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Abstract
The concept of perfect invisibility in free space implies an object neither reflects nor refracts optical waves coming from arbitrary directions, regardless of its shape and size. An optimal solution to realize such a peculiar phenomenon is to tune the constitutive parameters of the object to be identical to air. In particular, to render zero extinction from an existing object by covering some additional structures, is of importance for practical implementations, which is challenging. Here, we demonstrate and propose that a thin metallic wire can be tuned to be air-like under TE polarization, with the aid of an external enclosure. This is achieved through a precise dispersion engineering with independently controllable electric and magnetic responses. Consequently, an electrically large cluster composed of multiple thin wires can be safely hidden in free space, without any macroscopic cloaking structure, which is verified by full-wave simulations and experiments. The measured results on an electrically large airplane-like sample show the excellent performance of 2D omnidirectional invisibility at the designed frequency. This proposed metamaterial would be helpful in enhancing the mechanical stability, electrical conduction, and heat dissipation of a device (or system) by extra wires (or pipes), without disturbing its electromagnetic characteristics.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
If an object is not sensed by a specified detector, it has the ability of invisibility, which has been attracting tremendous interests in both the scientific and engineering communities. Traditional studies used to focus on the invisibility in some particular scenarios, e.g. back-ward scattering reduction through absorption [1] or antireflection [2], which concerns transparency by impedance matching. For the latter approach, various metasurfaces with full transmission have been developed, including the electromagnetically induced transparency [3–6], frequency selective structures [7–10] and the successful Huygens metasurfaces [11,12]. However, these metasurfaces usually take effect only under some specific incidence illuminations, due to their intrinsic confinements, i.e., the design procedure of these structures involving the prescribed electromagnetic quantities, or structures losing rotational symmetry. As a result, the application and implementation of these structures are limited.
In fact, there is a demand that an object can behave as omnidirectionally invisible, so that the drawbacks of those metasurfaces mentioned previously can be safely lifted. The typical examples of omnidirectional invisibility would be those cloaking devices with transformation optics (TO) [13,14], which employ complex inhomogeneous and anisotropic materials to guide the electromagnetic power flow around their inner region. However, such TO based cloaks are too difficult to realize with current fabrication techniques, even in 2D case. An alternative approach to achieve omnidirectional invisibility is the transparent body [15,16], which only requires the object itself has an electromagnetic (EM) response similar to the surrounding background. For electrically small objects, the EM scattering can be deeply suppressed by utilizing low or negative permittivity coatings, which help cancelling the majority of Mie scattering coefficients under some particular conditions [17–19]. Till now, various low-scattering designs of electrically small objects (based on the scattering cancellation technique) have been proposed and verified through computer based simulations and practical experiments [20–24]. It is shown that these designs work well with individual particles. Nevertheless, for a cluster composed of several particles, the scattering cancellation fails due to the enhancement of unwanted Mie coefficients aroused by the multiple scattering interaction, except that the whole composite can behave as air-like, i.e., effective permittivity and effective permeability are equal to unity. In [25], an integrated design of a metallic mesh structure is shown to be air-like, which indicates the possibility of invisibility for electrically large objects. Although, such an all-in-one structure does not exhibit flexibility in the practical implementations, since it may not be finely employed by an existing system. Hence, it would be much more convenient if the air-like EM response can be rendered through a coating approach.
In this paper, we propose a two-part design to realize perfect transparency and invisibility for thin metallic wire structures under TE polarization. We show that the electric and magnetic responses of the coated wires can be controlled independently by changing the external enclosure. With carefully tuning the dimensions of the composite shell, the scattering of an infinitely long metallic cylinder can be totally cancelled, which holds for a 2D electrically large cluster made of multiple cylinders. The omnidirectional invisibility effect is well analyzed with the effective medium and photonic crystal theories. Full-wave simulations and experimental measurements verify our new findings.
2. Theory and design
We begin by analyzing the electromagnetic characteristics of a periodical array of thin parallel metallic wires with the lattice constant p, as shown in the top left panel of Fig. 1(a). Such a dense array can be used to construct metamaterial with a negative permittivity [26]. It couples strongly to parallel incident electric fields in free space, inducing a strong electric resonance and exhibiting a Drude-model dielectric dispersion. In the quasi-static limit, its effective permittivity can be described in the form of ɛeff = 1-ω2p/ω2, where ω2p=2πc2/[p2ln(p/r1)] is the effective plasma frequency [26]. Here, r1 is the radius of metallic wires and c is the velocity of light in vacuum. A key observation, from the equation above, is that its effective permittivity is negative below the plasma frequency ωp and always smaller than unity in the whole band, leading to inevitable EM scattering. According to the mixing principle of media, we can tune the array’s effective permittivity by covering each single wire with a dielectric layer with a permittivity larger than unity, with doing this the overall dipole moment induced can be complemented [15], as shown in the top right panel of Fig. 1(a). Meanwhile, due to the presence of magnetoelectric coupling stemming from the finite phase velocity along the metamaterial array, the corresponding effective permeability (μeff) of wire array would exhibit an anti-resonant frequency dependence, accompany with the resonant dispersion of effective permittivity [27]. This unconventional magnetic effect makes the effective permeability be larger than unity, so a paramagnetic response would be observed macroscopically. Hence, it is essential that the outer dielectric layer should be diamagnetic, so that the macroscopic paramagnetic response is neutralized. Based on the diamagnetic property of periodical array of small metallic cubes or cylinders [28,29], here we introduce a non-resonance element into the cover dielectric layer to control overall magnetic response, as shown in the bottom panel of Fig. 1(a), wherein the effective permeability can be efficiently tuned in a wide frequency band by changing the volume ratio of metallic inclusion. Systematically, we can synthesize that the effective permeability and permittivity of the cover layer can be approximated by ucover_eff ≈1-F, ɛcover_eff ≈ ɛdielectric_host ×(1-F)−1, where F is the volume fraction of the hollow cylinder [28]. Thus, the overall effective permittivity and permeability of wire array can be controlled independently through tuning F.
Fig. 1. (a) Periodical array of thin metallic wires without (top left panel) and with (top right panel) diamagnetic dielectric cover layer, the lattice constant is p. The bottom panel shows the unit cell of thin metallic wire covered with an effective diamagnetic dielectric layer composed of a metallic hollow cylinder and a dielectric host. (b) Retrieved effective constitutive parameters (top panel) and effective refractive indexes (bottom panel) for a single layer composed of closely arranged unit cells in (a) along y and z axes, where the dielectric host is revised to be cube with side length p, as shown in the inset of bottom panel. The dimensions are p=12 mm, r1=0.75 mm, r2=1.73 mm, r3=4.6 mm, h=4.8 mm. The metal is copper with a conductance of 5.896 × 107 S/m, and the dielectric host is polysulfone with a dielectric constant of 3 and a loss tangent of 0.0013. (c) Calculated normalized scattering widths of a thin metallic metallic wire covered with a diamagnetic dielectric layer according to Eq. (1). The radius r1 of wire is 0.75 mm, and the permittivity and permeability of the diamagnetic dielectric layer are ɛcover_eff=3×(1-F)−1 and μcover_eff = 1-F. The radius of diamagnetic dielectric cover layer is R.
To verify our previous analysis, a perfectly transparent metamaterial in free space composed of previous unit cells is designed at 5 GHz. For the convenience of simulation and fabrication, the shape of dielectric host is revised to be square with side length p. We performed full-wave simulations on this structure using CST Microwave Studio by optimizing the permittivity of the dielectric host and the dimensions of hollow cylinder, i.e., r2, r3 and h. For the detailed optimized parameters, please refer to Fig. 1. The metal is copper with a conductance of 5.896 × 107 S/m, and the dielectric host is polysulfone with a dielectric constant of 3 and a loss tangent of 0.0013. By arranging previous unit cells closely along y and z axes into a single layer of slab, we simulated S parameters under z-polarized electric field incidence to extract its effective constitutive parameters [30]. Figure 1(b) shows the retrieved constitutive parameters (top panel) and refractive indexes (bottom panel). As we expected, its permittivity exhibits a Drude-model dispersion with a plasma frequency of 4.2 GHz, and Re(ɛz) = Re(μx/y) = 1 at 5 GHz with imaginary parts smaller than 0.002. Accordingly, the real part of its effective refractive index is also unity at 5 GHz, as the red line shows in the bottom panel. To show the validity of the homogenization, we also retrieved the effective refractive indexes while adding two air layers (t mm in the thickness) on the two sides of the metamaterial slab, i.e., the effective thickness of metamaterial slab is equal to p+2t, as shown in the inset of bottom panel. We can see that the refractive indexes keep invariant (i.e., unity) for all the cases at 5 GHz, even though they are all dispersive.
Previous retrieved results show that the designed metamaterial slab exactly exhibits the air-like response at the designed frequency. More importantly, such an air-like response is independent of the air space on both sides of the slab. This behavior can be explained by analyzing the scattering of a single thin metallic wire (with the radius r1) covered with a diamagnetic dielectric cover layer (with the radius R), which can be approximately derived via semi-analytical model [25,31,32]. With previous analysis, the effective permittivity and permeability of the covered diamagnetic dielectric layer are ɛcover_eff ≈ 3×(1-F)−1 and ucover_eff ≈ 1-F, respectively. For an incident wave with z-polarized electrical field, the scattering width σsca can be derived by MIE solution in Bessel (Jn) and Hankel (Hn) functions as:
Numerically, we plot three calculated normalized scattering widths (by the identical metallic wire) according to Eq. (1) for different F and R with r1 = 0.75 mm, as shown in Fig. 1(c). As we see, the normalized scattering widths are nearly as small as −60 dB at their desired frequencies (4.8, 5.0 and 5.2 GHz), respectively. It is evident that a single thin metallic wire could be perfectly transparent and invisible in free space by covering precisely designed diamagnetic dielectric layer, as long as the electric field is parallel to the metallic wire. Yet, it also implies that the thin metallic wire array can be randomly distributed provided the minimum distance between two adjacent wires is no less than 2R, and the design confinement of periodicity can be cancelled, due to the true air-like property.
To validate previous assertion, we show the simulated normalized scattering widths of single one designed composite wire in x-y plane for two incident angles in the left panel of Fig. 2(a), and its electric field scatterings in two cases at 5 GHz in the right panels. The relative bandwidth is about 4% where the normalized scattering widths are less than −30 dB. The inset shows the normalized scattering widths dependent on incident angles at 5 GHz, and the suppression of scattering width is up to 45 dB.
Fig. 2. (a) Simulated normalized scattering width of a single unit cell in x-y plane and its electric field scatterings under normal (I) and oblique (II) incidences at 5 GHz. The inset shows the normalized scattering widths dependent on incident angles at 5 GHz. The curves are normalized by the scattering width from a metallic cube with identical borders. (b) Equal-frequency contours in the first Brillouin zone of two-dimensional photonic crystal consisting of closely arranged unit cells in x-y plane, where the unit of frequency is gigahertz and the dashed white line denotes the equal-frequency contour of air at 5 GHz. (c) Simulated electric field distributions under an oblique plane wave incidence to a bulk prism-like designed sample (I) and array of thin metallic wires without covered composite shells (II) at 5 GHz.
Finally, we arrange the designed composite wires closely along x-y plane into a two-dimensional photonic crystal to study its electromagnetic response in a bulk structure. Its first-band equal-frequency contours in the first Brillouin zone are shown in Fig. 2(b), the equal-frequency contour at 5 GHz coincidences with that of air (dashed white line). Meanwhile, we performed another full-wave simulation to illustrate its omnidirectional air-like response, as shown in Fig. 2(c). A plane waves is incident on a prism-like bulk structure composed of closely arranged composite wires. The total electric fields at 5 GHz in the air stay almost undisturbed, showing a perfect transparency and invisibility. On the contrary, strong scattering fields are observed when the plan wave is incident on the prism-like metallic wire array without covered composite shells. So, we can assert that objects composed of either loosely or densely arranged designed composite wires can exhibit a two-dimensional omnidirectional transparency and invisibility in free space under TE polarization, regardless of its shape and size.
3. Experiment and discussion
For experimental verification, we fabricated an electrically large airplane-like sample as shown in Fig. 3(a) and Fig. 3(b). In the fabrication process, four polysulfone cover layer were firstly machined with small through holes and circular openings by 3D sculpture technology, and all hollow copper cylinders were embedded inside the circular openings and sandwiched between two adjacent polysulfone covers. Then, we drove all thin copper wires through the holes in four covers into a solid-state composite, as shown in Fig. 3(a). The final dimensions of sample are 396 × 300 × 36 mm3, as shown in Fig. 3(b). Note that the weight of each unit in our design is around 4.2 grams, where the copper cylinder plays a key role. To reduce its total weight in some specific applications, such as radome in aircraft, the solid copper cylinder can be replaced with a lightweight plastic core coated with thin conductor film by metal sputtering process.
Fig. 3. (a) Polysulfone covers, hollow copper cylinders and wires used to assemble the airplane-like sample. (b) Actual sample with a length of 396 mm, a width of 300 mm and a height of 36 mm. (c) Schematic of the experimental setup. A small coaxial connector with omnidirectional radiation is serving as a monopole antenna, and another identical one is sequentially placed in each cell to measure the amplitude and phase of the electric fields. The height of the parallel waveguide is 36 mm, where the upper plate is a perforated aluminum sheet to facilitate the measurements.
The experimental setup we used to measure the scattering fields of sample is depicted in Fig. 3(c). Since the scattering fields of interest is two-dimensional, the sample was placed inside a parallel-plate waveguide with a separation of 36 mm so that only a transverse electromagnetic wave mode can exist in it. The lower plate is a large copper-plated PCB board, and the upper one is a perforated aluminum sheet whose perforation radiuses are 2 mm with intervals of 12 mm. Four sides of the parallel plate waveguide were surrounded with pyramid absorber to mimic infinite extents. Note that a metal sputtering process was used to coat the upper and lower surfaces of the plane-like sample in actual measurement, keeping all copper wires embedded in polysulfone covers connect with parallel-plate waveguide.
In the measurement, a small coaxial connector with a two-dimensional omnidirectional radiation was placed inside one perforation serving as a monopole antenna, another identical one was sequentially placed in each perforation to measure the amplitude and phase of local electric field normal to the plate. These two coaxial connectors were connected to the output and input ports of Agilent E8361A network analyzer, respectively. For a comprehensive study, two sets of sample configurations were studied, i.e., placing the monopole source outside and inside of the sample. Meanwhile, for comparison, three measurements were performed for each set. The first one is to measure the electric field distribution for the empty parallel-plate waveguide (without sample), and the second one is for the designed sample while the third one is replacing the designed sample by an identical aluminum sample.
The measured results at 5 GHz are shown in Fig. 4, where we also show corresponding simulated results for comparison. Figure 4(a) shows the results where the source was placed outside of the sample. Model (I) shows simulated (top panel) and measured (bottom panel) instantaneous electric fields in the parallel-plate waveguide. We can see the propagation of a cylindrical wave in measured results except that there are some weak standing waves due to the imperfect absorber used in experiment. Model (II) shows the total electric field distributions for the designed sample. As expected, the simulated total electric fields in air stay undisturbed both in amplitude and phase without any observable standing wave. For the measured results, the electric fields in air also nearly stay the same with that for empty parallel-plate waveguide. The difference is that the power travelling through the electrically large airplane-like sample is a little smaller due to the inevitable loss of the designed sample. In model (III), the airplane-like aluminum samples both in simulation and experiment strongly scatters the incident cylindrical waves, agreeing well with each other. Figure 4(b) shows the results where the source was placed inside of the sample. The measured results in models (I), (II) and (III) keep in accordance with simulated ones. Although the imperfections of fabrication and experiment setup inevitably degrade the performance, the above results confirm that the fabricated sample is omnidirectionally transparent and invisible, regardless of shape and size.
Fig. 4. Instantaneous snapshots of the electric fields simulated (top panels) and measured (bottom panels) at 5 GHz when the source is placed outside (a) and inside (b) of samples. Models (I) are for empty parallel waveguide, models (II) are for fabricated sample, and models (III) are for aluminum sample with the same dimensions.
4. Conclusion
In conclusion, we have demonstrated a two-part design method to perfectly hidden a thin infinite metallic cylinder under TE wave incidence, as well as a cluster made of it. It is shown that the effective constitutive parameters can be efficiently engineered through manipulating the volume fraction of the outer metallic shell, i.e., the Drude dispersion of continuous wires and the non-resonance diamagnetic response of metallic shells are successfully mixed. It is shown that the composite structure (a metallic cylinder with outer shells) can behave completely identical to air, and this air-like property holds for either the periodic or the random case, which provides us a simple but powerful tool to tailor the EM scattering from a cluster made of wire-shaped structures in free space, regardless of its shape and size. We note that this approach can be directly adopted in all the frequency range, i.e., from microwave to terahertz, due to the low loss of metals. Meanwhile, the concept and methodology to render 2D omnidirectional transparency and invisibility by editing the additional enclosure can also be potentially extended to other physical systems, such as acoustic and seismic waves.
Funding
National Natural Science Foundation of China (61771422, 62071420, 61875051, 61771421, 61675013); Natural Science Foundation of Zhejiang Province (LR18F010001).
Acknowledgments
X. Hu, R. Li, D. Ye designed the research; X. Hu, R. Li, R. Wang, L. Peng, J. Huangfu, L. Ran, D. Ye performed the research. All authors contributed to data interpretation and the composition of the manuscript.
Disclosures
The authors declare no conflicts of interest.
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