New Metamaterial Absorber Based on Electromagnetic Coupling of Triangular SRR and Square SRRs for X-Band RADAR Applications

— In this paper, a new metamaterial absorber (MA) is presented. The proposed absorber is a microwave structure constituted by a network of four split ring resonators (SRRs) of magnetic resonance and negative permeability ( μ < 0); one resonator SRR central for triangular shape and three others resonators SRRs of the same square shape and the same dimensions. All resonators SRRs are printed on the upper surface of the FR4_Epoxy substrate ( 𝜀 𝑟 = 4.4; 𝑡𝑔𝛿 = 0.02), its dimensions are chosen to obtain the resonance in the X-band frequency. To eliminate the transmission, we add a copper conductive metal plate that will be etched on the upper face of the same substrate. The proposed MA is optimized for dimensions of (27.9 mm × 32 mm), its electromagnetic characteristics are studied for transverse electric (TE) polarization for different incidences and different inter-resonator spacing. The obtained results with the simulations performed by the high-frequency structure simulator (HFSS) show that our metamaterial absorber still has three peaks of different absorptions estimated at a maximum on the order of 98.76%. The main advantage of this study based on the proposed structure is that it is possible to control its absorption percentage for X-band radar applications.


I. INTRODUCTION
During the last decade, wireless communication systems using microwave devices have undergone remarkable development. The study of most microwave devices requires a remarkable knowledge of the physical characteristics of electromagnetic waves when they propagate in structures. These electromagnetic characteristics are often reflection, transmission, refraction, radiation, diffraction and also absorption [1][2][3][4][5].
The absorption of electromagnetic (EM) waves has been the subject of several recent studies [6][7][8][9], the control of the absorption percentage is becoming more and more essential to meet the needs of absorber performance. Nowadays, metamaterials absorbers offer a prestigious position in the world of telecommunications, especially for antennas [10] and radars [11].
Metamaterials are artificially designed materials with different properties than natural materials. This kind of medium was introduced for the first time by Victor Veselago [12] in 1967 after the Second World War. He showed that the propagation of electromagnetic waves in metamaterials is carried out in the opposite direction to that of natural materials. Previously, left-handed metamaterials, whose permittivity and permeability are negative [13] have been a favorite topic for millimeter-wave and for microwave societies because of their unique unusual phenomena, such as negative index refraction [14] and the generation of surface plasmon.
In this work, we propose a new metamaterial absorber (MA) consisting of four split ring resonators (SRRs). The overall shape of our absorber is based on a central resonator SRR with triangular shape surrounded by three resonators SRRs of the same square shape and also of the same dimensions (engraved on the upper face of the used substrate) in order to obtain resonances in the X-band. These square resonators SRRs are spaced apart by an inter-resonator distance (e), one of these three resonators SRRs is coupled to an etched copper conductive plate to prevent transmission of the overall structure. The polarization of our MA is TE for different incidences and the study is based on electromagnetic coupling of triangular resonator SRR to square resonator SRRs to have different absorption levels in the same X-band frequency.

II.1. DEPICTION
The resonator SRR is a metamaterial resonator proposed for the first time by J. Pendry and his research team [15]. Geometrically, the resonator SRR is formed by two outer and inner split rings with two opposing interrupts to have the capacitive effect. Physically, the resonator SRR can support too small wavelengths; see lengths of the order of a few microns [16].

II.1.1. TRIANGULAR SPLIT-RING RESONATOR
The triangular resonator SRR of period 1 is a metamaterial resonator formed by two inner and outer rings.
These two rings have a triangular shape (equilateral triangle) of and ribs for the outer and inner ring, respectively. All interrupts of the rings have the same value which is , the width is the same for both rings. The triangular resonator SRR is represented by Fig. 1.

Fig. 1 Triangular resonator SRR
The proposed triangular resonator SRR dimensions are shown in Table I. The study of the elementary components of a metamaterial resonator shows that the origin of the resonance comes mainly from the Lorentz dispersion [17], which led us to propose an equivalent electrical scheme for each resonator, this scheme is based on a resonant circuit.
The equivalent electrical circuit of the triangular resonator SRR is composed of three resonators each one formed by an inductance 1 and a capacitance 1 , these three resonators represent the outer ring of our triangular resonator SRR. The inner ring corresponds to a resonator formed by an inductance 2 and a capacitance 2 . The capacitance represents the coupling between the two inner and outer rings of the triangular resonator SRR. Fig. 2 shows the equivalent circuit model of the triangular resonator SRR.

II.1.2. SQUARE SPLIT-RING RESONATOR
As triangular resonator SRR, the square resonator SRR is also formed by two rings; inner of radius 1 and outer of radius 2 for square shape. The period of the proposed square resonator SRR is 2 , represents the spacing between the two rings that have the same width , the interruption gaps have the same value as the interrupt for the triangular resonator SRR.
The square resonator SRR and its equivalent circuit model are shown in Fig. 3.  Table II. The square resonator SRR can be mainly considered as a magnetic dipole, its equivalent circuit model behaves like a 0 0 resonator excited by a magnetic field perpendicular to the plane of the rings [18]. The equivalent circuit model of the square resonator SRR is shown in Fig. 3b.

II.2. PROPOSED METAMATERIAL ABSORBER
Our proposed metamaterial absorber (MA) consists of four metamaterial resonators SRRs; three resonators SRRs of square shapes (for dimensions shown in Table II) centered on a triangular resonator SRR (for dimensions shown in Table I)

III.1. TRIANGULAR SPLIT-RING RESONATOR BEHAVIOR
On    6 shows the behavior of the triangular resonator SRR based on its S11 parameter (module and phase).
For the amplitude of S11, we note that it is about two resonance frequencies in the X-band [8 -12] GHz; the frequency 1 = 8.91 GHz of the low resonance associated with the inner ring of the triangular resonator SRR and the frequency 2 = 9.73 GHz of the high resonance associated with the outer ring. For the S11 argument, we notice that the values vary in the interval [− , + ].
The triangular resonator SRR has characteristic impedance ( ) defined by the relation.
Where ( ) and ( ) represent the relative permeability and the relative permittivity of the triangular resonator SRR, respectively and 0 represents the characteristic impedance of the vacuum ( 0 ≈ 377 Ω.) We note that the triangular resonator is adapted for ( ( ) = 0 ).
The effective reduced impedance of the triangular resonator SRR is defined by [19].
For a zero transmission ( 21 ( ) = 0), then And also, In the HFSS simulator, we directly select both parts; real (with ′ ( ) > 0) and imaginary characteristic impedance. Fig. 7 shows the variation of these two impedance parts.

Fig. 7
Real and imaginary parts of the characteristic impedance of the triangular resonator SRR As shown in Fig. 7, at resonance frequency, the real part of the characteristic impedance of the triangular resonator SRR approaches to the vacuum impedance (i.e. approximately 377 Ω) while the imaginary part tends to 0. So, the energy that is not reflected is trapped and absorbed into the resonator. The triangular resonator SRR absorption is given by [20].

III.2. SQUARE SPLIT-RING RESONATOR BEHAVIOR
On the upper surface of the same substrate used for the triangular resonator SRR, the square metamaterial resonator SRR is etched for the same thickness ( = 15 μm). Fig. 9 shows this resonator in 3-D Modeler of The reflection and the absorption of square resonator SRR are shown in Fig. 10.

III.3. ELECTROMAGNETIC CHARACTERISTICS OF THE PROPOSED (MA)
To simulate the proposed MA consisting of three square resonators SRRs and a central triangular resonator SRR, we fixed simulation criteria which will be adapted to complicated microwave structures. So, two Master-Slave boundary conditions are used along the ⃗ and ⃗ ⃗ axes. To generate the incident wave (designed along the ⃗ axis) on the surface of our MA, we must use a Floquet-port that is assigned to the upper limit of the structure. The lower limit of the overall structure is indicated by the lower surface of the substrate (since a metal plate has been used on the upper surface of the substrate to prevent transmission). The absorption of our MA according to the inter-resonator spacing and the incidence angle (for TE polarization) is shown in Fig. 12 and Fig. 13, respectively.   The electric field mapping for the proposed MA at the central resonance (for the normal incidence) is represented by Fig. 15. On Figure 15 we note that the electric field at the resonance of 10.26 GHz is more condensed in the regions situated between the triangular resonator SRR and the square resonators SRRs, which justifies the effect of the electromagnetic coupling on the absorption of the structure. In the vicinity of the gaps of each metamaterial resonator constituting the absorber, it is also noted that the electric field can take considerable amplitudes which shows the capacitive effect of the resonators SRRs; triangular and squares in these region.

IV. CONCLUSIONS
In this work, we have proposed a new microwave structure that is a MA. Our proposed MA is based on the electromagnetic coupling between three resonators SRRs for one central triangular and square shape resonators. All the dimensions of these metamaterial resonators are chosen to have magnetic resonances in the X-band and thus to have the necessary absorption in the same band. We used a printed metal plate on the upper face of the used substrate to prevent transmission of the structure. We polarized our MA to have the TE polarization for different angles of incidence. During our study, we also varied the inter-resonator spacing. In our results, we have always found three absorption peaks relative to the coupling of the triangular resonator to the three square resonators where the biggest appeared around the resonance of each square resonator for the normal incidence. Based on these results, our proposed MA may represent the base cell for several future RADAR applications systems in the frequency X-Band.