H-shaped modifiers loaded mirror symmetric resonator based double negative metamaterial for multi-band wireless communications

In this article, a unique metamaterial (MTM) structure is presented that exhibits four resonances of transmission coefficient (S21) that fall into S, X, and Ku bands. The MTM design is initiated on a Rogers (RT5880) substrate with an electrical dimension of 0.088 λ × 0.088 λ (λ is calculated at 3.424 GHz). The resonating patch contains four quartiles connected by a central metallic strip. The placement of each quartile is such that the whole resonator is mirror symmetric about the vertical axis. Two H-shaped modifiers connect two quartiles of each vertical half of the resonator. These H-shaped modifiers form the resonance cavity in its vicinity, and thus help significantly to orient the overall resonances of the proposed MTM at 3.424 GHz, 10 GHz, 14.816 GHz, and 16.848 GHz. The resonance phenomena are examined through equivalent circuit modeling and verified in Advanced Design Software (ADS). Metamaterial properties of the proposed MTM are extracted and it exhibits negative permittivity, permeability, and refractive index. The prototype of the MTM is fabricated and measurement is taken. The measured S21 shows a close similarity with the simulated result. Moreover, effective medium ratio (EMR) is calculated for the proposed MTM and a high EMR of 10.95 is obtained that expresses its compactness. This compact MTM with negative permittivity, permittivity, and refractive index can be important component for improving the performance of the miniaturized devices for multi-band wireless communication systems.

The latest development of wireless technologies expedited the applications of multiband frequency in a single microwave device.To meet future demand these devices must attain the miniaturization feature and as well as operation in multi-frequency ranges with high gain.There are artificial materials with a symmetrical homogeneous structure known as metamaterials, which can exhibit these properties together [1][2][3] .These symmetrical homogeneous structures of metamaterials are one of the prime developments in the designing and miniaturization of multiband microwave devices.These artificial metamaterials can exhibit many exclusive features that are not present in the established conventional materials [4][5][6] .One of them is negative permeability and permittivity at the same frequency.A metamaterial can display these unique properties depending on the structure's orientation, geometry, and substrate materials.Nowadays, the research on metamaterials is one of the first growing research fields because of their small structure compared to the wavelength of the targeted electromagnetic wave 1,[7][8][9][10] .The metamaterial-based system can be used effectively in different microwave applications such as sensing 1,11 sound engineering, anomalous reflection, sub-wavelength focusing, and metallic cloaking 11,12 .Keshavarz et al. 13 demonstrated a mechanism to detect skin cancer, where they used a metamaterial-based system in the terahertz frequency range.Using conventional reflect-array wide-band dual frequencies cannot be shared by the same aperture, which was possible by replacing it with a metasurface as explained by Nayeri et al. 14 in 2018.In 15 metasurface was used effectively in Holography and nanoprinting.In 16 another ultra-compact metasurface was presented for polarization splitter-rotator application.A metamaterial-based active amplifier is presented in 17 , which can amplify and modify the magnitude of energy of the propagating spatial waves using digital coding.A metamaterial-based design to operate in the microwave frequency ranges is presented in 18 , which can cover wideband frequencies.In addition, this design of metamaterial can exhibit a high value of the effective medium ratio (EMR), negative permittivity, and refractive index close to zero.The metamaterial with the split ring is used in 19 to achieve high EMR and negative permittivity.The proposed metamaterial of 19 can cover frequencies of S, C, and X-bands.Misran et al. 20 demonstrated the design of another split ring metamaterial that observed the impact of parameter variation with the help of thickness change and permittivity of the substrate material.To perform linear polarization Wang et al. 21presented a dual-band metamaterial-based converter.The model showed insensitive behavior to the polarization angle, which helped to reduce the RCS radar, imaging, and communication system 21 .Xie et al. 22 proposed a Fabry-Perot antenna to reduce the RCS of radar, which used metamaterial in both transmitter and receiver surfaces, obtained high gain, and reduced the RCS of radar significantly.
Numerous research works have been conducted on metamaterial-based systems for multiband microwave applications.To facilitate the overall performance of the microwave system the performance of the antenna is very vital and can be evaluated by the bandwidth, gain, radiation efficiency, and size of the antenna.Bougoutaia et al. 23 designed an antenna to attain high gain and wide bandwidth that used a dual ring metamaterial resonator in the antenna.The metamaterial resonator along with partial ground has helped the antenna to exhibit impedancematching phenomena 23 .Van Yem et al. 24 also improved the gain and bandwidth of the antenna by including a metamaterial structure on the ground plane of the antenna.A metamaterial-loaded mushroom-shaped antenna displayed circular polarization with high gain and wide bandwidth 25 .Along with high bandwidth, the efficiency of the antenna can also be improved by using metamaterial which is demonstrated in 26 where the antenna is designed to attain the application-oriented frequency of 2.4 GHz.Pyo et al. 27 improved the efficiency of the antenna-based transmission line model that used metamaterial in both central-fed and offset-fed antennas of the model.In 28 the compactness of the antenna was achieved by the use of metamaterial in the design which reduced the size of the antenna substantially compared to the conventional antennas.To improve the antenna performance metamaterial-based split ring is presented in 29,30 .In 29 a compact design of metamaterial was developed by tuning the split ring inductively which can provide negative permittivity and close to zero refractive index.To get these properties and improvement of antenna gain the model of 30 used a symmetrically shaped split ring with the coupled gap.Moreover, the metamaterial-based resonators can also be implemented in sensing applications.Using metamaterial in the structure of the sensor, the optical, electromagnetic, and mechanical properties of the sensors can be improved 31 .
Based on the above literature study, a double negative metamaterial is presented in this paper that has a high possibility of being used in future for the wireless communication applications like the performance improvement of antenna used in microwave communication systems and sensing devices.The unique features of the proposed MTM are: (i) it contains four quartiles placed in a 2 × 2 matrix where quartiles are connected at the center with a copper strip.The total structure is mirror symmetric about the vertical axis, which helps to reduce the crosscoupling effect between the array elements.(ii) The H-shaped modifiers are placed between two adjacent quartiles of the same column that help to improve the frequency response covering the low-frequency range to a high frequency.(iii) Resonances in different other frequencies can be selected by placing H-shaped modifiers at different other quartiles.(iii) Moreover, the H-shaped modifier also helps to improve the EMR value significantly, representing the compactness of the design.(iv) Additionally, the proposed MTM exhibits both permittivity and permeability negative in the vicinity of resonance frequencies of S 21 .Because of these unique features, the proposed double negative metamaterial can be utilized to develop a compact high-gain antenna.Moreover, the proposed MTM can also be used for the reduction of coupling effects in MIMO antennas.In addition to this, it can be used as a band-stop filter that can be used to hinder unwanted transmitted signals.Thus, the multiband resonance characteristics of this compact MTM make it suitable for use directly in various miniaturized microwave systems, or as a part of an antenna for performance enhancement.This MTM-loaded antenna can be employed in several applications such as in 5G communications, weather monitoring systems, amateur radio and VSAT systems as the designed frequencies of the proposed MTM fall in the S, X, and Ku bands.The rest of the paper is organized as follows.The design of the MTM unit cell is presented in section two.This section also includes step-by-step design procedures, electromagnetic field and current analysis, and effective parameter extraction methods.The equivalent circuit model is demonstrated in section three.In section four, the result is analyzed, which includes simulation and measurement results, analysis of effective parameters, effects of substrate change of the designed MTM, comparison of the unit cell of the proposed MTM with its different arrays, impact of oblique incident angle change of the proposed MTM, a comparative study of the effects of H-shaped modifiers at different positions, Far-field analysis of the proposed MTM and comparison of proposed model with relevant works.Finally, a conclusion is drawn in section five that includes the major outcome of this work.

Development of the structure of the unit cell of the proposed model
The schematic diagram of the unit cell of the proposed model is given in Fig. 1.As the model is targeting wide ranges of frequency bands, Rogers RT5880 is suitable for the application.The motivation behind selecting this material as the substrate because it can provide minimum moisture absorption and minimum electrical losses.At the same time, over a wide range of frequency bands, it can exhibit identical electric properties.For the proposed model the thickness of the substrate is selected to 1.57 mm with dielectric constants of 2.2 and loss tangent of 0.0004.To make the dimension of the unit cell small compared to the wavelength, an 8 × 8 mm 2 substrate is chosen for the unit cell.The frequency range for the system is considered 2 to 18 GHz.This material is used as the substrate of the designed resonator patch and on top of this conducting metal strip is used with a thickness of 0.035 mm.The patch is constructed by combining four identical segments.Each quartile has two square-shaped split ring resonators (SRR) and one circular split ring resonator (CSRR) that are connected by three metal strips.Then these four segments are connected by a central rectangular conducting metal strip.The upper two quartiles are connected with the lower quartiles by two H-shaped modifiers.The dimension of the unit cells is provided in Fig. 1.The various segments are presented in Table 1.
To prepare the simulation setup and evaluate the properties of the proposed model of metamaterial, its unit cell is sited in the middle of positive and negative Z direction of the wave-guide ports of the CST Studio Suite 2019 simulator is shown in Fig. 2. For the simulation, the E field is set in the X and H field is set in Y direction.

Steps towards the formation of the proposed model
The design of the unit cell of the proposed model is developed with the help of a step-by-step modification process.The design steps are presented in Fig. 3.In each step, the response of the transmission coefficients (S 21 )

Electric field, magnetic field, and surface current analysis of proposed model
The influence of the electric field, magnetic field, and surface current on the unit cell of the proposed MTM can be observed in Figs. 5, 6, and 7 respectively for the resonance frequencies of 3.424 GHz, 10 GHz, 14.816, and 16.848 GHz.There is a correlation among these parameters, which can be expressed mathematically using Maxwell's equations as explained in 32 .At

Effective parameters extraction procedure
The effective parameters of the proposed model can be extracted by the Nicolson-Ross-Weir (NRW) method that is explained in 33,34 .To extract permittivity ε r , permeability μ r , normalized impedance Z, and refractive index η r the values of scattering parameters S 21 and S 11 are used from the CST simulation.As explained in Ref 29,33,35,36 the effective permittivity, ε r and permeability, μ r can be calculated using the following Eqns.: and, (1) The normalized impedance can be calculate as: The effective refractive index η r is calculated from S 11 and S 21 using direct refractive strategy, where c represents the velocity of light, f is the frequency of the signal and d is the thickness of the substrate.A MATLAB code is used where equations from (1) to ( 4) are used to calculate the permittivity, permeability, and normalized impedance, and refractive index of the proposed MTM.The effective parameters can also be extracted from CST simulation which uses Drude-Lorentz model 29 for S-parameters identification and built in post processing module for effective parameters.

Analysis of simulation and measurement results
The array of the proposed metamaterial-based model is given in Fig. 10.The prototype of the array is fabricated with the unit cell dimension of 8 × 8 mm 2 for the measurement purpose.The performance of the prototype is analyzed using Agilent N5227A, Vector Network Analyzer (VNA) for determining the scattering parameters of the proposed unit cell.The vector network analyzer is calibrated with the help of electronic calibration kit (model: N4694-60001).The measurement setup is given in Fig. 11.The data recorded for S 21 from the measurement is compared with the simulation results of CST, which is depicted in Fig. 12. From the measurement, the resonances of S 21 are found at 3.4 GHz, 9.878 GHz, 14.76 GHz, and 16.849 GHz respectively whereas the simulation results provided the corresponding resonances of S 21 at 3.424 GHz, 10 GHz, 14.816 GHz, and 16.848 GHz respectively that are plotted together in Fig. 12.After analyzing these two sets of data it is found that, from the simulation results there are frequency deviations of 0.7%, 1.22%, and 0.38% in the first three resonances of S 21 respectively, whereas the fourth resonance frequency matches with the simulation result.The measurement data From the analyses, it can be commented that the deviation of resonance frequencies from the simulation results to the measurement results are very negligible which implies that the resonance frequencies of the simulation are matched very closely with the measurement.However, there are disparities in the negative peak values of S 21 between measurement results.A few aspects of the prototype design and measurement environment may be responsible for these inconsistencies.To be more specific, construction errors due to very tiny metal strips with miniaturization of slots, and calibration errors of the VNA may have occurred.However, the overall  www.nature.com/scientificreports/measurement response can be considered to have a significant level of matching between the simulation results, which can be observed in Fig. 12.The model performed very well in the high-frequency ranges.Irrespective of these inconsistencies, the deviation is not severe, and the experimental result exhibits similar behavior within the S, X, and Ku bands.

Analysis of effective parameters
The S-parameters of the proposed MTM are presented in Fig. 13a.The values of permittivity and permeability are extracted using the Eqs.( 1) and ( 2) respectively which require the values of S 21 and S 11 .The permittivity and permeability plots are presented in Fig. 13b,c respectively.Table 4 summarizes the frequency ranges of the permittivity and permeability, normalized impedance, and refractive index of the proposed model near the www.nature.com/scientificreports/resonance frequencies.As explained in 37 , the relation between permittivity and plasma frequency is established by the following Eq.( 5): where ω represents the frequency of the incident EM wave and the plasma frequency is represented by ω p .When the frequency of the EM wave is less than the plasma frequency the permittivity becomes negative.It becomes zero if the frequency of the EM wave is equal to the plasma frequency.By observing the real part of the permittivity, ε of the proposed model, it is realized that permittivity undergoes transition from positive peak having magnitude of 2381 to negative peak of magnitude − 1596 at 3.424 GHz, from 1684 to − 945 at 10 GHz, and from 992 to -67 at 16.84 GHz which are significantly large.On the other hand, the real part of the permeability shows negative values of − 0.04827 at 3.456 GHz, − 0.070934 at 10 GHz, − 0.039874 at 14.816 GHz and − 0.085298 at 16.848 GHz.
From Table 4 it is observed that both permittivity and permeability are negative in the frequency ranges of 3.433-3.5131GHz, 10.013-10.387GHz, 14.828-14.87GHz, and 16.886-17.527GHz.The double negative properties of the metamaterials can be achieved using a split-ring resonator (SRR) that exhibits negative values of the permeability and micro-strip metallic lines or micro-structured array of wires to obtain negative permittivity that is followed by the original work of J. B Pendry et al.9][40] are some examples that follow these principles to obtain the double negative properties of the metamaterial.Using of micro-structured array of wires and SRR helps to tune the magnetic and electric resonance separately and thus, the magnitude of the permittivity and permeability can be controlled robustly through structural design.2][43][44] in which complementary split ring resonators are used to obtain the double negative characteristics.In the present work, a one-sided design approach has been followed.Since both electrical and magnetic resonances are required to obtain both negative permittivity and permeability simultaneously, the proposed MTM is so designed that each quartile of this design contains three interconnected complementary split rings.Moreover, the quartiles are so arranged that they are mirror images of one another.Due to this structural design, an antiparallel surface current is flowing through various segments when the MTM is excited with electromagnetic waves.The analysis of surface current distribution at 3.424 GHz reveals that strong anti-parallel currents flow through the vertical arms of the outer split rings of resonator quartiles as shown in Fig. 7a.Compared to this, the inner arms of this ring contain almost zero currents.Thus, the magnetic dipole is formed between two vertical sides of the outer ring that contributes to magnetic oscillation with a result of shifting the permeability values from positive to negative values.On the other hand, a strong electric field concentrated near the innermost arms of the outer ring contributes to the electrical resonance and thus it assists in the transition of permittivity between positive and negative values.Similarly, the anti-parallel currents flown through various segments and rings of MTM at 10 GHz, 14.816, and 16.848 GHz as shown in Fig. 7b-d respectively triggers the magnetic resonances.Thus, magnetic as well as electric field distribution in different segments of the MTM contributes to double negative characteristics of the permittivity and permeability at these resonance frequencies.
Lorentz model is utilized for material characterization, which utilizes the information related to electron motion such as acceleration, damping force, and restoring force associated with it to relate to the electric field.The interrelation among these parameters can be presented in the Lorentz model using the mathematical form presented in Ref. 29,45 , As discussed in Ref 29 , electrical susceptibility can be determined from the solution of this equation of the Lorentz model.From this electrical susceptibility, permittivity can be determined.Similarly, using a magnetic counterpart instead of the electrical one, such as a magnetic field, the magnetic polarization Lorentz model for magnetic property can be developed and a solution of it provides magnetic susceptibility.This magnetic susceptibility helps to determine the permeability of the material.By neglecting the restoring force, from the Lorentz model Drude model is introduced.In CST, iterative simulation is performed to obtain the S 11 and S 21 .In this method, S-parameter values are so optimized that the obtained results comply with the values of the Drude-Lorentz model and reproduce the behavior of the MTM cell 29,46 .Now, the permeability of the MTM cell has been determined using two different methods: (a) using Eq. ( 2) namely the NRW method, (b) using the CST post-processing module that explores the robust retrieval method.In both methods same S-parameter values obtained from the simulation in CST are used so that permeability can be obtained obeying the principle of the Drude-Lorentz model.The resulting outcomes are presented in graphical form in Fig. 13c.As depicted in Fig. 13c, both methods of permeability extraction provide the same real values for permeability at the resonance frequencies of S 21 .The real and imaginary part of the permeability follows the same changing patterns without any frequency shifting.A little deviation in maximum values of real parts and minimum values of imaginary parts between these two methods are observed.This is due to the fact that the two methods consider two different www.nature.com/scientificreports/equations as solutions for obtaining the permeability.Despite this dissimilarity, both method ensures negative permeability at the frequencies of interest.The normalized impedance, Z can be determined using the mathematical relation, Z = √ µ r /ε r .The cal- culated Z values are then plotted in Fig. 13d and the near-zero values are presented in Table 4.At 3.424 GHz, 10 GHz, 14.816 GHz where the resonances occurred the extracted normalized impedances are 0.000965 + j0.0047, 0.000596 + j0.0064, 0.00314 + j0.0086 and 0.000524 + j0.00918, respectively.It is a noticeable fact that the normalized impedance has far deviated from the value 1 + j0 at every frequency of resonances of S 21 .The normalized impedance 1 + j0 indicates that the impedance of metamaterial will be essentially equal to the free space impedance.That happens when permittivity and permeability both are equal.But, in case to make the permittivity and permeability equal, the S 11 and S 21 need to be zero as per the Eqs.( 1) and (2).That is the condition of the perfect absorber, in which all the signal will be absorbed and no signal will be transmitted or reflected from it.For the omission of the transmission in the absorber, full metallic backplane needs to be employed on one side of the substrate and on the opposite side, the resonating patch is utilized for making the reflection coefficient near zero at the targeted frequencies.Thus, permittivity and permeability become nearly equal and Z becomes closer to 1 + j0.Since the present work contains only the resonating patch over the substrate and no metallic backplane is used, a portion of the incident wave is transmitted and the rest is reflected back.Therefore, both S 11 and S 21 never become zero simultaneously.Thus, permeability and permittivity become unequal resulting in normalized impedance deviating from the value Z = 1 + j0.As expressed in Fig. 13b,c the scale of permittivity is higher than the permeability.The metamaterial exhibits high electric field distribution as depicted in Fig. 5.The maximum value of the electrical field is around 10,000 V/m in the region where electrical dipoles are formed.Unlikely, the magnetic field distribution presented in Fig. 6 reveals that maximum field strength is around 50 A/m.The electric dipole formed by the high electric field causes strong electrical resonances.On the other hand, the magnetic resonance is not so strong due to the comparatively lower strength magnetic dipole.Thus, permittivity is higher in scale than the permeability at the frequency of resonances.The refractive index of the proposed MTM is presented in Fig. 13e and the ranges of negative refractive index are presented in Table 4.

Effects of substrate change of the designed MTM
In the proposed model of MTM, Rogers (RT5880) is used as the substrate material.However, to analyze the impact of substrate change on the transmission and reflection coefficients, the simulation is also conducted for the FR4 epoxy substrate of the designed MTM.The S 21 and S 11 spectra for both types of substrates are presented in Fig. 14a Due to the use of RT5880 as the substrate in the proposed MTM, we can cover the frequencies of S, X, and Ku bands.Whereas if we use FR4 epoxy as the substrate in the designed MTM, the frequency bands will shift to S, C, and X bands.19a illustrates the power density for 3.424 GHz which provides the maximum radiated power is 5.757 × 10 −7 W/m 2 .Moreover, at this frequency, the radiation efficiency of the MTM is only 0.0165.At 10 GHz, the maximum obtained power is 8.15 × 10 −8 W/m 2 and radiation efficiency is 0.0006.The power distribution pattern for this frequency is expressed in Fig. 19b.As illustrated in Fig. 19c, at 14.816 GHz, the pattern becomes more concentric toward the − z direction compared to the earlier two distribution patterns.It exhibits a low amount of power with a maximum value of 5.228 × 10 −5 W/m 2 and the radiation efficiency is 0.01247.The directivity further increases at 16.848 GHz as shown in Fig. 19d where the maximum power is 3.38 × 10 −8 W/m 2 and radiation efficiency is 0.0001.The far-field radiative power analysis indicates that almost zero electromagnetic radiative power is emitted from the MTM with very negligible efficiency (nearly zero).Thus, the MTM does not act as a radiator.Moreover, transmission coefficients at the frequency of interest are nearly zero which provides the reflection coefficients of 0.998, 0.998, 0.986, and 0.998 at 3.424 GHz, 10 GHz, 14.816 GHz, and 16.848 GHz respectively.Thus, the MTM acts as a good reflector at the discussed frequencies of interest and also as a good stop-band filter for the omission of transmitted signals at these frequencies.

Comparison of proposed model with relevant works
A comparative analysis is presented in this section with the help of Table 7 where the proposed model is compared with other relevant research works on metamaterials.The comparison is made based on the dimension, substrate material, resonance frequency, effective medium ratio (EMR), and covering frequency bands.The EMR is calculated using the formula, EMR = l where wavelength λ is considered at the lowest resonance frequency and l is the longer dimension of the proposed MTM unit cell.The EMR value of the MTM represents the compactness of the unit cell.High EMR indicates more compactness of The MTM.The consideration of EMR in MTM design is very important from the perspective of miniaturization of the device where the MTM can be implemented.Small-dimensioned MTM (having high EMR) can be used with the miniaturized antenna to improve the gain and directivity.Thus, EMR exhibits its impact on MTM as well as on the antenna.9][50][51] mentioned in Table 7 used FR4 material as the substrate of the unit cell.FR4 is the lossy medium, and MTM constructing with FR4 substrate suffers from increased energy loss, especially when the frequency is over 10 GHz.However, in our proposed model, Rogers (RT5880) is used which can minimize this limitation and can be more suitable for high-frequency applications.On the other hand, Refs. 36,48,50,52have larger dimensions than the proposed MTM.Moreover, the proposed MTM exhibits a higher EMR of 10.95 than the MTMs of 36,49,52 , which indicates the superiority of the proposed design in terms of compactness over those MTMs.Additionally, The MTMs of Refs. 48,491][52] .Thus, the proposed MTM can be a good candidate as a component of high frequency application devices due to its compact dimension, multi-frequency responses compared to other MTMs.

Conclusion
In this paper, an H-shaped modifier loaded mirror-symmetric metamaterial is presented for multi-band wireless communication.The proposed model exhibits negative permittivity, permeability, and refractive index.The EMR of the model is found 10.95, which indicates the compactness of it.The resonances of S 21 are found at 3.424 GHz, 10 GHz, 14.816 GHz, and 16.848 GHz.The simulated outcome is compared with the measurement results of the prototype using VNA where the frequency deviation found was very small.This indicates that the simulation result is well matched to the measurement result.The resonance phenomena is further studied through electro-magnetic field and surface current analysis, and equivalent circuit modeling.Along with the proposed model, two other versions of H-shaped modifier-loaded metamaterial were also developed named Model-1 and Model-2.From the comparative analysis, it is found that between 6 and 15 GHz, these two models can also cover six different resonance frequencies.Because of the compact size, negative permittivity, and permeability of the proposed metamaterial, it can be utilized to improve the performances of microwave communication elements such as implementation as a part in antenna, sensor, and band-stop filter.As the proposed MTM can cover S, X, and Ku bands it can be implemented in 5G devices, satellites for weather monitoring systems, and dish antennas for VSAT to improve their performances.

Figure 1 .
Figure 1.Dimension of the unit cell of the proposed model.
3.424 GHz, a strong electric field appears near the outer vertical segment of the first rectangular ring and the inner half of the second split ring of each quartile of the resonator as shown in Fig.5a.The electric field distribution has changed at 10 GHz, where it is reduced in the inner vertical parts of the first and second rectangular rings and increased significantly in the outer vertical parts of the first and second rectangular rings of each quartile as exposed in Fig.5b.At 14.816 GHz, the electric field strength is high near the outer vertical segment of the first and second rectangular rings, the inner horizontal segment of the second rectangular rings, and the third circular ring as depicted in Fig.5c.At 16.848 GHz, the electric field increased significantly in the upper half of the inner vertical region of the outer rectangular ring of each quartile as shown in Fig.5d.The magnetic field distribution became very strong in the outer region of the first rectangular ring of each quartile and the H-shaped modifiers at 3.424 GHz which is presented in Fig.6a.A substantial magnetic field appeared in the inner part of the second ring of each quartile and the H-shaped modifier segment but disappeared from most of the part of the first outer ring at 10 GHz frequency, as shown in Fig.6b.However, at 14.816 GHz, the magnetic field disappeared from the H-shaped modifiers whereas it became very strong at circular split rings and most of the parts of the second rings as shown in Fig.6c.At 16.848 GHz, a strong magnetic field appeared in the outer horizontal segments of the first and second rectangular rings of each quartile and the H-shaped modifiers of the resonator as shown in Fig.6d.The impact of the magnetic field can also be justified through the image of the surface current as presented in Fig.7.As with the magnetic field, the surface current became very strong in the outer region of the first rectangular ring of each quartile, and the H-shaped modifiers at 3.424 GHz that are presented in Fig.7a.At 10 GHz frequency, the surface current is very strong in in the inner part of the second ring of each quartile and the H-shaped modifier segment.Surface current is also very large at the horizontal H-shaped modifiers as shown in Fig.7b.At 14.81 GHz the surface current of the H-shaped modifiers becomes very small whereas it becomes very high at the circular split ring and most of the part of the second ring of each quartile as shown in Fig.7c.At 16.848 GHz, the high current distribution is observed in the outer horizontal segments of the first and second rectangular rings of each quartile and the middle of H-shaped modifiers of the resonator as shown in Fig.7b.

Figure 4 .
Figure 4. Scattering parameters: (a) S 21 , and (b) S 11 for systematic development of the unit cell.

Figure 8 .
Figure 8. Equivalent circuit of the proposed model.

Figure 9 .
Figure 9. S 21 spectra for the simulation of: (a) unit cell in CST and equivalent circuit of the proposed model in ADS, and (b) Frequency selective surface (FSS) and equivalent circuit of the proposed model in ADS.
,b respectively.For Rogers (RT5880) substrate, the resonances of S 21 occurred at 3.424 GHz, 10 GHz, 14.816 GHz, and 16.848 GHz with peak values of − 39.86 dB, − 51.65 dB, − 39.58 dB, and − 57 dB respectively.Whereas for the FR4 epoxy substrate, the resonance of S 21 occurred at 2.7 GHz, 7.84 GHz, 11.68 GHz, and 13.32 GHz with magnitudes of − 27.07 dB, − 28.86 dB, − 15.07 dB, and − 28.37 dB respectively.The resonances of S 11 occurred at 4.385 GHz, 11.712 GHz, and 15.008 GHz with peak values of − 38.84 dB, − 21.52 dB, and − 22 dB respectively for our proposed MTM.The resonances of S 11 using FR4 epoxy substrate are attained at 3.424 GHz and 9.08 GHz with peak values of − 23.14 dB, and − 11.51 dB respectively.Because of using FR4 epoxy instead of RT5880 substrate the resonances of both S 21 and S 11 are shifted towards the lower frequencies as shown in Fig. 14a,b respectively.In addition, the peak values of both S 21 and S 11 both decreased significantly for using FR4 epoxy substrate.

Figure 18 .
Figure 18.Scattering parameters: (a) S 21 , and (b) S 11 for different positions of H-shaped modifiers in the unit cell.

Table 1 .
Dimensions of the proposed model.

Table 2 .
The resonance frequencies and their corresponding bandwidths of S 21 for systematic development of the unit cell.

Table 3 .
The resonance frequencies and their corresponding bandwidths of S 11 for systematic development of the unit cell.

Table 4 .
Effective parameters with frequency ranges of the proposed model.

Table 5 .
Resonance frequencies and bandwidths of S 21 for different Models of the unit cell.

Table 7 .
Comparison of the proposed model with other reported works.