Quad-Band Polarization-Insensitive Square Split-Ring Resonator (SSRR) with an Inner Jerusalem Cross Metamaterial Absorber for Ku- and K-Band Sensing Applications

The development of metamaterial absorbers has become attractive for various fields of application, such as sensing, detectors, wireless communication, antenna design, emitters, spatial light modulators, etc. Multiband absorbers with polarization insensitivity have drawn significant attention in microwave absorption and sensing research. In this paper, we propose a quad-band polarization-insensitive metamaterial absorber (MMA) for Ku- and K-band applications. The proposed patch comprises two square split-ring resonators (SSRR), four microstrip lines, and an inner Jerusalem cross to generate four corresponding resonances at 12.62 GHz,14.12 GHz, 17.53 GHz, and 19.91 GHz with 97%, 99.51%, 99%, and 99.5% absorption, respectively. The complex values of permittivity, permeability, refractive index, and impedance of MMA were extracted and discussed. The absorption mechanism of the designed MMA was explored by impedance matching, equivalent circuit model, as well as magnetic field and electric field analysis. The overall patch has a rotational-symmetrical structure, which plays a crucial role in acquiring the polarization-insensitive property. The design also shows stable absorption for both transverse electric (TE) and transverse magnetic (TM) modes. Its near-unity absorption and excellent sensing performance make it a potential candidate for sensing applications.


Introduction
A metamaterial is a non-natural material structure that possesses rare material properties, such as negative permittivity, negative permeability, reverse doppler effect, and negative refractive index, known as metamaterial (MTM) properties [1]. MTM properties depend on the geometry of the unit cell structure with a stable structural composition. These extraordinary physical properties make MTMs appropriate for numerous applications, such as sensing [2,3], imaging [4], metamaterial coding [5], lensing [6], reflect arrays [7], terahertz applications [8], invisible clocks [9], antennae [10][11][12], absorbers [13], programable analog differentiators [14], etc. The perfect or near-perfect metamaterial absorber has the ability to absorb a specific frequency by preventing reflection and transmission of electromagnetic (EM) waves at a given frequency [15][16][17][18][19]. MTMs have attracted significant attention due absorption behavior. The designed MMA simulated for TM and TE modes, and all simulation setups resulted in similar absorption curves due to the symmetrical rotational design. We evaluated the proposed MMA in order to understand the effect of structural design on absorption behavior. In the following sections, we discuss the metamaterial properties, normalized input impedance, polarization conversion ratio (PCR), and H-field and E-fields with respect to absorption behavior. The advantages of the designed MMA include its quad-band absorption peaks with near-unity and polarization insensitivity.

Unit Cell Design and Absorption Calculation
In his section, we discuss the design of an MMA unit cell with an absorption mechanism. The square split-ring resonator (SSRR) achieves quad-band near-unity absorption peaks. FR4 substrate materials with 1.6 mm thickness were selected for the absorber design due to their low cost, zero water absorption, and versatility, making them commercially attractive. The dielectric constant, thermal conductivity, and loss tangent of the substrate are 4.3, 0.3 W/K/m, and 0.025, respectively. Copper was used for the patch and ground design, with an electrical conductivity (ρ) of 5.96 × 10 7 S/m. Figure 1 shows a front view of the MMA unit cell with a sketch of all required dimensions. The MMA patch design consists of a Jerusalem cross, two square split rings, and four microstrip lines. The unit cell dimensions are 10 × 10 × 1.6 mm 3 , and all the design parameters are recorded in Table 1. The proposed MMA was designed and simulated using the CST microwave studio [50], where the unit cell boundary conditions were applied along the Y-and X-axes, and electromagnetic waves were applied along the negative Z-axis. The absorption behavior A(ω) was determined according to Equation (1) [27].
where S 11 and S 21 are reflection and transmission coefficients, respectively, as shown in Figure 2, and four near-zero reflection coefficient (S 11 ) resonance peaks are achieved at 12.62 GHz, 14.12 GHz, 17.53 GHz, and 19.91 GHz. A copper ground of 0.035 mm thickness results in a zero transmission coefficient (S 21 ), which can be obtained by calculation of the skin depth [27].
where permeability (µ) is 1, resistivity (ρ) is 1.72Ω − m, with lower frequency defined as f = 12.62GHz. The skin depth becomes δ = 0.0065 mm, which completely blocks the electromagnetic (EM) wave transmission through the MMA. Therefore, Equation (1) becomes: The peak 97% absorption at 12.62 GHz and 99% absorption at 14.12 GHz, 17.53 GHz, and 19.91 GHz were attained for the proposed MMA presented in Figure 2. The high-quality (Q) factor represents high sensitivity, where the Q factor is calculated by Q = fc/FWHM, where f C is the center frequency, and FWHM is the full wave of half maximum [51].

Evaluation of MMA and Metamaterial Property Analysis
The evaluation of the proposed MMA towards SSRR for achieving quad-band absorption is shown in Figure 3. In order to understand the absorption mechanism of the MMA impedance, analysis is vital. The reflection coefficient (S 11 ) depends considerably on the effective impedance (Z e ), as shown in Equation (4). where Z e = µ 0 µ r (ω)/ε 0 ε r (ω) Z 0 = 377Ω = µ 0 /ε 0 is the free space impedance; and µ 0 , ε 0 , µ r (ω), and ε r (ω) are the free space permeability, free space permittivity, frequencydependent permeability, and permittivity, respectively. The normalized impedance can be calculated by Z = Z e f f /Z o = µ r /ε r . Near-unity absorption is achieved by impedance matching with free space. The near-unity value of the real part and the near-zero value of the imaginary part represent the normalized impedance matched with free space [52,53]. The relation between the absorption and metamaterial properties can be understood by calculating Equations (3) and (4) [54].         Figure 4. Table 2 lists the metamaterial properties for various design evaluations. Metamaterial properties such as permittivity, permeability, refractive index, and normalized impedance of different designs are presented in Figure 5.   The metamaterial attributes of the absorber are determined by the Nicolson-Ross-Weir (NRW) formula [55], where ω = 2π f , and c is the velocity of light.
Initially (design 1), a square ring resonator (SRR) is placed on top of the substrate materials, achieving only 14% absorption at a 12.25 GHz resonance frequency with (single negative) SNG metamaterial properties. The absorption percentage slightly increases to 30% at a 12.30 GHz resonance frequency using two square ring resonators because of coupling capacitance between the two SRRs, where SNG metamaterial properties are achieved. In design 3, four splits are made in the middle of each SRR, which significantly increases the capacitance in the splits, resulting in 96.37% and 98.64% absorption peaks appearing at 13.01 GHz and 17.46 GHz resonance frequency, respectively, with DNG metamaterial properties. Three absorption peaks are achieved by inserting four microstrip lines in the  Figure 4. Table 2 lists the metamaterial properties for various design evaluations. Metamaterial properties such as permittivity, permeability, refractive index, and normalized impedance of different designs are presented in Figure 5.

Equivalent Circuit Model
The proposed MMA equivalent circuit model was designed and simulated via ADS (advanced design system) [56], as shown in Figure 6 [27,[57][58][59]. Each resonant peak is constituted by the inductance and capacitance of separate elements, such as the inner Jerusalem cross, the two splits ring, and the external microstrip line, indicated different colors in Figure 6a. An RLC circuit is considered for each resonant frequency in the equivalent circuit design shown in Figure 6b. The series capacitances, C1, C2, C3, and C4, are calculated by Equation (8), where the resonant frequency is f, and the associated series inductance is L (L1, L2, L3, and L4).

TE and TM Mode Analysis
The designed MMA was simulated in both TE and TM modes. Unit cell boundary conditions were applied for TM and TE simulation. Figure 7a-d presents the absorption, permittivity, permeability, and refractive index plot for all three modes, which show a feature of uniform absorption behavior. Both modes obtain the near-uniform metamaterial properties. Table 3 shows the metamaterial properties of the proposed absorber at the resonant frequency. The DNG metamaterial property appears at 14.12 GHz, 17.53 GHz, and 19.91 GHz in TM propagation mode. However, at 12.62 GHz, SNG behavior is exhibited. The dispersion diagram also validates the metamaterial properties plotted by Equa- L=13  The inductance (L1, L2, L3, and L4) is generated by different elements, which are calculated by Equation (9), where the substrate length is l; and w and t are the width of the strapline and the substrate thickness, respectively, in inches. The coupling capacitance (C5, C6, C7, and C8) between the elements and ground is estimated by Equation (10), where d is the gap between the strip, and A represents the area of the strip. Associated series resistance is estimated by tuning for the increment and reduction in the S 11 value. Figure 6c is an S 11 plot of both CST and ADS simulations.

TE and TM Mode Analysis
The designed MMA was simulated in both TE and TM modes. Unit cell boundary conditions were applied for TM and TE simulation. Figure 7a-d presents the absorption, permittivity, permeability, and refractive index plot for all three modes, which show a feature of uniform absorption behavior. Both modes obtain the near-uniform metamaterial properties. Table 3 shows the metamaterial properties of the proposed absorber at the resonant frequency. The DNG metamaterial property appears at 14.12 GHz, 17.53 GHz, and 19.91 GHz in TM propagation mode. However, at 12.62 GHz, SNG behavior is exhibited. The dispersion diagram also validates the metamaterial properties plotted by Equation (11) [24], where d is the MMA unit cell thickness and the propagation phase constant. Figure 8 presents the dispersion curve of the designed MMA during TM mode simulation. The positive slope of the curve represents the right-hand (R) region or SNG metamaterial. The phase and group velocity are parallel in the R region. The DNG metamaterial behavior is represented by the negative slope in the left-hand (L) region, where group velocity and phase are antiparallel. In TM mode, the upper three frequencies, 14.12 GHz, 17.53 GHz, and 19.91 GHz, are located in the L region, which represents doublenegative metamaterial behavior. The SNG behavior of the lower 12.62 GHz frequency is understood from the right-hand R region. The similarity of these two methods validates the metamaterial behavior of the MMA.

Polarization Insensitivity
The H field ( H ) and E field ( E ) vector direction of the incident EM wave is presented in Figure 9a,b of the regular incident angle (θ = 0°) for TE and TM mode. The k vector towards the z-axis represents the propagation direction of the EM wave. In TE mode, there is no H vector in the z-axis, whereas no E vector exists in TM-mode propagation. Polarization-insensitive behavior of the proposed MMA for normal incident angle is plotted in Figure 10 for both TM and TE modes. The constant absorption plot for different polarization incident angles (0° to 90°) increases MMA eligibility for various applications. The reason behind the polarization-insensitive behavior is the symmetrical structural design of the proposed MMA. The designed SSRR is rotationally symmetrical, which indicates no effects on absorption at the rotation of incident EM wave vector on the XY-axis with respect to the Z-axis for circular or any other polarization of the incident wave, as shown in Figure 10a,b. Figure 10c,d shows the oblique incident angle impact TE and TM mode, respectively. In TE mode for the increment of the oblique incident angle, the absorption at 14.12 GHz shows stability up to 45°, but other resonances are either slightly shifted or reduced. On the other side, in TM mode, the absorption at both middle frequencies shows stability, whereas the upper and lower absorption peaks are shifted with the increment of oblique incident angle.

Polarization Insensitivity
The H field ( → H) and E field ( → E) vector direction of the incident EM wave is presented in Figure 9a,b of the regular incident angle (θ = 0 • ) for TE and TM mode. The k vector towards the z-axis represents the propagation direction of the EM wave. In TE mode, there is no H vector in the z-axis, whereas no E vector exists in TM-mode propagation. Polarizationinsensitive behavior of the proposed MMA for normal incident angle is plotted in Figure 10 for both TM and TE modes. The constant absorption plot for different polarization incident angles (0 • to 90 • ) increases MMA eligibility for various applications. The reason behind the polarization-insensitive behavior is the symmetrical structural design of the proposed MMA. The designed SSRR is rotationally symmetrical, which indicates no effects on absorption at the rotation of incident EM wave vector on the XY-axis with respect to the Z-axis for circular or any other polarization of the incident wave, as shown in Figure 10a,b. Figure 10c,d shows the oblique incident angle impact TE and TM mode, respectively. In TE mode for the increment of the oblique incident angle, the absorption at 14.12 GHz shows stability up to 45 • , but other resonances are either slightly shifted or reduced. On the other side, in TM mode, the absorption at both middle frequencies shows stability, whereas the upper and lower absorption peaks are shifted with the increment of oblique incident angle.
with respect to the Z-axis for circular or any other polarization of the incident wave, as shown in Figure 10a,b. Figure 10c,d shows the oblique incident angle impact TE and TM mode, respectively. In TE mode for the increment of the oblique incident angle, the absorption at 14.12 GHz shows stability up to 45°, but other resonances are either slightly shifted or reduced. On the other side, in TM mode, the absorption at both middle frequencies shows stability, whereas the upper and lower absorption peaks are shifted with the increment of oblique incident angle.

E-Field and H-Field Distributions
The absorption mechanism can also be understood through (Magnetic field) H-field and (Electric field) E-field analysis [60]. The inter-relationship of these features can be assumed through the Maxwell equation [61][62][63]. The E-field is resonantly confined at a particular portion of the symmetrical structure. Figure 11 shows the E-field and H-field at in TE mode, where at 12.62 GHz frequency E-field is highly confined at the upper side of the external ring, and the strong H-field appears at the four corners of the outer ring. The intense magnetic field achieves absorption peaks at 14.12 GHz contributed by the vertical bar of the inner Jerusalem cross. On the other side, the E-field is strong in the left and right portions of the outer ring. The near-unity absorption at 17.53 GHz is contributed by the strong H-field of the right and left sides of the inner and outer ring, where less intensity appears in the E-field. The microstrip line on the outer ring's external side influence the absorption peaks at 19.91 GHz. The two opposite sides of the microstrip line have an in-

E-Field and H-Field Distributions
The absorption mechanism can also be understood through (Magnetic field) H-field and (Electric field) E-field analysis [60]. The inter-relationship of these features can be assumed through the Maxwell equation [61][62][63]. The E-field is resonantly confined at a particular portion of the symmetrical structure. Figure 11 shows the E-field and H-field at in TE mode, where at 12.62 GHz frequency E-field is highly confined at the upper side of the external ring, and the strong H-field appears at the four corners of the outer ring. The intense magnetic field achieves absorption peaks at 14.12 GHz contributed by the vertical bar of the inner Jerusalem cross. On the other side, the E-field is strong in the left and right portions of the outer ring. The near-unity absorption at 17.53 GHz is contributed by the strong H-field of the right and left sides of the inner and outer ring, where less intensity appears in the E-field. The microstrip line on the outer ring's external side influence the absorption peaks at 19.91 GHz. The two opposite sides of the microstrip line have an intense E-field, and the center shows high H-field intensity. Figure 12 shows the H-field and E-filed allocations in TM mode, where field intensity is similar to that in TM mode but rotated at 90 degrees.

Sensing Applications
The absorption attributes of the designed MMA depend on impedance matching, which relies on the complex value of relative permittivity and permeability. The metamaterial property can be handled by variation of the substrate thickness and dielectric property. Hence, the absorption of MMA varies with substrate thickness and dielectric constant. MMAs can be used for sensing applications in two ways: by placing a sensor layer on top of the MMA patch [34] or by placing the sensing layer between the patch substrate and substrate ground [13,30,35]. Different mechanisms of absorption-based sensor applications have been proposed from microwave to THz frequency, such as permittivity sensors [32,33], refractive index sensors [34], grin sensors [35], density sensors, tem-

Sensing Applications
The absorption attributes of the designed MMA depend on impedance matching, which relies on the complex value of relative permittivity and permeability. The metamaterial property can be handled by variation of the substrate thickness and dielectric property. Hence, the absorption of MMA varies with substrate thickness and dielectric constant. MMAs can be used for sensing applications in two ways: by placing a sensor layer on top of the MMA patch [34] or by placing the sensing layer between the patch substrate and substrate ground [13,30,35]. Different mechanisms of absorption-based sensor applications have been proposed from microwave to THz frequency, such as permittivity sensors [32,33], refractive index sensors [34], grin sensors [35], density sensors, tem-

Sensing Applications
The absorption attributes of the designed MMA depend on impedance matching, which relies on the complex value of relative permittivity and permeability. The metamaterial property can be handled by variation of the substrate thickness and dielectric property. Hence, the absorption of MMA varies with substrate thickness and dielectric constant. MMAs can be used for sensing applications in two ways: by placing a sensor layer on top of the MMA patch [34] or by placing the sensing layer between the patch substrate and substrate ground [13,30,35]. Different mechanisms of absorption-based sensor applications have been proposed from microwave to THz frequency, such as permittivity sensors [32,33], refractive index sensors [34], grin sensors [35], density sensors, temperature sensors [30], glucose sensor [64], etc. A permittivity sensing model using the proposed MMA is presented in Figure 13a. The relation between the dielectric constant and permittivity can be understood according to the equation k = ε/ε 0 , where k is the dielectric constant, ε is permittivity, and ε 0 is the permittivity of the vacuum. The dielectric constant is the ratio of how fast an electric field travels through a material compared to a vacuum medium. For the investigation of permittivity sensing, an air gap of 1 mm is maintained between two FR-4 substrate materials as a sensing layer. The patch was designed on the upper surface of FR4 substrate 1, and no copper layer was used on the lower side. On the other hand, no copper was used on the upper side of substrate material 2, and full copper was used on the bottom side. Different hydrocarbons with individual dielectric constants were inserted in the air gap in the range of 1.8 to 2.2. The absorption curve of the MMA changes due to the overall thickness and variation of different dielectric constants of hydrocarbon that used in the sensing layer. As a result, the absorption of the lower two bands and the one upper band out of the quad band decreases. Only one absorption band shows near-unity absorption. The absorption plots for different hydrocarbon materials are shown in Figure 13b. Figure 13 shows a zoomed-in version of the absorption peaks zooming in to facilitate understanding of the resonant frequency shift with respect to the dielectric constant. The resonant frequency shifts towards a lower-frequency region with the increment of the dielectric constant by a measurable frequency interval, as shown in Figure 13d. Another permittivity sensor model for solid material sensing is shown in Figure 14a, where the sensing layer is placed on the MMA patch. Various Arlon substrate materials were chosen, with dielectric constants between 2.2 and 3.5. The integration of the sensing layer with the MMA results in a change in peak absorption due to the overall thickness and dielectric constant variation of the MMA. These changes shift the resonance frequency of the MMA, as shown in Figure 14c. The Arlon solid material sensing sensitivity is presented in Figure 14d. Figure 15 shows the measurement setup of the proposed MMA. The first three frequency bands were measured with the setup shown in Figure 15a. A vector network analyzer (VNA), coaxial cable, and waveguide to the coaxial adapter (P/N: 75WCAS, P/N: 51WCAS_Cu) and 1 × 2-unit cell prototype were used in this setup. The upper resonance frequency was measured by a horn antenna with 10 × 10-unit cells in the prototype design, as shown in Figure 15b. The agreement of the measurement and simulated values of the S 11 (dB) phase in degree and absorption % are shown in Figure 16a  lyzer (VNA), coaxial cable, and waveguide to the coaxial adapter (P/N: 75WCAS, P/ 51WCAS_Cu) and 1 × 2-unit cell prototype were used in this setup. The upper resonan frequency was measured by a horn antenna with 10 × 10-unit cells in the prototype desig as shown in Figure 15b. The agreement of the measurement and simulated values of t S11 (dB) phase in degree and absorption % are shown in Figure 16a,b, respectively. T measured absorption values are indicated in Figure 16b. The measured Q-factor is 28.

Comparison
A detailed comparative study was performed of the proposed MMA vs. existing MMAs, as shown in Table 4. Different parameters of MPA were considered, such as MPA design, size, substrate, frequency, absorption, polarization insensitivity, and applications. As discussed in previous works, an MMA that exhibits multiple absorption bands is preferable. Different MMAs were designed previously for C-, Ku-, and K-band applications. Some MMAs show absorption in other frequency spectra, such as the S and X bands. On the other side, some show polarization sensitivity, which may degrade the absorption performance at various polarization incident angles. This article represents a low-cost FR-4 substrate-based, polarization-insensitive quad-band MMA, which shows four nearunity absorption peaks in the Ku-and K-band frequencies. The proposed MMA exhibits good sensing performance for different values of permittivity.

Comparison
A detailed comparative study was performed of the proposed MMA vs. existing MMAs, as shown in Table 4. Different parameters of MPA were considered, such as MPA design, size, substrate, frequency, absorption, polarization insensitivity, and applications. As discussed in previous works, an MMA that exhibits multiple absorption bands is preferable. Different MMAs were designed previously for C-, Ku-, and K-band applications. Some MMAs show absorption in other frequency spectra, such as the S and X bands. On the other side, some show polarization sensitivity, which may degrade the absorption performance at various polarization incident angles. This article represents a low-cost FR-4 substrate-based, polarization-insensitive quad-band MMA, which shows four near-unity absorption peaks in the Ku-and K-band frequencies. The proposed MMA exhibits good sensing performance for different values of permittivity.

Conclusions
In this article, we proposed a quad-band SSRR metamaterial absorber for Ku-and K-band applications. The evaluation of the MMA unit cell, impedance matching of MMA, and equivalent circuit design were discussed to understand the absorption behavior. The metamaterial property of the designed unit cell was verified by the NRW method and the dispersion calculation formula. Due to its symmetrical rotational structure, uniform absorption and polarization insensitivity has been achieved. So, the absorption performance was not verified in TE and TM simulation modes. The proposed MMA shows four absorption peaks at 12.62 GHz, 14.12 GHz, 17.53 GHz, and 19.91 GHz with absorption rates of 97 %, 99.51%, 99% and 99.5 %, respectively. The sensing performance was investigated in two modes, verifying the sensing performance of the developed MMA. Therefore, the proposed MMA is potentially appropriate for Ku-and K-band absorption and sensing applications.