Introduction

Metamaterials are synthetic materials with electromagnetic properties that do not exist in nature. The physical properties of MTMs are highly dependent on the shape, design, orientation, and dimensions of their unit cells. Metamaterials are good candidates for focusing electromagnetic waves in near field region. This property makes metamaterials to be suitable for sensing applications. On the other hand, different techniques were introduced material classifications based on their electromagnetic properties at high frequencies like cavity perturbation method1 free-space method2,3, planar resonator method4 and transmission-line method5.

Recently, metamaterial-based sensors were developed to classify different materials for different applications6,7,8,9. This technique is mainly based on the shift in the measured resonance frequency for these materials. Romera et al. presented a technique for measuring the thickness and relative permittivity of solid and liquid materials by using two split-ring resonator (SRR) in a frequency range less than 2 GHz10. The sensing process in this case is based on notches in the corresponding transmission coefficients. Abdulkarim et al. presented another metamaterial sensor for the detection of liquid chemicals11. Different liquids including clean and waste transformer oil, corn oil, cotton oil and olive oil were classified by using this method. A reflected mirror rectangular split-ring resonator-shaped metamaterial sensor is also designed for detecting type and thickness of different materials12. Tumkaya et al. introduced a microwave sensor for distinguishing between branded and unbranded fuel samples13,14. Another metamaterial sensor based on adjacent triple circle SRR shaped within the X band is introduced for the identification of various oils, fluids, and chemicals using microwave frequencies. This MTM sensor exhibits a good quality factor and high sensitivity in both frequency shifts and amplitude variations15.

Islam et al. presented a tri-circle SRR metamaterial sensor, specifically designed for X-band detection and classification of different liquids, including coconut, olive, clean, sunflower and canola oils. This sensor achieves real-time, reliable, and specific recognition of various samples16. An oval-shaped MTM sensor for evaluating glucose levels in watery mixtures is also presented in Ref.17. Its impressive sensitivity of 0.037 GHz per 30 mg/dL of glucose solution makes it a powerful tool for glucose detection. Euclides et al., presented a microwave sensor for liquid dielectric characterization based on MTM complementary SRR at 2.4 GHz18. The liquid sample fills a glass capillary tube, inserted into a hole within the center of the complementary SRR. This hole is designed to match the capillary's external diameter, ensuring optimal interaction with both the CSRR and the surrounding transmission line. A flexible double-sided microwave sensor based on nested-complementary split ring resonator loaded U-shaped microstrip structure for dielectric constant monitoring of liquids is presented by Jianbing et al.19. A material detection sensor utilizing a Substrate Integrated Waveguide (SIW) cavity resonator is introduced in Ref.20. Three conductive vias define the three electric walls of the SIW cavity resonator, while the fourth wall is realized by a quarter-wavelength stub, influencing the modal characteristics and electromagnetic field distribution. Partial removal of the dielectric substrate creates a cavity below the stub, forming a sensitive region for sample interaction. Introducing a liquid or material within this cavity modifies the effective permittivity experienced by the stub, leading to a shift in the cavity resonator's resonant frequency due to altered modal characteristics.

Zhang et al. introduced a microwave metamaterial absorber specifically designed for non-destructive sensing in the grain industry, potentially improving efficiency and minimizing waste within the agricultural and food sectors21. Islam et al. developed a metamaterial sensor using a unique star-enclosed split ring resonator design. This sensor effectively detects adulteration in gasoline and oil22. The research by Yu et al. explores a new application to act as sensors for terahertz metamaterial absorbers. This dual functionality is particularly attractive for compact or integrated systems23. The liquid or solid sample under test (SUTs) can then be placed in the container, which is sandwiched between the chiral metamaterial structures. Alternatively, the SUTs can be positioned at the front or back of the metamaterial sensing surface. This can be achieved by placing the SUTs in a waveguide adjuster, which serves as a holder for the SUTs24. A star-shaped, dual-band (C and X band) tunable microwave sensor designed for high-performance sensing of both solid and liquid materials, including FR-4 substrates, Rogers laminates (RO3035, RO5880, RT6202), and various liquids (milk, oil, water, and even an energy drink). The metamaterial array and its liquid reservoir positioned between the waveguide structures, eliminating the need for complete enclosure within the waveguide cavity25. A key feature of waveguide sensor topology is the use of chiral metamaterials. These materials strategically arrange resonators in an asymmetric manner, leading to unique benefits for sensor performance26. To achieve negative refraction more efficiently, the design utilizes resonators with chiral asymmetry. These resonators reside on opposing sides of the substrate and exhibit a geometry that prevents perfect mirroring. This configuration offers additional advantages through mutual coupling effects27. One example of this concept is the use of split-ring resonators (SRRs) in these double-sided chiral structures28.

MTM sensors have emerged applications in various fields, including biological and medical diagnostics, agricultural monitoring, and environmental sensing29,30,31. This paper presents a sensor based on one-port waveguide with a modified F-shape unit cell to classify different powder in X band. The paper is organized as follows: Section “Design of metamaterial unit cell sensor” introduces the unit cell sensor design. Section “Equivalent circuit of the F-shape unit cell sensor” equivalent circuit and field distribution. Section “Analysis and design of F-shape sensor inside WG” operation of one-port waveguide sensors with MTM unit cell. Finally, conclusion is presented in Section “Conclusion”.

Design of metamaterial unit cell sensor

The numerical studies of the F-shaped resonator are designed and analyzed using finite element method (FEM) based HFSS software. The proposed sensor design operates in the X-band frequency regime. The dimensions of unit cell are adjusted to fill the waveguide section WR-90 with inner dimensions 22.86 × 10.16 mm2, as shown in Fig. 1. This size selection facilitates compatibility with an X-band waveguide for experimental work using the waveguide measurement method. To determine the optimal dimensions for the proposed unit cell sensor, a parametric analysis is performed to be suitable for the analysis in the frequency region from 9 to 11 GHz. The top and the bottom layers of the MTM unit cell are illustrated in Fig. 1b and c. This unit cell is printed on FR4 dielectric substrate with a dielectric constant \({\varepsilon }_{r}=\) 4.3 and loss tangent tan \(\delta =\) 0.02. The substrate thickness is 1.6 mm. Figure 2, shows the reflection and transmission coefficients of this unit cell.

Fig. 1
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(a) Geometry of the proposed antenna, (b) top, (c) bottom.

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Fig. 2
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Simulated reflection and transmission coefficients for the proposed MTM structure.

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The equivalent metamaterial characteristics of this unit cell can be obtained by using the resulting complex reflection and transmission coefficients as follows32:

$$n= \frac{1}{kd}{\text{cos}}^{-1}\left[\frac{1}{2{S}_{21}}\left(1-{S}_{11}^{2}+{S}_{21}^{2}\right)\right]$$
(1)
$$z=\sqrt{\frac{{\left(1+{S}_{11}\right)}^{2}-{{S}_{21}}^{2}}{{\left(1-{S}_{11}\right)}^{2}-{{S}_{21}}^{2}}}$$
(2)
$$\varepsilon = \frac{n}{z}$$
(3)
$$\mu ={n}^{2}/\varepsilon $$
(4)

The effective parameters (ε, μ, n and z) are shown in Fig. 3a–c. It can be noted that negative real permittivity for this unit cell lies in the frequency ranges from 9.785 GHz to 10.3 GHz and 10.66 GHz to 10.96 GHz. On the other hand, negative real permeability lies in the frequency ranges from 10.3 GHz to 10.44 GHz and 10.52 GHz to 10.71 GHz. Negative real refractive index is observed over the frequency ranges from 9.96 GHz to 10.43 GHz and 10.55 GHz to 10.95 GHz.

Fig. 3
figure 3

(a) Relative permittivity for the proposed MM structure (b) Relative permeability for the proposed MM structure (c) Refractive index for the proposed MM structure.

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Equivalent circuit of the F-shape unit cell sensor

The equivalent circuit of the designed F-shape unit cell sensor is shown in Fig. 4a. The unit cell can be divided into five parts such as TL1, TL2, TL3, G1, and G2 as shown in Fig. 4b.

Fig. 4
figure 4

Equivalent circuit of the F-shape unit cell sensor.

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Transmission lines inherently introduce inductive effects due to their physical characteristics. These effects can be defined as L1, L2, L3 respectively. The presence of a gap is equivalent to C1 and C2 which correspond to the capacitive coupling between the conductors. The unit cell's behavior can be accurately modeled using an RLC circuit, as illustrated in Fig. 4a.

The impedance of the F-shape unit cell sensor is defined as Refs.33,34

$${Z}_{t}= {R}_{t }+j\omega {L}_{t}+\frac{1}{j\omega {C}_{t}}$$
(5)

where \({Z}_{t}\), \({R}_{t}\), \({L}_{t}\), \({C}_{t}\) are respectively denoting the total impedance, total resistance, total inductance and total capacitance of the unit cell structure. The resonance frequency is given by Refs.33,34

$${f}_{r}= \frac{1}{2\pi \sqrt{{L}_{t}{C}_{t}}}$$
(6)

The performance of the unit cell by using HFSS and the corresponding equivalent circuit by using ADS is shown in Fig. 5. Table 1, presents the different components values of the equivalent circuit.

Fig. 5
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Comparison of unit cell’s reflection coefficient using ADS and HFSS.

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Table 1 Values of different components of the Equivalent circuit.
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Analysis and design of F-shape sensor inside WG

Figure 6 shows the configuration of the proposed sensor for classifying powder materials. It consists of a unit cell of metamaterial embedded inside on the open end of a rectangular waveguide. The powder material is placed in dielectric container attached to the open end of the waveguide. The sample container is a hollow cube of outer length 40 mm and thickness 1.5 mm made by using a material of εr = 3.6. The basic theory of the present sensor is that the metamaterial unit cell is used to focus the fields inside the sample container to enhance the reflection sensitivity measured by the open-ended waveguide section. The dielectric properties of the material under test changes the resonant frequency of the reflection coefficient. This change in resonant frequency is used to classify different materials33. The container is filled with different powder materials under test and is hold attached to the waveguide as shown in Fig. 6. The reflection coefficient is measured in the frequency range from 9 to 11 GHz. The dielectric constant (\({\varepsilon }_{r}\)) and loss tangent (tan \(\delta \)) of different samples are previously obtained experimentally by using Dielectric Assessment Kite (DAK) are listed in Table 2. These values are used in the present study to introduce the simulation results for the proposed sensor to discriminate between these different materials. These simulation results are verified experimentally to introduce the applicability of this sensor for fast discrimination between these materials. The proposed materials are mainly used in civil engineering. Thus, it is expected that this simple sensor can be quite useful for onsite tests for civil engineering.

Fig. 6
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System diagram of the microwave sensing process.

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Table 2 Measured average dielectric constant (\({\varepsilon }_{r}\)) and Tan \(\delta \) of powder materials under test.
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Figures 7 and 8 illustrate, respectively, the electric field and surface current distributions within the sand sample at the resonant frequency of 10.48 GHz. Figure 7 highlights how, for air, the electric field primarily concentrates near the resonator's surface. While electromagnetic fields can travel through conductive cables, the field within the sensor is expected to be in the Transverse Electromagnetic (TEM) mode. This mode dictates that the electric field component is zero. Analyzing the distributions of both the electric field and surface current is crucial to comprehend the underlying theory of the sensor's design. These distributions offer insights into the energy storage and loss mechanisms within the device, as changes in these fields reveal information about the contained energy and any energy dissipation.

Fig. 7
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Surface current distribution for the proposed design.

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Fig. 8
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Electric field distribution for the F-shape sensor.

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The distribution of surface currents flowing along the edges of the F-shaped sensor at its resonant frequency of 10.48 GHz (when a sand sample is present), as shown in Fig. 8. Red arrows visualize the direction of current flow. The currents are strongest and most concentrated at the top and bottom of the sensor, flowing in clockwise and counter-clockwise directions.

Figure 9, shows the reflection coefficient for these different powder samples without the MTM unit cell and with MTM unit cell. It can be noted that the MTM unit cell enhances the discrimination between different samples by introducing sharp clear different resonances for these different materials. The obtained resonance frequencies with MTM are 9.82 GHz, 9.92 GHz and 10.22 GHz for the cement with sand, clay and sand with − 26.53 dB, − 25.95 dB and -24.78 dB magnitude, respectively. Whereas, for cement and clay with sand, the magnitude values are − 26.03 dB at 10.42 GHz and − 23.33 dB at 10.66 GHz, respectively.

Fig. 9
figure 9

Simulated reflection coefficient of the designed sensor for different materials (a) without MTM unit cell (b) with MTM unit cell.

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Experimental verification

The measured and simulated reflection coefficient for the proposed unit cell inside WG is shown in Fig. 10. It can be noted that there is a good agreement between the measured and simulated results. However, little fabrication and calibration errors introduce minor discrepancies between them. Significant noise observed in the results, due to fabrication and calibration tolerances produce some minor performance variations.

Fig. 10
figure 10

Measured and simulated reflection coefficient of the MTM unit cell inside WG Section.

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The proposed setup for powder material classification is shown in Fig. 11. When designing an effective sensor to distinguish among powder samples, the frequency band should be carefully determined because the dielectric permittivity depends on the frequency. The network analyzer and dielectric probe kit which are used to measure the dielectric permittivity of the samples are adjusted to be in the frequency range from 8 to12 GHz.

Fig. 11
figure 11

(a) Front view of the fabricated metamaterial-based sensor, (b) back view, (c) Unit cell inside waveguide and (d) experimental setup with waveguide configuration.

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During the measurements, certain oscillatory fluctuations were detected on the VNA. These fluctuations are attributed to the combined effects of waveguide coupling and MTM sensor fabrication tolerances within the prototype FR-4 substrate layer. Fluctuations were additionally influenced by the dielectric properties of the substrate and environmental factors affecting the measurement.

Figure 12 illustrates the simulated and experimental results for reflection coefficients of different powder samples. It can be noted that experimental results align with the numerical study. It is concluded that from these figures without MTM structure, there were no transition in the resonance frequency for different powder samples which leads to difficulty in the classification process. On the other hand, using MTM unit cell introduces different resonance frequencies for powder samples. This can be explained due to the field enhancement by the MTM unit cell which acts as a lens for electromagnetic waves, focusing them onto the sample under test. This concentrated energy makes it easier to distinguish between different samples based on their interactions with the incident waves.

Fig. 12
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Measured S11 response of powder samples (a) with MTM structure (b) without MTM structure.

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Table 3 shows the responses of reflection coefficients for different powder samples with/without the MTM structure.

Table 3 Comparison for different samples with/without the MTM structure.
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Comparison with other related works

The proposed sensor performance metrics, including frequency band, material under test, sensing parameters, and resonant frequency shift, are compared with those of established microwave sensors documented in the literature, as shown in Table 4. Unlike other microwave sensors which are developed to measure liquid materials based on both S11 and/or S21 response, the present sensor is used to classify powder samples by analyzing S11 only with frequency shifts ranging from 30 to 60 MHz between different samples.

Table 4 Comparative evaluation of performance Metrics: Our Work versus previous work.
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Conclusion

This paper presents a modified F-shaped unit cell sensor for the classification of various powder materials based on a one-port waveguide measurement. The classification performance of various powder samples was compared with and without the use of an MTM structure by using HFSS. The frequency-shifting property allows the sensor to achieve high sensitivity in distinguishing between different samples. The dimensions of the designed sensor are 22.86 × 10.16 mm2, making it perfectly compatible with X-band waveguide dimensions. The equivalent circuit of the F-shape unit cell sensor was studied by using ADS. The proposed sensor utilizes frequency shifting to achieve precise discrimination between various samples. The simulation and experimental results demonstrate that the presence of an MTM structure significantly enhances the classification accuracy for different powder samples. The recommended sensor can be used in various applications, including the detection of powder materials and industrial applications.