Terahertz (THz) waves is located in the frequency range of 0.1–10 THz [1, 2], which has revealed more and more unique applications in biomedical fields such as image [3] label-free detection [4] and recognition [5]. Metamaterials (MMs) are artificially designed electromagnetic materials composed of periodically arranged sub-wavelength elements [6–17]. Since Veselago defined and analyzed the properties of MMs with negative dielectric constant and negative permeability in 1967 [18], research on MMs biosensors at THz frequency has achieved great progress in recent years for MMs' strong electromagnetic response [19–22]. For example, Dong demonstrated a biosensor with resonators on a silicon substrate, its sensitivity is 85 GHz/RIU [23]. Sam et al. presented a refractive index MMs biosensor with a sensitivity of 300 GHz/RIU and thickness sensitivity of 23.7 GHz/μm [24]. Zhang et al. proposed a high-sensitivity MMs biosensor with a sensitivity of 638 GHz/RIU [25]. Furthermore, a metamaterial based double Corrugated Metal stripe label-free biosensor was modeled with sensitivity of 1,750 GHz/RIU [26]. Niknam et al. have also presented a metamaterial absorber sensor with refractive index sensitivity of 1.966 THz per unit refractive index variation and the thickness sensitivity of 52.5 GHz/μm [27]. Although biosensors based on MMs have been studied extensively, the thickness and refractive index of sensitivity still needs to be improved for practical applications.

In this study, we designed an ultrasensitive MMs sensor composed of centrosymmetric double F-shaped metal resonators (CDFMR) array. The simulation results show that its average absorption rate is 0.95, the Q-factor of the resonant peaks reaches 49.6, display excellent ability on frequency selectivity. Furthermore, the sensor shows ultra-high sensitivity on the variation of refractive index and thickness of analyte. The result will shed light on better application prospect in THz biosensors and detectors.

Figure 1A shows the schematic of the proposed metamaterial sensor. Figure 1B is the unit cell of the presented sensor, which consists of two gold layers on the top and in the bottom of the structure. The top layer is double F-shaped gold resonators layer with a thickness of h₁, l₁, and w₁ are the length and width of the metal strips, respectively, three gaps with width of w₂ are formed between the two resonators. While the bottom layer is a continuous gold plate with a thickness of h₃, the conductivity of gold is set as σ = 4.09 × 10⁷S/m [24], the dielectric medium between them is polytetrafluoroethylene (Teflon), its dielectric constant is ε_r + jε_j = 2.1 + j0.01 [24] with a thickness of h₂. The analysis and design of the structure is based on the Full Vector Finite Element Method [28]. The period of the unit cell are P_x = P_y = 36 μm in x and y directions, separately, h₁ = 0.2 μm, h₂ = 5 μm, h₃ = 1 μm, l₁ = 20 μm, and w₁ = w₂ = 2.5 μm.

Excited by a linearly p-polarized plane incident wave (with electric component along the x direction), the absorption curve of the sensor without analyte is shown in Figure 2A, a perfect absorption peak at 5.95 THz is obtained. The full-width half-maximum value (FWHM) of the absorption peak is 0.12 THz, the quality factor (Q-factor) equal to 49.6 which is defined as Q = f/FWHM, where f = 5.95 THz is the central resonance frequency and FWHM = 0.12 THz is the full-width at half-maximum [29].

The electricfield (E-field) distribution and surface current distribution of the sensor at the resonance frequency of 5.95 THz are simulated and analyzed. Figure 2B demonstrate the E-field are concentrate near the gaps of the resonance. Correspondingly, we can observe from Figure 2C that the current distribute mainly on the metal strips of the double F-shaped resonance, and there are strong induced current distributions on the bottom metal plane due to the magnetic resonance effect in the structure as shown in Figure 2D. According to the equivalent circuit theory, The F-shaped metal strips and the metal base plate form a current loop. The gaps form equivalent capacitances C₁, C₂, and C₃ and the metal strips form equivalent inductances L₁, L₂, L₃, and L₄ as shown in Figure 2E.

Effective capacitances of the structure also come from the top analyte and the dielectric layer sandwiched between the two mental layers, and assuming they are defined as C_sensor and C_d, separately. So, there are a total inductance L_e = L₁ + L₂ + L₃ + L₄, a total device capacitance C_e = C_d + C₁ + C₂ + C₃ and a sensing capacitance C_sensor. The value of C_sensor will vary with the refractive index n and thickness h₀ of the surface analyte. Then, equivalent circuit model of CDFMR can be simplified as Figure 2F for convenient analysis of the sensor properties in the following discussion. The resonance frequency of the sensor is expressed as

The equivalent device capacitance C_e can be much smaller than C_sensor once the relative dielectric constant of dielectric is small and the gaps between the double F are narrow. So that C_sensor will take charge of equivalent capacitance of the sensor, and further brings a prominent shift of resonance frequency when there is a minor variation of analyte refractive index, finally realizes high sensitivity.

With a fixed thickness t = 5 μm, the corresponding absorption curves are described in Figure 3A when the surface analyte on the sensor possess different refractive indexes n = 1.0, 1.1, 1.2, 1.3, 1.4, respectively. It can be seen that the resonance frequency of the sensor will red-shift when the refractive index n of the analysis layer increases. The result can be explained by the equivalent circuit theory, the dielectric constant ε is proportional to the refractive index n with εμ = n² [30]. Therefore, the equivalent capacitance C_sensor of the analyte will increase with n, and resonance frequency will increase according to formula (1), the increasing scale is near linearity as shown in Figure 3B. The sensitivity of a sensor is normally defined as S = Δf/Δn, where Δf is the offset of resonance frequency, Δn is the change rate of refractive index n [23], and the ultra-high sensitivity of 1,800 GHz/RIU can be obtained for the presented sensor. Furthermore, the FOM value take absorption bandwidth into account but only offset of resonance frequency, it is a more commonly used parameter for better evaluation of the synthetical performance of a sensor and the calculation formula is defined as Fom = S/FWHM [29], where S is the sensitivity of the sensor. Obviously, for a certain S, the smaller the 3 dB bandwidth FWHM of the resonance frequency band is, the higher the FOM value can be achieved. The FOM value for the proposed sensor is as high as 15. It is worth noting that the refractive index of typical biomedical samples is usually between 1.3 and 1.4. For example, the refractive index of blood for healthy human being is 1.35, and the n of blood samples infected with T-type leukemia (Jurkat) is 1.39 [31]. Remarkable offset of absorption band can be observed in Figure 3A when n varying with a step of 0.1, and the deviation of resonance peaks still keep distinct even though the variation step of n is only 0.02 in the range of 1.3–1.4. Obviously, the device can act as a supersensitive biosensor with high sensitivity and high Q-value.

The influence of the geometrical parameters of the double F-shaped resonator on the sensing performance are analyzed for the gap width w₂, the strip width w₁ and the strip length L₂. As shown in Figure 4A, when w₂ increases from 2.25 to 3 μm, the resonance frequency is blue-shifted, and the peak of the absorption spectrum decreases at the same time accompany with an absorption bandwidth broadening. According to formula (1), the increase of w₂ will reduce the equivalent capacitances C₁, C₂, and C₃, and the blue shift happens for the resonance frequency. Simultaneously, the reduction of the equivalent capacitances will weaken the absorption ability of the structure to the incident EM wave.

Increasing width w₁ of the metal strip of the F-shaped resonance will induce larger value of its inductance L_e and capacitance C₁ + C₂ + C₃, which bring with a blue shift of the resonant frequency. Obviously, the result is agreement well with the evolution of the absorption curves shown in Figure 4B. Meanwhile, there is a decrease of the absorption peak and the Q-value.

Finally, we discussed the effect of the metal strip length l₁ on the resonance frequency. As shown in Figure 4C, red shift of the resonance frequency happens as l₁ increases, which is due to the increase of the total inductance L_e. It is noteworthy that the absorption rate and the Q-value of the absorption band will increase with increasing l₁.

The thickness of the analyte layer will also impact the sensing performance. For a typical biological analyte slice with refractive index of n = 1.3, Figure 5A shows the absorption curves vs. thickness of analyte h₀, it hints that the resonance frequency will red shift non-uniformly when h₀ increasing from 0 to 6 μm with step of 1 μm, the absorption spectrum band get narrower and more sharp. Furthermore, there is a long span offset for the case of the thickness of surface analyte change from 0 to 1 μm, which represent that of without or with surface analyte on the sensor, evidently, the proposed sensor unfolds a better performance with analyte loaded.

Figure 5B declares the red shift of resonance frequency with the increase of the analyte thickness. It can be seen that the deviation of the resonance frequency will tend to be gentle on per unit increase of thickness primarily, and become negligible when the thickness of the analyte exceeds 4 μm. Considering the thickness sensing is defined as S = Δf/Δh₀ [24], in which Δf is the resonance frequency offset and Δh₀ is the thickness variation of analyte slice. When the thickness of the analyte changes from 0 to 4 μm, the sensitivity of the proposed sensor can reach S = 134 GHz/μm.

In summary, a metamaterial biosensor with good performances is designed and proposed, ultrahigh sensitivity and high Fom value are obtained, the sensing characteristics and resonance mechanism are discussed in detail. The results show that the sensor can realize an average absorption rate of 0.95 and a Q factor of 49.6, the sensitivity can reach 1,800 GHz/RIU and the Fom value is 15, which realizes high sensitive and high Q factor refractive index sensing in THz frequency band. At the same time, it shows a high thickness sensitivity of 134 GHz/μm when the thickness of the analyte changes from 0 to 4 μm. The proposed sensor has important application in THz ultrasensitive biomedical sensor and detector.

All datasets generated for this study are included in the article/supplementary material.

AM and RZ conceived the idea of the research, carried out the whole simulation, performed the acquisition and analysis of data, and they also wrote the manuscript. All authors contributed to the final manuscript.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.