Miniaturized and Wide-Range Microwave-Permittivity Sensor Based on Electromagnetic-Induced Transparency

Abstract

In this paper, we had designed a microwave band permittivity sensor based on analog electromagnetic-induced transparency (A-EIT). By comparing the S-parameter changes of the tested sample before and after measurement, we can calculate the permittivity of the tested sample then distinguish material types with similar appearances. The transmission line had used impedance transformation structure, and the open circuit branch is vertically connected to the transmission line. The open circuit branch will have a coupling effect with the spiral cross structure and can also simulate the A-EIT phenomenon. The above design has potential applications in the miniaturization of sensors.

1. Introductions

Electromagnetic-induced transparency (EIT) is a quantum optics phenomenon in atomic systems [1,2,3,4,5,6]. In a medium that absorbs light or electromagnetic waves, the destructive interference between two excitation paths results in a transparent window. Furthermore, there are many other ways to simulate the EIT, including metamaterial, photonic crystals, topological structures [7,8,9], and so on, also known as analog electromagnetic-induced transparency (A-EIT). In recent years, researchers had done a lot of work on the theoretical exploration of EIT phenomena, but research on the engineering application of EIT is relatively rare. Given the characteristics of A-EIT, we have applied the A-EIT phenomenon to the design of microwave sensors, thereby expanding the potential applications of A-EIT.

Microwave sensors have received widespread attention from scholars due to their non-invasive, low-radiation, high-sensitivity, and strong anti-interference ability [10,11,12,13,14]. They have been widely used in communication, antenna, radar, and remote sensing fields [15,16,17,18]. The permittivity is the main parameter of the dielectric and polarization properties of the feedback medium under the action of electromagnetic waves, which belongs to the inherent characteristics of the material independent of the external electromagnetic field [12,19,20]. Through this characteristic, it is possible to distinguish some substances with similar appearances but different permittivity. Although there are many existing works on the design of microwave sensors for detecting permittivity [21,22,23,24], most current designs have drawbacks such as large-volume and complex manufacturing processes, which cannot effectively suit the measurement requirements of permittivity sensors in special environments.

However, we have noticed that the BICs (bound states in the continuum) [25,26,27] phenomenon and EIT have certain similarities in mechanism and manifestation. The similarity between BIC and EIT is that they both come from the excitation of resonance modes and also caused absorption attenuation. The difference is that BIC usually refers to localized bound states that exist within the continuous spectral energy range, while EIT is a high Q-value state caused by destructive interference.

2. Mechanism of A-EIT Sensors

The A-EIT structure has the characteristic of high Q-value, and the transmission characteristics of A-EIT structure are very sensitive to changes in external permittivity. According to this characteristic of A-EIT structure, high-precision measurement of the permittivity for the measured object can be achieved, making A-EIT structures have broad application prospects in the field of sensors.

Due to the mutual coupling between the external electric field and the EIT structure, varying the permittivity of the EIT structure can cause changes in the electromagnetic wave transmission spectrum, making it possible for the EIT permittivity sensor. When the working frequency of the EIT permittivity sensor is in the microwave frequency range, the distributed capacitance and inductance of the EIT resonant structure will vary with the change of the permittivity of the sample being tested, resulting in a shift in the resonance frequency of the EIT structure. Therefore, the working principle of the EIT permittivity sensor is based on comparing the changes in the permittivity of the tested sample before and after loading, which will affect the distributed capacitance and inductance of the EIT resonance circuit, and further cause significant changes in the EIT resonance frequency and amplitude.

In terms of equivalent circuit, the EIT permittivity sensor can be equivalent to a harmonic oscillator model. When the resonant frequency of the harmonic oscillator is close to the frequency of the external electromagnetic field, the oscillator obtains the energy of the external electric field and the amplitude of the harmonic oscillator increases under the excitation of the external field. On the other hand, the excited current in the harmonic oscillator will generate external radiation, thus losing the energy of the harmonic oscillator and forming an electromagnetic transmission peak at this frequency. The linear response of the resonance frequency of an A-EIT resonator composed of distributed capacitors and distributed inductors in an EIT structure to the permittivity is the foundation of an EIT permittivity sensor. The resonant frequency f₀ of the EIT permittivity sensor can be written as:

$$f_0\approx {\displaystyle \frac{1}{2\pi \sqrt{L_{eff}{C}_{eff}}}}$$

(1)

In the Equation (1), L_eff and C_eff represent the equivalent distributed capacitance and equivalent distributed inductance of the A-EIT structure. When the EIT permittivity sensor is introduced into the tested sample with unknown material, the distribution parameters introduced by the tested sample will affect the inherent distribution parameters of the A-EIT structure, causing the resonance frequency to change with the addition of the tested sample:

$$f_0\approx {\displaystyle \frac{1}{2\pi \sqrt{(L_{eff}+L_s)(C_{eff}+{\mathrm{C}}_s)}}}$$

(2)

In Equation (2), L_s and C_s represent the distributed inductance and distributed capacitance introduced by the tested sample, which depend on the permittivity of the tested sample.

Sensitivity (S) refers to the ratio of output to input of a sensor under steady-state operation, while quality factor (FOM) is the amount of energy change in the feedback-resonant element. Both of them are important performance parameters of the sensor, and can be defined as:

$$\mathrm{S}={\displaystyle \frac{\Delta \lambda }{\Delta n}}$$

(3)

$$\mathrm{FOM}={\displaystyle \frac{S}{FWHM}}$$

(4)

Δλ indicates wavelength offset, Δn represents refractive index offset, while FWHM (full width at half height) represents the 3 dB bandwidth.

In the field of microwave engineering, the electric size is usually used to distinguish whether a device belongs to lumped or distributed parameters. The electric size refers to the comparison between the geometric dimensions of a device and its operating wavelength. Obviously, we cannot directly judge the degree of miniaturization of a device based on its geometric dimensions. By comparing the electric size between various devices instead of geometric dimensions, we just can determine their degree of miniaturization.

3. Design of A-EIT Permittivity Sensor

Previously, we had mentioned that there had been relatively little research on the application of class EIT in practical engineering. Furthermore, the class EIT implemented in a single structure (different from the periodic structure of a single unit cell) is even rarer. In periodic structures, the simulations of A-EIT structures can be achieved by using a combination of CW + SRR at a specific frequency. However, if the CW + SRR structure is directly applied in a single microstrip feeding structure, it is usually unable to get an A-EIT effect. We are interested in whether the “bright-dark mode” theory in periodic A-EIT structures is still applicable if A-EIT structures are implemented in other individual structures. Our work is aimed at the above issues.

Based on the mechanism of A-EIT, we had proposed a miniaturized microwave permittivity sensor structure. The proposed A-EIT sensor consists of a microstrip feed structure, with a pair of SMA connectors (version: KHD9) welded at both ends for single-side feeding, similar in shape to a “spider web”, as shown in Figure 1.

The substrate material selection is FR4 (permeability μ = 1.0, permittivity ε = 4.3) The transmission line and sensing area are made of pure copper with a thickness of 0.035 mm. The connection between two SMA connectors uses the impedance transformation design, which can greatly reduce unnecessary coupling between the transmission line and the sensing area at the high-frequency range. The transmission line and open circuit branch are perpendicular to each other. The cross-shaped structure composed of eight cut wires (CW) divides the lower area into a spiral cross-shaped structure, which is located at the bottom left of the transmission line and open circuit branch. There are six “L”-shaped structures within each quadrant, with open and short circuits alternating with each other. We refer to the cross-shaped structure and all “L”-shaped structures together as “spiral cross structures”. Compared with a single CW-SRR (split-ring resonator) structure (the periodic CW-SR metamaterial structure is a very classic metamaterial simulation EIT structure [5,28,29,30]), the above design can effectively realize the miniaturization of A-EIT sensors. The permittivity of the dielectric block to be tested can be measured by directly contacting the substrate surface below the transmission line, as shown in Figure 1.

4. Simulations of Permittivity Sensor Based on A-EIT Structure

The simulation model of an A-EIT sensor is constructed by using the simulation commercial software CST studio 2022, and its S-parameters are calculated by the mesh-generation algorithm. In order to improve simulation accuracy, we have established the simulation models for a pair of SMA connectors instead of directly setting waveguide ports on both sides of the substrate. In addition, set the plane perpendicular to the outer wall metal of the SMA connectors (outside the substrate) as the waveguide port; its sizes are equal to the port area. The SMA connectors and excitation source are connected through the coaxial cables. By setting a frequency range of 1.3 GHz to 3.3 GHz in the frequency-domain solver, we can obtain the S-parameters of the proposed A-EIT sensor, as shown in Figure 2. From the S₂₁ results, it can be observed that there is a sharp transmission peak at the frequency of 2.64 GHz, with a transmission rate exceeding 0.77, which is very similar to the EIT phenomenon in the quantum system.

However, relying solely on the results of the solid green line in Figure 2 is not sufficient to indicate that the generated peak is an A-EIT transmission peak. Since the structure proposed by us to realize A-EIT belongs to a single-unit microstrip feed structure, which is different from the A-EIT structure realized by periodic metamaterial structure, the A-EIT theory of periodic structure cannot be directly copied. It is necessary to first determine whether the bright-dark mode theory is still applicable to the un-periodic single-microstrip feed structure. To explore this issue, we removed the spiral cross structure from the substrate and only reserving transmission lines and open circuit branch on the substrate. This structure was simplified as a microstrip feed structure without near-field coupling, and its corresponding S₂₁ showed a transmission valley with a frequency of 2.618 GHz. Therefore, this transmission valley can be regarded as the bright mode for exciting A-EIT. Using the same method, if we remove the open circuit branches and preserve the transmission line and spiral cross structure on the substrate, we find that S₂₁ tends to be a straight line close to 0 dB, which means that the transmission line cannot directly generate near-field coupling with the spiral cross structure without extending the open circuit branch. This reason is that the distance between the transmission line and the spiral cross structure is too long to generate near-field coupling, and the frequency of the transmission line is also far away from the resonant frequency of the spiral cross structure. The transmission line and open circuit branch are considered as bright mode together, and then the open circuit branch transmits energy to the spiral cross structure through near-field coupling, while the spiral cross structure is considered as dark mode. Bright and dark modes with the same frequencies can usually excite the A-EIT phenomenon. By comparing the results of the S-parameters mentioned above with the EIT theory of periodic structures, we can conclude that the “bright-dark mode” theory is also effective in single-unit microstrip feeding structures.

It should be emphasized that in order to effectively distinguish the “bright/dark mode” of periodic structure metamaterial and single unit structure, we need to redefine the bright mode under single unit structure: namely, the resonant mode that was caused by the direct excitation of the feed. For the dark mode, the definition of the dark mode of the periodic single unit is similar to that in the periodic structure metamaterial, that is, the energy can only be obtained through the near-field coupling from the bright mode. Taking the A-EIT metamaterial structure of the classical CW-SRR combination in the periodic structure as an example, observing the S-parameter of an individual dark mode requires directly stimulating the SRR to form an individual dark mode by making the incident magnetic field perpendicular to the entire substrate. It is obvious that since the structure proposed in this work belongs to active devices, the above approach cannot be implemented in a single microstrip feeding structure. To overcome this trouble, we can conduct the upper CW and transmission line between the first and second quadrants, allowing the spiral cross structure to receive power from the waveport to observe the S-parameters of a single dark mode. The difference between this observation method and the dark mode of periodic structures is very obvious, as shown in Figure 3 and its inset. As can be seen, there is a clear resonance valley at the frequency of 2.614 GHz, and this resonance valley is also close to the frequency of the A-EIT transmission peak. In addition, we had also summarized the characteristics of the single unit structure and periodic structure bright/dark modes of A-EIT, as shown in

Table 1. Separate bright mode and dark mode under different excitation ways.

Excitations	Single Unit	Periodic Structure
Bright mode	Removing the parts of dark mode	Removing the parts of dark mode
Dark mode	Removing the parts of bright mode and connecting the parts of dark mode to the source	Removing the parts of bright mode and changing the polarization direction to excite the dark mode directly

. It is worth mentioning that if the waveport and SMA connector models are removed from the above structures and the relevant settings of periodic structures are used for simulation, the results often show significant differences from the S-parameter of the single un-periodic structure, in which the S-parameter is no longer a sharp transmission peak but an irregular curve shape.

In order to further understand the working principle of A-EIT sensors, just like analyzing periodic structures of A-EITs, we also need to explore their current distributions as shown in Figure 4. Three current monitors were still set up in the simulation, with working frequencies of two resonant valleys (f₁ = 2.54 GHz and f₃ = 2.714 GHz) and one transmission peak (f₂ = 2.64 GHz). At frequency f₁, the current of the transmission line is in the negative x-direction, and the voltage of the open branch is in the positive y-axis direction. In the spiral cross structure, the current intensity gradually decreases from the outer ring to the inner ring, while their directions alternate clockwise and counterclockwise. At frequency f₂, the current intensity of the transmission line and open circuit branch decreases, and their directions are no longer consistent. Due to the high Q-value, the current intensity of the spiral cross structure reaches its maximum at f₂. Finally, at frequency f₃, the current distribution of the transmission line and open circuit branch is mostly same as that at f₁. In the spiral cross structure, the current intensity of the first four turns from the outside to the inside is relatively high, while the current intensity of the last two turns is relatively low. We noticed that the current flow direction of f₂ at the open branch is opposite to that of frequency f₁ and f₃, while at the spiral cross structure, the current flow trend of f₁ is the same as that of frequency f₂ but opposite to frequency f₃. In terms of current distributions, the excitation source transfers energy from the transmission line to the open-circuit branch, which excites the resonance of the spiral cross structure through near-field coupling energy, thus simulating the EIT phenomenon.

5. Characteristic Analysis of Permittivity Sensors

In order to verify the sensing characteristics of the proposed model, we need to investigate the changes in the S-parameter of the sensor when the tested sample is in a loaded and unloaded state. Considering the two most common substrate materials used for manufacturing electronic components in communication engineering, FR4 and Roges 5880 (ε = 2.2), we have simulated the changes in S-parameters of the A-EIT sensor when loaded with the aforementioned material to be tested, as shown in Figure 5. For the convenience of experiments and simulations, the geometric dimensions of the samples we used are equivalent to the substrate size of the A-EIT sensor. In the simulation, set the sample to be tested to cover under the SMA connector bracket. It should be pointed out that regardless of whether the sensor is loaded with the test sample or not, the coupling between the transmission line and the spiral cross structure cannot be completely eliminated by increasing the coupling distance. Therefore, their S-parameters have a slight collapse in the high-frequency range (which is also the reason for impedance transformation design and can have a certain decoupling effect). It can be seen that when the tested sample Roges 5880 is loaded, the entire S-parameter curve shifts red, and there is a slight collapse in the high-frequency band, followed by a slight shift of the absorption peak to the low-frequency band. When the sample to be tested is FR4, the overall redshift of the S-parameter curve is more significant, and the collapse is also significantly enhanced.

We know that the placement of the test sample will disturb the S-parameter of the sensor. For different permittivity of the test samples, the resonant frequencies of the sensor and the Q-value of the S-parameter are obviously different. By analyzing the changes in transmission peak frequency and Q-value before and after loading, the corresponding relationship between permittivity and S₂₁ can be quantitatively analyzed, as shown in Equations (5) and (6):

$$\left[\begin{array}{c}\Delta f_t\\ \Delta Q\end{array}\right]=\left[\begin{array}{cc}{a}_1& a_2\\ b_1& b_2\end{array}\right]\left[\begin{array}{c}\Delta {\epsilon }^{\prime }\\ \Delta {\epsilon }^{″}\end{array}\right]$$

(5)

$$\begin{array}{l}\Delta {\epsilon }^{\prime }={{\epsilon }^{\prime }}_u-{{\epsilon }^{\prime }}_r\\ \Delta {\epsilon }^{″}={{\epsilon }^{″}}_u-{{\epsilon }^{″}}_r\\ \Delta f_t=f_u-f_r\\ \Delta Q=Q_u-Q_r\end{array}$$

(6)

Among them, the subscript u represents the unknown sample to be measured, and the subscript r represents the reference sample with a known permittivity. We can obtain f_r and Q_r by placing reference samples with known permittivity, and we can derive unknown coefficients of the feature matrix from experimental data of specific samples. The units of a₁ and a₂ are GHz, while b₁ and b₂ are dimensionless. Due to the substrate width being much larger than the microstrip line width, according to the relevant theory of microwave circuits [31,32,33], we can obtain the expression of the characteristic impedance Z₀ of the sensor as:

$${\mathrm{Z}}_0={\displaystyle \frac{120\pi }{\sqrt{\epsilon }[(\frac{W}{d})+1.393+0.667\mathrm{In}(W/d+1.444)]}}$$

(7)

where W and d are the width of the sensor and the width of the microstrip line, and their units are millimeters, respectively. Meanwhile, the maximum range f₀ of the sensor can be calculated by the following equation:

$$f_0={\displaystyle \frac{75}{2.085\sqrt{\epsilon -1}}}$$

(8)

Among them, 2.085 is the thickness of the sensor substrate and its unit is also millimeter, which can be substituted into the data to obtain a maximum range of 19.80 GHz. Therefore, the designed sensor has a wider range. According to Equation (3), we can also calculate the sensitivity of the sensor to be 7.5 per unit.

6. Experimental Results

We had manufactured an A-EIT sensor sample using printed circuit board technology and soldered a pair of SMA connectors onto the corresponding reserved solder joints. Collect S-parameters through a vector network analyzer (Version: Agilent E5071C, Santa Clara, CA, USA) and connect an A-EIT sensor and a vector network analyzer with a pair of coaxial cables. When the test samples loaded by the sensor are air, FR4, and Roges 5880, the corresponding S-parameters of the sensor are collected, as shown in Figure 6.

It can be seen that whether the test samples are loaded or unloaded, the simulation results are very consistent with the experimental results, but there are still existing slight spectral shifts and distortions. We speculate that this is caused by the fluctuation of permittivity during substrate processing and the limited geometric accuracy of printed circuit boards. It is worth noting that when FR4 is loaded, the collapse of the high-frequency band becomes more significant. Although the loss of FR4 is relatively small at the frequency band less than 5 GHz, the collapse caused by loss cannot be completely eliminated when the sensor is loaded with FR4, even in low-frequency operating conditions. However, this has almost no impact on the performance of the sensor.

7. Conclusions

In this work, we have designed a permittivity microwave sensor based on A-EIT. Under the 2.64 GHz working frequency, its electric size is only 4.73λ₀ × 4 73λ₀ × 0.41λ₀ wavelength with wide range characteristics. The no-loading and loading experimental results are in good agreement with the simulation results. In addition, the “bright-dark mode” theories of metamaterials A-EIT are further extended to a single-unit microstrip feed structure. The work of this paper has made contributions to both the theoretical analysis and potential application for EIT.