development of double c-shaped left-handed metamaterial

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Citation: Sifat, R.; Faruque, M.R.I.; Hossain, M.B.; Abdullah, M.; Islam, M.T.; Khandaker, M.U.; Tamam, N.; Sulieman, A. Development of Double C-Shaped Left-Handed Metamaterial for Dual-Band Wi-Fi and Satellite Communication Application with High Effective Medium Radio and Wide Bandwidth. Crystals 2022, 12, 836. https://doi.org/10.3390/ cryst12060836 Academic Editors: Liangchi Zhang, Zhen Li, Yang He and George Kenanakis Received: 13 May 2022 Accepted: 9 June 2022 Published: 13 June 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). crystals Article Development of Double C-Shaped Left-Handed Metamaterial for Dual-Band Wi-Fi and Satellite Communication Application with High Effective Medium Radio and Wide Bandwidth Rasheduzzaman Sifat 1 , Mohammad Rashed Iqbal Faruque 1, * , Md Bellal Hossain 1 , Mardina Abdullah 1 , Mohammad Tariqul Islam 2 , Mayeen Uddin Khandaker 3 , Nissren Tamam 4 and Abdelmoneim Sulieman 5 1 Space Science Centre (ANGKASA), Institute of Climate Change (IPI), Universiti Kebangsaan Malaysia, Bangi 43600, Selangor, Malaysia; [email protected] (R.S.); [email protected] (M.B.H.); [email protected] (M.A.) 2 Department of Electrical, Electronic & Systems Engineering, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor, Malaysia; [email protected] 3 Centre for Applied Physics and Radiation Technologies, School of Engineering and Technology, Sunway University, Bandar Sunway 47500, Selangor, Malaysia; [email protected] 4 Department of Physics, College of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia; [email protected] 5 Department of Radiology and Medical Imaging, Prince Sattam Bin Abdul Aziz University, Alkharj 16278, Saudi Arabia; [email protected] * Correspondence: [email protected] Abstract: The development and improvement of the dual-band 802.11ac standard Wi-Fi and wide bandwidth satellite communication devices are currently research subjects that have garnered sig- nificant interest. In this paper, double C-shaped two split-ring resonator (SRR) bounded unit cells were developed, which are applicable for S, C, and X band applications, including dual-band Wi-Fi communication devices and satellite communication applications for its effective medium ratio (EMR) of 15.6, which results in a 2.4 GHz resonance frequency and wide bandwidth (S21 < -10 dB) of 1650 MHz at an 11.5 GHz resonance frequency. A copper resonator and the popular substrate material Rogers RT 5880 (thickness of 1.575 mm) were adopted for analyzing the characteristics of this unit cell. The 8 × 8 mm 2 structure was designed and simulated using a commercially available electromagnetic simulator CST (Computer Simulation Technology) Studio Suite 2019, which was utilized at four resonance frequencies: 2.4 GHz, 5.6 GHz, 8.93 GHz, and 11.5 GHz. The electric field, magnetic field, and surface current distribution were examined by modifying the metamaterial unit cell design structure, showing effective results. To confirm the CST simulation results, the newly designed double C-shaped double-negative metamaterial (DNG) was also simulated with the Ansys High-Frequency Structure Simulator (HFSS) and compared with the extracted results. The suggested metamaterial is advised for usage in Wi-Fi and satellite communication applications for superior long-distance communication performance and efficiency with the compactness of the structure. Keywords: double negative metamaterial; double C shape; effective medium ratio; Wi-Fi application; satellite application 1. Introduction In recent decades, metamaterials have received a lot of attention in the scientific community because of their extraordinary electromagnetic properties. In microwave engi- neering, metamaterials are used to build manmade dielectric electromagnetic waves [1] that are being controlled. The development of metamaterials is inextricably linked to the progress of manmade material design that interacts with microwave, radio, and optical frequency bands. The double negative (DNG) metamaterial is known as the negative index metamaterial (NIM); they are also sometimes referred to as left-handed metamaterials Crystals 2022, 12, 836. https://doi.org/10.3390/cryst12060836 https://www.mdpi.com/journal/crystals

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Citation: Sifat, R.; Faruque, M.R.I.;

Hossain, M.B.; Abdullah, M.; Islam,

M.T.; Khandaker, M.U.; Tamam, N.;

Sulieman, A. Development of Double

C-Shaped Left-Handed Metamaterial

for Dual-Band Wi-Fi and Satellite

Communication Application with

High Effective Medium Radio and

Wide Bandwidth. Crystals 2022, 12,

836. https://doi.org/10.3390/

cryst12060836

Academic Editors: Liangchi Zhang,

Zhen Li, Yang He

and George Kenanakis

Received: 13 May 2022

Accepted: 9 June 2022

Published: 13 June 2022

Publisher’s Note: MDPI stays neutral

with regard to jurisdictional claims in

published maps and institutional affil-

iations.

Copyright: © 2022 by the authors.

Licensee MDPI, Basel, Switzerland.

This article is an open access article

distributed under the terms and

conditions of the Creative Commons

Attribution (CC BY) license (https://

creativecommons.org/licenses/by/

4.0/).

crystals

Article

Development of Double C-Shaped Left-Handed Metamaterialfor Dual-Band Wi-Fi and Satellite Communication Applicationwith High Effective Medium Radio and Wide BandwidthRasheduzzaman Sifat 1, Mohammad Rashed Iqbal Faruque 1,* , Md Bellal Hossain 1 , Mardina Abdullah 1 ,Mohammad Tariqul Islam 2 , Mayeen Uddin Khandaker 3 , Nissren Tamam 4 and Abdelmoneim Sulieman 5

1 Space Science Centre (ANGKASA), Institute of Climate Change (IPI), Universiti Kebangsaan Malaysia,Bangi 43600, Selangor, Malaysia; [email protected] (R.S.); [email protected] (M.B.H.);[email protected] (M.A.)

2 Department of Electrical, Electronic & Systems Engineering, Universiti Kebangsaan Malaysia,Bangi 43600, Selangor, Malaysia; [email protected]

3 Centre for Applied Physics and Radiation Technologies, School of Engineering and Technology,Sunway University, Bandar Sunway 47500, Selangor, Malaysia; [email protected]

4 Department of Physics, College of Sciences, Princess Nourah Bint Abdulrahman University,P.O. Box 84428, Riyadh 11671, Saudi Arabia; [email protected]

5 Department of Radiology and Medical Imaging, Prince Sattam Bin Abdul Aziz University,Alkharj 16278, Saudi Arabia; [email protected]

* Correspondence: [email protected]

Abstract: The development and improvement of the dual-band 802.11ac standard Wi-Fi and widebandwidth satellite communication devices are currently research subjects that have garnered sig-nificant interest. In this paper, double C-shaped two split-ring resonator (SRR) bounded unit cellswere developed, which are applicable for S, C, and X band applications, including dual-band Wi-Ficommunication devices and satellite communication applications for its effective medium ratio(EMR) of 15.6, which results in a 2.4 GHz resonance frequency and wide bandwidth (S21 < −10 dB)of 1650 MHz at an 11.5 GHz resonance frequency. A copper resonator and the popular substratematerial Rogers RT 5880 (thickness of 1.575 mm) were adopted for analyzing the characteristics ofthis unit cell. The 8× 8 mm2 structure was designed and simulated using a commercially availableelectromagnetic simulator CST (Computer Simulation Technology) Studio Suite 2019, which wasutilized at four resonance frequencies: 2.4 GHz, 5.6 GHz, 8.93 GHz, and 11.5 GHz. The electric field,magnetic field, and surface current distribution were examined by modifying the metamaterial unitcell design structure, showing effective results. To confirm the CST simulation results, the newlydesigned double C-shaped double-negative metamaterial (DNG) was also simulated with the AnsysHigh-Frequency Structure Simulator (HFSS) and compared with the extracted results. The suggestedmetamaterial is advised for usage in Wi-Fi and satellite communication applications for superiorlong-distance communication performance and efficiency with the compactness of the structure.

Keywords: double negative metamaterial; double C shape; effective medium ratio; Wi-Fi application;satellite application

1. Introduction

In recent decades, metamaterials have received a lot of attention in the scientificcommunity because of their extraordinary electromagnetic properties. In microwave engi-neering, metamaterials are used to build manmade dielectric electromagnetic waves [1]that are being controlled. The development of metamaterials is inextricably linked to theprogress of manmade material design that interacts with microwave, radio, and opticalfrequency bands. The double negative (DNG) metamaterial is known as the negative indexmetamaterial (NIM); they are also sometimes referred to as left-handed metamaterials

Crystals 2022, 12, 836. https://doi.org/10.3390/cryst12060836 https://www.mdpi.com/journal/crystals

Crystals 2022, 12, 836 2 of 20

(LHM), which exhibit negative electric permittivity and negative magnetic permeability.In a particular frequency range, a metamaterial can act as a single negative metamate-rial that shows only negative permittivity or negative permeability [2,3]. These unusualfeatures are not typically encountered in nature. Tweaking the metamaterial design canprovide the electromagnetic field a large range of potentiality including the development ofsubstrates [4], reconfigurable antennas [5], absorbers [6–8], microwave devices such as Wi-Fi, GPS [9], imaging [10], study of SAR reduction [11], metamaterial sensor [12], filter [13],perfect lens [14], perfect tunneling [15], optics [16–18], invisible cloaking [19], radar andsatellite communication [20], information metamaterial [21], terahertz metamaterial [22,23],programmable modulator [24]; these benefits afford metamaterials wide applicability inmany fields.

It is highly requested in many application fields to design the required system for highperformance with better device compactness and higher bandwidth capacity. EMR refersto the design’s compactness and effectiveness in long-distance communication systems,which can be added to the design’s novelty. In this literature, recent progress on EMR-basedmetamaterial design is discussed. In 2017, a double C shape metamaterial was developedby Faruque et al. [25]. The frequency bands were S, C, and X-band, the dimension of thatunit cell was 12× 12 mm2, and the EMR was 7.427. In the same year, Marathe et al. [26]reported a very compact size metamaterial design with a higher EMR of 11.5. The size of thereported open delta loops-based metamaterial was 6× 6 mm2. Another double L shape [27]metamaterial was designed two years later in 2019. The structure was 10× 10 mm2 indimension and developed for long-distance, military, and satellite communication appli-cations. The EMR of that proposed metamaterial was lower than the previous one of 3.9.In 2020, Afsar et al. [28] proposed a new inverse epsilon-shaped metamaterial unit cellthat has a higher EMR of 12.61, where the unit cell was 10× 10 mm2 in dimension and theresonance frequencies were in the S, C, and X bands. The developed metamaterial wassuggested for distance radar communication and satellite communication applications. Inthe same year, more research was established on the metamaterial unit cell EMR properties.Sifat et al. [29] developed a hook C-shaped metamaterial design with a higher EMR of 12.78.The compactness of that design also established the effective electric field characteristicsunder the S band. The dimension of that design was 8× 8 mm2 and the metamaterial washighly suggested for airport surveillance radar systems. In the same year, Islam et al. [30]designed a new square circle shape metamaterial with the dimension of 8× 8 mm2. Themetamaterial unit cell with a higher EMR of 14.3 presents its effectiveness and compactnessfor airport surveillance radar systems. In the following year, 2021, Islam et al. [31] devel-oped a compact-sized semi-circle-shaped meander-lines-based metamaterial unit cell thatoperates under S, C, X, and Ku bands. The EMR and the dimension of the unit cell were15.1 and 8× 8 mm2 respectively.

The U-NII (Unlicensed National Information Infrastructure) radio band [32], whichwas established by the United Federal Communications Commission, is part of the mi-crowave frequency spectrum from 5.150 to 7.125 GHz. This frequency band is used byWLAN devices and wireless ISPs. Wireless ISPs generally use a 5.825–7.725 GHz band span.In March 2021, U-NII provided a total of eight ranges, which were segmented as U-NII-1–U-NII-8. U-NII-1 to U-NII-4 ranges are for 5 GHz WLAN, which are 802.11 a and laterstandards; U-NII-5 to U-NII-8 areas are for 6 GHz WLAN, which are 802.11 ax standards;UNII-2 is divided into three sub-range sections through A to C. Licensed amateur radiooperators are authorized to use 5.650–5.925 in the USA. Due to a shared IEEE standard,many countries use similar bands for wireless communication. The European HiperLANstandard operates in the same frequency band as the U-NII. The U-NII-1, U-NII-2A, andU-NII-3 bands are also used for Wi-Fi as well, being used both indoors and outdoors forhigher bandwidth capacity. The concept of dual-band Wi-Fi comes from the need for extradata capacity and coverage; the dual-band architecture of 2.4 GHz and 5.6 GHz bands ingateways and end notes have become the most popular. The users are allowed to connectmore devices to the Internet using the 5 GHz spectrum in a more effective way when a home

Crystals 2022, 12, 836 3 of 20

mesh system with several routers is used to cover a bigger area; the UNII band 5.6 GHz canbe worked as a dedicated communications connection between the two routers, speedingup the overall system using a dual-band [33] configuration.

In this study, two SRR-constrained double C-shaped metamaterials are presentedfor S, C, and X band applications. The proposed design provides a unique shape with aminiaturized size: a dimension of 0.0156λ × 0.0156λ. The proposed metamaterial producedquadruple resonance covering for Wi-Fi and satellite communication applications. More-over, it can provide a wider bandwidth of 1.65 GHz at 11.5 GHz. The developed doubleC-shaped left-handed metamaterial exhibited a highly effective medium ratio (EMR) of15.6 that showed compactness, which is relatively high in this regard compared to therecently proposed metamaterials. The S band is very popular with a 2.4 GHz resonancefrequency for Wi-Fi and other applications such as mobile services, satellite communica-tions, and optical communications. The C band with 5.6 GHz resonance frequency canbe used for dual-band Wi-Fi communication along with the 2.4 GHz. It is also applicablein WLAN/WiMAX and radar applications with its large bandwidth of 600 MHz. Theother two resonance frequencies, 8.93 GHz and 11.5 GHz are also highly applicable forlong-distance communication devices. The 11.5 GHz under the X band has a high band-width of 1650 MHz, which can be employed in long-distance satellite communicationapplications. Metamaterials are presently a prominent focus of study to build lightweight,small, and low-cost devices for improving radar and satellite application functionality. Theproposed unit cell was developed with the high-performance Rogers RT5990 substrateand the design is achieved with an EMR of 15.6, which is better than the existing works.Moreover, the demonstration is observed with the suggested design’s compactness andeffectiveness. The CST studio suite 2019 and the finite integration technique (FIT) were usedto design and analyze the considered metamaterial properties that are broadly described inthis manuscript.

2. Design of the Metamaterial Unit Cell

In the unit cell construction, a mutually linked double C-shaped metal with an inter-connected double SRR was proposed. The design structure is shown in Figure 1a, whichpresents the geometric structure of the metamaterial unit cell with a front view of thestructure. The design of the proposed metamaterial unit cell was implemented with aRogers RT5990 substrate with a dimension of 8 × 8 mm2 and a substrate thickness of1.575 mm. The dielectric constant and loss tangent of the substrate is εr = 2.2 and δ = 0.0009,respectively. The used copper coating has a thickness of 0.035 mm and a width of 0.4 mm,with an electrical conductivity of σ = 5.8× 107 S/m. The double SRR attached doubleC-shaped metamaterial schematic and 3D diagram are shown in Figure 1b–d. Figure 1bexhibits the layers of the metamaterial unit cell where there is a substrate layer and a coppercoating layer; Figure 1c shows the perspective view of the unit cell; Figure 1d indicatesthe side view of the design. The unit cell consists of two square SRR bounded with twoC-shaped interconnected parts. The design is achieved with modification of the position,length, and width of the shapes by several numerical simulations executed in the CSTMicrowave Studio Suite (2019).

Figure 2 represents the design progress from beginning to end; Figure 3 representsthe transmission coefficients and reflection coefficients from the different design structures.The design was attempted with an outer SRR, which is shown in Figure 2a-Design 1. Thegap between the edge of the substrate and the outer SRR is 0.2 mm. The length, width, andheight of the very first SRR are 7.6 mm, 7.6 mm, and 0.035 mm, respectively. There is asplit gap of 0.2 mm at the top-right side of the SRR. When the incident wave is propagatedon the device, the resonance is observed there by the SRR as the conducting part of theSRR shows inducting properties and the split gap creates the capacitance. As shown inFigure 3a, there are three resonances of transmission coefficient found because of the outerSRR at 3.53 GHz, 10.29 GHz, and 13.42 GHz.

Crystals 2022, 12, 836 4 of 20

Crystals 2022, 12, x FOR PEER REVIEW 4 of 24

shown in Figure 3a, there are three resonances of transmission coefficient found because of the outer SRR at 3.53 GHz, 10.29 GHz, and 13.42 GHz.

(a) (b)

(c) (d)

Figure 1. (a) Unit cell design parameters and (b–d) schematic and 3D structure of the proposed metamaterial unit cell.

Figure 2. Design evolution of metamaterial unit cell.

Figure 1. (a) Unit cell design parameters and (b–d) schematic and 3D structure of the proposedmetamaterial unit cell.

Crystals 2022, 12, x FOR PEER REVIEW 4 of 24

shown in Figure 3a, there are three resonances of transmission coefficient found because of the outer SRR at 3.53 GHz, 10.29 GHz, and 13.42 GHz.

(a) (b)

(c) (d)

Figure 1. (a) Unit cell design parameters and (b–d) schematic and 3D structure of the proposed metamaterial unit cell.

Figure 2. Design evolution of metamaterial unit cell.

Figure 2. Design evolution of metamaterial unit cell.

Crystals 2022, 12, 836 5 of 20Crystals 2022, 12, x FOR PEER REVIEW 5 of 24

Figure 3. (a) Transmission coefficient (S21); (b) reflection coefficient (S11) based on the evaluation of metamaterial unit cell design.

It is observed that the four resonance frequencies are in three different bands, the S, X, and Ku bands, respectively. The reflection coefficient is shown in Figure 3b, where two strong resonances are observed at 5.2 GHz and 12.6 GHz. In Figure 2b-Design 2, when the second outer SRR is introduced at the inner part of the existing SRR, we observed there is a left shifting of the resonance frequencies. The updated transmission coefficients are 3.4 GHz, 9.2 GHz, and 12.9 GHz—see Figure 3a; the updated reflection coefficients are 4.6 GHz and 11.3 GHz—see Figure 3b. In Figure 2c-Design 3, the C-shape SRR is introduced at the inner part of the existing two SRRs; we find that a new resonance frequency is added with a strong bandwidth at 8.7 GHz.

The new transmission coefficient is shown in Figure 3a along with the other reso-nance frequencies, 3.4 GHz, 8.7 GHz, 9.2 GHz, and 12.8 GHz, respectively. The new re-flection coefficient at 10.8 GHz is also compared in Figure 3b with the other frequencies, 4.5 GHz, 10.8 GHz, and 11.2 GHz, respectively. In Figure 2d-design 4, we introduce a new C-shape SRR in the very inner part of the whole structure and we find almost the same resonance frequencies over the transmission coefficient (S21) in Figure 3a and reflection coefficients (S11) in Figure 3b. The transmission coefficients and reflection coefficients are 3.4 GHz, 8.7 GHz, 9.2 GHz, and 12.8 GHz and 4.5 GHz, 10.8 GHz, and 11.2 GHz, respec-tively. Finally, in Figure 2e-Proposed design, we interconnect the C-shape SRRs to make a double C-shape and interconnect the outer two SRRs. The outer two SRRs and the inner double C-shape are interconnected with a metallic stripe; as a result, we obtain tremen-dous results with a strong lower frequency in this compact size structure. The new design is adopted with the frequencies shifted towards the lower frequencies where the mutual coupling is introduced and magnitudes are changed. The shifted transmission coefficients are 2.4 GHz, 5.6 GHz, 8.9 GHz, and 11.5 GHz with a magnitude of −32.77, 38.28, −26, and −44.7 dB, respectively, which are shown in Figure 3a; the reflection coefficients are 2.8 GHz, 6.14 GHz, 9.1 GHz, and 12.6 GHz with a magnitude of −35.9, −14.8, −17.54, and −7.04 dB, respectively, which are shown in Figure 3b. We also observed that the resonance fre-quency under the Ku band is shifted towards the X band. The resonance frequencies are found under the S, C, and X bands in the proposed structure. The parameters and dimen-sions of the proposed unit cell are shown in Table 1.

The metallic part of the design was tweaked until we obtained good results in the computer simulation technology (CST) studio suite (2019). In this study, different sub-strates were utilized with different thicknesses, dielectric constants, and loss tangents. The design began with a single SRR on the FR-4 substrate and ended with two SRR bounded

Figure 3. (a) Transmission coefficient (S21); (b) reflection coefficient (S11) based on the evaluation ofmetamaterial unit cell design.

It is observed that the four resonance frequencies are in three different bands, the S,X, and Ku bands, respectively. The reflection coefficient is shown in Figure 3b, where twostrong resonances are observed at 5.2 GHz and 12.6 GHz. In Figure 2b-Design 2, when thesecond outer SRR is introduced at the inner part of the existing SRR, we observed thereis a left shifting of the resonance frequencies. The updated transmission coefficients are3.4 GHz, 9.2 GHz, and 12.9 GHz—see Figure 3a; the updated reflection coefficients are4.6 GHz and 11.3 GHz—see Figure 3b. In Figure 2c-Design 3, the C-shape SRR is introducedat the inner part of the existing two SRRs; we find that a new resonance frequency is addedwith a strong bandwidth at 8.7 GHz.

The new transmission coefficient is shown in Figure 3a along with the other resonancefrequencies, 3.4 GHz, 8.7 GHz, 9.2 GHz, and 12.8 GHz, respectively. The new reflectioncoefficient at 10.8 GHz is also compared in Figure 3b with the other frequencies, 4.5 GHz,10.8 GHz, and 11.2 GHz, respectively. In Figure 2d-design 4, we introduce a new C-shapeSRR in the very inner part of the whole structure and we find almost the same resonancefrequencies over the transmission coefficient (S21) in Figure 3a and reflection coefficients(S11) in Figure 3b. The transmission coefficients and reflection coefficients are 3.4 GHz,8.7 GHz, 9.2 GHz, and 12.8 GHz and 4.5 GHz, 10.8 GHz, and 11.2 GHz, respectively. Finally,in Figure 2e-Proposed design, we interconnect the C-shape SRRs to make a double C-shapeand interconnect the outer two SRRs. The outer two SRRs and the inner double C-shapeare interconnected with a metallic stripe; as a result, we obtain tremendous results with astrong lower frequency in this compact size structure. The new design is adopted with thefrequencies shifted towards the lower frequencies where the mutual coupling is introducedand magnitudes are changed. The shifted transmission coefficients are 2.4 GHz, 5.6 GHz,8.9 GHz, and 11.5 GHz with a magnitude of −32.77, 38.28, −26, and −44.7 dB, respectively,which are shown in Figure 3a; the reflection coefficients are 2.8 GHz, 6.14 GHz, 9.1 GHz,and 12.6 GHz with a magnitude of −35.9, −14.8, −17.54, and −7.04 dB, respectively, whichare shown in Figure 3b. We also observed that the resonance frequency under the Ku bandis shifted towards the X band. The resonance frequencies are found under the S, C, and Xbands in the proposed structure. The parameters and dimensions of the proposed unit cellare shown in Table 1.

Table 1. Proposed unit cell parameters values.

Parameter a & b l & w l1 & l2 l3 l4 w1 & c3 w2

Value 8 7.6 2.3 5.8 3.4 1.7 4.9Parameter w3 w4 g1,g2,g3,g4 c1 & c2 c4 c5 m

Value 5.8 0.8 0.2 3.4 2 0.9 0.2

Crystals 2022, 12, 836 6 of 20

The metallic part of the design was tweaked until we obtained good results in thecomputer simulation technology (CST) studio suite (2019). In this study, different substrateswere utilized with different thicknesses, dielectric constants, and loss tangents. The designbegan with a single SRR on the FR-4 substrate and ended with two SRR bounded doubleC-shaped metallic copper coatings on the Rogers RT5880 substrate. The outer two SRRsare interconnected and there is a connection with the inner design of the double C-shapedmetallic part. The inner metallic parts relate to each other at the top and bottom area, wherethey appear as a bold C shape. The width and length of the double C shape are w3 andl3, respectively. The width of the outer C is denoted by c1, and the length of the outer C isdenoted by c2. The inner C shape is denoted by c3, c4, which are the width and length ofthe inner C shape, respectively. The free space between the head and tail of the C shape isidentified by g4.

The whole double C shape is attached to an SRR where l3 is denoted for the length.The SRR has two split gaps at the top and bottom area; the length is 0.02 mm for eachgap denoted by g2 and g3. The single SRR-attached design is also bounded with anotherSRR, and they are interconnected with two metallic parts; the metallic part is denotedby m. The height and width of those connectors are identified as m = 0.2 and g4 = 0.5,respectively. The gap length between the two SRRs is 0.5 mm. The length and width ofthe most outer SRR are denoted by l and w. Finally, the whole copper coating structure isplaced over a Roger RT5880 substrate, which has a length and weight that are denoted by aand b. The transmission coefficient (S21) and reflection coefficient (S11) of the designs areshown in Figure 3 based on the design evaluation. The results of the polarization angleand the incident angle of the incident wave are shown in Figure 4. Figure 4a displaysthe S21 comparison for distinct incident wave polarization, indicating that the suggestedmetamaterial design has a similar response in different circumstances. This polarizationangle effect is analyzed by varying the polarization angle, Φ, from 0◦ to 90◦, with fouridentical steps. The S21 response was also observed from different angles of the incidentwave, which is represented in Figure 4b. The effect of this oblique incidence is analyzedby varying the incident angle, θ, from 0◦ to 90◦. The transmission coefficient is unaffectedby changes in polarization and incident angle, demonstrating that the suggested designstructure has a consistent response for every angle of incidence. As a result, the suggestedmetamaterial structure is insensitive to changes in polarization and oblique incidence angle.

Crystals 2022, 12, x FOR PEER REVIEW 6 of 24

double C-shaped metallic copper coatings on the Rogers RT5880 substrate. The outer two SRRs are interconnected and there is a connection with the inner design of the double C-shaped metallic part. The inner metallic parts relate to each other at the top and bottom area, where they appear as a bold C shape. The width and length of the double C shape are w3 and l3, respectively. The width of the outer C is denoted by c1, and the length of the outer C is denoted by c2. The inner C shape is denoted by c3, c4, which are the width and length of the inner C shape, respectively. The free space between the head and tail of the C shape is identified by g4.

The whole double C shape is attached to an SRR where l3 is denoted for the length. The SRR has two split gaps at the top and bottom area; the length is 0.02 mm for each gap denoted by g2 and g3. The single SRR-attached design is also bounded with another SRR, and they are interconnected with two metallic parts; the metallic part is denoted by m. The height and width of those connectors are identified as m = 0.2 and g4 = 0.5, respec-tively. The gap length between the two SRRs is 0.5 mm. The length and width of the most outer SRR are denoted by l and w. Finally, the whole copper coating structure is placed over a Roger RT5880 substrate, which has a length and weight that are denoted by a and b. The transmission coefficient (S21) and reflection coefficient (S11) of the designs are shown in Figure 3 based on the design evaluation. The results of the polarization angle and the incident angle of the incident wave are shown in Figure 4. Figure 4a displays the S21 comparison for distinct incident wave polarization, indicating that the suggested met-amaterial design has a similar response in different circumstances. This polarization angle effect is analyzed by varying the polarization angle, Φ, from 0° to 90°, with four identical steps. The S21 response was also observed from different angles of the incident wave, which is represented in Figure 4b. The effect of this oblique incidence is analyzed by var-ying the incident angle, θ, from 0° to 90°. The transmission coefficient is unaffected by changes in polarization and incident angle, demonstrating that the suggested design structure has a consistent response for every angle of incidence. As a result, the suggested metamaterial structure is insensitive to changes in polarization and oblique incidence an-gle.

Figure 4. S21 response for different (a) polarization angles; (b) oblique incident angles.

Table 1. Proposed unit cell parameters values.

Parameter a & b l & w l1 & l2 l3 l4 w1 & c3 w2 Value 8 7.6 2.3 5.8 3.4 1.7 4.9

Parameter w3 w4 g1,g2,g3,g4 c1 & c2 c4 c5 m Value 5.8 0.8 0.2 3.4 2 0.9 0.2

Figure 4. S21 response for different (a) polarization angles; (b) oblique incident angles.

3. Metamaterial Simulation and Methodology

The various models were utilized to investigate different property parameters for themetamaterial. The CST Microwave Studio simulation software was used to realize theperformance and compute the S-parameters of the proposed unit cell. The finite integrationtechnique (FIT), including simulation and analysis, was used in this study following fromReference [34]. The numerical approach of the FIT is used to extract the transmissioncoefficient (S21) and reflection coefficient (S11), which indicate return loss and insertion loss,

Crystals 2022, 12, 836 7 of 20

respectively. The two waveguide ports are utilized to generate electromagnetic waves andtransmitted in the Z-axis direction. The boundary conditions are realized to induce thenegative electric and negative magnetic responses to the X and Y-axis. The polarizationhappens while propagating the incoming electromagnetic wave through the E-field andH-field. The X-axis is approved as a perfect electric conductor and the Y-axis as a perfectmagnetic conductor. For free space simulation, a frequency domain solver-based simulationwas utilized. This metamaterial structure implies the equivalent LC circuit where the splitgap acts as a capacitor and the resonator strip plays as an inductor. The inductance of theacting inductor and capacitance of the acting capacitor were modified with the width of themetallic part and the split gap. The simulation was performed from the 1 GHz to 14 GHzmicrowave range. The boundary conditions and the wave ports are shown in Figure 5.

Crystals 2022, 12, x FOR PEER REVIEW 9 of 24

Figure 5. Simulation setup of metamaterial unit cell in computer simulation technology (CST).

Table 2. Proposed unit cell parameters values.

Structure Design 1 Design 2 Design 3 Design 4 Proposed design

Resonance frequencies

3.53, 10.29, 13.42 GHz

3.41, 9.19, 12.9 GHz 3.41, 8.72, 9.25, 12.87 GHz

3.43, 8.77, 9.25, 12.85 GHz

2.4, 5.6, 8.93, 11.5 GHz

Magnitude in dB −40.79, −47.37, −34.61

−42.49, −44.98, −38.36

−41.38, −35.89, −35.68, −40.44

−39.9, −35.11, −39.9, −23.43

−32.27, −38.28, −25.99, −44.7

Bandwidth Span (under −10 dB)

3.25–3.8, 9.38–11.1, 13.2–13.8

3.1–3.6, 8.3–9.8, 12.5–13.36

3.18–3.6, 8.27–8.88, 9.0–9.7, 12.55–13.19

3.19–3.6, 8.28–8.87, 9.0–9.7, 12.5–13.15

2.3–2.49, 5.27–5.87, 8.81–8.98, 10.61–

12.26

4. Equivalent Circuit and Design Analysis Numerous approaches can be taken for remodeling the equivalent circuit. The

lumped equivalent circuit approach is one of the approaches that consider the microwave elements, including the inductance, resistance, capacitance, and conductance [38]. The metallic conductor is addressed with the inductor property when the equivalent circuit model is developed. The capacitive impact is represented by the split gap. Every SRR serves as a combination of inductance L and capacitance C. The split ring acts as a reso-nator, resonating at a specific frequency. The proposed structure is based on double SRR

Figure 5. Simulation setup of metamaterial unit cell in computer simulation technology (CST).

The property of effective permittivity (εr), permeability (µr), and refractive index (η)are extracted from the S-parameters using the Robust technique [35]. Throughout thewhole procedure, Equations (1)–(7) were performed to calculate the parameters [36]. FromEquations (1) and (2), the reflection coefficient (S11) and transmission coefficient (S21) canbe formed.

S11 =R01 (1−

Crystals 2022, 12, x FOR PEER REVIEW 7 of 24

3. Metamaterial Simulation and Methodology The various models were utilized to investigate different property parameters for the

metamaterial. The CST Microwave Studio simulation software was used to realize the performance and compute the S-parameters of the proposed unit cell. The finite integra-tion technique (FIT), including simulation and analysis, was used in this study following from Reference [34]. The numerical approach of the FIT is used to extract the transmission coefficient (S21) and reflection coefficient (S11), which indicate return loss and insertion loss, respectively. The two waveguide ports are utilized to generate electromagnetic waves and transmitted in the Z-axis direction. The boundary conditions are realized to induce the negative electric and negative magnetic responses to the X and Y-axis. The polarization happens while propagating the incoming electromagnetic wave through the E-field and H-field. The X-axis is approved as a perfect electric conductor and the Y-axis as a perfect magnetic conductor. For free space simulation, a frequency domain solver-based simulation was utilized. This metamaterial structure implies the equivalent LC cir-cuit where the split gap acts as a capacitor and the resonator strip plays as an inductor. The inductance of the acting inductor and capacitance of the acting capacitor were modi-fied with the width of the metallic part and the split gap. The simulation was performed from the 1 GHz to 14 GHz microwave range. The boundary conditions and the wave ports are shown in Figure 5.

The property of effective permittivity (εr), permeability (μr), and refractive index (𝜂) are extracted from the S-parameters using the Robust technique [35]. Throughout the whole procedure, Equations (1)–(7) were performed to calculate the parameters [36]. From Equations (1) and (2), the reflection coefficient (S11) and transmission coefficient (S21) can be formed. 𝑆 = 𝑅 (1 − ℮ )1 − 𝑅 ℮ (1)

𝑆 = (1 − 𝑅 )℮1 − 𝑅 ℮ (2)

where 𝑅 = The metamaterial is identified as a passive medium. In such a situation, the real com-

ponent and the imaginary portion of the refractive index and impedance are determined in the following manner. z (real) ≥ 0 (3)𝜂 (imaginary) ≥ 0 (4)

The refractive index (𝜂) and the impedance (z) are derived from Equations (1) and (2),

𝑧 = ± (1 + 𝑆 ) − 𝑆(1 − 𝑆 ) − 𝑆 (5)

℮ = 𝑋 ± 𝑖 1 − 𝑋 (6)

where 𝑋 = ( ) 𝜂 denotes refractive index value and can be achieved from Equation (7) using Equa-tion (6) 𝜂 = 1𝑘 𝑑 [ln (℮ )]” + 2𝑚𝜋 − 𝑖[ln (℮ )] (7)

where m denotes an inextricable link to the index of 𝜂 and k denotes the free space wave vector. The thickness of the proposed structure is denoted by d. The imaginary component

i2nk0d)

1− R012

Crystals 2022, 12, x FOR PEER REVIEW 7 of 24

3. Metamaterial Simulation and Methodology The various models were utilized to investigate different property parameters for the

metamaterial. The CST Microwave Studio simulation software was used to realize the performance and compute the S-parameters of the proposed unit cell. The finite integra-tion technique (FIT), including simulation and analysis, was used in this study following from Reference [34]. The numerical approach of the FIT is used to extract the transmission coefficient (S21) and reflection coefficient (S11), which indicate return loss and insertion loss, respectively. The two waveguide ports are utilized to generate electromagnetic waves and transmitted in the Z-axis direction. The boundary conditions are realized to induce the negative electric and negative magnetic responses to the X and Y-axis. The polarization happens while propagating the incoming electromagnetic wave through the E-field and H-field. The X-axis is approved as a perfect electric conductor and the Y-axis as a perfect magnetic conductor. For free space simulation, a frequency domain solver-based simulation was utilized. This metamaterial structure implies the equivalent LC cir-cuit where the split gap acts as a capacitor and the resonator strip plays as an inductor. The inductance of the acting inductor and capacitance of the acting capacitor were modi-fied with the width of the metallic part and the split gap. The simulation was performed from the 1 GHz to 14 GHz microwave range. The boundary conditions and the wave ports are shown in Figure 5.

The property of effective permittivity (εr), permeability (μr), and refractive index (𝜂) are extracted from the S-parameters using the Robust technique [35]. Throughout the whole procedure, Equations (1)–(7) were performed to calculate the parameters [36]. From Equations (1) and (2), the reflection coefficient (S11) and transmission coefficient (S21) can be formed. 𝑆 = 𝑅 (1 − ℮ )1 − 𝑅 ℮ (1)

𝑆 = (1 − 𝑅 )℮1 − 𝑅 ℮ (2)

where 𝑅 = The metamaterial is identified as a passive medium. In such a situation, the real com-

ponent and the imaginary portion of the refractive index and impedance are determined in the following manner. z (real) ≥ 0 (3)𝜂 (imaginary) ≥ 0 (4)

The refractive index (𝜂) and the impedance (z) are derived from Equations (1) and (2),

𝑧 = ± (1 + 𝑆 ) − 𝑆(1 − 𝑆 ) − 𝑆 (5)

℮ = 𝑋 ± 𝑖 1 − 𝑋 (6)

where 𝑋 = ( ) 𝜂 denotes refractive index value and can be achieved from Equation (7) using Equa-tion (6) 𝜂 = 1𝑘 𝑑 [ln (℮ )]” + 2𝑚𝜋 − 𝑖[ln (℮ )] (7)

where m denotes an inextricable link to the index of 𝜂 and k denotes the free space wave vector. The thickness of the proposed structure is denoted by d. The imaginary component

i2nk0d (1)

S21 =(1− R01

2)

Crystals 2022, 12, x FOR PEER REVIEW 7 of 24

3. Metamaterial Simulation and Methodology The various models were utilized to investigate different property parameters for the

metamaterial. The CST Microwave Studio simulation software was used to realize the performance and compute the S-parameters of the proposed unit cell. The finite integra-tion technique (FIT), including simulation and analysis, was used in this study following from Reference [34]. The numerical approach of the FIT is used to extract the transmission coefficient (S21) and reflection coefficient (S11), which indicate return loss and insertion loss, respectively. The two waveguide ports are utilized to generate electromagnetic waves and transmitted in the Z-axis direction. The boundary conditions are realized to induce the negative electric and negative magnetic responses to the X and Y-axis. The polarization happens while propagating the incoming electromagnetic wave through the E-field and H-field. The X-axis is approved as a perfect electric conductor and the Y-axis as a perfect magnetic conductor. For free space simulation, a frequency domain solver-based simulation was utilized. This metamaterial structure implies the equivalent LC cir-cuit where the split gap acts as a capacitor and the resonator strip plays as an inductor. The inductance of the acting inductor and capacitance of the acting capacitor were modi-fied with the width of the metallic part and the split gap. The simulation was performed from the 1 GHz to 14 GHz microwave range. The boundary conditions and the wave ports are shown in Figure 5.

The property of effective permittivity (εr), permeability (μr), and refractive index (𝜂) are extracted from the S-parameters using the Robust technique [35]. Throughout the whole procedure, Equations (1)–(7) were performed to calculate the parameters [36]. From Equations (1) and (2), the reflection coefficient (S11) and transmission coefficient (S21) can be formed. 𝑆 = 𝑅 (1 − ℮ )1 − 𝑅 ℮ (1)

𝑆 = (1 − 𝑅 )℮1 − 𝑅 ℮ (2)

where 𝑅 = The metamaterial is identified as a passive medium. In such a situation, the real com-

ponent and the imaginary portion of the refractive index and impedance are determined in the following manner. z (real) ≥ 0 (3)𝜂 (imaginary) ≥ 0 (4)

The refractive index (𝜂) and the impedance (z) are derived from Equations (1) and (2),

𝑧 = ± (1 + 𝑆 ) − 𝑆(1 − 𝑆 ) − 𝑆 (5)

℮ = 𝑋 ± 𝑖 1 − 𝑋 (6)

where 𝑋 = ( ) 𝜂 denotes refractive index value and can be achieved from Equation (7) using Equa-tion (6) 𝜂 = 1𝑘 𝑑 [ln (℮ )]” + 2𝑚𝜋 − 𝑖[ln (℮ )] (7)

where m denotes an inextricable link to the index of 𝜂 and k denotes the free space wave vector. The thickness of the proposed structure is denoted by d. The imaginary component

ink0d

1− R012

Crystals 2022, 12, x FOR PEER REVIEW 7 of 24

3. Metamaterial Simulation and Methodology The various models were utilized to investigate different property parameters for the

metamaterial. The CST Microwave Studio simulation software was used to realize the performance and compute the S-parameters of the proposed unit cell. The finite integra-tion technique (FIT), including simulation and analysis, was used in this study following from Reference [34]. The numerical approach of the FIT is used to extract the transmission coefficient (S21) and reflection coefficient (S11), which indicate return loss and insertion loss, respectively. The two waveguide ports are utilized to generate electromagnetic waves and transmitted in the Z-axis direction. The boundary conditions are realized to induce the negative electric and negative magnetic responses to the X and Y-axis. The polarization happens while propagating the incoming electromagnetic wave through the E-field and H-field. The X-axis is approved as a perfect electric conductor and the Y-axis as a perfect magnetic conductor. For free space simulation, a frequency domain solver-based simulation was utilized. This metamaterial structure implies the equivalent LC cir-cuit where the split gap acts as a capacitor and the resonator strip plays as an inductor. The inductance of the acting inductor and capacitance of the acting capacitor were modi-fied with the width of the metallic part and the split gap. The simulation was performed from the 1 GHz to 14 GHz microwave range. The boundary conditions and the wave ports are shown in Figure 5.

The property of effective permittivity (εr), permeability (μr), and refractive index (𝜂) are extracted from the S-parameters using the Robust technique [35]. Throughout the whole procedure, Equations (1)–(7) were performed to calculate the parameters [36]. From Equations (1) and (2), the reflection coefficient (S11) and transmission coefficient (S21) can be formed. 𝑆 = 𝑅 (1 − ℮ )1 − 𝑅 ℮ (1)

𝑆 = (1 − 𝑅 )℮1 − 𝑅 ℮ (2)

where 𝑅 = The metamaterial is identified as a passive medium. In such a situation, the real com-

ponent and the imaginary portion of the refractive index and impedance are determined in the following manner. z (real) ≥ 0 (3)𝜂 (imaginary) ≥ 0 (4)

The refractive index (𝜂) and the impedance (z) are derived from Equations (1) and (2),

𝑧 = ± (1 + 𝑆 ) − 𝑆(1 − 𝑆 ) − 𝑆 (5)

℮ = 𝑋 ± 𝑖 1 − 𝑋 (6)

where 𝑋 = ( ) 𝜂 denotes refractive index value and can be achieved from Equation (7) using Equa-tion (6) 𝜂 = 1𝑘 𝑑 [ln (℮ )]” + 2𝑚𝜋 − 𝑖[ln (℮ )] (7)

where m denotes an inextricable link to the index of 𝜂 and k denotes the free space wave vector. The thickness of the proposed structure is denoted by d. The imaginary component

i2k0d (2)

where R01 = z−1z+1 .

Crystals 2022, 12, 836 8 of 20

The metamaterial is identified as a passive medium. In such a situation, the realcomponent and the imaginary portion of the refractive index and impedance are determinedin the following manner.

z (real) ≥ 0 (3)

η (imaginary) ≥ 0 (4)

The refractive index (η) and the impedance (z) are derived from Equations (1) and (2),

z = ±

√√√√ (1 + S11)2 − S21

2

(1− S11)2 − S21

2(5)

Crystals 2022, 12, x FOR PEER REVIEW 7 of 24

3. Metamaterial Simulation and Methodology The various models were utilized to investigate different property parameters for the

metamaterial. The CST Microwave Studio simulation software was used to realize the performance and compute the S-parameters of the proposed unit cell. The finite integra-tion technique (FIT), including simulation and analysis, was used in this study following from Reference [34]. The numerical approach of the FIT is used to extract the transmission coefficient (S21) and reflection coefficient (S11), which indicate return loss and insertion loss, respectively. The two waveguide ports are utilized to generate electromagnetic waves and transmitted in the Z-axis direction. The boundary conditions are realized to induce the negative electric and negative magnetic responses to the X and Y-axis. The polarization happens while propagating the incoming electromagnetic wave through the E-field and H-field. The X-axis is approved as a perfect electric conductor and the Y-axis as a perfect magnetic conductor. For free space simulation, a frequency domain solver-based simulation was utilized. This metamaterial structure implies the equivalent LC cir-cuit where the split gap acts as a capacitor and the resonator strip plays as an inductor. The inductance of the acting inductor and capacitance of the acting capacitor were modi-fied with the width of the metallic part and the split gap. The simulation was performed from the 1 GHz to 14 GHz microwave range. The boundary conditions and the wave ports are shown in Figure 5.

The property of effective permittivity (εr), permeability (μr), and refractive index (𝜂) are extracted from the S-parameters using the Robust technique [35]. Throughout the whole procedure, Equations (1)–(7) were performed to calculate the parameters [36]. From Equations (1) and (2), the reflection coefficient (S11) and transmission coefficient (S21) can be formed. 𝑆 = 𝑅 (1 − ℮ )1 − 𝑅 ℮ (1)

𝑆 = (1 − 𝑅 )℮1 − 𝑅 ℮ (2)

where 𝑅 = The metamaterial is identified as a passive medium. In such a situation, the real com-

ponent and the imaginary portion of the refractive index and impedance are determined in the following manner. z (real) ≥ 0 (3)𝜂 (imaginary) ≥ 0 (4)

The refractive index (𝜂) and the impedance (z) are derived from Equations (1) and (2),

𝑧 = ± (1 + 𝑆 ) − 𝑆(1 − 𝑆 ) − 𝑆 (5)

℮ = 𝑋 ± 𝑖 1 − 𝑋 (6)

where 𝑋 = ( ) 𝜂 denotes refractive index value and can be achieved from Equation (7) using Equa-tion (6) 𝜂 = 1𝑘 𝑑 [ln (℮ )]” + 2𝑚𝜋 − 𝑖[ln (℮ )] (7)

where m denotes an inextricable link to the index of 𝜂 and k denotes the free space wave vector. The thickness of the proposed structure is denoted by d. The imaginary component

ink0d = X ± i√

1− X2 (6)

where X = 12S21(1−S11

2+S212)

.η denotes refractive index value and can be achieved from Equation (7) using Equation (6)

η =1

k0d{[[ln (

Crystals 2022, 12, x FOR PEER REVIEW 7 of 24

3. Metamaterial Simulation and Methodology The various models were utilized to investigate different property parameters for the

metamaterial. The CST Microwave Studio simulation software was used to realize the performance and compute the S-parameters of the proposed unit cell. The finite integra-tion technique (FIT), including simulation and analysis, was used in this study following from Reference [34]. The numerical approach of the FIT is used to extract the transmission coefficient (S21) and reflection coefficient (S11), which indicate return loss and insertion loss, respectively. The two waveguide ports are utilized to generate electromagnetic waves and transmitted in the Z-axis direction. The boundary conditions are realized to induce the negative electric and negative magnetic responses to the X and Y-axis. The polarization happens while propagating the incoming electromagnetic wave through the E-field and H-field. The X-axis is approved as a perfect electric conductor and the Y-axis as a perfect magnetic conductor. For free space simulation, a frequency domain solver-based simulation was utilized. This metamaterial structure implies the equivalent LC cir-cuit where the split gap acts as a capacitor and the resonator strip plays as an inductor. The inductance of the acting inductor and capacitance of the acting capacitor were modi-fied with the width of the metallic part and the split gap. The simulation was performed from the 1 GHz to 14 GHz microwave range. The boundary conditions and the wave ports are shown in Figure 5.

The property of effective permittivity (εr), permeability (μr), and refractive index (𝜂) are extracted from the S-parameters using the Robust technique [35]. Throughout the whole procedure, Equations (1)–(7) were performed to calculate the parameters [36]. From Equations (1) and (2), the reflection coefficient (S11) and transmission coefficient (S21) can be formed. 𝑆 = 𝑅 (1 − ℮ )1 − 𝑅 ℮ (1)

𝑆 = (1 − 𝑅 )℮1 − 𝑅 ℮ (2)

where 𝑅 = The metamaterial is identified as a passive medium. In such a situation, the real com-

ponent and the imaginary portion of the refractive index and impedance are determined in the following manner. z (real) ≥ 0 (3)𝜂 (imaginary) ≥ 0 (4)

The refractive index (𝜂) and the impedance (z) are derived from Equations (1) and (2),

𝑧 = ± (1 + 𝑆 ) − 𝑆(1 − 𝑆 ) − 𝑆 (5)

℮ = 𝑋 ± 𝑖 1 − 𝑋 (6)

where 𝑋 = ( ) 𝜂 denotes refractive index value and can be achieved from Equation (7) using Equa-tion (6) 𝜂 = 1𝑘 𝑑 [ln (℮ )]” + 2𝑚𝜋 − 𝑖[ln (℮ )] (7)

where m denotes an inextricable link to the index of 𝜂 and k denotes the free space wave vector. The thickness of the proposed structure is denoted by d. The imaginary component

ink0d)]′′+ 2mπ]− i[ln (

Crystals 2022, 12, x FOR PEER REVIEW 7 of 24

3. Metamaterial Simulation and Methodology The various models were utilized to investigate different property parameters for the

metamaterial. The CST Microwave Studio simulation software was used to realize the performance and compute the S-parameters of the proposed unit cell. The finite integra-tion technique (FIT), including simulation and analysis, was used in this study following from Reference [34]. The numerical approach of the FIT is used to extract the transmission coefficient (S21) and reflection coefficient (S11), which indicate return loss and insertion loss, respectively. The two waveguide ports are utilized to generate electromagnetic waves and transmitted in the Z-axis direction. The boundary conditions are realized to induce the negative electric and negative magnetic responses to the X and Y-axis. The polarization happens while propagating the incoming electromagnetic wave through the E-field and H-field. The X-axis is approved as a perfect electric conductor and the Y-axis as a perfect magnetic conductor. For free space simulation, a frequency domain solver-based simulation was utilized. This metamaterial structure implies the equivalent LC cir-cuit where the split gap acts as a capacitor and the resonator strip plays as an inductor. The inductance of the acting inductor and capacitance of the acting capacitor were modi-fied with the width of the metallic part and the split gap. The simulation was performed from the 1 GHz to 14 GHz microwave range. The boundary conditions and the wave ports are shown in Figure 5.

The property of effective permittivity (εr), permeability (μr), and refractive index (𝜂) are extracted from the S-parameters using the Robust technique [35]. Throughout the whole procedure, Equations (1)–(7) were performed to calculate the parameters [36]. From Equations (1) and (2), the reflection coefficient (S11) and transmission coefficient (S21) can be formed. 𝑆 = 𝑅 (1 − ℮ )1 − 𝑅 ℮ (1)

𝑆 = (1 − 𝑅 )℮1 − 𝑅 ℮ (2)

where 𝑅 = The metamaterial is identified as a passive medium. In such a situation, the real com-

ponent and the imaginary portion of the refractive index and impedance are determined in the following manner. z (real) ≥ 0 (3)𝜂 (imaginary) ≥ 0 (4)

The refractive index (𝜂) and the impedance (z) are derived from Equations (1) and (2),

𝑧 = ± (1 + 𝑆 ) − 𝑆(1 − 𝑆 ) − 𝑆 (5)

℮ = 𝑋 ± 𝑖 1 − 𝑋 (6)

where 𝑋 = ( ) 𝜂 denotes refractive index value and can be achieved from Equation (7) using Equa-tion (6) 𝜂 = 1𝑘 𝑑 [ln (℮ )]” + 2𝑚𝜋 − 𝑖[ln (℮ )] (7)

where m denotes an inextricable link to the index of 𝜂 and k denotes the free space wave vector. The thickness of the proposed structure is denoted by d. The imaginary component

ink0d)]′} (7)

where m denotes an inextricable link to the index of η′ and k denotes the free spacewave vector. The thickness of the proposed structure is denoted by d. The imaginarycomponent of η is known just once, while the real part is complicated by the subfunctionsof the logarithm function. To calculate the true fraction of effective parameters, the usualextraction procedure is utilized. From the effective parameter analysis, the resonancefrequencies are displayed. The real part of the effective parameters is determined using theconventional extraction procedure. The effective parameter analysis reveals the resonancefrequencies. The negative effective permeability is influenced by a series of gaps, which areadded together to form a narrow band gap where permittivity and permeability emergeclose to the resonance frequency, and the real value of the effective permittivity, permeability,and refractive index can be calculated using Equations (8)–(10) [37].

εr =c

jπfd× (1− V1)

(1 + V1)(8)

µr =c

jπfd× (1− V2)

(1 + V2)(9)

ηr =c

jπfd×

√√√√ (S21 − 1)2 − S112

(S21 + 1)2 − S112

(10)

The obtained resonance frequencies are 2.4 GHz, 5.6 GHz, 8.93 GHz, and 11.5 GHzin the proposed structure. The final structure is developed by changing many structureswith the variation of the resonance frequencies. The bandwidths are also varied due totheir design pattern. According to the different design structures, the transmission-basedresonance frequencies are 2.4 GHz, 5.6 GHz, 8.93 GHz, and 11.5 GHz, respectively. Thevariation of the designs at their different resonance frequencies and bandwidths are shownin Table 2, which indicates the evolution of the designs and the outcome of the proposeddesign from the design evolution. The magnitudes and bandwidth spans of the differentdesign patterns are also attached to Table 2.

Crystals 2022, 12, 836 9 of 20

Table 2. Proposed unit cell parameters values.

Crystals 2022, 12, x FOR PEER REVIEW 9 of 24

Figure 5. Simulation setup of metamaterial unit cell in computer simulation technology (CST).

Table 2. Proposed unit cell parameters values.

Structure Design 1 Design 2 Design 3 Design 4 Proposed design Resonance frequencies

3.53, 10.29, 13.42 GHz

3.41, 9.19, 12.9 GHz 3.41, 8.72, 9.25, 12.87 GHz

3.43, 8.77, 9.25, 12.85 GHz

2.4, 5.6, 8.93, 11.5 GHz

Magnitude in dB −40.79, −47.37, −34.61

−42.49, −44.98, −38.36

−41.38, −35.89, −35.68, −40.44

−39.9, −35.11, −39.9, −23.43

−32.27, −38.28, −25.99, −44.7

Bandwidth Span (under −10 dB)

3.25–3.8, 9.38–11.1, 13.2–13.8

3.1–3.6, 8.3–9.8, 12.5–13.36

3.18–3.6, 8.27–8.88, 9.0–9.7, 12.55–13.19

3.19–3.6, 8.28–8.87, 9.0–9.7, 12.5–13.15

2.3–2.49, 5.27–5.87, 8.81–8.98, 10.61–

12.26

4. Equivalent Circuit and Design Analysis Numerous approaches can be taken for remodeling the equivalent circuit. The

lumped equivalent circuit approach is one of the approaches that consider the microwave elements, including the inductance, resistance, capacitance, and conductance [38]. The metallic conductor is addressed with the inductor property when the equivalent circuit model is developed. The capacitive impact is represented by the split gap. Every SRR serves as a combination of inductance L and capacitance C. The split ring acts as a

Crystals 2022, 12, x FOR PEER REVIEW 9 of 24

Figure 5. Simulation setup of metamaterial unit cell in computer simulation technology (CST).

Table 2. Proposed unit cell parameters values.

Structure Design 1 Design 2 Design 3 Design 4 Proposed design Resonance frequencies

3.53, 10.29, 13.42 GHz

3.41, 9.19, 12.9 GHz 3.41, 8.72, 9.25, 12.87 GHz

3.43, 8.77, 9.25, 12.85 GHz

2.4, 5.6, 8.93, 11.5 GHz

Magnitude in dB −40.79, −47.37, −34.61

−42.49, −44.98, −38.36

−41.38, −35.89, −35.68, −40.44

−39.9, −35.11, −39.9, −23.43

−32.27, −38.28, −25.99, −44.7

Bandwidth Span (under −10 dB)

3.25–3.8, 9.38–11.1, 13.2–13.8

3.1–3.6, 8.3–9.8, 12.5–13.36

3.18–3.6, 8.27–8.88, 9.0–9.7, 12.55–13.19

3.19–3.6, 8.28–8.87, 9.0–9.7, 12.5–13.15

2.3–2.49, 5.27–5.87, 8.81–8.98, 10.61–

12.26

4. Equivalent Circuit and Design Analysis Numerous approaches can be taken for remodeling the equivalent circuit. The

lumped equivalent circuit approach is one of the approaches that consider the microwave elements, including the inductance, resistance, capacitance, and conductance [38]. The metallic conductor is addressed with the inductor property when the equivalent circuit model is developed. The capacitive impact is represented by the split gap. Every SRR serves as a combination of inductance L and capacitance C. The split ring acts as a

Crystals 2022, 12, x FOR PEER REVIEW 9 of 24

Figure 5. Simulation setup of metamaterial unit cell in computer simulation technology (CST).

Table 2. Proposed unit cell parameters values.

Structure Design 1 Design 2 Design 3 Design 4 Proposed design Resonance frequencies

3.53, 10.29, 13.42 GHz

3.41, 9.19, 12.9 GHz 3.41, 8.72, 9.25, 12.87 GHz

3.43, 8.77, 9.25, 12.85 GHz

2.4, 5.6, 8.93, 11.5 GHz

Magnitude in dB −40.79, −47.37, −34.61

−42.49, −44.98, −38.36

−41.38, −35.89, −35.68, −40.44

−39.9, −35.11, −39.9, −23.43

−32.27, −38.28, −25.99, −44.7

Bandwidth Span (under −10 dB)

3.25–3.8, 9.38–11.1, 13.2–13.8

3.1–3.6, 8.3–9.8, 12.5–13.36

3.18–3.6, 8.27–8.88, 9.0–9.7, 12.55–13.19

3.19–3.6, 8.28–8.87, 9.0–9.7, 12.5–13.15

2.3–2.49, 5.27–5.87, 8.81–8.98, 10.61–

12.26

4. Equivalent Circuit and Design Analysis Numerous approaches can be taken for remodeling the equivalent circuit. The

lumped equivalent circuit approach is one of the approaches that consider the microwave elements, including the inductance, resistance, capacitance, and conductance [38]. The metallic conductor is addressed with the inductor property when the equivalent circuit model is developed. The capacitive impact is represented by the split gap. Every SRR serves as a combination of inductance L and capacitance C. The split ring acts as a

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Figure 5. Simulation setup of metamaterial unit cell in computer simulation technology (CST).

Table 2. Proposed unit cell parameters values.

Structure Design 1 Design 2 Design 3 Design 4 Proposed design Resonance frequencies

3.53, 10.29, 13.42 GHz

3.41, 9.19, 12.9 GHz 3.41, 8.72, 9.25, 12.87 GHz

3.43, 8.77, 9.25, 12.85 GHz

2.4, 5.6, 8.93, 11.5 GHz

Magnitude in dB −40.79, −47.37, −34.61

−42.49, −44.98, −38.36

−41.38, −35.89, −35.68, −40.44

−39.9, −35.11, −39.9, −23.43

−32.27, −38.28, −25.99, −44.7

Bandwidth Span (under −10 dB)

3.25–3.8, 9.38–11.1, 13.2–13.8

3.1–3.6, 8.3–9.8, 12.5–13.36

3.18–3.6, 8.27–8.88, 9.0–9.7, 12.55–13.19

3.19–3.6, 8.28–8.87, 9.0–9.7, 12.5–13.15

2.3–2.49, 5.27–5.87, 8.81–8.98, 10.61–

12.26

4. Equivalent Circuit and Design Analysis Numerous approaches can be taken for remodeling the equivalent circuit. The

lumped equivalent circuit approach is one of the approaches that consider the microwave elements, including the inductance, resistance, capacitance, and conductance [38]. The metallic conductor is addressed with the inductor property when the equivalent circuit model is developed. The capacitive impact is represented by the split gap. Every SRR serves as a combination of inductance L and capacitance C. The split ring acts as a

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Figure 5. Simulation setup of metamaterial unit cell in computer simulation technology (CST).

Table 2. Proposed unit cell parameters values.

Structure Design 1 Design 2 Design 3 Design 4 Proposed design Resonance frequencies

3.53, 10.29, 13.42 GHz

3.41, 9.19, 12.9 GHz 3.41, 8.72, 9.25, 12.87 GHz

3.43, 8.77, 9.25, 12.85 GHz

2.4, 5.6, 8.93, 11.5 GHz

Magnitude in dB −40.79, −47.37, −34.61

−42.49, −44.98, −38.36

−41.38, −35.89, −35.68, −40.44

−39.9, −35.11, −39.9, −23.43

−32.27, −38.28, −25.99, −44.7

Bandwidth Span (under −10 dB)

3.25–3.8, 9.38–11.1, 13.2–13.8

3.1–3.6, 8.3–9.8, 12.5–13.36

3.18–3.6, 8.27–8.88, 9.0–9.7, 12.55–13.19

3.19–3.6, 8.28–8.87, 9.0–9.7, 12.5–13.15

2.3–2.49, 5.27–5.87, 8.81–8.98, 10.61–

12.26

4. Equivalent Circuit and Design Analysis Numerous approaches can be taken for remodeling the equivalent circuit. The

lumped equivalent circuit approach is one of the approaches that consider the microwave elements, including the inductance, resistance, capacitance, and conductance [38]. The metallic conductor is addressed with the inductor property when the equivalent circuit model is developed. The capacitive impact is represented by the split gap. Every SRR serves as a combination of inductance L and capacitance C. The split ring acts as a

Structure Design 1 Design 2 Design 3 Design 4 Proposed design

Resonancefrequencies

3.53, 10.29,13.42 GHz 3.41, 9.19, 12.9 GHz 3.41, 8.72, 9.25,

12.87 GHz3.43, 8.77, 9.25,

12.85 GHz 2.4, 5.6, 8.93, 11.5 GHz

Magnitude in dB −40.79, −47.37,−34.61

−42.49, −44.98,−38.36

−41.38, −35.89,−35.68, −40.44

−39.9, −35.11,−39.9, −23.43

−32.27, −38.28,−25.99, −44.7

Bandwidth Span(under −10 dB)

3.25–3.8, 9.38–11.1,13.2–13.8

3.1–3.6, 8.3–9.8,12.5–13.36

3.18–3.6, 8.27–8.88,9.0–9.7, 12.55–13.19

3.19–3.6, 8.28–8.87,9.0–9.7, 12.5–13.15

2.3–2.49, 5.27–5.87,8.81–8.98, 10.61–12.26

4. Equivalent Circuit and Design Analysis

Numerous approaches can be taken for remodeling the equivalent circuit. The lumpedequivalent circuit approach is one of the approaches that consider the microwave elements,including the inductance, resistance, capacitance, and conductance [38]. The metallicconductor is addressed with the inductor property when the equivalent circuit modelis developed. The capacitive impact is represented by the split gap. Every SRR servesas a combination of inductance L and capacitance C. The split ring acts as a resonator,resonating at a specific frequency. The proposed structure is based on double SRR withsome modifications. The length and spacing of the ring resonator may be adjusted tomodify the resonance frequency.

f =1

2π√

LC(11)

The total inductance L and capacitance C of the proposed unit cell can be achievedfrom Equations (12) and (13), respectively [39].

L = 0.01× µ0

2(d + g + h)2

(2w + g + h)2 +

√(2w + g + h)2 + l2

(d + g + h)

t (12)

C = ε0

[2w + g + h

2π(d + h)2 ln{

2(d + g + h)(a− l)

}]t (13)

where µ0 = 4π × 10−7 H/m, µ0 = 8.854 × 10−12 F/m, h = thickness of the substrate,d = split distance, l = resonator length, w = resonator width, t = thickness of the copperresonator, and g = split gap of the ring.

The equivalent circuit of the unit cell and the S21 response from the CST and ADSsimulator are illustrated in Figure 6. Table 3 represents the values of the circuit components.The inductances L1 and L2 with the collaboration of capacitances C1 and C2 indicate themodel of the equivalent circuit of the outer SRR of the design. At the same time, inductancesL3 and L4 and capacitances C3 and C4 represent the inner SRR as an equivalent circuit.The outer and inner SRR relate to two metallic stripes, which are represented with the LCcombination of L7, C7, and L8, C8, respectively. The inductances and capacitances of theDouble C shape are indicated by the components of L5, L6, C5, and C6. This part of thecircuit is related to the inner SRR, whereas component C9 is made by the split gap. Thesimulation software Advanced Design System (ADS) was used to determine the values ofthese circuit components; the acquired values are characterized in Table 3. These values areconsidered from the unit cell resonances of S21. It can be seen in Figure 6b that both resultsshow slight variations, as the ADS simulator was used to provide the estimated structureof the lumped elements with manual fitting and lower boundary values, whereas the CSTsimulator used the finite integration method with a computing mesh algorithm. After

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studying the unit cell design and equivalent circuit model, the responsible componentsthat trigger the resonance at a certain frequency are identified. The L1, L3, C1, C3, L8, andC8 are responsible for the resonance of 2.4 GHz, whereas the L3, C3, L7, and C7 representthe resonance of 5.6 GHz. The resonance of 8.93 GHz is responsible for the components ofC9, L5, and C5. The resonance frequency at 11.5 GHz is triggered by the components of L6and C6. Controlling the values of these components can change the resonance frequencies.

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with some modifications. The length and spacing of the ring resonator may be adjusted to modify the resonance frequency. 𝑓 = 12𝜋√𝐿𝐶 (11)

The total inductance L and capacitance C of the proposed unit cell can be achieved from Equations (12) and (13), respectively [39].

𝐿 = 0.01 × 𝜇 2(𝑑 + 𝑔 + ℎ)(2𝑤 + 𝑔 + ℎ) + (2𝑤 + 𝑔 + ℎ) + 𝑙(𝑑 + 𝑔 + ℎ) 𝑡 (12)

𝐶 = 𝜖 2𝑤 + 𝑔 + ℎ2𝜋(𝑑 + ℎ) ln 2(𝑑 + 𝑔 + ℎ)(𝑎 − 𝑙) 𝑡 (13)

where 𝜇 = 4𝜋 × 10 H/m, 𝜇 = 8.854 × 10 F/m, h = thickness of the substrate, d = split distance, l = resonator length, w = resonator width, t = thickness of the copper reso-nator, and g = split gap of the ring.

The equivalent circuit of the unit cell and the S21 response from the CST and ADS simulator are illustrated in Figure 6. Table 3 represents the values of the circuit compo-nents. The inductances L1 and L2 with the collaboration of capacitances C1 and C2 indi-cate the model of the equivalent circuit of the outer SRR of the design. At the same time, inductances L3 and L4 and capacitances C3 and C4 represent the inner SRR as an equiva-lent circuit. The outer and inner SRR relate to two metallic stripes, which are represented with the LC combination of L7, C7, and L8, C8, respectively. The inductances and capaci-tances of the Double C shape are indicated by the components of L5, L6, C5, and C6. This part of the circuit is related to the inner SRR, whereas component C9 is made by the split gap. The simulation software Advanced Design System (ADS) was used to determine the values of these circuit components; the acquired values are characterized in Table 3. These values are considered from the unit cell resonances of S21. It can be seen in Figure 6b that both results show slight variations, as the ADS simulator was used to provide the esti-mated structure of the lumped elements with manual fitting and lower boundary values, whereas the CST simulator used the finite integration method with a computing mesh algorithm. After studying the unit cell design and equivalent circuit model, the responsi-ble components that trigger the resonance at a certain frequency are identified. The L1, L3, C1, C3, L8, and C8 are responsible for the resonance of 2.4 GHz, whereas the L3, C3, L7, and C7 represent the resonance of 5.6 GHz. The resonance of 8.93 GHz is responsible for the components of C9, L5, and C5. The resonance frequency at 11.5 GHz is triggered by the components of L6 and C6. Controlling the values of these components can change the resonance frequencies.

(a) (b)

Figure 6. (a) Equivalent circuit model of metamaterial unit cell and (b) transmission coefficients S21from CST and ADS simulator.

Table 3. Circuit components and values of the components.

Capacitor Value (pF) Inductor Value (nH) Capacitor Value (pF) Inductor Value (nH)

C1 0.2 L1 0.5 C6 1.45 L6 1.61C2 1.5 L2 0.258 C7 0.775 L7 0.85C3 0.85 L3 1.33 C8 0.76 L8 0.408C4 1.8 L4 4.42 C9 4.405C5 1.02 L5 1.5

5. Parametric Study: Changing Effects of Length and Split Gaps

The length and split gap are the most important property for metamaterial perfor-mance. Because of the split gap and length, the inductance and capacitance are altered.The metamaterial’s resonance frequencies are affected by the modification of the splitgaps. The split gap in SRR has the most influence on the proposed metamaterial unit cell’sresponse. Due to the relationship between capacitance and resonance frequency, the changein capacitance value impacts the resonance of the unit cell. The split gaps g1 and g3 aremodified on the proposed unit cell for analyzing the resonance results. The split gap g1 isdesigned in the outer SRR and g3 is developed in the inner SRR. In this study, the lengthsof these two split gaps are varied once at a time, whereas the lengths of the other split gapremain fixed. The effects of changing the split gaps are shown in Figure 7. The split gapg1 has an effect on the resonance at 5.6 GHz, 8.93 GHz, and 11.5 GHz, which is shownin Figure 7a. As the split gap g1 decreases from higher gap length to lower gap length,the capacitance increases steadily; this causes the resonance frequency to trend towardthe lower values by following Equation (11). The impact of changing the split gap g3 inthe inner SRR is shown in Figure 7b. The modification of capacitance value due to thechange in g3 causes a minor resonance to exist around 2.4 GHz, though the variation of theresonance frequency is lesser when compared to the effect of the change of g1. The splitgap g3 in the inner SRR shows its impact around the resonances within 7 GHz and 14 GHz.As a result, the split gaps play an important role in regulating the modulator’s capacitance,and the resonance frequency may be controlled by modifying the gap length. The effect

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of changing the length of the metamaterial design is also observed in this study. l1 and l2represent the length of the outer and inner SRR copper parts of the design, respectively.The length modification strongly affects the inductance and influences the resonance of theproposed metamaterial. The resonance shifting results based on the modification of thelength of the outer and inner SRR are shown in Figure 7c,d, where the lengths are tweakeduntil we obtained the desired resonances.

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Figure 7. S21 of the proposed metamaterial unit cell based on the (a) split gap variation of g1; (b) split gap variation of g3; (c) length variation of l1; (d) length variation of l2.

6. Results and Discussion In this part, the metamaterial property of the proposed design is extracted and ana-

lyzed to identify the feature of the introduced design. The EMR on the design evolution is also analyzed here along with the discussion. The array was designed, and the property analysis of the metamaterial array is also introduced here. The metamaterial was used as an array most of the time; thus, it was also necessary to examine the performance of vari-ous arrays of metamaterial because of the validity of the design. The frequency hopping properties of the outer two SRRs were explored using numerical simulation by mirroring the unit cell position in the array. In this part, the metamaterial’s performance is compared to some current research works.

6.1. Electric Field, Magnetic Field, and Surface Current Analysis With the help of mathematics and physics, the electric field distribution at resonance

frequencies of 2.4 GHz, 5.6 GHz, 8.9 GHz, and 11.5 GHz was investigated. The propaga-tion constant (𝛾) of the medium is responsible for frequency (𝜔), permittivity (𝜀), perme-ability (𝜇), and conductivity (𝜎). The propagation constant of the medium is adopted by E-field propagation. For the E-field, we may obtain the Helmholtz equation [40] from Equation (14). 𝛻 𝐸 − 𝛾 𝐸 = 0 (14)

Figure 7. S21 of the proposed metamaterial unit cell based on the (a) split gap variation of g1;(b) split gap variation of g3; (c) length variation of l1; (d) length variation of l2.

6. Results and Discussion

In this part, the metamaterial property of the proposed design is extracted and ana-lyzed to identify the feature of the introduced design. The EMR on the design evolution isalso analyzed here along with the discussion. The array was designed, and the propertyanalysis of the metamaterial array is also introduced here. The metamaterial was usedas an array most of the time; thus, it was also necessary to examine the performance ofvarious arrays of metamaterial because of the validity of the design. The frequency hoppingproperties of the outer two SRRs were explored using numerical simulation by mirroringthe unit cell position in the array. In this part, the metamaterial’s performance is comparedto some current research works.

6.1. Electric Field, Magnetic Field, and Surface Current Analysis

With the help of mathematics and physics, the electric field distribution at resonancefrequencies of 2.4 GHz, 5.6 GHz, 8.9 GHz, and 11.5 GHz was investigated. The prop-agation constant (γ) of the medium is responsible for frequency (ω), permittivity (ε),permeability (µ), and conductivity (σ). The propagation constant of the medium is adoptedby E-field propagation. For the E-field, we may obtain the Helmholtz equation [40] fromEquation (14).

∇2Em − γ2Em = 0 (14)

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Em indicates the propagation of electric field and γ indicates propagation constant.∣∣∣γ2∣∣∣ = ωµ

√σ2 + ω2ε2 (15)

Equation (14) can be generated by combining the given parameters and form toEquation (16), where it is satisfied with a linear homogeneous differential equation.[

d2

dz2 − γ2]

Exm(z) = 0 (16)

At a resonance frequency, Equation (16) gives the properties to the electric field.In Figure 8, the E-field distribution over the outer SRRs is seen while simulating wavepropagation along the z-axis. The properties of electric fields are also observed in the innerdouble C shape area of the metamaterial unit cell. At different resonances, for the proposedquad resonance frequencies, a high-intensity E-field produces a significant dipole momentwhen mutual coupling occurs, and this moment is shared equally by the symmetric andasymmetric parts of the structure. We adjusted the planned unit cell with a connectingslab based on the E-field. The introduced copper metallic slab inductor was placed inthe gap between the outer two SRR areas at 1.7 mm from the left and 4.9 mm from theright of the outer SRR. We also introduced another metallic stripe at 4.9 mm from the leftand 1.7 mm from the right of the outer cell between the two outer SRR gap. Fortunately,the feedback is produced by the electric field and resonance frequencies after connectingthe two outer SRRs. There is another connecting slab used between the inner SRR anddouble C shape gap, which also shows effective results on electric field distribution. Thismodifying technique of the metallic part in the unit cell is inspired by Ahamed et al. [41].The resonance frequencies are implemented in this design at 2.4 GHz, 5.6 GHz, 8.9 GHz,and 11.5 GHz; the bandwidth was observed at or below−10 dB and achieves distinguishedresults, which can be discussed further in the study.

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Figure 8. Electric field distribution at (a) 2.4 GHz; (b) 5.6 GHz; (c) 8.9 GHz; (d) 11.5 GHz.

The electric field (E-field), magnetic field (H-field), and surface current distribution of the proposed metamaterial were analyzed for quad resonance frequency and are shown in Figures 8–10. At the resonance frequency of 2.4 GHz, a strong electric field is seen at the top-right area of the metallic part of the structure, including two outer SRRs; there is an electric field also observed in the inner split of the outer SRRs at the bottom-left area due to the capacitive effect in Figure 8a. At the same time, the magnetic field is observed in the inner double C shape area on the left side of the structure in Figure 9a, where it indicates the opposite reaction from the electric field. Figure 10a shows that a higher sur-face current is observed in those areas where the magnetic field is present.

Figure 8. Electric field distribution at (a) 2.4 GHz; (b) 5.6 GHz; (c) 8.9 GHz; (d) 11.5 GHz.

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The electric field (E-field), magnetic field (H-field), and surface current distribution ofthe proposed metamaterial were analyzed for quad resonance frequency and are shown inFigures 8–10. At the resonance frequency of 2.4 GHz, a strong electric field is seen at thetop-right area of the metallic part of the structure, including two outer SRRs; there is anelectric field also observed in the inner split of the outer SRRs at the bottom-left area due tothe capacitive effect in Figure 8a. At the same time, the magnetic field is observed in theinner double C shape area on the left side of the structure in Figure 9a, where it indicatesthe opposite reaction from the electric field. Figure 10a shows that a higher surface currentis observed in those areas where the magnetic field is present.

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Figure 9. Magnetic field distribution at (a) 2.4 GHz; (b) 5.6 GHz; (c) 8.9 GHz; (d) 11.5 GHz.

Figure 9. Magnetic field distribution at (a) 2.4 GHz; (b) 5.6 GHz; (c) 8.9 GHz; (d) 11.5 GHz.

These characteristics fulfill the criteria of Maxwell’s equation. At the resonance fre-quency of 5.6 GHz in Figure 8b, there is a strong electric field observed at both the top-rightand bottom-left outer SRR area. At the same resonance frequency, the magnetic field isalso observed strongly at the top-left area where the two outer SRRs are connected inFigure 9b. A strong surface current flow is observed in the same area where the magneticfield occurred—see Figure 10b. This high current concentration creates a powerful magneticdipole through the top-right and bottom-left outer SRR. At the resonance frequency of8.9 GHz, in the metamaterial unit cell structure, a strong electric field is observed in boththe outer two SRRs and the inner double C shape. In the meantime, a strong magneticfield is observed at the connecting strip between the outer SRR and the inner double Cshape part—see Figure 9c. The surface current flow is observed in the same area wherethe strong magnetic field exists in Figure 10c. At the resonance frequency of 11.5 GHz, astrong magnetic field appears at the split gap between the outer SRR and inner SRR inFigure 9d. A dense magnetic field is observed throughout the structure where there is

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less of an electric field. A strong magnetic field appears in the inner SRR bottom-left areabecause of the low impedance path—see Figure 9d. At the same time, the surface currentflow is observed in the same area where the magnetic field density is achieved.

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Figure 10. Surface current distribution at (a) 2.4 GHz; (b) 5.6 GHz; (c) 8.9 GHz; (d) 11.5 GHz.

These characteristics fulfill the criteria of Maxwell’s equation. At the resonance fre-quency of 5.6 GHz in Figure 8b, there is a strong electric field observed at both the top-right and bottom-left outer SRR area. At the same resonance frequency, the magnetic field is also observed strongly at the top-left area where the two outer SRRs are connected in Figure 9b. A strong surface current flow is observed in the same area where the magnetic field occurred—see Figure 10b. This high current concentration creates a powerful mag-netic dipole through the top-right and bottom-left outer SRR. At the resonance frequency of 8.9 GHz, in the metamaterial unit cell structure, a strong electric field is observed in both the outer two SRRs and the inner double C shape. In the meantime, a strong magnetic field is observed at the connecting strip between the outer SRR and the inner double C shape part—see Figure 9c. The surface current flow is observed in the same area where the strong magnetic field exists in Figure 10c. At the resonance frequency of 11.5 GHz, a strong magnetic field appears at the split gap between the outer SRR and inner SRR in Figure 9d. A dense magnetic field is observed throughout the structure where there is less of an electric field. A strong magnetic field appears in the inner SRR bottom-left area be-cause of the low impedance path—see Figure 9d. At the same time, the surface current flow is observed in the same area where the magnetic field density is achieved.

Figure 10. Surface current distribution at (a) 2.4 GHz; (b) 5.6 GHz; (c) 8.9 GHz; (d) 11.5 GHz.

6.2. Metamaterial Unit Cell Property Extraction Analysis

The transmission coefficient (S21) and reflection coefficient (S11) obtained from theCST studio suite 2019 are plotted in Figure 11a. The results were analyzed using MATLABcode from Equations (6) and (13) to determine the relative permittivity, relative permeabil-ity, refractive index, and impedance. The graphs are plotted in Origin Pro 2018 using theexported data from MATLAB. Figure 11b shows the negative permittivity in four separaterange frequencies of 2.42–2.71 GHz, 5.64–6.15 GHz, 8.9–9.1 GHz, and 11.57–12.64 GHz,respectively. Another resonance frequency is seen near 6.2 GHz, whereas the other fourindicate a strong contribution to negative permittivity characteristics. The positive permit-tivity imaginary obtains the metamaterial behavior criteria. In Figure 11c, the permeabilitygraph is plotted where three district areas are identified with negative permeability of near2.4 GHz, 5.5 GHz, and 11.2 GHz, which strongly established itself as a double negativemetamaterial. To confirm the results from the CST simulator, another popular simulator, theAnsys High-Frequency Structure Simulator (HFSS), was utilized to extract the transmissioncoefficient (S21) and reflection coefficient (S11) data under the simulator’s proper setupconditions. The compared results of the S21 and S11 from the CST and HFSS simulator areillustrated in Figure 11e. They have almost the same results, which validates the designstructure of the metamaterial unit cell.

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Figure 11. (a) Transmission coefficient and reflection coefficient, the real and imaginary part; (b) relative permittivity; (c) relative permeability; (d) refractive index; (e) transmission coefficient re-flection coefficient results between CST and HFSS simulator; (f) simulated S21 phase of unit cell and arrays.

6.3. Metamaterial Array Analysis In this study, four different sizes of array structures were investigated. The examina-

tion was held under consideration of the resonance and different characteristics of the array at different positions. To evaluate the effects of coupling between the unit cell, dif-ferent layouts of an array need to be described. We call it mirror positioning when one unit cell is positioned as a mirror to its neighbor unit cell. Moreover, we can classify the array evolution into two types: (A) without mirror positioning; (B) with mirror position-ing—inspired by Reference [29]. The top and bottom positions of the two-unit cells were used to place them face to face in a mirror positioning array. In Figure 12, two different types of positioning 1 × 2 sized arrays are illustrated; Figure 12a indicates the without

Figure 11. (a) Transmission coefficient and reflection coefficient, the real and imaginary part; (b) rela-tive permittivity; (c) relative permeability; (d) refractive index; (e) transmission coefficient reflectioncoefficient results between CST and HFSS simulator; (f) simulated S21 phase of unit cell and arrays.

The refractive index is plotted in Figure 11d, which indicates the negative refrac-tive index (real) in the frequency range of 2.4–2.74 GHz, 5.6–6.1 GHz, 8.9–9 GHz, and11.5–12.6 GHz. The imaginary part of the refractive index indicates positive values in thefrequency range of 2.4–2.7 GHz, 5.6–6.1 GHz, 8.9–9 GHz, and 11.6–12.6 GHz, respectively.The incident wave within the metamaterial structure decreases when the refractive indexhas a positive imaginary value. For the validation of the suggested design, the extractedresults from the HFSS simulation software are also compared with the CST simulator,which is illustrated in Figure 11e. The magnitude negative values of the S21 from the HFSSare slightly higher than in the CST simulator, where the resonance frequencies are placedat almost the same points. The S11 values from the HFSS simulator are slightly shiftedright than the CST results. This comparison establishes the validity of the design structurebased on different simulation software, which is mostly popular for microwave simulations.

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The simulated S21 phase of the metamaterial unit cell and different size array is shown inFigure 11f.

6.3. Metamaterial Array Analysis

In this study, four different sizes of array structures were investigated. The examina-tion was held under consideration of the resonance and different characteristics of the arrayat different positions. To evaluate the effects of coupling between the unit cell, differentlayouts of an array need to be described. We call it mirror positioning when one unit cell ispositioned as a mirror to its neighbor unit cell. Moreover, we can classify the array evolutioninto two types: (A) without mirror positioning; (B) with mirror positioning—inspired byReference [29]. The top and bottom positions of the two-unit cells were used to place themface to face in a mirror positioning array. In Figure 12, two different types of positioning1 × 2 sized arrays are illustrated; Figure 12a indicates the without mirror positioning array(the normal placement); 12b indicates the mirror positioning array where the top unit cellis mirrored horizontally in its place. Another scenario is presented in Figure 12c,d, wherea 2 × 1 sized array is examined, where 12 c indicates a general positioned unit cell and12d indicates a transformed unit cell on top position where it transformed to 180◦ in theZ-axis at its position. The transmission coefficients from that without mirror positioningand transformed positioning yield almost similar results to that of the metamaterial ar-ray characteristics. In normal unit cell placement in 1 × 2 sized arrays, the resonancefrequencies shifted to 2.63 GHz, 5.8 GHz, 8,2 GHz, and 11.8 GHz from 2.4 GHz, 5.6 GHz,8.93 GHz, and 11.5 GHz, respectively. It is also observed that with mirror positioning, theresonance frequencies in the same sized array shift back to 2.43 GHz, 5.64 GHz, 9.93 GHz,and 11.55 GHz. The same shifting is occurred in the 2 × 1 sized transformed positioningarray structure. Utilizing this mirror positioning, the 2 × 2 and 4 × 4 sized metamaterialarrays are formed and shown in Figure 12e,f, respectively. The graph visualization oftransmission coefficients of different-sized metamaterial arrays is shown in Figure 13.

The relevant transmission coefficients of the differently sized metamaterial arrays,including their different positioning of the unit cell where the mirror positioning andtransformed positioning array, almost achieved the same resonances. The 1 × 2 and 2 × 1normal positioning arrays fluctuated at their desired resonance frequencies, whereas themirror positioning array in different sizes 1 × 2, 2 × 1, 2 × 2, and 4 × 4 display almostthe same resonance frequencies. For the proposed structure, we are able to discuss thehomomorphism [42] of the design. The transmission coefficient results of the unit cell anddifferent arrays vary slightly due to the coupling effect; however, when applied to themirror symmetry method in an array, the transmission coefficient results of both are thesame due to less coupling effect.

6.4. Effective Medium Ratio (EMR) Analysis and Comparison

The effective medium ratio represents the compactness of the unit cell. In Table 4,the proposed unit cell is compared with a few of the recent existing works, includingreferences, year of development, shape, dimension, resonance frequencies, EMR, andfrequency bands. The presented comparison shows that the proposed design has thehighest effective medium ratio. The wavelength at the lowest resonance frequency isdivided by the unit cell maximal size to achieve the EMR. A metamaterial unit cell can beeither single negative or double negative once the EMR should be larger than 4 in order toestablish its efficiency. The EMR is calculated from Equation (17) [29]. The wavelength anddimension are denoted by λ and L.

EMR =λ

L(17)

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Figure 12. Metamaterial (a) 1 × 2 sized arrays without mirror positioning; (b) 1 × 2 sized array with mirror positioning; (c) 2 × 1 sized array with normal positioning; (d) 2 × 1 sized array with transform positioning; (e) 2 × 2 sized array with mirror positioning; (f) 4 × 4 sized array with mirror position-ing.

The relevant transmission coefficients of the differently sized metamaterial arrays, including their different positioning of the unit cell where the mirror positioning and transformed positioning array, almost achieved the same resonances. The 1 × 2 and 2 × 1 normal positioning arrays fluctuated at their desired resonance frequencies, whereas the mirror positioning array in different sizes 1 × 2, 2 × 1, 2 × 2, and 4 × 4 display almost the same resonance frequencies. For the proposed structure, we are able to discuss the homo-morphism [42] of the design. The transmission coefficient results of the unit cell and dif-ferent arrays vary slightly due to the coupling effect; however, when applied to the mirror symmetry method in an array, the transmission coefficient results of both are the same due to less coupling effect.

Figure 12. Metamaterial (a) 1 × 2 sized arrays without mirror positioning; (b) 1 × 2 sized arraywith mirror positioning; (c) 2 × 1 sized array with normal positioning; (d) 2 × 1 sized array withtransform positioning; (e) 2 × 2 sized array with mirror positioning; (f) 4 × 4 sized array withmirror positioning.

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Figure 13. Transmission coefficient (S21) of differently sized metamaterial arrays with positioning.

6.4. Effective Medium Ratio (EMR) Analysis and Comparison The effective medium ratio represents the compactness of the unit cell. In Table 4, the

proposed unit cell is compared with a few of the recent existing works, including refer-ences, year of development, shape, dimension, resonance frequencies, EMR, and fre-quency bands. The presented comparison shows that the proposed design has the highest effective medium ratio. The wavelength at the lowest resonance frequency is divided by the unit cell maximal size to achieve the EMR. A metamaterial unit cell can be either single negative or double negative once the EMR should be larger than 4 in order to establish its efficiency. The EMR is calculated from Equation (17) [29]. The wavelength and dimension are denoted by λ and L. 𝐸𝑀𝑅 = 𝜆𝐿 (17)

According to Table 4, it is observed that the lower dimension of the unit cell with lower resonance frequencies can achieve a higher EMR. Though the material from Refer-ence [26] represents a much smaller size unit cell of 6 × 6 mm in dimension, it also has a high resonance frequency at a lower band among the compared metamaterial structures. We also obtained two frequency bands, where the double L-shaped unit cell with the di-mension of 10 × 10 mm has three frequency bands, although the EMR is very low. The developed structure competes with the square circle shape structure [30], where the num-ber of bands (S, C, and X bands) are the same, but the following semi-circle shape structure [31] has the same number of resonance frequencies of four. From Reference [29], the unit cell provided only one resonance frequency under the S band. Because of its narrow band, the metamaterial unit cell also provided a high EMR at that point. The proposed unit cell obtains the miniaturization and higher EMR with quad-band resonance frequencies, indi-cating the metamaterial design was the most effective when compared to all other studies presented in Table 4. The compactness and quad-band properties indicate this metamate-rial unit cell can be used for a variety of small-sized devices and could be useful in a wide array of applications.

Figure 13. Transmission coefficient (S21) of differently sized metamaterial arrays with positioning.

According to Table 4, it is observed that the lower dimension of the unit cell with lowerresonance frequencies can achieve a higher EMR. Though the material from Reference [26]represents a much smaller size unit cell of 6× 6 mm2 in dimension, it also has a highresonance frequency at a lower band among the compared metamaterial structures. Wealso obtained two frequency bands, where the double L-shaped unit cell with the dimensionof 10× 10 mm2 has three frequency bands, although the EMR is very low. The developedstructure competes with the square circle shape structure [30], where the number of bands(S, C, and X bands) are the same, but the following semi-circle shape structure [31] hasthe same number of resonance frequencies of four. From Reference [29], the unit cellprovided only one resonance frequency under the S band. Because of its narrow band,the metamaterial unit cell also provided a high EMR at that point. The proposed unitcell obtains the miniaturization and higher EMR with quad-band resonance frequencies,indicating the metamaterial design was the most effective when compared to all otherstudies presented in Table 4. The compactness and quad-band properties indicate thismetamaterial unit cell can be used for a variety of small-sized devices and could be usefulin a wide array of applications.

Table 4. Comparison between proposed metamaterial and recently developed metamaterials basedon resonance frequencies, dimension, and EMR.

References Year Shape Dimensions (mm) ResonanceFrequencies (GHz) EMR Frequency Bands

[25] 2017 Double C 12 × 12 3.36, 8.57, 11.57 7.42 S, C, and X[26] 2017 Delta loop 6 × 6 4.3, 7.6, 9.8 11.5 C and X[27] 2019 Double L 10 × 10 7.69, 8.47, 12.04, 13.14 3.9 C, X and Ku[28] 2020 Inverse-epsilon 10 × 10 2.38, 4.55, 9.42 12.61 S, C and X[29] 2020 Hook-C shape 8 × 8 2.93 12.78 S-band[30] 2020 Square-Circle 8 × 8 2.6, 6.3, 9.3 14.3 S, C, and X[31] 2021 Semi-Circle 8 × 8 2.48, 4.28, 9.36, 13.7 15.1 C, S, X and Ku

Proposed 2022 Double C shaped 8 × 8 2.4, 5.64, 8.93, 11.5 15.6 S, C, and X

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7. Conclusions

In this study, two SRRs bounded to a double C-shape double-negative left-handedmetamaterial were simulated using the CST Microwave Studio Suite 2019. We comparedthe results with the extracted results from Ansys High-Frequency Structure Simulator HFSS.The equivalent circuit analysis and its electric, magnetic, and surface current distributionanalysis were also used rigorously in this study. The resonance frequencies are 2.4 GHz,5.6 GHz, 8.9 GHz, and 11.5 GHz, indicating the multi-band performance of this device. Thehigh EMR of the device at the lower resonance frequency of 2.4 GHz compared to otherexisting designs strongly indicates its novelty. The proposed developed structure can beemployed in Wi-Fi applications with dual-band facilities. It is also suggested to employ thedesign in satellite communication applications for its high bandwidth.

Author Contributions: Conceptualization, R.S. and M.R.I.F.; methodology, R.S. and M.R.I.F. software,R.S.; validation, R.S., M.R.I.F. and M.B.H.; formal analysis, R.S.; investigation, R.S. and M.R.I.F.data curation, R.S.; writing—original draft preparation, R.S., writing—review and editing, M.R.I.F.,M.A., M.T.I. and M.U.K.; visualization, R.S., M.R.I.F., M.B.H., M.T.I., M.A., M.U.K., N.T., and A.S.;supervision, M.R.I.F., M.T.I. and M.A.; project administration, M.R.I.F.; funding acquisition, A.S. andN.T. All authors have read and agreed to the published version of the manuscript.

Funding: The authors express their gratitude to Princess Nourah bint Abdulrahman UniversityResearchers Supporting Project (Grant No. PNURSP2022R12), Princess Nourah bint AbdulrahmanUniversity, Riyadh, Saudi Arabia. The authors also thank the research Universiti Grant, UniversitiKebangsaan Malaysia, GUP-2021-074, who helped conduct the research work.

Institutional Review Board Statement: Not applicable.

Informed Consent Statement: Not applicable.

Data Availability Statement: All the data are available within the manuscript.

Conflicts of Interest: The authors declare no conflict of interest.

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