse front method  in LiNbO3 doped with 1% MgO to prevent photorefractive damage. A pair of off-axis paraboloidal mirrors (OPM 1 and OPM 2 with f1 = 25.4 mm and f2 = 516.8 mm) expands and collimates the THz beam with a diameter of 73 mm, which is measured at the position of the target and defined as the full width at half maximum (FWHM) of the peak electric field amplitude measured by a knife-edge scanning experiment. The target, mounted on a computer-controlled rotation stage to adjust the rotation angle θ, is placed at a stand-off distance of 1200 mm from OPM 2.
The THz wave scattered off the target is picked up at a small bistatic angle (6.6°), defined by the dimensions of OPM 2 and the plane mirror PM which is also centered 1200 mm from the target. After the plane mirror, OPM 3 focuses the scattered THz radiation onto the electro-optic detection crystal (2 mm thick ZnTe crystal) where the time-dependent electric field of the THz signal is measured by free-space electro-optic sampling [21–23]. For this purpose, the second portion of the laser beam is delayed by a time τ and directed through a small central hole in OPM 3 for collinear transmission through the ZnTe crystal with the THz beam. The THz-induced birefringence at delay time τ is detected with a quarter-wave plate, polarizer, and two photodiodes (PD 1-2). The difference signal is detected by a lock-in amplifier, locked to the frequency (500 Hz) of an optical chopper in the THz generation beam path. The insets of Fig. 4 show the time-domain (top) and frequency-domain (bottom) representation of a reference signal recorded from the specular reflection of a large, planar reflector positioned at the location of the target.
The RCS of the sample is defined on the basis of the received power relative to the transmitted power via the standard radar range equation ,
Figure 5 shows the RCS of the sample as function of sample rotation angle relative to the incident THz wave for 0.40 THz (black curve), 0.87 THz (red curve), and 1.30 THz (blue curve). The RCS curves have been normalized to the RCS at the opposite side of the sample where the surface is bare Spectroscopy, terahertz, averaged over the angle range 170-190°. The data are directly comparable with the data shown in Fig. 3(b). The slight differences in the frequency indications arise from a different temporal step size and scan lengths used in the recording of the data in the two experiments. The center of the MM film faces the THz beam at a rotation angle of 0°.
The frequency-dependent RCS of a metallic cylinder is , where the equality sign holds for specular reflection at normal incidence. At the frequencies 0.40, 0.87 and 1.3 THz used in Fig. 5 the absolute RCS at normal incidence and 180° rotation angle is 107, 232 and 347 cm2, respectively. Notice that these cross sections are significantly larger than the projected cross section of the cylinder of 2.54 cm2.
Common features for the three frequencies are the uniform RCS at the back side of the sample (angle region 90-270°) and the reduction of the RCS in the regions near 90° and 270°. These reductions are due to the mounting of the MM film on the cylinder with double-sided sticky tape. This results in a small surface kink which acts as an efficient scatterer. The gradual decrease of RCS at 1.30 THz in the region 180-270° is most probably due to an unintentional tilt of the sample which results in a slight asymmetry in the RCS pattern.
The interesting features are observed when the MM film faces the THz beam. The RCS is reduced significantly at the resonance frequency of 0.87 THz, corresponding to the region of low reflectivity observed in Fig. 3(a). The reduction is greatest in a narrow angular range, by a factor of 384 from 232 cm2 to 0.60 cm2, and by an average factor of at least 10 in the angular range 340-20°. Comparison with the position dependent reflectivity in Fig. 3(b) (red curve) shows good agreement, even on the quantitative level. Figure 3(b) shows that the minimum reflectivity is −27 dB at the position of −3 mm, and the RCS is reduced with almost the same amount (−10log(384) = −26 dB) at a rotation angle of approximately 10°. Our measurements therefore indicate that the structure observed in the angular dependence of the RCS is due to the slight variation of the LC resonance frequency across the film.
At 1.30 THz there are two minima in the RCS in the region of interest (at 320° and 30°) with similar good correspondence to the position-dependent point measurement shown in Fig. 3(b) (blue curve). As seen in Fig. 3(a), these positions correspond to the shifted resonance frequencies near the MM area edges.
At 0.40 THz, which is selected as a reference frequency, we observe a rather constant RCS across the MM region of the sample. The slight reduction of the RCS with respect to the back side of the sample (bare aluminum) can be traced to the mounting of the MM film on the cylinder. Additionally, there is a slight crimping at the edges of the film. This crimping could result in scattering of the incident field away from the bistatic angle, leading to an apparent reduction of the RCS of the metallic cylinder. This effect is not observed in Fig. 3(a) and (b) where the measurements are carried out with a small THz spot size away from the edges of the thin film.
The close correspondence between the normal-incidence reflectivity spectra in Fig. 3 and the angle-dependent RCS in Fig. 5 indicates that there is a close relation between the two measurement methods. The spatial resolution in the point measurements in Fig. 3 is given by the spot size of the THz beam, measured to be 0.9 mm by a knife edge scan. The spatial resolution of the RCS measurement system is, in contrast, not determined by the spot size (here 73 mm, much larger than the sample), but rather by the aperture of the detection system as shown in Fig. 6 . With a cylindrical target we can estimate the displacement of an incident ray on the sample that will result in a reflected ray missing the aperture of the detection system. This displacement provides an estimate of the spatial resolution in the rotational direction on the cylinder.
The incident beam, displaced from the center of the cylinder to reproduce the experiment’s bistatic angle , is reflected off the cylindrical target and hits the center of the aperture a located at a distance R from the target.
A ray displaced Δ (corresponding to the angular displacement indicated by the blue-shaded triangle construction) from the beam center leaves the target with an angular offset of with respect to the main beam, as indicated by the orange-shaded triangle. Relating these expressions gives the estimated resolution,
The above arguments show that, for the cylindrical target used here, the on-target lateral resolution obtainable in the RCS experimental setup (Fig. 4) can be similar to or even better than what can be obtained by tight focusing in a conventional reflection-type setup (Fig. 2). While we did not perform a characterization of the angular resolution of the RCS measurement we observe consistent variations of the RCS within a few degrees change of the rotational angle.
Summarizing our findings, in absolute numbers the RCS, at 0.87 THz, was reduced from 232 cm2 to 0.60 cm2 for a cylinder with projected cross section of 2.54 cm2. As could be expected, the RCS reduction is very closely related to the 27 dB reduction of the reflectivity of the sample at the resonance frequency. Due to the very sharp LC resonance in the film studied here we found that slight variations of the resonance frequency across the active metamaterial area are observed as a significant angular dependence of the RCS at a specific frequency. With a thin, flexible film such as the one used in our experiments the handling and mounting of the film is delicate, and unintentional stretching or other deformations of the film may lead to the observed minor variations. We observed clear signatures of the mounting of the film on the cylinder in the RCS, and scattering effects were clearly visible at the transition between the MM film and the bare aluminum cylinder.
We found a close correspondence between the position-dependent reflectivity and angular dependence of the RCS pattern. Edge effects, which strongly influence the resonance frequency in the measured position-dependent reflectivity spectra, were directly visible in the RCS measurements. The origin of these edge effects is under further investigation and will be scrutinized elsewhere. The spatial resolution in the RCS measurement approaches the sub-mm range with a 73-mm diameter THz beam at our stand-off distance of 1200 mm.
In summary, we have measured the bistatic radar cross section of a metal cylinder wrapped in a perfect metamaterial absorber. We have demonstrated that flexible metamaterial films with high resonant absorption can reduce the radar cross section of a metallic object by a factor of nearly 400. With metamaterials, it is possible to further tailor the response. For example, dual-frequency absorbers have been demonstrated and highlight that multiband reduction of the scattering cross section is feasible . In principle, it is even possible to create dynamically tunable stealth materials. Finally, given the scale invariance of metamaterials, we note that these results are relevant to other frequency ranges.
We acknowledge partial support from the Danish Defense Acquisition and Logistics Organization, the Carlsberg Foundation, NSF under Contract No. ECCS 0802036, and AFOSR under Contract No. FA9550-09-1-0708.
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