1. Introduction

Invisibility devices in electromagnetic frequency range basically require low reflectivity in observer’s sight under wave source illumination. Many structures and materials have been developed under this physical prospect including electromagnetic absorbers [1–3], cloak with transformation optics and other mechanism [4–10], electromagnetic meta-surface [11–13] and frequency selective surfaces [14,15]. And most of structures are based on periodic unit arrangements, which could guarantee maximum spatial usage and homogeneous effective material property [16–19]. Meanwhile non-periodic unit structures are also been investigated due to its flexibility and complexity [12–29].

Wide band character is one of few major pursuing goals for researcher working on invisible devices and structures in electromagnetic frequency. Some structures’ corresponding mechanism are naturally wide band including electromagnetic absorbers constructed with resistive patterned layers and spacing foam [30]; effective medium based mechanism are sometimes narrow band including transformation optics; meta-surface and frequency selective surface sometimes has directivity which remains as a study topic recently. Applicable structures tend to be shell like including closed spherical shell or half-closed cylindrical shell. Another issue for invisibility device communication because invisibility means absorption of electromagnetic wave. PEC lining of Radar absorbing structures always prevent possible transmission window. Current radome constructed with frequency selective surface has directionality and often involve aperture connection problem with shell itself, because radome needs to open up aperture on structure shell.

Non-periodic unit structures could be constructed by placing metallic unit in random positions on a regular lattice grid for stochastic description, and non-periodic unit arrangement has an intrinsic characteristic of band-expanding effect. However, 3-dimensional non-periodic unit structure has not been studied thoroughly as it has complexity comparing to 2-dimensional random unit surface showing some interesting features in wide band [22,24]. However, 3-dimensional non-periodic structure might implicit unknown mechanisms and has some engineering value.

From application level, it is interesting to probe new mechanism in shell and coating structures which could operate in wide band, wide incidence angle and wide observation angle to realize the absolute invisibility characteristic. Mechanism fitting arbitrary structure shape or figure is also interesting to tackle complex oblique incidence situation and overcome manufacturing difficulty for non-developable curved surface. New mechanism might realize different functionality with quite simple basic unit cell and random position and probability density distribution. And random position forms basic frame for this structure which is referred as hyper-structure here, as a further development of metamaterial which depends more on effective material property of periodical unit cell.

So we propose Murky Diffusion Shell (MDS) to investigate what real 3D structure could bring to the overall properties of a quasi-periodic material. Since it is different from periodic structure in metamaterials, it could be categorized into a new concept: Hyper-structure. Please note that all the building units are identical, so structure—how they are arranged—functions more dominative to decide the final overall property. For example, MDS is invisible (indicated by a low RCS reduction) in frequency band as periodic structure shows a quite strong reflection near unity. Another reason for investigation of MDS is that it’s a real 3-D random structure. Comparing to 2D meta-surface which has been studied for quite a while, it has more structural degree of freedom and more design space. MDS doesn’t need metallic lining so it could remain passing frequency band for possible communication demand which is very practical.

Murky media concept utilizes reflection characteristic of unit cell rather than effective material properties, thus opens up new manner to realize low scattering structures [31,32]. Absorption in optical scattering media is found beneficial to enhance observable image resolution through random scattering media under certain circumstance [33]. There are a common natural object—vapor cloud—which is opaque in some circumstance but transparent in other circumstance, as illustrated in Fig. 1(a) and (b), respectively. Thus a murky media in electromagnetic frequency range is expectable under proper geometry setups.

 

Fig. 1 Invisibility and transparency in light scattering medium. (a) opaque cloud which could hide object inside; (b) seemingly transparent cloud.

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In Fig. 1(a), murky media needs to have enough thickness to keep the incident light from penetrating the media to impinging the object, thus avoid possible scattering from the inclusion object. And in Fig. 1(b), murky media might manage to have some transparent effect under light illumination. Such a murky media shell has been realized in light frequency [31] and we wonder if similar theory is applicable in electromagnetic frequency, especially in microwave frequency. 2D murky media, referred as non-periodic meta-surface, has been proved to have reflection controlling effect [11]. So a 3D murky diffusion shell structure is proposed here to investigate murky media theory for electromagnetic invisible device.

A typical diffusive media similar to water vapor forming matter in cloud is considered here. A light scattering media—like water vapor–has a typical mass density value of 0.6kg/m³ under 100 degree centigrade, in which H₂O molecule has a much larger average interval than water to allow light scattering. Then consider more dense matter form—like water or ice, in which H₂O molecule is in a closely arranged manner or lattice and have a density (1000kg/m³) 3 orders larger than water vapor. The formula for water vapor is${\rho }_{\text{vapor}}\text{~}0.\text{00}1{\rho }_{\text{ice}}\Rightarrow {\text{p}}_{average}\text{~}10\cdot d_{molecule}$, in which ${\text{p}}_{average}$is average distance between H₂O molecules in water vapor and $d_{molecule}$ is molecule diameter. Here considering the low scattering requirement for electromagnetic media, a density ~0.1 is enough to generate low reflectance. So possible formula for diffusive medium operational in electromagnetic frequency is (${\text{p}}_{average}$ is the average distance between units):

Simulation shows reflection coefficient reduces to −10dB in a wide band if ${\rho }_{unit}$ is reduced to 0.15 from unity. And for invisible murky media device, its scattering reduction comparing to metallic object could reach$RCS{R}_{Backword}~-10dB$ and $RCS{R}_{Bistatic}~-10dB$. And for an ideal communication shell, shell structure transmission coefficient without inclusion object under plane wave incidence could reach ${\text{S21}}_{\text{I}nclusion}~0dB$ in order to function as a communication shield layer.

2. MDS design, simulation and configuration

Design of MDS requires two intrinsic elements: scattering units or particles and appropriate sparse unit position distribution configuration. Scattering feature ensures the impinging wave is sheltered from inclusion structure. And wide band reflection is realizable with appropriate unit. Unit position distribution under appropriate sparse density permits the pass for impinging field. Stochastic arrangement [11,28] of units is required to form diffusive media instead of periodical arrangement [15].

In scattering unit cells or particles level, unit cell needs to have anisotropic reflection coefficient near unity and unit size as small as possible to accommodate enough particles in a limited space for shell in order to make diffusion scattering. Subwavelength feature of metamaterial units naturally fits to small size demand. Double faced resonator type unit with dielectric substrate structure is able to reach a wide reflective or transmissive band in which coefficient is close to 0dB. Relative high permittivity of substrate is found to be able to avoid zero-value sunken in reflection band, and also helps to increase S11 reflection coefficient close to unity (0dB). Performance of unit cell has reflection band (S11>-1.5dB) reaching wide frequency range between 8GHz~18GHz. Selected unit cell is in cube shape with side length 2.5mm, which keeps subwavelength ratio comparing to lowest frequency 8GHz.

Considering unit pattern, performance of three typical patterns are compared and illustrated in Fig. 2 including square ring (black line), split ring resonator (SRR, red line) and blocking gate resonator (BGR, blue resonator). Unit dimension in BGR unit is a₀ = 2.5mm, d₀ = 2.35mm, d_0B = 2.146mm, s = 0.77mm, s₁ = 0.182mm, g = 0.12mm, g₁ = 0.12mm, r₁ = 0.04mm, r₂ = 0.02mm, r₃ = 0.02mm. Dielectric substrate selects polytetrafluoroethylne board with thickness 0.254mm and permittivity $\epsilon$ = 6.15, loss tangent t_d = 0.001 at 10GHz and double faced Copper films of unit pattern are 17$\mu m$thick. BGR unit has higher and more consecutive S11 coefficient when considering wave incidence on side direction (peak frequency 18.14GHz) and facial direction (peak frequency 14.79GHz). Only BGR unit fit standard of reflection band (S11>-1.0dB) between (10, 19) GHz. So the presented BGR unit is chosen to study the scattering medium mechanism. Experimental measured S11 of a periodical resonator array of BGR is retrieved from measured S21 to verify unit cell pattern design and sample fabrication. Experiment (peak frequency 14.08GHz) and simulation results are coincident approximately as shown in purple dash-dotted line and blue line in Fig. 2(a), respectively.

 

Fig. 2 Reflection coefficient comparison of different subwavelength unit used as cell blocks of diffusive metamaterial in TE polarization wave illumination: (a), incidence on facial direction; (b), incidence on side direction; (c), periodic BGR array sample picture corresponding to reflectivity indicated by purple dash-dotted line in (a).

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In unit position distribution configuration, unit density with the order of 10⁻¹ is required to form a murky diffusion medium, which is the highest occupation ratio for gas-like medium. Scattering performance under different probability density is investigated under a configuration of 8-unit array on side incidence direction and 4 by 4 array on facial incidence direction. Results in Fig. 3 shows when probability p = 0.15, reflection coefficient in 8-12GHz band is well below −10dB. In facial direction low reflection band (S11<-8dB) exist in interval of (8, 15.4) GHz. So murky shell still perform in frequency band above 12GHz. Unit probability density adopts 0.12 after we confirm unit cluster arranged below density of 0.15 shows rather low reflection coefficient.

 

Fig. 3 S-parameter of different unit densities array shows formation prerequisite of murky media indicating by Eq. (1).

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Since unit cell density is with order of 10⁻¹, total layer number should have order of 10 at least. A layer number of 12 gives an effective probability density of 1.44, which we think a probability value above unity could well shelter inclusion object from electromagnetic wave illumination and reach invisibility with low scattering of murky medium. For sample fabrication convenience, slice pile-up structure is selected as illustrated in Fig. 5. BGR unit (Fig. 5(a)) is placed in random position on dielectric substrate board with pre-designed circular patch (Fig. 5(b)). Then circular rings are glued together with foam spacer layers (Fig. 5(c)) to form a hemispherical shell, and two half shells form a spherical MDS shell (Fig. 5(d)). Fabricated sample pictures are shown in lower row respectively.

MDS is designed as spherical shell with external latitudinal diameter 140mm and internal diameter 80mm as shown in Fig. 4. MDS shell thickness is 30mm which equals to 12 units. Shell thickness might be compressed because it is found unit with small thickness could also have similar isotropic scattering features to those shown in Fig. 2. Thickness of foam spacer is 2.3mm, and total thickness per layer is 2.588mm. The actual external diameter in longitudinal direction is 142.052mm. Total 27 variety of stochastic unit distribution position are designed to reach murky media character.

 

Fig. 4 Overall cell unit configuration of murky diffusion shell (MDS). Upper row: design illustration; Lower row: fabricated sample. (a) BGR unit; (b) PCB with random BGR unit position; (c) PCB with spacer layer; (d) spherical shell.

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Fig. 5 MDS momostatic scattering reduction in TE and TM polarizations.

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3. MDS sample and experiment

In MDS sample preparation, printed circuit boards (PCB) are fabricated with a predefined random unit positions as shown in Fig. 4. Sample spacer layer select PMI foam with thickness 2.3mm and they are glued together with 3M 9460PC non-base material double faced adhesive tape with nominal thickness 0.05mm. In order to characterize MDS performance, following properties are measured: monostatic scattering reduction, bi-static scattering reduction, transmission coefficient with inclusion object. Experiment measurement scenario is illustrated in Fig. 5, Fig. 6 and Fig. 7 respectively. Considering heterogeneous structure and diffusion scattering nature of MDS, impedance analysis is no longer applicable, which is a main difference between MDS and periodic structures [3,20].

 

Fig. 6 Bi-static scattering of MDS in TE and TM polarizations.

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Fig. 7 Transmission coefficients of MDS in TE and TM polarizations with inclusion ball, empty MDS and sole inclusion.

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A standard arch framing measurement system with arch radius 2000mm is adopted to conduct experiment as shown in Fig. 5(c). The experiment is conducted in 3 steps: confirmation of calibration and measurement setting, calibration and test measurement to verify measurement accuracy, and MDS sample measurement. In calibration and measurement setting, calibration reference object is kept in the same position and state to guarantee effectiveness of the sample measurement. A Ceyear AV3672D phase network analyzer is used as source signal generator. Polarization direction of antenna is shown in Fig. 5(a), Fig. 6(a) and Fig. 7(a), respectively. Time domain gating is opened in measurement process to avoid unwanted electromagnetic noise from environment. Figure 5(b) shows MDS hemisphere padding with reflective PEC plate adopted both in monostatic and bi-static scattering measurement. Figure 5(c) shows the measurement scenario in monostatic scattering coefficient. Figure 6(b) shows measurement scenario in bi-static scattering coefficient. Figure 7(b) shows transmission aperture setup used in transmission coefficient measurement. Figure 7(c) and Fig. 7(d) show MDS transmission coefficient measurement scenario on incidence face side and receiving face side, respectively. MDS is placed in a customized ellipse aperture with radius 70mm and 70.5mm. Figure 7(e) shows the transmission measurement aperture setup and transmitting double ridge antenna.

In scattering reduction measurement scenario, we consider rigorous condition in which PEC surface reflector plate has a diameter same as shell’s out diameter 140mm, which is shown as red plate in inset of Fig. 5(a). The bare PEC surface reflector is used for calibration (left inset in Fig. 5(a)), and MDS hemisphere padding with PEC surface reflector is used to measure the reflection control effect as sample is shown in Fig. 5(b). Transmitting and receiving antenna is placed with angle of inclination 5 degree, which could be considered equivalent to monostatic scattering measurement. Monostatic scattering reduction coefficient (RCSR) is shown in Fig. 5(d). MDS shows similar reduction effect in both polarizations, because homogeneity on both polarization directions guarantees near identical trend. A reduction crest −33.23dB located at 15.42GHz shows up in TM polarization, which is consistent with reflection coefficient simulation in Fig. 2(b). −15dB attenuation is in a range of (10, 18) GHz which indicates 3D murky media could show rather deep attenuation effect. −10dB attenuation is in a range of (8.74, 18) GHz, and highest frequency on −10dB is above 18GHz (value shown in Fig. 2(b) indicate it is around 19GHz). MDS shows a similar reduction effect in TE polarization with TM polarization.

In bi-static scattering measurement, rigorous condition in which PEC surface reflector plate has a diameter of 140mm is adopted. In this measurement scenario, transmitting and receiving antenna is placed with angle of inclination 45 degree as shown in inset of Fig. 6(a). PEC plate is used for calibration corresponding to strong scattering situation. And MDS hemisphere padding with PEC plate reflector used for measurement (sample shown in Fig. 5(b)). Bi-static scattering reduction coefficient is shown in Fig. 6(c). In both polarizations, MDS shows very similar reflection attenuation effect as monostatic scattering, and −15dB attenuation is in a range of 9~18 GHz in TE polarization and −10dB attenuation is in 8~18 GHz in TM polarization. This proves proposed mechanism and design to be reasonable.

Transmission coefficient of MDS is measured with tailored aperture customized for the external profile of MDS specimen. Coefficient value is measured in calibration with empty aperture to inspect transmitted energy power, as shown in left inset in Fig. 7(a). Then MDS transmission coefficient measurement is conducted with PEC inclusion and empty in each polarization. PEC inclusion is steel hollow spherical ball with diameter 76mm and thickness 1.5mm.

In TM polarization, MDS shows total transparent state indicating by transmission coefficient near 0dB as red dash-dotted line in Fig. 7(e), which is a results of anisotropic unit setup shown in Fig. 2(b). MDS is completely transparent in TM polarization. MDS with inclusion shows a very similar transmission character with situation without inclusion, and inclusion ball could cause S21 drop from near 0dB to near −4dB, which also indicates inclusion ball intercepts some of incident EM wave energy for possible wave energy transfer. In TE polarization, MDS shows transmission window in low frequency range near 5.5GHz, indicating by black dash line circle in Fig. 7(e). Between 4.5GHz and 6.5GHz, inclusion ball apparently intercepts part of the incident wave energy, indicating by transmission coefficient rise for empty MDS. In this frequency range MDS shows transparent radome effect which possess feature for communication window. MDS shows non-transparent effect in high frequency range with strong diffuse scattering effect. And it is predicable by subwavelength unit design shown in Fig. 2.

4. Conclusion

In conclusion, a MDS murky media hyper-structure is proposed under natural diffusive cloud concept and constructed, experimentally measured. The experimental work realizes invisibility effect for hyper-structure in electromagnetic frequency band, which creates all-directional low reflection effect through electromagnetic wave diffusion so that wave field is avoided to reach inclusion object. Experiment measurements show monostatic scattering reduction reaches well below −10dB in 8.74-18GHz and bi-static scattering reduction reaches well below −10dB in 7.46-18GHz when PEC disk object is wrapped by MDS, indicating obvious scattering reduction in arbitrary selected bi-static observation angle. Experiment also shows certain unit density could reach remarkable shielding effect. The proposed MDS structure has super-wide transparency band for certain polarization and transmission angles for possible communication brought by feature of constructing subwavelength unit particles. The obtained scattering and transmission feature obtained in hyper-structure experiment is not usually seen in previous proposed effective material property medium.

MDS murky media hyper-structure has many simple and engineering features: single kind of subwavelength unit and homogeneous probability density distribution could guarantee low reflection characteristic. To reach the diffusion effect, unit cell arrangement adopts stochastic manner. Diffusion shell requires only enough thickness to function and no PEC lining, and this feature makes it suitable for a wide variety of 3D shell shapes. A spherical shell shape built with cubic unit cell demonstrates the scattering trace characteristic universally. Those features make MDS suitable for future transporter or an engineering functional shell structure with communication demands.