1 Introduction

The main consideration in the design of military platforms is the reduction of radar coverage (RCS). Two methods for RCS reduction are commonly available in the literature: changing the object structure to redirect the scattered waves away from the incidence direction and loading radar absorbing material (RAM) on the object (Singh and Jha 2015; Cos et al. 2010). The drawbacks of both methods are a complex design, large volume and small bandwidth. Meta-surfaces have been adopted to overcome the aforementioned drawbacks. The RCS reduction can be achieved while using meta-surfaces consisting of equivalent perfect electric conductors (PEC) and artificial magnetic conductors (AMC) unit cells. Metamaterial provides a new way to manipulate electromagnetic (EM) waves and achieves the broadband and low-reflection materials. In many situations, the application scope of the three-dimensional (3D) metamaterials is limited due to their large volumes. The meta-surface is a 2D equivalent of metamaterials (Singh and Marwaha Jan 2015), which are usually constituted by inhomogeneous arrays of sub wavelength resonators. However, once the structure-only metamaterials (i.e. passive metamaterial) are fabricated, their functions will be fixed. To control the EM waves dynamically, active devices are integrated into the structure, yielding active metamaterials. Traditionally, the active metamaterials include tunable metamaterials and reconfigurable metamaterials, which have either small-range tenability or a few numbers of reconfigurability. Recently, a special kind of active metamaterials, digital coding and programmable metamaterials, haven been presented, which can realize a large number of distinct functionalities and switch them in real time with the aid of field programmable gate array (FPGA). Coding metamaterials offered a novel way to manipulate the backscatter performance by different codes (Hao et al. 2019). Several methods have been used to reduce the backscatter using metamaterial (Cos et al. 2010; Failed 2018; Zhang et al. 2012). In these methods, the meta-surface enables high efficiency propagating-wave to surface-wave conversion, deflected reflection, or diffused reflection if appropriately designed. The chessboard surface is another essential technique for RCS reduction. The chessboard surface is similar to shaping technology, and the design of chessboard configuration is easier. The working mechanism of the chessboard artificial magnetic conductor (AMC) for RCS reduction is that the backscattered field will cancel when the phase difference of the reflected fields between the two kinds of AMC units is 180°. Paguay et. al combined perfect electric conductor (PEC) and AMC in chessboard arrangement in Paquay et al. (2007). The reflect energy was scattered into four diagonal directions, and the RCS in the normal direction was almost zero. A method utilized two kinds AMC units is proposed in Chen et al. (2015). Tao et al. put two kinds of AMC units cell in triangle arrangement in Song et al. (2018). Chen et.al put the same units in different sizes randomly in Chen et al. (2017), which redistributed the scattering energy from the surface toward all the directions. Coding metamaterials concept is proposed by Cui et.al, realize different functionalities by means of biased diode, field-programmable gate array (FPGA) and different codes in Giovampaola and Engheta (2014).

In this paper, different configured chessboard plasma-based DRA is proposed by increasing the number of interfaces between adjacent unit-cells and thus redirecting the incident wave into different reflected lobes. As a result, the RCS is highly attenuated. The size of super-cell is investigated for RCS reduction over the operating bandwidth. Different arrangements of super-cells with uniform and non-uniform coding arrangements are investigated.

2 Design of plasma-based DR unit-cell

The detailed configuration of the proposed plasma-based dielectric resonator (DR) unit-cell structure is shown in Fig. 1a. It consists of dielectric container of dielectric constant \(\varepsilon\) rc = 3.4 with cylindrical core of radius Ro = 3 mm, surrounded by cylindrical ring of radius R1 = 5 mm, width W1 = 0.82 mm, and height Hc = 1.2 mm. The dielectric container is placed on Ls × Ls × Hs = 15 × 15 × 2 mm3 grounded FR4 substrate of \(\varepsilon\) rd = 4.6 and tanδ = 0.036. The container is injected with argon-noble gas occupying a height of Hp = 1 mm and connected with voltage source for plasma ionization. The dispersive plasma material characteristics is calculated from Malhat et al. Oct. (2015):

$${\varepsilon }={\varepsilon }_{o}\left[1-\frac{{\omega }_{p}^{2}}{\omega \left(\omega -j{v}_{p}\right)}\right]$$
(1)

where \({\varepsilon }_{o}\) is the free space permittivity, \(\omega\) is the angular operating frequency, \({v}_{p}\) is the collision frequency, and \({\omega }_{p}\) is the plasma angular frequency which is related to the electron density \({n}_{e}\) as

$${\omega }_{p}=\sqrt{\frac{{n}_{e}{e}^{2}}{{m}_{e}{\varepsilon }_{o}}}$$
(2)

where \(e\mathrm{ and }{m}_{e}\) are the electron charge and mass. The electron density of the ionized plasma medium is controlled by the applied voltage as given by Zainud-Deen et al. Dec. (2019)

$${V}_{B}={\left(\frac{{n}_{e}\sqrt{ek{T}_{e}}{H}_{p}^{2}}{{\varepsilon }_{0}}\right)}^{2/3}$$
(3)

where K is Boltzmann constant, and \({T}_{e}\) is the electron temperature. Figure 1b shows the frequency response of plasma dispersive properties for \({\upsilon }_{p}\)=2 GHz and \({T}_{e}\)=300 K at \({\omega }_{p1}\)=7.44 × 1011 rad/sec and \({\omega }_{p2}\)=1.4 × 1012 rad/sec. In the frequency range from 7 to 12 GHz, the real part of dielectric constant is increased while the imaginary part is decreased with increasing the operating frequency. The plasma conductivity is decreased with increasing the operating frequency, while it has a tunable response with varying the plasma frequency. At fixed frequency of 9.5 GHz, the plasma conductivity is increased with increasing \({\omega }_{p}\) from 7.44 × 1011 to 1.4 × 1012 rad/sec. The frequency response of the reflection coefficient is calculated using the waveguide simulator at \({\omega }_{p1}\)=7.44 × 1011 rad/sec and \({\omega }_{p2}\)=1.4 × 1012 rad/sec as shown in Fig. 2a. The zero-crossing frequency of the reflection phase curve are 9.2 GHz and 10 GHz, for \({\omega }_{p1}\) and \({\omega }_{p2}\) respectively. The reflection phase difference is 180° ± 37° within the range between 9.2 and 9.8 GHz. At 9.5 GHz the two unit cells have identical reflective amplitudes of − 4 dB and opposite reflective phases of 180°. The structure with \({\omega }_{p1}\) denotes logic “0” and the other with \({\omega }_{p2}\) denotes logic “1”. Figure 2b shows the arrangement of uniform super-cell consists of 4 × 4 plasma DR unit-cell used as a building block of RCS reduction surfaces.

Fig.1
figure 1

a The configuration of the reconfigurable plasma ring unit-cell. b The dispersion properties of the plasma material

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Fig. 2
figure 2

a The reflection coefficient phase and magnitude for logic 0 and 1 versus frequency, b The geometry for 4 × 4 uniform super-cell

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3 RCS reduction theory of operation

To reduce the scattered field from metallic plate surface, it is covered by the plasma DR unit-cell elements energized into two different plasma frequencies, \({\omega }_{p1}\) and \({\omega }_{p2}\) called coding configuration. When illuminated by normal incident plane- wave, the scattered fields are directed into different directions according to the reflection phases of the plasma DR elements (i.e. coding configurations). The scattering field pattern from 2-D coding-surface is calculated using the antenna array principles given by,

$$F\left(\theta ,\phi \right)=\mathrm{field\; of\; reference\; element }\times \mathrm{array\; factor}$$
(4)

The array factor M × N array elements is expressed by

$$AF\left( {\theta ,\phi } \right) = \sum\limits_{{m = 1}}^{M} {\sum\limits_{{n = 1}}^{N} {{\text{exp}}} } j\left[ {\phi _{{m,n}} + \beta D_{x} \left( {m - \frac{1}{2}} \right)\left( {u - u_{o} } \right) + \beta D_{y} \left( {n - \frac{1}{2}} \right)\left( {v - v_{o} } \right)} \right]$$
(5)

where\(u=sin\theta\; cos\phi\),\(v=sin\theta\; sin\phi\),\({u}_{o}=sin{\theta }_{i}\; cos{\phi }_{i}\),\({v}_{o}=sin{\theta }_{i}\; sin{\phi }_{i}\), \({\theta }_{i}\) is the pitching angle of incident wave and \({\phi }_{i}\) is the azimuth angle of incident wave. Supposing that \({\phi }_{m,n}\) of coding unit-cell element “1” has the value of\(\pi\), \({\phi }_{m,n}\) of coding unit-cell element “0” has the value of 0, Eq. (5) is then rewritten as

$$AF\left(\theta ,\phi \right)= \sum_{m=1}^{M}\mathrm{exp}j [\beta {D}_{x}\left(m-\frac{1}{2}\right) \left(u-{u}_{o}\right)+m\pi ]+\sum_{n=1}^{N}\mathrm{exp}j\left[\beta {D}_{y}\left(n-\frac{1}{2}\right) \left(v-{v}_{o}\right)+n\pi \right]$$
(6)

The amplitude of the \(AF\left(\theta ,\phi \right)\) is deduced as

$$\left|AF\left(\theta ,\phi \right)\right|=MN sinc\left(\frac{m\pi }{2}- \frac{m}{2} {\beta D}_{x} \left(u-{u}_{o}\right)+pm\pi \right)+ sinc\left(\frac{n\pi }{2}- \frac{n}{2} {\beta D}_{y} \left(v-{v}_{o}\right)+qn\pi \right)$$
(7)

in which\(sinc\left(x\right)=\frac{\mathrm{sin}(x)}{x}\), \({D}_{x}\) and \({D}_{y}\) are the inter-element distance in x- and y-direction and p, q = 0, ± 1, ± 2,…... It is clear that, under normal incidence, the maximum values of \(\left|AF\left(\theta ,\phi \right)\right|\) appears at the direction of elevation angles

$$\phi =\pm \mathrm{atan}\frac{{D}_{x}}{{D}_{y}} and\; \phi = =\pi \pm \mathrm{atan}\frac{{D}_{x}}{{D}_{y}}$$
(8)

And azimuth angle

$$\theta =\mathrm{asin }[ \frac{\lambda }{2} \sqrt{\frac{1}{{D}_{x}^{2}}+\frac{1}{{D}_{y}^{2}}} ]$$
(9)

These expressions indicate the possibility to realize the beam sweeping at the same frequency by changing the super-cell size and the distribution of the digital codes.

Figure 3a shows the arrangement of 6 × 6 uniform super-cells (24 × 24 unit-cells) with all unit-cells are energized using ωp2 = 1.40 × 1012 rad/sec to represent the uniform coding sequence “1”. The normal incidence plane-wave is mainly reflected to a single main beam at broadside with a scattering level of …dBm2, as depicted from the 3D RCS pattern at 9.5 GHz shown in Fig. 3b. Figure 3c shows the backscattering versus frequency for the unloaded metallic plate and the loaded plate with coding structure “1”. Using the coding structure “1”, the RCS reduction varies from − 1 dBm2 to − 7 dBm2 at different frequencies from the unloaded case. Figure 4a shows the periodic sequence of 111,111/000000, the normal incident plane wave is mainly reflected to two symmetrical beams. The black patches denote logic “0” and the white patches denote logic “1”. The 3-D RCS at 9.5 GHz shown in Fig. 4b indicates that the two beams are directed to − 15° and at + 15°, respectively. The backscattering versus frequency in Fig. 4c shows a high RCS reduction over the frequency band with − 21 dBm2 at 9.4 GHz and − 10 dBm2 reduction bandwidth from 8.6 to 9.7 GHz using the 111,111/000000 coding structures. Figure 5a shows a periodic sequence of 010101/101010 chessboard arrangement. The normal incident plane wave is mainly reflected to four symmetrical beams as shown in Fig. 5b. The main lobes are directed to 45°, 135°, 225°, and 315°. The backscattering has a minimum reduction RCS of − 18 dBm2 with − 10 dBm2 reduction bandwidth extends from 8.65 to 9.75 GHz as shown in Fig. 5c.

  1. A.

    RCS reduction using uniform coding supper-cells

Fig. 3
figure 3

The bistatic RCS from code (111111….) 6 × 6 super-cells using all (1) 4 × 4 uniform super-cell. b The 3-D RCS versus angle at 9.5 GHz, c The backscattering versus frequency

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Fig. 4
figure 4

The bistatic RCS from code (111111/000000….) 6 × 6 plasma ring surface using 4 × 4 uniform super-cell. b The 3-D RCS versus angle at 9.5 GHz, c The backscattering versus frequency

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Fig. 5
figure 5

The bistatic RCS from code (010101/101010) 6 × 6 plasma ring surface using 4 × 4 uniform super-cell. b The 3-D RCS versus angle at 9.5 GHz, c The backscattering versus frequency

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The effect of changing the size of the super-cell consisting of uniform identical plasma DR unit-cells on the direction of the main scattered beams is explained in this section. The size of the super-cell is adjusted to control the beam directions of periodic coding patterns and the level of random diffusions. The super-cells are consisting of 3 × 3, 4 × 4, 6 × 6, 8 × 8, and 12 × 12 plasma DR unit-cells. The RCS from uniform super-cells ionized using \({\omega }_{p1}\)=7.44 × 1011 rad/sec and \({\omega }_{p2}\)=1.4 × 1012 rad/sec at 9.5 GHz are plotted in Fig. 6a and b, respectively. In both cases, increasing the super-cell size increases the RCS reflected in the illumination direction and the beam width is decreased. The peak RCS is − 15.1 dBm2, − 3.97 dBm2, and 6.43 dBm2 for 3 × 3, 6 × 6, and 12 × 12 super-cells arrangements at \({\omega }_{p1}\)=7.44 × 1011 rad/sec and the RCS is − 19 dBm2, − 5.93 dBm2, and 2.88 dBm2 for 3 × 3, 6 × 6, and 12 × 12 super-cells at \({\omega }_{p2}\)=1.4 × 1012 rad/sec. Figure 7 introduces the scattering properties of chessboard arrangement of coding sequence of 101010/010101 using different sizes of uniform super-cell. For different sizes of the super-cells, the scattered field is splinted into four beams with deflection angle decrease with increasing the super-cell size. The scattered beams are directed to (± 30°, 180° ± 30°), (± 25°, 180° ± 25°), (± 20°, 180° ± 20°), (± 15°, 180° ± 15°) and (± 10°, 180° ± 10°) for 3 × 3, 4 × 4, 6 × 6, 8 × 8, and 12 × 12 uniform super-cells, respectively. The RCS is reduced over a wide angle range reduction with − 18 dBm2 at the broadside direction and below − 32 dBm2 over the angular range from − 90° to 90° according to the super-cell size. The frequency responses of the backscattered RCS are plotted in Fig. 8a. Changing the super-cell size doesn’t affect the RCS reduction values where all the super-cell sizes share the same RCS reduction bandwidth from 8.7 to 9.8 GHz with highest reduction of − 23 dBm2 at 9.4 GHz. Figure 8b shows the bistatic RCS versus angle in the plane φ = 45° for different uniform super-cell sizes. The deflected beam angle is increased with reducing the super-cell size. The deflected RCS beam amplitude is decreased by − 2 dBm2 with decreasing the super-cell size.

  1. 2

    RCS reduction using non-uniform coding supper-cells

Fig. 6
figure 6

The 3D-RCS from uniform super-cells with different sizes at 9.5 GHz

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Fig. 7
figure 7

The RCS response from 6 × 6 reconfigurable coding structure consisting of different sizes of uniform super-cells

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Fig. 8
figure 8

a The backscattered RCS versus frequency. b The scattered beam angle versus size of super-cell at 9.5 GHz

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In this case, non-uniform super-cells consists of 8 × 8 plasma DR unit-cells ionized non-uniformly using \({\omega }_{p1}\)=7.44 × 1011 rad/sec and \({\omega }_{p2}\)=1.4 × 1012 rad/sec in different arrangement are considered. Figure 9 shows the RCS from different non-uniform super-cell using 8 × 8 plasma DR unit-cells configurations size at 9.5 GHz. The RCS varies between 2.9 and 3.19 dBm2 for different configurations. Figure 10 introduces the RCS characteristics from 3 × 3 super-cells with individual 24 × 24 plasma DR unit-cells. The super-cells are arranged in checkboard like format to satisfy 180° progressive phase criteria to result in null in boresight direction under the normal incidence waves. In Fig. 10a, super-cell arrangement (1) consists of triangle-type checkerboard surface, two opposite triangle are excited using \({\omega }_{p1}\)=7.44 × 1011 rad/sec and the opposite triangles are excited using \({\omega }_{p2}\)=1.4 × 1012 rad/sec. The backscattered RCS shows wideband reduction of 1 GHz with peak reduction of − 17 dBm2. The 3-D RCS shows null at the broadside direction. In super-cell arrangement (2), H-shaped unit-cells are excited using \({\omega }_{p1}\) and the surrounding unit-cells are excited using \({\omega }_{p2}\) as in Fig. 10b. Wideband RCS reduction of − 15 dBm2 over the reduction bandwidth of 1.2 GHz with scattered beams in different directions. Figure 10c shows the arrangement of super-cell (3) in which the unit-cells are diagonally divided into two triangles excited using two frequencies, \({\omega }_{p1}\) and \({\omega }_{p2}\). The RCS reduction bandwidth extended from 8.5 to 9.65 GHz. The scattered 3D RCS pattern at 9.5 GHz shows two beams at ± 20°. The arrangements using super-cell (4), super-cell (5) and super-cell (6) in which different distributions of excited unit-cells are depicted in Fig. 10d, e and f, respectively. The scattered beam produces null in the broadside direction with wideband RCS reduction.

Fig. 9
figure 9

The 3D-RCS from non-uniform super-cells at 9.5 GHz

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Fig. 10
figure 10

The RCS response from 6 × 6 reconfigurable coding structure consisting of 4 × 4 non-uniform super-cells arrangements

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4 Conclusion

The RCS reduction using plasma DR unit-cells chessboard arrangement is investigated in this paper. The scattering from the unit-cell is tuned using the plasma frequency with 180° degrees phase shift. The logic “0” state and logic “1” state are achieved using \({\omega }_{p}= 7.44\times {10}^{11} rad/sec \mathrm{and} {\omega }_{p}=1.4\times {10}^{12} rad/sec\), respectively. The reflection phase difference is 180° ± 37° within the range between 9.2 and 9.8 GHz. At 9.5 GHz the two unit-cells have identical reflective amplitudes of − 4 dB and opposite reflective phases of 180°. Different chessboard arrangements of uniform plasma DR unit-cells are investigated. High RCS reduction over the frequency band with − 21 dBm2 at 9.4 GHz and − 10 dBm2 reduction bandwidth from 8.6 to 9.7 GHz using the 111111/000000 coding structures. Super-cells consisting of 3 × 3, 4 × 4, 6 × 6, 8 × 8, and 12 × 12 plasma DR unit-cells are investigated. Increasing the super-cell size increases the RCS reflected in the illumination direction and the beam width is decreased. The RCS is reduced over a wide angle range reduction with − 18 dBm2 at the broadside direction and below − 32 dBm2 over the angular range from − 90o to 90° according to the super-cell size. Non-uniform super-cells consisting of 8 × 8 plasma DR unit-cells are investigated. The RCS reduction bandwidth extended from 8.5 to 9.65 GHz. The scattered 3D RCS pattern at 9.5 GHz shows two beams at ± 20° and produces null in the broadside direction with wideband RCS reduction.