In this paper, design and fabrication of a dual-band near-zero index metamaterial (MTM) structure using copper on an epoxy resin fiber (FR-4) dielectric substrate is reported for refractive index sensing applications. The primary objective is to achieve dual-band operation spanning a 1–15 GHz frequency range, with a specific focus on achieving a broad bandwidth in the C-band. The resonance of the MTM structure was ascribed to the coupling of plane electromagnetic waves with surface plasmon polaritons on the structure, resulting in a quadrupole plasmon resonance mode. Furthermore, transmission characteristics of the fabricated MTM structure were experimentally measured and found to align closely with the simulated results obtained through the finite element method in COMSOL Multiphysics. The designed MTM structure demonstrates negative and near-zero permittivity at resonance frequencies, enabling left-handed and near-zero index behavior in dual microwave frequency bands. Under room temperature conditions, the MTM sensor exhibited sensitivities of 1 GHz/RIU and 3 GHz/RIU at resonance frequencies of 2.7 and 7.3 GHz, respectively. Consequently, the MTM structure exhibits significant potential for diverse applications, serving as a valuable component in sensors, detectors, and optoelectronic devices operating in the GHz region.

The S (2–4 GHz) band and the C (4–8 GHz) band hold significant importance across a spectrum of applications due to the unique electromagnetic characteristics of these frequency ranges. Modern optoelectronic devices developed for these bands are essential for various purposes, including wireless communications,1 radar navigation,2 remote sensing,3 etc. However, effective utilization of the S and C bands often encounters challenges, primarily associated with the limitations of conventional materials and components in achieving the desired performance levels. These limitations can impede progress in the above-mentioned application and beyond. Metamaterials (MTMs) represent a groundbreaking solution that has revolutionized the world of electromagnetic engineering. These artificially engineered materials are engineered to manipulate electromagnetic waves in unconventional ways that were previously thought impossible.4–6 One of the most remarkable feats achieved by metamaterials is the creation of a negative refractive index, allowing waves to bend in unconventional directions.7 However, the evolution of metamaterials extends beyond this milestone, delving into the realm of zero-index materials—a cutting-edge development within the field. The zero-index metamaterials (ZIMs), a subset of metamaterials, present unique advantages that render them highly valuable for applications such as electromagnetic cloaking, tunneling, and beam splitting.8 With a refractive index of zero, these materials exhibit remarkable properties that can significantly enhance the performance and efficiency of devices across various frequency ranges. These capabilities open new avenues for manipulating and controlling electromagnetic waves, promising a new range of advantages and applications that go beyond the capabilities of conventional materials.

MTMs can be classified according to their effective permittivity ( ε eff .) and effective permeability ( μ eff .) parameters, resulting in categories such as single negative (SNG), double negative, and double positive metamaterials. Within the SNG metamaterials, there are two types known as ε-negative (ENG) and μ-negative (MNG) materials, depending on whether ε eff . or μ eff . is negative.9 Exploration of metamaterials in the GHz and THz frequency ranges has revealed their distinctive properties such as negative permeability ( μ), negative permittivity ( ε), and negative refractive index ( η). As a result, these MTMs have found diverse applications in microwave and optical domains,10 ranging from reconfigurable antennas,11 satellites,12 and dual-band sensors13 to applications like invisibility cloaking,14 tunable perfect reflectors,15 filters,16 self-adjustable smart metamaterial waveguides,17 and super-lenses.18,19 In recent investigations, there has been extensive exploration of sensors operating in several gigahertz ranges, leveraging MTMs. It has been shown that a relatively straightforward geometric structural design can yield impressive sensing capabilities across various applications. Enhanced sensitivity is crucial in sensing applications as it enables the detection of subtle changes in the surrounding environment. The MTM design has shown its great potential in sensing applications. The specific metamaterial belongs to the targeted sensing application as shown by Banerjee et al. SRR type of metasurface showed a sensitivity of 0.742 THz/RIU for ultrathin subwavelength films sensing through excitation of dark modes in the THz region.20 Navaratna et al. showed all silicon topological waveguide cavity chips with a honeycomb lattice design operating in the THz range for biomolecule sensing applications.21 Gupta and Singh22 showed that a large Q/V meta-sensor emphasizing a high quality factor and a small mode volume with an I-shaped metasurface which resonates at 0.6  THz has a sensitivity of 18 GHz/RIU. Hyperbolic meta-sensors are known for their high-resolution sensing capabilities. Sreekanth et al. showed phase change materials based on low-loss visible frequency hyperbolic metamaterials for ultrasensitive label free biosensing applications.23 Absorptive liquid meta-sensors are optimized for liquid environments of water methanol mixtures. Chen et al. showed high sensitivity due to multiple resonances, i.e., Fano resonance and dipole resonance, in the THz region metamaterial of highly absorptive water–methanol mixtures.24 Microfluidic meta-sensors integrate fluidic channels for enhanced analyte interaction with dual torus (doughnut-shaped object) toroidal metasurfaces.25 This designed structure is fabricated using single step lithography and shows a high sensitivity of 0.129 THz/RIU for 28 μm thick microfluidic layers of different mixed ethanol–water solutions. Lim et al. reviewed the high-Q planar Fano resonant metamaterial sensors that leverage interference effects to achieve high sensitivity toward futuristic technologies.26 In this continuous development of metamaterial advancement in sensor applications, our study has shown that the MTM sensor utilizes quadrupole plasmon resonance to achieve high sensitivity in dual frequency bands in the GHz range of the S and C bands of microwave regions. This distinct mechanism not only provides high sensitivity but also ensures broad bandwidth coverage in the GHz range, which is a unique feature in the advancement of refractive index sensing. In 2017, Tian et al. developed an SRR configuration to create a refractive index sensor achieving a sensitivity of up to 1.69 GHz/RIU in the C-band.54 Meanwhile, Hu and Liu29 devised a microwave resonator measuring 18 × 18 mm2 but failed to achieve significant sensitivity in the C-band. Additionally, Dadouche et al. obtained a corona-shaped metamaterial resonator for the S-band with low sensitivity in 2023.55 Nevertheless, existing literature has identified constraints in these described MTM structures, underscoring the need for an enhanced dual-band MTM tunable sensor structure capable of achieving high sensitivities in both S- and C-bands.

Over the past several years, numerous MTM structures including V-shaped, modified H-shaped, oval-shaped, I-shaped, and Z-shaped designs have been developed to cater the increasing demands in antenna design for sensor, satellite, and radar communication applications.30–34 The main goal has been aimed to improve the antenna's efficiency. Achieving compactness and miniaturization of MTMs relies on enhancing the bandwidth, which is a crucial factor in MTM research. In 2020, Rashedul Islam et al.35 introduced an 8 × 8 mm2 square enclosed circle split ring resonator (SRR) designed for satellite communications in the S, C, and X bands. This SRR had bandwidths of 0.11, 0.79, and 0.15 GHz in these respective bands. Similarly, Islam et al.36 introduced an MTM structure designed to operate in the S, C, X, and Ku bands, exhibiting bandwidths of 0.19, 0.14, 1.3, and 0.6 GHz, respectively. Moniruzzaman et al.37 suggested a symmetric resonator for the C, X, and Ku bands with bandwidths of 0.72, 1.55, and 0.24 GHz, respectively. Bellal Hossain et al.38 presented a symmetric hexagonal split ring resonator MTM with dual-band operation and a wide bandwidth of 1.67 in the C-band for Wi-Fi applications. More recently, Hossain et al.39 proposed an MTM structure with a bandwidth of 0.94 GHz in the C-band. However, the literature has shown limitations in these reported MTM structures, highlighting the necessity for an improved dual-band MTM structure with a wide bandwidth in the C-band.

In this current research, we have fabricated and examined a novel metamaterial (MTM) structure designed for dual-band operation, showcasing a broad bandwidth in the C-band for refractive index sensing applications. The MTM unit cell, also called meta-atom's scattering parameter, was studied using FEM based simulation, and the results were validated using experimentally measured results. Analysis of the proposed MTM structure reveals the presence of negative and near-zero effective refractive index (NZI) and epsilon near zero (ENZ) in the dual-band operation range, covering the S and C bands within the microwave region. The designed MTM structure demonstrates a high EMR of up to 6.93, which confirms the compactness of the proposed design. This study suggests that the MTM structure has the potential to significantly enhance the efficiency and compactness of devices and components used in wireless communication systems with its compact size, dual-band resonance, and wide bandwidth in the C band. Utilizing the proposed MTM as a refractive index sensor results in high sensitivity, specifically 1 and 3 GHz/RIU. To create high-performance multi-function sensors with exceptional sensing capabilities, this study presents a viable alternative technique. These sensors would be ideal for use in biochemical sensing, medical detection, and diagnostics.

The schematic representation of the meta-atom of the designed MTM structure is demonstrated in Fig. 1(a), which is similarly used for simulation purposes. Figure 1(b) displays the fabricated prototype array of the same, periodically extended on all sides with a periodicity of 16 × 16 mm2. The top view of the fabricated meta-atom (unit cell) structure is displayed in Fig. 1(c). The designed MTM is composed of a copper (Cu) material resonating patch impinges on a 1.6 mm thick ( t s) epoxy resin fiber substrate. Fabrication of the unit cell of dimension 16 × 16 mm2 and a prototype array of 10 × 10 is achieved using a computer numerical control (CNC) machine, shown in Fig. 1(b). The fabrication process begins with creating a design layout using computer-aided design (CAD) or similar software, serving as the blueprint for the MTM structure. Next, the design is transferred onto a screener mask for subsequent printing. Material deposition onto the substrate follows using screen printing, a technique for depositing materials onto substrates. This step involves applying the desired material onto the substrate according to the design pattern. Etching is then performed to refine the geometry of the MTM structure by removing excess materials from the substrate. The final stages entail cleaning the fabricated MTM to eliminate any residues or contaminants remaining from the fabrication process. All the above fabrication processes are presented using a flow chart as shown in Fig. 1(d). All necessary physical parameters are listed in Table I.

FIG. 1.

(a) The meta-atom or unit cell of the simulated MTM design from an orthogonal view. (b) The physical prototype array of the fabricated MTM design, (c) the top view of the meta-atom of the fabricated sample, and (d) flow chart representing the complete process of fabrication of the simulated MTM design.

FIG. 1.

(a) The meta-atom or unit cell of the simulated MTM design from an orthogonal view. (b) The physical prototype array of the fabricated MTM design, (c) the top view of the meta-atom of the fabricated sample, and (d) flow chart representing the complete process of fabrication of the simulated MTM design.

Close modal
TABLE I.

The parameters of the fabricated and simulated designed unit cell MTM structure.

ParameterValue (mm)Description
lm 15 Length of the material 
G 1.5 Middle gap 
ls 16 Length of the substrate 
wr 1.5 Width of the resonator 
ts 1.6 Thickness of the substrate 
tm 0.35 Thickness of the resonator 
ParameterValue (mm)Description
lm 15 Length of the material 
G 1.5 Middle gap 
ls 16 Length of the substrate 
wr 1.5 Width of the resonator 
ts 1.6 Thickness of the substrate 
tm 0.35 Thickness of the resonator 

The proposed structure is designed and simulated using the FEM based COMSOL Multiphysics simulation software, as depicted in Fig. 1(a). The copper material patch in the design has a thickness ( t m) of 0.35 mm with an electrical conductivity ( σ) of 5.99 × 107 S/m.38 The dielectric substrate used in this study has a loss tangent ( δ) of 0.025 radians and permittivity ( ε) of 4.3.36,38

Scattering parameters of the simulated design structure were computed using the Drude–Lorentz variables. A configuration with two waveguide ports was used, where port 1 acted as the signal transmitter, and port 2 served as the receiver [Fig. 2(a)]. The x axis was implemented with a perfect magnetic conductor (PMC), while the y axis had a perfect electric conductor (PEC) with periodic boundary conditions in x and y axes. The electromagnetic wave propagated vertically along the z axis. This setup allowed for precise simulations and analysis of the electromagnetic behavior of the proposed design.

FIG. 2.

(a) Simulation analysis, (b) experimental measurement setup of the designed MTM, and (c) flow chart representing the complete process of the measurement process of the simulated MTM design.

FIG. 2.

(a) Simulation analysis, (b) experimental measurement setup of the designed MTM, and (c) flow chart representing the complete process of the measurement process of the simulated MTM design.

Close modal

The experimental configuration used for S21 measurement involves an antenna test setup illustrated in Fig. 2(b). This setup comprises connectors, RF cables, and calibration standards necessary for accurate measurements. A vector network analyzer (VNA-MS2028C) is employed for this purpose. The device under test (DUT), a fabricated planar frequency selective surface (FSS), is positioned within the test setup. The VNA determines the transmitted signal (S21) through the DUT. One port of the VNA connects to the transmitting horn antenna, while the other end is attached to the receiver horn antenna, with the DUT positioned between them. The entire antenna setup is placed in an anechoic chamber to minimize external interference and reflections. Calibration of the VNA is vital for obtaining precise measurements and involves the use of short-open-load-through (SOLT) calibration standards connected to the VNA's ports to establish accurate reference points. The VNA generates a swept RF signal transmitted through the DUT, and the transmitted signal is measured by the VNA in terms of magnitude and phase (expressed in dB). Detailed measurement processes are illustrated in a flow chart, as depicted in Fig. 2(c). Figure 3(a) depicts a comparative representation between the simulated and experimentally observed responses of the transmission coefficient (S21) for the fabricated designed structure. Furthermore, the phase plot of the scattering parameters is shown in Fig. 3(b).

FIG. 3.

(a) Transmission coefficient (S21) for the simulated and measured response and (b) the phase plot of the scattering parameter at different incident wave frequencies of the unit cell structure.

FIG. 3.

(a) Transmission coefficient (S21) for the simulated and measured response and (b) the phase plot of the scattering parameter at different incident wave frequencies of the unit cell structure.

Close modal

The experimental observations align well with the simulation results within the limits of the experimental setup. As depicted in Fig. 3(a), there is a very small and minor mismatch between the experimentally measured and simulated transmission coefficient (S21) outcomes. This mismatch may be attributed due to factors like manufacturing variations, signal interference, reflection noise, and other similar effects. The experimental setup has certain limitations, wherein achieving the desired performance depends on the precise alignment of the two horn antennas. To ensure accurate experimental findings, it is crucial to calibrate the network analyzer properly. All these constraints contribute to a slight shift in resonance frequencies, as evident in the measurement results. Nevertheless, the simulated and experimentally measured data cover the S and C frequency bands. The study on the S21 parameter of the designed MTM unit cell indicates the presence of two resonance frequencies at specific points, namely, 2.7 and 7.3 GHz. These resonance frequencies fall within the microwave region, corresponding to the S-band and the C-band, which are commonly used in wireless communication applications. In contrast, Fig. 3(b) illustrates the phase plot of output scattering parameters (S11 and S21), demonstrating variations from −π to +π values with a total phase change of 2π. The bandwidth of S21, which is significant for wireless communication, is shown to be considerable in different frequency bands. For instance, it spans 0.44 GHz (2.42–2.86 GHz) and 1.98 GHz (6.10–8.08 GHz) for the S and C bands, respectively. Importantly, the proposed MTM unit cell has a relatively wider bandwidth for the C band as compared to previously published data,35–39 as detailed in Table II. This makes it suitable for various wireless communication applications, including satellite and Wi-Fi technologies.38 

TABLE II.

Comparison of different bandwidths of the proposed work with the previously published work and boldface values denotes the effective bandwidth for C-band.

ReferencesDimension (physical and electrical)Resonance frequencies (GHz)Frequency bandEffective Bandwidth (GHz)
35  8 × 8 mm2 (0.070λ × 0.070λ) 2.61, 6.32, 9.29 S, C, X 0.11, 0.79, 0.15 
36  8 × 8 mm2 (0.06λ × 0.06λ) 2.48, 4.28, 9.36, 13.7 S, C, X, Ku 0.19, 0.4, 1.3, 0.6 
37  10 × 10 mm2 (0.14λ × 0.14λ) 4.20, 10.14, 13.15, 17.1 C, X, Ku 0.72, 1.55, 0.17, 0.24 
38  10 × 10 mm2 (0.17λ × 0.17λ) 5.0, 6.88, 8.429 C, X 1.67, 0.52, 0.98 
39  15 × 15 mm2 (0.20λ × 0.20λ) 3.36, 7.41, 10.16 S, C, X 1.51, 0.94, 0.89 
Present work 16 × 16 mm2 (0.07λ × 0.07λ) 2.7 and 7.3 S, C 0.44, 1.98 
ReferencesDimension (physical and electrical)Resonance frequencies (GHz)Frequency bandEffective Bandwidth (GHz)
35  8 × 8 mm2 (0.070λ × 0.070λ) 2.61, 6.32, 9.29 S, C, X 0.11, 0.79, 0.15 
36  8 × 8 mm2 (0.06λ × 0.06λ) 2.48, 4.28, 9.36, 13.7 S, C, X, Ku 0.19, 0.4, 1.3, 0.6 
37  10 × 10 mm2 (0.14λ × 0.14λ) 4.20, 10.14, 13.15, 17.1 C, X, Ku 0.72, 1.55, 0.17, 0.24 
38  10 × 10 mm2 (0.17λ × 0.17λ) 5.0, 6.88, 8.429 C, X 1.67, 0.52, 0.98 
39  15 × 15 mm2 (0.20λ × 0.20λ) 3.36, 7.41, 10.16 S, C, X 1.51, 0.94, 0.89 
Present work 16 × 16 mm2 (0.07λ × 0.07λ) 2.7 and 7.3 S, C 0.44, 1.98 
To observe the frequency-dependent behavior of the metamaterial, researchers have explored several models. Among these models, the Lorentz model is frequently employed for MTM characterization which involves the response of electrons to an electric field (E) by undergoing damped harmonic oscillations, resulting in a polarization field (P). The mathematical representation of the relationship between the polarization field (P) and the electric field (E) can be expressed as follows:40,
d 2 d t 2 P i + Γ L d d t P i + ω 0 2 P i = ε 0 χ L E i .
(1)
In Eq. (1), the terms on the left side correspond to the acceleration of charges, damping coefficient ( Γ L), and the restoring force, which are represented by the first, second, and third terms, respectively. On the right-hand side, the excitation field, also known as the driving field, is present along with the coupling coefficient, χ L. Employing Eq. (1), researchers assess the electric susceptibility [ χ e , Lorentz ( ω )], which can be expressed as follows:40 
χ e , Lorentz ( ω ) = P i ( ω ) ε 0 E i ( ω ) = χ L ω 2 + j Γ L ω + ω 0 2 .
(2)
By utilizing Eq. (2), researchers calculate the electric permittivity ( ε Lorentz)40 of the Lentz model, which can be expressed as the following equation:
ε Lorentz ( ω ) = ε 0 [ 1 + χ e , lorentz ( ω ) ] .
(3)
The Drude model is derived from the Lorentz model of electromagnetic characteristics by eliminating the restoring force from the left side of Eq. (1). Solving this modified equation results in an equation for the electric susceptibility [ χ e , Drude ( ω )] of the Drude model, which can be represented as follows:40 
χ e , Drude ( ω ) = χ D j Γ D ω + ω 0 2 ,
(4)
where Γ D is the Drude damping coefficient.
Plasma frequency of the Drude model is determined using the following relationship:40 
χ D = ω p 2 .
(5)
The assessed plasma frequency can serve as an alternative to the coupling coefficient ( χ L) in the Lorentz model. For instance, when the coupling coefficient is positive, the Lorentz model exhibits a narrow band of negative real permittivity at frequencies beyond the resonance frequencies. On the other hand, the Drude model shows a wide spectral negative permittivity for frequencies below ω < ω p 2 Γ D 2. To analyze the metamaterial's scattering parameters, researchers utilized the Drude–Lorentz variables as parameters in numerical simulations. Ziolkowski et al. proposed a mathematical method to extract effective parameters such as ε eff ., μ eff ., and n eff . using the NRW method, which is a widely used approach for effective parameter extraction. The NRW method employs transmission coefficient (S21) and reflection coefficient (S11) to derive the effective electromagnet parameters. The simplified equations used in this process are as follows:41–44 
ε eff . = 2 j k 0 d × ( 1 V 1 ) ( 1 + V 1 ) = c j π ν d ( 1 S 21 S 11 ) ( 1 + S 21 + S 11 ) ,
(6)
μ eff . = 2 j k 0 d × ( 1 V 2 ) ( 1 + V 2 ) = c j π ν d ( 1 S 21 + S 11 ) ( 1 + S 21 S 11 ) ,
(7)
n eff . = ε eff . × μ eff . = c j π ν d { ( S 21 1 ) 2 ( S 11 ) 2 ( S 21 + 1 ) 2 ( S 11 ) 2 } .
(8)
In the given context, the parameters are defined as follows:
V 1 = | S 21 | + | S 11 | ,
(9)
V 2 = | S 21 | | S 11 | ,
(10)
k 0 = 2 π ν c .
(11)
Here, d represents the metamaterial slab thickness and c represents the velocity of light.
The normalized impedance (Z) can be computed using the following formula:45,46
Z = ( 1 + S 11 ) 2 S 21 2 ( 1 S 11 ) 2 S 21 2 .
(12)

According to the data presented in Figs. 4(a) and 4(b), it is evident that the effective permittivity ( ε eff .) of the proposed MTM structure is negative at resonance frequencies of 2.7 and 7.3 GHz, while it approaches near to zero (ENZ) at these frequencies as well [shown in the inset of Fig. 4(a)]. On the other hand, the effective permeability ( μ eff .) remains positive across all resonance frequencies for the designed metamaterial structure, as shown in Fig. 4(b). Furthermore, Fig. 4(c) shows that the effective refractive index ( η eff .) exhibits negative and near-zero values at dual resonance frequencies, which correspond to the S and C bands [shown in the inset of Fig. 4(c)]. In Fig. 4(d), the normalized impedance (Z) demonstrates positive and near-zero real values across the resonance frequencies [represented in the inset of Fig. 4(d)]. Smaller values of normalized impedance at resonance frequencies indicate the passive nature (i.e., which have fixed properties determined by their structural design) of the designed metamaterial unit cell. Table III provides a summary of the overall parameter properties.

FIG. 4.

(a)–(c) illustrate the graphical representations of real and imaginary μ eff ., ε eff ., and η eff .. for the proposed metamaterial unit cell structure.

FIG. 4.

(a)–(c) illustrate the graphical representations of real and imaginary μ eff ., ε eff ., and η eff .. for the proposed metamaterial unit cell structure.

Close modal
TABLE III.

Effective parameter property.

ParametersResonance Frequency (GHz)MagnitudeExtracted property
Effective permittivity ( ε eff .2.7, 7.3 −0.085, −0.588  ε eff . < 0 (ENG), ε eff . 0 (ENZ) 
Effective permeability (μeff.2.7, 7.3 9.118, 14.493 μeff. > 0 (SNG) 
Refractive index (ηeff.2.7, 7.3 −0.144, −0.017 ηeff. < 0 (LHM), ηeff. ∼  0 (NZI) 
Impedance (Z) 2.7, 7.3 0.0030, 0.0019 Z  ∼  0 
ParametersResonance Frequency (GHz)MagnitudeExtracted property
Effective permittivity ( ε eff .2.7, 7.3 −0.085, −0.588  ε eff . < 0 (ENG), ε eff . 0 (ENZ) 
Effective permeability (μeff.2.7, 7.3 9.118, 14.493 μeff. > 0 (SNG) 
Refractive index (ηeff.2.7, 7.3 −0.144, −0.017 ηeff. < 0 (LHM), ηeff. ∼  0 (NZI) 
Impedance (Z) 2.7, 7.3 0.0030, 0.0019 Z  ∼  0 
EMR plays a crucial role in metamaterial design and development as it contributes to the compactness of the structure. Effective medium theory (EMT) is employed in designing the metamaterial structure, and according to EMT, the unit cell dimension should be smaller than the operating wavelength.47 In the case of the proposed structure, it is observed that the unit cell size is 16 mm, which is significantly smaller than the operating wavelength for all quad-frequency bands. As a result, the proposed structure meets the EMT condition, leading to the desired metamaterial (MTM) characteristics. The formula provided below can be used to calculate EMR,47 
EMR = Operating Wavelength for the unit cell length of the unit cell .
(13)

The proposed MTM unit cell exhibits a relatively high EMR and compact dimensions, enabling it to cover all dual frequency bands (S and C) commonly used in satellite and multi-band applications. The calculated EMR value for the designed metamaterial at its operating resonance frequency of 2.7 GHz is 6.93. The relatively high EMR value contributes to the improved compactness of the structure, making it a promising choice for various practical applications.

The optimization process for the proposed MTM structure involves five design steps, as depicted in Fig. 5. Design 1 consists of four L-shaped metallic strips placed at the corners of the substrate, resulting in resonance frequencies at 11.65 GHz for the transmission scattering parameter (S21), as shown in Fig. 6. Moving on to design 2, four horizontal metallic wires are added to the middle edges, leading to resonance frequencies at 7.6 GHz. Design 3 involves the addition of a central metallic strip incorporated into design 2, generating resonance frequencies at 7.45 GHz. All these designs resonate in single S bands.

FIG. 5.

The methodological approach employed in creating the MTM structure.

FIG. 5.

The methodological approach employed in creating the MTM structure.

Close modal
FIG. 6.

The variation of the scattering parameter S21 (transmission coefficient) concerning the frequency of the incident electromagnetic plane wave, observed across different MTM structures.

FIG. 6.

The variation of the scattering parameter S21 (transmission coefficient) concerning the frequency of the incident electromagnetic plane wave, observed across different MTM structures.

Close modal
Design 4 builds upon design 3 by adding four more vertical metallic strips, resulting in resonance frequencies at 6.25 and 14.6 GHz. But this design results in narrow band resonance frequencies although dual-band resonance occurs. Finally, in design 5, two vertical strips are joined at their ends in the center of design 4, forming an MTM with a mirror image shape. This design reflects dual-band operating resonance frequencies at 2.7 and 7.3 GHz in the S and C bands, respectively, within the microwave region, as depicted in Fig. 6. The resonance frequencies of the designed structure are due to the formation of a capacitor and an inductor for the gap region and metallic strips, respectively, which becomes an LC circuit like an LCR tank circuit.48 The resonance frequency ( f) can be found using the formula:49 
f = 1 2 π L C .
(14)

The presence of induced current in the metallic component of metamaterials (MTMs) leads to the generation of a scattering field when a plane wave interacts with an MTM surface. Maxwell's equations provide a comprehensive explanation for how the electric field (E), surface current (J), and magnetic field (B) interact within an MTM. When a current flows through MTM conducting elements, it generates a magnetic field. However, any change in the magnetic field can induce an electromotive force. Consequently, Maxwell's formulation of Ampere's and Faraday's laws yields a set of four differential equations that establish connections between electric and magnetic fields, elucidating these phenomena.50 The behavior of electromagnetic waves in a medium is influenced by several key factors, including permeability ( μ), permittivity ( ε), and conductivity ( σ) of that medium. These material properties, along with the boundary conditions of the medium, play a significant role in determining the electromagnetic characteristics.

Magnetic field distributions for two resonance frequencies, i.e., 2.7 and 7.3 GHz are shown in Figs. 7(a) and 7(b), respectively. Magnetic field and surface current density are correlated, as per Maxwell's equations. In Fig. 7(a), high magnetic field intensities are shown on the inner side of the structure, near the edges where a larger current density is observed. In Fig. 7(b), a magnetic field with low intensity is depicted, attributed to the low current intensity at this frequency. However, the field intensity remains low in other regions of the MTM structure.

FIG. 7.

Magnetic field distribution corresponding to resonance frequencies at (a) 2.7 GHz and (b) at 7.3 GHz.

FIG. 7.

Magnetic field distribution corresponding to resonance frequencies at (a) 2.7 GHz and (b) at 7.3 GHz.

Close modal

Figures 8(a) and 8(b) display the electric field distribution. It is evident that changes in the magnetic field affect the induced electric field. Intense electric fields are observed in areas where magnetic fields experience the most rapid rate of change, as illustrated by the comparison between Figs. 8(a) and 7(a). Due to the capacitive effect, a strong electric field is detected near the gap in the MTM structure. As a result, at 2.7 GHz, the outer and middle horizontal edges exhibit a stronger electric field than the remaining area. On the other end, in Fig. 8(b), at 7.3 GHz, a low electric field intensity is observed due to low electric current resulting in less magnetic field intensity. Furthermore, the electric field is neutralized when the magnetic field is constant in the resonator. Due to the interconnected nature of electromagnetic fields and currents, both play a vital role in the resonances at the frequencies mentioned above. In Figs. 8(c) and 8(d), the field distribution of the x-component of electric field ( E x) is presented which indicates the formation of electric quadrupole mode resonance at the metal–dielectric interface. The proposed structure's resonance is primarily caused by the excitation of surface plasmon polaritons (SPPs) due to electric quadrupole mode resonance, as indicated by the field distribution, which also shows the accumulation of positive and negative charges in the gap region of the resonator structure.13,51–53

FIG. 8.

Electric field distribution corresponding to resonance frequencies at (a) 2.7 GHz and (b) at 7.3 GHz. Electric field x-component showing electric quadrupole mode resonance at (c) 2.7 GHz and (d) 7.3 GHz.

FIG. 8.

Electric field distribution corresponding to resonance frequencies at (a) 2.7 GHz and (b) at 7.3 GHz. Electric field x-component showing electric quadrupole mode resonance at (c) 2.7 GHz and (d) 7.3 GHz.

Close modal

1. Effect of resonator width (wr) on resonance frequency

Figure 9(a) demonstrates the relationship between the scattering parameter (S21) and the resonator width ( w r). Altering the width has an impact on inductance, consequently leading to changes in the resonance frequency of the proposed MTM structure.37,38 Notably, a significant blue shift is observed in the S21 parameter when w r is increased from 1 to 1.8 mm leading to a rise in inductance, indicating an increase in the resonance frequency. The observed shift in resonance frequencies also imparts tunability characteristics of the designed MTM structure.

FIG. 9.

The response of the scattering parameter (S21) relating to (a) different resonator widths ( w r) and (b) different substrate thicknesses ( t s).

FIG. 9.

The response of the scattering parameter (S21) relating to (a) different resonator widths ( w r) and (b) different substrate thicknesses ( t s).

Close modal

2. The impact of varying the thickness (ts) of the FR-4 dielectric substrate

Substrate FR-4 thickness ( t s) is varied from 0.4 to 2.2 mm to analyze its influence on the scattering parameter (S21), as shown in Fig. 9(b). Substrate thickness has less impact on resonance frequency, although this change is less observed at the lower-valued resonance frequency (in the S-band). However, at high values, particularly in the C band, the resonance frequency shift becomes more noticeable with increasing thickness of the FR-4 substrate. This is because the substrate functions as a dielectric medium, leading to the creation of capacitance between the two waveguide ports. As the substrate thickness increases, parallel capacitance also increases, causing a decrease in the resonance frequency.38  Figure 9(b) illustrates that the MTM unit cell achieves the required resonance frequencies in both S and C bands when the substrate thickness is set at 1.6 mm. Therefore, this variation of w r and t s shows the tunability characteristics of the designed structure with a shift in the resonance frequency.

3. Effect of different dielectric substrate materials

This study examines how changing the dielectric substrate material affects the performance of MTMs. When using Roger's versions instead of the FR-4 substrate, the frequency response of S21 shifts toward higher frequencies. This shift indicates that the choice of substrates significantly influences MTM performance, as depicted in Fig. 10. Each Roger's version demonstrates dual resonance frequencies in S and X bands with varying magnitudes, but not in C-bands. In contrast, the FR-4 substrate exhibits dual resonances at 2.7 and 7.3 GHz in S and C bands, with magnitudes of −40.6 and −50.7 dB, respectively. The discussion clarifies the significance of the FR-4 dielectric material as a suitable substrate for the proposed MTM structure. These above findings are summarized in Table IV.

FIG. 10.

The variation of the scattering parameter (S21) with different materials as substrates.

FIG. 10.

The variation of the scattering parameter (S21) with different materials as substrates.

Close modal
TABLE IV.

Various properties and S21 parameter results of different substrate materials.

S. No.SubstrateElectric permittivityTangent lossResonance frequency of S21 (GHZ)Frequency bandMagnitude of S21 (dB)
1. Roger's RT6002 2.94 0.0012 3.1 and 8.4 S and X −31.9 and −47.3 
2. Roger's RT6202 2.90 0.0015 3.1 and 8.4 S and X −37.9 and −45.1 
3. Roger's RT5880 2.20 0.0009 3.3 and 9.1 S and X −37.4 and −45.2 
4. FR−4 4.30 0.025 2.7 and 7.3 S and C −40.6 and −50.7 
S. No.SubstrateElectric permittivityTangent lossResonance frequency of S21 (GHZ)Frequency bandMagnitude of S21 (dB)
1. Roger's RT6002 2.94 0.0012 3.1 and 8.4 S and X −31.9 and −47.3 
2. Roger's RT6202 2.90 0.0015 3.1 and 8.4 S and X −37.9 and −45.1 
3. Roger's RT5880 2.20 0.0009 3.3 and 9.1 S and X −37.4 and −45.2 
4. FR−4 4.30 0.025 2.7 and 7.3 S and C −40.6 and −50.7 
The transmission coefficient (S21) change with respect to various refractive index (RI) values has been examined in the following section to evaluate RI sensitivity. The study of RI sensing properties involves altering the surrounding environment of the MTM to correspond with changes in its refractive index, consequently inducing a shift in the resonance frequency of the proposed MTM, as shown in Fig. 11(b). Sensitivity (SR) serves as a crucial benchmark for evaluating sensing performance and is defined as follows:27 
S R = Δ f Δ n .
(15)
FIG. 11.

(a) Transmission coefficient (S21) spectra of the proposed MTM sensor using different RI values of the surrounding environment. (b) The variation of simulated resonance frequency (square and circle symbols) and linear fitting (solid line) with different RI values of the surrounding environment.

FIG. 11.

(a) Transmission coefficient (S21) spectra of the proposed MTM sensor using different RI values of the surrounding environment. (b) The variation of simulated resonance frequency (square and circle symbols) and linear fitting (solid line) with different RI values of the surrounding environment.

Close modal

Transmission coefficient spectra show a red shift as the refractive index of the surrounding environment changes from 1.00 to 1.20, as shown in Fig. 11(a). Figure 11(b) illustrates the correlation between the shift in resonance frequency shift ( Δ f) and the variations in refractive index ( Δ n) of the surrounding environment. Additionally, the resonance frequency of the proposed MTM exhibits a linear decrease with the rise in the refractive index of the surrounding environment. Moreover, it is clarified that sensitivities SR1 and SR2, corresponding to the first and second resonance peaks in the S and C bands, are about 1 and 3 GHz/RIU, respectively. These sensitivities surpass those of the previously reported MTM sensors, as reported in Table V. Thus, it can be said that in the GHz band, the suggested MTM sensor has a high refractive index sensitivity.

TABLE V.

Comparison of the sensitivity of the proposed MTM structure with the previous literature work.

ReferenceDesigned structureFrequency bandSensitivity
54  SRR Single band (C band)  S R = 1.69 GHz / RIU 
27  Frequency selective surface (FSS) Single band (X band)  S R = 1.31 GHz / RIU 
28  Periodical circle rings resonator Single band (C band)  S R = 0.3537 GHz / RIU 
29  Microwave resonator Dual band (C and X bands)  S R 1 = 1.116 GHz / RIU
S R 2 = 2.357 GHz / RIU 
55  Corona-shaped metamaterial resonator Single band (S band)  S R = 0.1825 GHz / RIU 
This work Metamaterial structure Dual band (S and C bands)  S R 1 = 1 GHz / RIU
S R 2 = 3 GHz / RIU 
ReferenceDesigned structureFrequency bandSensitivity
54  SRR Single band (C band)  S R = 1.69 GHz / RIU 
27  Frequency selective surface (FSS) Single band (X band)  S R = 1.31 GHz / RIU 
28  Periodical circle rings resonator Single band (C band)  S R = 0.3537 GHz / RIU 
29  Microwave resonator Dual band (C and X bands)  S R 1 = 1.116 GHz / RIU
S R 2 = 2.357 GHz / RIU 
55  Corona-shaped metamaterial resonator Single band (S band)  S R = 0.1825 GHz / RIU 
This work Metamaterial structure Dual band (S and C bands)  S R 1 = 1 GHz / RIU
S R 2 = 3 GHz / RIU 

The designed MTM structure is highly suitable for chemical and biological sensing applications, offering high sensitivity of 1 and 3 GHz/RIU at dual resonance frequencies. The MTM structure's dual-band operation within the GHz frequency range makes it a promising candidate for advanced optoelectronic devices. Its near-zero index and left-handed behavior are particularly advantageous for non-destructive testing and evaluation methods,56 which are critical for material characterization and quality control in manufacturing industries.

This study has focused on developing technology that is both easy to fabricate and straightforward to implement within the GHz frequency range. This focus on simplicity and ease of production ensures that this technology can be readily adopted and scaled up for mass production. The level of accuracy achieved in the design process allows the technology to be classified within the microwave region of the electromagnetic spectrum, which spans from 1 to 15 GHz frequencies. This classification is important because a variety of applications, such as radar systems satellite and wireless telecommunications, depend on technology that operates in the microwave region. These technologies are very fascinating for commercial and industrial use due to their high-precision production capabilities and ease of fabrication. This easy manufacturing procedure lowers expenses and increases mass productivity, allowing for the large-scale production of these technologies. Therefore, this study's emphasis on easy-to-fabricate and implement technologies in the GHz region positions it well within the current technological landscape. This compatibility with mass production systems further boosts its potential for widespread adoption and integration into various applications that rely on microwave technology.

The current study presents a novel design, fabrication, and simulation of an MTM structure capable of dual-band operation with a wide bandwidth in the C band and refractive index sensing application. The FEM-based high-frequency electromagnetic simulator in the frequency domain is used to design, simulate, and extract the MTM's scattering parameter. The experimental measurements were compared to the simulated results and found to be well-matched. The resonance frequencies showed minimal frequency shift, indicating that any differences between the simulated and measured values fell within the acceptable range. This study investigated the effective medium parameters of the designed MTM structure within the frequency range of 1–15 GHz using the NRW method. The analysis of the proposed mirror-shaped metamaterial revealed the presence of effective negative and near-zero refractive index (NZI) and effective negative and near-zero epsilon (ENZ) for dual-band operations. The electromagnetic field distributions were also plotted at the resonance frequencies. The EMR of the designed structure was measured to be 6.93, which confirms the compactness of the metamaterial and its applicability across all dual-frequency bands in the microwave region. Utilizing the suggested MTM as a refractive index sensor has the potential to attain significant sensitivity, specifically 1 GHz/RIU and 3 GHz/RIU. This research introduces a potential alternative approach for creating advanced multi-function sensors with exceptional sensing capabilities, making them suitable for applications in medical diagnostics, detection, and biochemical sensing.

The authors gratefully acknowledge the initiatives and support from the TIFAC—Centre of Relevance and Excellence in Fiber Optics and Optical Communication at Delhi College of Engineering, now DTU, Delhi, under the Mission REACH program of Technology Vision-2020, Government of India. One of the authors, Mr. Ankit, would like to acknowledge (i) the Central Research Facility (CRF) of IIT-Delhi for facilitating with measurement of fabricated design using RF and Antenna Measurement setup and (ii) Delhi Technological University, Delhi, for support in terms of Research Fellowship.

The authors have no conflicts to disclose.

Ankit: Investigation (lead); Methodology (lead); Resources (equal); Software (lead); Validation (equal); Visualization (equal); Writing – original draft (lead). Monu Nath Baitha: Formal analysis (supporting); Supervision (equal); Writing – review & editing (equal). Kamal Kishor: Formal analysis (equal); Resources (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal). Ravindra Kumar Sinha: Resources (equal); Supervision (lead); Writing – review & editing (equal).

The data that support the findings of this study are available within the article.

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