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Cross-wavelength invisibility integrated with various invisibility tactics

A cross-wavelength invisibility concept is proposed, inspired by a natural predator-prey relationship.


INTRODUCTION
In the open ocean, becoming transparent, thus allowing light to pass through the body, provides a superior self-protection strategy for midwater prey (1), such as the hyperiid amphipod crustacean Cystisoma in Fig. 1A. As Cystisoma is almost transparent except for some necessary organs, such as the eyes, its substantially reduced scattering cross section enables it to avoid detection by most predators. However, a few predators can still use cross-spectra vision (2) to detect and successfully attack this kind of prey because of the special capabilities of the predator eyes. If a prey could break the balanced prey-predator interaction by concealing itself completely from the cross-spectra vision of predators, then the possibility of survival in the midwater ocean would be much higher.
Here, we adopt a Boolean metamaterial design procedure to combine the functionalities of each micro/nanostructure required for different invisibility tactics. As proof of concept, we successfully demonstrate an optically transparent microwave cloak that integrates longwave cloaking and shortwave transparency simultaneously. The device is constructed of macroscopic metallic networks (extremely high local electrical conductivity) with microscopic silver/nickel (Ag/Ni) wires (extremely low global optical conductivity) through nanoimprinting fabrication (28). The experimental results demonstrate a substantial reduction in the scattering cross section in the microwave regime from 6 to 10 GHz and optical transparency from 400 to 760 nm.

RESULTS
A schematic of the optically transparent microwave cloak is illustrated in Fig. 1B. With a transparent body, the cloak should be penetrated by visible light (blue and yellow rays) with negligible loss, decreasing the optical scattering cross section and allowing the internal observer to simultaneously see outside freely. Meanwhile, both the amplitude and phase of the reflected microwave beam should be the same as those for the ground reflection case when microwave waves (green rays) interact with the metasurface cloak. For comparison with the schematic view, the sample realized in practice is shown in Fig. 1C. The geometrical dimensions of the fabricated cloak are D = 114.8 mm, d = 42 mm, and h = 21 mm. The cloak is fully transparent, and the internal object (i.e., the metallic badge with the words "Jilin University") can be seen from the outside. This phenomenon indicates that the internal observer can see outside freely and that the visible dimensions of the cloak are obviously decreased compared to a fully opaque cloak. Our optically transparent microwave invisibility cloak consists of two metasurfaces imprinted on flexible polyethylene terephthalate 2 of 8 (PET) films and isolated by a curved transparent PET spacer with a relative permittivity of 3.37 at 1 MHz (29). The thickness of the PET films is 0.15 mm, while the thickness of the spacer is 2.16 mm for the top cover and 1.8 mm for the sidewall of the cloak. The inner-layer metasurface acts as a perfect electric conductor (PEC) boundary, while the ring resonators on the outer-layer metasurface provide proper phase compensation and amplitude preservation effects.
We start the design by engineering the electromagnetic response for microwave invisibility. According to the generalized Snell's law (10,18), metallic ring resonators should provide a phase response ∆ =  − 2k 0 h u cos  to compensate for the phase error induced by the height of the bump. Here, k 0 and h u represent the wave number in free space and the height of the unit cell center, respectively. In total, eight kinds of ring resonators with periodicity p = 6 mm are used to build the cloak and are named ring N (N = 1, 2, …, 8) from the bottom to the top (see fig. S1). The angle  at which a microwave encounters a ring resonator on the sidewall can be written as  = (18), and the incident direction-dependent phase response is studied in Fig. 2 (A and B), for the cases of transverse electric (TE)-and transverse magnetic (TM)-polarized incidence, respectively. One can see that the phase responses are close to the ideal phase shift at  = 10°, 20°, 30°, and 40° for the TE case, while the phase responses of the resonators have a slight deviation with different  for the TM case. Since our carpet cloak design is based on phase compensation of the metasurface (10,18), which reconstructs the reflected wave so that it is the same as the wave reflected from the original ground plane, it does not have the apparent height problem and the lateral shift of scattering waves (30).
Designing only unit cells for microwave invisibility is not enough to realize cross-wavelength invisibility. On the one hand, microwave cloaking structures producing the proper phase shift and preserved amplitude response require a material with ultrahigh electrical conductivity, which is usually found in natural homogeneous metals. On the other hand, the metastructures should present an extremely high transmitted light intensity, which requires ultralow optical conductivity. To match the material requirements of an optically transparent microwave cloak, we prepare a transparent silver mesh to achieve extremely high global electrical conductivity and ultralow global optical conductivity as the first step. A schematic view of this silver mesh with a square lattice in air is shown in Fig. 2C. The silver structure is described by the Drude model (31). That is, the relative permittivity can be expressed by , where the plasma frequency  p = 1.39 × 10 16 s −1 and the collision frequency  c = 3.23 × 10 13 s −1 . The bulk conductivity of silver can be expressed by  =  of light, we suppose that all the light that illuminates the silver cannot penetrate the metallic mesh. With this assumption, the light transparency can be estimated by T = S metal _ S lattice under normal incidence, and the effective optical conductivity is estimated by (33). Then, an acceptable balance between the contradictory requirements of ultrahigh electrical conductivity at microwave frequencies and ultralow optical conductivity at visible frequencies could be found with a proper w m /p m ratio. For instance,  microw = 2.65 × 10 6 S/m and  opt = 6.98 × 10 2 S/m (equivalent to R s, mesh = 0.1 ohms/□ and T = 0.95; see also section S3) can be proposed when w m /p m = 0.025.
Then, we adopt a Boolean metamaterial design procedure to merge these metastructures for single-band functional realization into an integrated one. For example, to achieve cross-wavelength invisibility with optical transparency and microwave-bypassing ability, we can integrate the metastructures for the microwave regime M(x m , y m , z m ) and visible regime V(x v , y v , z v ) by adopting a Boolean logical multiplication (denoted by ∧ or AND), i.e., BM(x bm , y bm , Fig. 2D. Here, the metastructures in each frequency regime are treated as the inputs of the Boolean AND gate in an integrated circuit. Through this procedure, the integrated metastructures are equal to the macroscopic metallic network formed by mapped microscopic metal wires, which exhibit an extremely high local electrical conductivity while preserving an extremely low global optical conductivity. The amplitude response of the unit cells is calculated to quantitatively study the potential reflection attenuation with different sheet resistances. From the results in Fig. 3A, one can see that the suitable sheet resistances that match the requirements of the cloak are very limited. When the sheet resistance of the material is outside of this suitable region, the ohmic loss in the unit cells will attenuate the amplitude of the reflected electromagnetic waves and unfavorably deteriorate the cloaking effect (7,34). Achieving the material parameters that work for our design is very challenging in practice. For example, transparent conducting materials, e.g., indium tin oxides, graphene, and carbon nanowires, usually have good optical transparency only with a higher than 1 ohm/□ sheet resistance (35,36). However, from the results in Fig. 3A, we find that this kind of metasurface cannot achieve amplitude preservation when the sheet resistance is higher than 1 ohm/□. In other words, such transparent conducting materials may not meet the critical requirements for our cross-wavelength invisibility tactic, although they have been widely used in the demonstration of microwave absorbers (37)(38)(39)(40) and other microwave devices (see section S8). To avoid unnecessary ohmic loss, the width-period ratio w m /p m cannot be less than 0.025 locally for the outer-layer metasurface. In addition, considering the vision resolution of the naked eye, we set the width of the metal wires w m to not exceed 6 m for the Boolean procedure. The amplitude and phase response of the unit cells after the Boolean procedure are investigated as well. As shown in the inset of Fig. 3A, all the reflection coefficients |R| are close to unity, with the lowest amplitude of the reflection coefficient of 0.89 for ring 5 at 7 GHz. Figure 3 (B and C) presents the phase response of the unit cells at 7 GHz under the illumination of TE waves and TM waves, respectively. The phase responses of all the unit cells are very consistent with the ideal (theoretical) case. Furthermore, the phase response of each unit cell after the Boolean procedure is almost identical to that before the Boolean procedure (Fig. 2, A and B).
Because both a large-area metasurface for concealing macroscopic objects at the microwave scale and high-precision fabrication of microscopic metal wires at the micrometer scale should be guaranteed, an advanced nanoimprinting technique (28) is chosen to realize the optically transparent microwave cloak. The optical characterization of the outer-layer and quasi-PEC metasurfaces on PET substrates by scanning electron microscopy (SEM) is provided in Fig. 4 (A and  B, respectively). The outline of the macroscopic ring resonator is formed by metallic circular wires, and several straight shorting wires oriented along the radial direction are used to connect the circular metal wires. For a ring resonator with a larger width, more concentric circular metal wires could be adopted to preserve the widthperiod ratio w m /p m . In contrast to the ring resonators, hexagonal metal-wire networks are used as the quasi-PEC layer. The microscopic profiles of the interline junctions provided in the insets of Fig. 4 (A and B) present good electrical connections, indicating that the metal wires effectively form macroscopic effective circuits. Because of the metallic networks and good electrical connection, a local high electrical conductivity is achieved over the patterned areas at the microwave scale. The optical transparency is characterized in Fig. 4C. For the case of the outer-layer metasurface, the transmitted light intensity can be higher than 85% over the whole visible wavelength spectrum from 400 to 760 nm, and the highest transmittivity can reach 90% at approximately 660 nm. For the quasi-PEC layer, the average transmitted light intensity is higher than 82% over the full visible range. After stacking up the bilayer metasurface structure, the average transparency could be 72% over the wavelength range from 400 to 760 nm. The optical see-through ability of the optically transparent microwave cloak is experimentally proven in a field test, as shown in Fig. 4D. Compared to the case of direct observation without the cloak (e.g., Fig. 4E), the internal observer can see through the cloak and observe the environment freely with little visual distortion (see movie S1 that mimics the vision of a driver who drives a transparent invisible vehicle).
The microwave cloaking performance is demonstrated experimentally under both TE-polarized and TM-polarized incidence. As shown in Fig. 5A, the reflected beam distributions for the cloak case are identical to those for the ground case shown in Fig. 5B, which indicates that the reflected beam can be recovered when the cloak covers a bump. For comparison to the cloak and ground cases, Fig. 5 (C and D) shows the reflected beam distributions for the case of bumps made from transparent quasi-PEC film and aluminum film, respectively. In both cases, the reflected beams separate into several parts, the patterns of which are completely different from those in the ground case. One can see that the reflected beam distribution for the case of the transparent PEC is almost identical to that for the case of the aluminum bump, which provides unambiguous evidence that the metallic networks have extremely high conductivity and can act as quasi-PECs at microwave frequencies. The experimental results of the reflected beam distributions under TM-polarized incidence at 7 GHz are plotted in Fig. 5 (F to I). Similar to the TE cases, the reflected magnetic field distributions for the cloak case are in good agreement with those for the flat ground case. Furthermore, the total scattering reduction for our sample over different frequencies is studied experimentally. The total scattering reductions are calculated through  reduction,TE =  Fig. 5J. Here, ∅ represents the azimuthal angle from −90° to 90°. Both the electric field and magnetic field are in complex form, i.e., E z = E Rz + iE Iz and H z = H Rz + iH Iz , where subscripts R and I represent the real part and imaginary parts, respectively, of the electric field and magnetic field. The substantial reduction of the total scattering also indicates that the phase and amplitude of the wave reflected from the cloak is the same as those of the wave reflected from the ground plane (12,19). For the TE case, the cloak can decrease the total scattering of the object over the frequency range from 6 to 10 GHz, where the best 3-dB bandwidth is approximately 27.9% (from 6.65 to 8.81 GHz,  = 6°). Furthermore, the total scattering can be decreased to 14.5% at 7.57 GHz when  = 6°, which is shifted slightly compared to the designed frequency (i.e., 7 GHz) and designed incident angle ( = 10°). For the TM case, the total scattering can be decreased to 25.0% at 7.16 GHz and  = 16°, which is slightly higher than that in the TE case. The best 3-dB bandwidth in the TM case is approximately 18.9% (from 6.46 to 7.81 GHz,  = 16°). In addition, the numerical electromagnetic field distribution away from the cloak and the experimental differential scattering of the cloak (19) are provided in figs. S2 and S8, respectively.

DISCUSSION
The above results indicate achievement of cross-wavelength invisibility with preserved amplitude and undistorted phase at microwave frequencies, as well as omnidirectional transparency over the visible spectrum. Compared to previous carpet cloaks ( [14][15][16][17][18][19][20][21][22][23][24][25][26][27], our work presents an experimental demonstration of achieving invisibility over cross-wavelength wide regimes by integrating various invisibility tactics. Our work not only exhibits the advantages of polarization independence (15,(19)(20)(21)24), wide incident angle allowance (21,24,26,27), and remarkable bandwidth (14,15,(17)(18)(19)(20)(21)(22)(24)(25)(26) in the cloaking/longwave region but also features body transparency in the shortwave region. Such cross-wavelength invisibility integration is in line with the technical trend of stealth technology and can be practically more available with advanced nanofabrication technologies. Longwave detection is the technical trend of advanced long-distance detection technologies, because electromagnetic waves with longer wavelengths can propagate over a larger distance even in severe weather. In contrast to long waves, short waves cannot propagate over these long distances but are very helpful for people seeking a high resolution. The combination of longwave cloaking and shortwave transparency allows the eyes of a stealth system to clearly observe the external world while the system remains undetectable. Furthermore, it is possible to integrate transparent components underneath our cloak to enable a comprehensive system (see section S8).
On the basis of previous methods for controlling electromagnetic waves (1,(3)(4)(5)(6)(7)(8)(9)(10)(11), our Boolean metamaterial design procedure provides the possibility to combine various invisibility tactics, which is a general-purpose methodology for cross-wavelength invisibility integration. Moreover, triggered by the concept of integrated logic circuits, our work may eliminate concerns regarding compact designs with divergent functional requirements and thereby pave the way toward the integrated realization of multifunctional or even multiphysics devices with compact dimensions.

Boolean metamaterial design procedure
Here, we experimentally demonstrate the cross-wavelength invisibility device as only one example of the Boolean metamaterial design procedure. More generally, this procedure can be expressed as where R t is the target metastructure, R i (N = 1,2, …, N) is the metastructure of the Nth function/frequency regime, and "BF" represents the Boolean functions (e.g., AND, OR, and NOR) or their logical combinations adopted for the corresponding metastructures. In the first step of the procedure, metastructures with divergent spectral responses are achieved individually in their corresponding frequency regime. In this step, the metastructures in each frequency regime are treated as the inputs of relevant Boolean gates in an integrated circuit. As long as the functionality of the metastructures is dispersion independent, we can merge the geometries of the metastructures with single-band engineered dispersion into an integrated structure with multiband engineered dispersive properties following suitable Boolean operations or their combinations. Last, practical multifunctional or multifrequency devices based on Boolean metamaterials can be realized with the use of proper advanced nanofabrication technologies to support the multilevel geometrical degree of freedom in Boolean metamaterials. More details of this procedure are discussed in section S4.

Fabrication
The transparent metasurfaces are fabricated through an advanced nanoimprinting technique, the procedure of which is illustrated in fig. S6. First, photolithography is used to produce a Ni master plate with convex patterns as the imprinting template. Second, a layer of ultraviolet (UV) glue is used to cover a PET substrate, and then, the Ni master plate is imprinted into the UV glue layer ( fig. S6A). This step is carried out to form grooves with high aspect ratios, as shown in fig. S6B. Third, nano-Ag ink is poured into the grooves as the electroplating seed layer shown in fig. S6C. Last, metallic Ni is electroplated on top of the microscopic Ag wires inside the grooves ( fig.  S6D). The proposed electroplating step is performed to further increase the height of the microscopic metal wires, which could decrease the sheet resistance. The purpose of using Ag is to realize extremely low sheet resistance with relatively low loss in visible transmittance, while electroplating of Ni is carried out to prevent the Ag-based metasurface from being oxidized, expecting to obtain a long service life in practical application scenarios. The width, period, and arrangement of the metal wires are optimized slightly in the fabrication.

Microwave experiment
All the microwave measurements are carried out in a microwave absorber chamber, and a schematic view of the microwave experimental setup is illustrated in fig. S7. All the original experimental data are obtained automatically with the use of a Linbou threedimensional near-field scanning system. A laptop with the measurement operation system and postprocessing software is connected simultaneously to a Keysight E5071C vector network analyzer (VNA) and an electrical control box by cables. Two ports of the VNA are connected to a horn antenna as the transceiver and a probe as the receiver. The transmitting antenna used in the experiment is an HD-100LHA250SZJ high-gain directive horn antenna from Xi'an Hengda Microwave Technology Development Co. Ltd. A monopole probe is used to detect the electric field for TE-polarized incidence, while a commercial 100A Beehive EMC (electromagnetic compatibility) probe is used to detect the magnetic field for TMpolarized incidence. During the measurement, a half-circular path of ∅ ∈ (−90°, 90°) with a radius of 250 mm is used to obtain the reflected fields. The azimuthal resolution is 1° in the experiment.

Optical characterization
Both the outer-layer and inner-layer metasurfaces are cut into small pieces for optical characterization. A UV-visible spectrophotometer (UV-2550) is adopted to determine the transmitted light intensities, and a JSM-7500F SEM is used to observe the microscopic geometries of metal wires. The sheet resistance of the quasi-PEC layer is determined with the use of a four-probe detector (ST-21H, 4 Probes Tech). A micro wireless surveillance camera (JOOAN JA-A4) is used in the field test to mimic the vision of a driver inside an optically transparent microwave invisibility cloak (car).