Introduction

Metamaterials [1] are artificial structures with unique characteristics that can be created by smaller elements in size than the external stimulus. Metamaterials consist of two layers of metal separated by dielectric layer. The resultant permittivity ε(ω) and permeability μ(ω) can’t be achieved by conventional materials [2] which depend on the geometrical properties of metallic patch shape and mutual distance between them [3, 4]. Metamaterials, in particular, have become increasingly popular in recent years for a variety of purposes; such as negative refraction [5], polarization rotation [6], source imaging [7], energy harvesting [8], sensor technology [9], perfect absorption [10], super lenses [11], and antennas [12].

Metamaterials have become one of the most promising materials in attempt to achieve perfect absorption. The use of metamaterial absorbers has also been explored for bio-monitoring purposes in the terahertz domain. High-flexible absorber has been fabricated with absorptivity of 0.97 at f = 1.6 THz [13]. Areed et al. have proposed a near-perfect metamaterial absorbance with an absorbency of 0.97 across the visible wavelength range [14]. Metamaterial right/left-handed transmission line has been studied for sensing applications [15]. Lee et al. have also introduced metamaterial sensor based on split ring resonators [16]. A nearly zero permittivity metamaterial biosensor with enhanced sensitivity has proposed [17]. Another design of nearly perfect metamaterial absorber was suggested and analyzed for terahertz sensing applications with absorptivity of 0.99 at f = 2.249 THz [18]. A highly sensitive sensor for virus detection was presented using terahertz nano-gap metamaterials [19]. Further, microbial detection using a metamaterial absorption absorber was introduced in [20]. A metamaterial sensor was designed for non-destructive evaluation of dielectric substrates [21]. Dual band metamaterial cancer cell sensor with a maximum sensitivity of 196.5 GHz/RIU has been proposed [22]. Additionally, a hyperbolic metamaterial sensor with a maximum sensitivity of 500 nm/RIU has been introduced for the detection of cancer cells [23].

Haemoglobin (Hb) is located in red blood cells and is responsible for O2 transport in the circulatory system. Polycythemia is diagnosed when the Hb level in the blood is greater than the maximum limits. However, Anaemia is detected when the Hb level is less than the minimal limit. There is a need for immediate detection and easy technique to measure the (Hb) level in the blood. In this context, different types of electrical, and optical sensors were proposed for the detection of Hb concentrations. A dual-core photonic crystal fiber (PCF) sensor has been introduced for Hb concentration monitoring in the blood [24]. A two-dimensional photonic crystal-based for hemoglobin biosensor with a sensitivity and quality factor of 272.43 nm/RIU and 3000, respectively, have been proposed [25]. Further, highly sensitive one-dimensional photonic crystal (1D PhC) sensor for hemoglobin (Hb) concentration monitoring is proposed and analysed [26]. A highly sensitive PCF hemoglobin sensor was also numerically simulated and studied with sensitivity of 2080 RIU − 1 with a resolution of 4.80 × 10 − 6 RIU at a hemoglobin refractive index of 1.38 [27]. Moreover, El-Khozondar et al. [28] have suggested plasma blood sensor with sensitivity of 51.4 nm/RIU at concentration range of (0–50 g/L). Additionally, an optical sensor system for hemoglobin measurement was implemented in [29]. A multi-wavelength light absorption device to measure hemoglobin concentration was reported in [30]. However, the design of metamaterial sensor for Hb concentration is very limited in the literature.

According to the International Agency for Research on Cancer (IARC), cancer is the second leading cause of death worldwide. Cancer is a malignant genetic disorder that can be produced by a malfunction in the division of cells in the human body. Nowadays, a lot of research is conducted to explore the possibility of detecting tumors in the human body using microwave signals. The primary benefit of microwave imaging is its nonionizing nature and, as a rule of thumb, its cost-effectiveness. Cancer detection must be conducted at the cellular level in the early stages of cancer in order to enable the patient to receive early detection and treatment. In recent years, a number of research papers has been published using metamaterial biosensor for the cancer early detection. In this context, Cong and Singh [31] have presented a metamaterial absorber sensor with sensitivity of 163 GHz/RIU, and Q-factor of 7.036. Additionally, metamaterial terahertz biosensor was proposed for early-stage detection of cervical cancer tissue using with two resonant absorption frequencies [32]. Zhang et al. [33] introduced MM-based THz biosensor to analyze the apoptosis of dried cancer cells. Han et al. [34] employed MM-based THz biosensor with theoretical sensitivity of the MMs sensor is about 287 GHz/RIU. Additionally, Manikandan et al. [35] have suggested dual-band metamaterial cancer cell sensor with sensitivity of 196.5 GHz/RIU, and Q- factor of 165. Moreover a graphene-based metamaterial sensor has been implemented for different types of cancer cells with a sensitivity of 207.14 GHz/RIU, a quality factor of 13 [36].

In this paper, THz asymmetric metamaterial design is proposed and analyzed for biomedical applications including Hb concentration detection and cancer cell detection. The geometrical parameters are studied to maximize the sensor sensitivity. The simulation results are obtained using full vectorial finite element method. It is found that high sensor sensitivity of 1.08 GHz/g/dL is achieved through hemoglobin (Hb) concentration change from 5 g/dL to 20 g/dL. The potential of using the reported design for cancer early detection is also demonstrated with an average sensitivity of 556.325 GHz/RIU. The reported biosensor has a higher sensitivity than those suggested in [31, 33, 35, 36] for cancer early detection.

Design and Fabrication Considerations

Figure 1 shows the suggested design of asymmetric metamaterial biosensor. The proposed structure is composed of two layers of gold, which are separated by a dielectric material. The top layer of thickness h1 has an array of metallic patches. Each patch consists of a rectangle resonator with line width s, and gap G as shown in Fig. 1(a). A single bottom layer of gold is used with a thickness of h1 as a lossy media with conductivity independent of frequency σ = 4.09 \(\times\) 107 S/m [13]. The dielectric medium is polyimide with a thickness h2 = 8.5 µm and refractive index n = 2.88 – 0.09j [37]. In the suggeted design, the parameters a and d are used to control the shift of the central gap in x and y directions, respectively.

Fig. 1
figure 1

a Two- and b three- dimension schematic diagrams of the unit cell of the reported metamaterial biosensor and c the proposed patch array

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Metamaterials are engineered materials that possess distinct properties, with a permittivity (ε) that is smaller than the free space permittivity (ε0), and a permeability < free space permeability (μ0). In this study, the effective permittivity (εeff), and effective permeability (μeff) are obtained through the S-parameters as given by [38]:

$${\varepsilon }_{eff}=1+\frac{2j}{{K}_{o}{h}_{2}}(\frac{1-{S}_{11}}{1+{S}_{11}})$$
(1)
$${\upmu }_{eff}=1+\frac{2j}{{K}_{o}{h}_{2}}(\frac{1+{S}_{11}}{1-{S}_{11}})$$
(2)

where Ko is the free space wave number, h2 is the substrate thickness, and S11 is the reflection coefficient. The frequency dependent relative permittivity εr and relative permeability µr of the reported design are shown in Fig. 2. It may be seen that both εr and µr have negative real parts through the frequency range from 1.15 THz to 1.28 THz, hence the proposed metamaterial has double negative feature. Therefore, it is expected that a resonance can occur with maximum absorption in this region.

Fig. 2
figure 2

Frequency dependent a effective permittivity, and b effective permeability of the reported metamaterial absorber

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The impedance (Z) of the ideal absorber should be closely matched to the free space impedance in order to reduce the reflection from the surface [39].

$$Z=\pm \sqrt{\frac{{(1+{S}_{11}(\omega ))}^{2}-{S}_{21}^{2}(\omega )}{{(1-{S}_{11}(\omega ))}^{2}-{S}_{21}^{2}(\omega )}}$$
(3)

where S21 is the transmission coefficient, and \(\omega\) is the angular frequency. Figure 3 shows the real and imaginary parts of the relative impedance of the proposed design. It may be seen that at the resonance frequency 1.25 THz, the real part and imaginary part of relative impedance are close to 1, and zero, respectively. Consequently, at the resonance frequency, the incident light will be transmitted and absorbed by the metamaterial design.

Fig. 3
figure 3

The real part and imaginary part of the relative impedance for the resonance peak

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Using equivalent circuit theory, it is possible to understand the change in the resonance peaks as follows [40]:

$$f=\frac{1}{2\pi \sqrt{{L}_{eq}{C}_{eq}}}$$
(4)

where f is the resonance frequency, and Leq, and Ceq are the equivalent inductance and capacitance of the sensor. It is possible to infer that the frequency of resonance corresponds to the inverse square root of the corresponding capacitance, which is increased by the increase in the analyte Refractive Index (RI). Therefore, the resonance frequency is red shifted by increasing the analyte RI, which may be also explained by the first order electromagnetic perturbation theory [41]. Additionally, the positive charges are concentrated at the bottom metallic layer, acting as a weak electric dipole, while the negative charges are focused at the top metallic strip [42].

Symmetric structure is first studied with a = d = 0, as shown in the inset of Fig. 4. The initial design parameters are L = W = 38 µm, c = 12 µm, s = 3 µmm, G = 2 µm, x = y = 50 µm. The simulation of the symmetrical sensor design is based on the full vectorial finite element approach [43] utilizing the COMSOL Multiphysics Software Package (comsol.com) [44]. Using a non-uniform mesh, the 3D computational unit cell is discretized into 367,299 tetrahedral domain elements, 47,706 boundary elements, and 1864 edge elements with a minimum element size of 7.2 nm. Moreover, boundary condition of perfect electric conductor is applied in y-direction while perfect magnetic conductor is used in x-direction. This is equivalent to applying Floquet periodic boundary condition (FPBC) in x- and y-directions to reduce the computational domain. Further, the ground plane and top metal patches are subjected to impedance boundary and transition boundary conditions, respectively.

Fig. 4
figure 4

Frequency dependent absorption of the symmetric metamaterial sensor

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A plane wave is also excited using a single port with a power 1W with a normal incidence. The electric field also has unity in the y-direction. The light absorption A through the suggested design can be calculated as follows

$$A=1- {S}_{11}^{2}-{S}_{21}^{2}$$
(5)

Because of the bottom gold layer, which behaves as an optical mirror in the used frequency range, S21 = 0. Figure 4 shows the absorption spectra where the resonance occurs at f = 1.25 THz, which is compatible with that presented in [13]. At the resonance frequency, the field is confined in the gap region as shown in the inset of Fig. 4. It is expected that the resonance frequency will be sensitive to the surrounding variation in the refractive index of the medium.

To demonstrate the accuracy of our model, a comparison study is conducted using the simulated and experimental absorption spectra of the metamaterial absorber reported in [7]. It may be seen from Fig. 5 that a good agreement is achieved between the simulation results. Additionally, the simulated resonance frequency is compatible with the measured resonance frequency [7] which guarantees the accuracy of our model.

Fig. 5
figure 5

Comparison between the measured and calculated frequency dependent absorptions of the metamaterial absorber reported in [7] and our calculations

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Hemoglobin Concentration Measurement Biosensor

To test the potential of using the studied design as a biosensor, a hemoglobin sample is placed over the metamaterial as shown in the inset of Fig. 6. The wavelength dependent refractive index \({n}_{Hb}\) of the hemoglobin depends on its concentration \({C}_{Hb}\) as given by:

Fig. 6
figure 6

Dependence of the resonance frequency on the analyte thickness

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$$n_{Hb}\left(\lambda,C_{Hb}\right)=n_{H_2o}\left(\lambda\right)\lbrack\beta(\lambda)C_{Hb}+1\rbrack$$
(6)

where \({n}_{{H}_{2}o}\left(\lambda \right)\) is the wavelength-dependent water refractive index, β(λ) is a wavelength-dependent increase in the water’s refractive index in (g/dL) [45], and \({C}_{Hb}\) is the concentration of the hemoglobin in g/dL [46]. Figure 7 shows the effect of analyte thickness on resonance frequency. It is evident that that the resonance frequency does not change significantly beyond 9 µm analyte thickness which will be used for the subsequent simulation.

Fig. 7
figure 7

Variation of the absorption of the metamaterial biosensor with the frequency at different hemoglobin concentrations

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Figure 5 shows the frequency dependence of the absorption curve on different hemoglobin concentrations. It may be seen that the resonance frequency slightly increases by increasing the hemoglobin concentration. Therefore, \({C}_{Hb}\) change can be detected using the resonance shift and the sensor sensitivity is calculated as follows [18]:

$$\text{Sensitivity}=\frac{\Delta\;Resonance\;frequency }{\Delta\;{C}_{Hb}}$$
(7)

The quality factor (Q) of the reported sensor is also calculated [18]:

$$Q=\frac{{f}_{res}}{FWHM}$$
(8)

where \({f}_{res}\) is the resonance frequency and FWHM is the full width at half maximum of the absorption peak.

It is aimed to maximize the sensor sensitivity; therefore, parametric sweep study is performed on the different geometrical parameters. It should be noticed that the geometrical parameters alter the equivalent circuit's values for inductance and capacitance, which affects the resonance frequency. Figure 8(a) shows the effect of the line width s on the biosensor sensitivity. However, the other geometrical parameters are fixed at their initial values. As shown in Fig. (8-a), the biosensor sensitivity has a maximum value at line width 3.8 µm where the electric field is more confined in the gap region (as shown in the inset field plot of the Ex-component of X-polarized mode). Figure (8-b) illustrates the dependence of the sensor sensitivity on the gap size G at s = 3.8 µm. It may be seen that the optimum value for the gap is 2.75 µm where the biosensor sensitivity is maximum of 0.866 GHz/g/dL. Figure (8-c) shows the biosensor sensitivity as a function of the capacitor length at s = 3.8 µm and G = 2.75 µm where the electric field is more confined between gap at c = 3.8 µm. Changing the gap side length, gap, and line width affects the equivalent capacitance and the equivalent inductance, which change the resonance frequency.

Fig. 8
figure 8

The dependence of the biosensor sensitivity on the geometrical parameters; a line width s, b gap G and c capacitive line length C

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The optimum geometric parameters for the symmetric structure are s = 3.8 µm, G = 2.75 µm, c = 4 µm and plyimide thickness of 8.5 µm for optimum sensitivity. These geometrical parameters are chosen to improve the sensitivity of the sensor. To increase the biosensor sensitivity, asymmetric structure is used as revealed from Fig. 1(a). Figure 9(a) illustrates the effect of the shift distance (a) while the impact of d at a = 2 µm is illustrated in Fig. 9(b). It is evident form Fig. 9 that the asymmetric structure increases the biosensor sensitivity from 0.9 GHz/g/dL at a = d = 0 to 1.01 GHz/gm/dL at a = 2 µm and to 1.08 GHz/gm/dL at d = 3 µm. Figure 10 shows the absorption of the reported asymmetric metamaterial biosensor at different Hb concentrations. The resonance frequency is varied from 1115 to 1095 GHz by increasing the Hb concentration from 5 g/dL to 20 g/dL. Additionally, high quality factor of 74.333 is achieved at Hb concentration of 5 g/dL.

Fig. 9
figure 9

The effect of the asymmetric parameters a a, and b d at a = 2 µm on the biosensor sensitivity

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Fig. 10
figure 10

Frequency dependent absorption of the metamaterial absorber bio-sensor at different concentrations using asymmetric metamaterial biosensor

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The linear performance of the reported biosensor is analyzed within the given frequency range. The variation of the resonance frequency with the Hb concentration is shown in Fig. 11. It may be seen that a linear fitting can be obtained for the suggested biosensor as given by

Fig. 11
figure 11

Variation of the resonance frequency with the Hb concentration. Also, the linear fitting is demonstrated by black line

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$$resonance\;frequency\;\left(GHz\right)=-1.32\times {10}^{-3}\times {C}_{Hb}\left(THz\right)+1.121\;(THz)$$
(9)

The fitting line has R-square value of 0.9986 with high linear performance. A comparison is also made as revealed from Table 1 to show the merits of the proposed metamaterial biosensor. It may be seen that our suggested sensor has a higher linear sensitivity than the early presented sensors in the literature.

Cancer Early Detection Biosensor

The reported design is also investigated for early cancer detection including basal, breast, cervical, and jurkat cells. The normal and cancerous studied cells have refractive indices presented in Table 1 [47]. Figure 12 shows the absorption spectra using normal and cancerous cells where the resonance frequencies are summarized in Table 2. The sensor sensitivity is calculated using the resonance frequency shift as given by

Fig. 12
figure 12

The absorption spectrum of the metamaterial biosensor using different normal and cancerous cells

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Table 1 The sensor performance of the reported biosensor for basal, breast, cervical, and jurkat cells
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Table 2 The average sensitivity of the reported biosensor compared to the recent biosensors
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$$\text{sensitivity}=\frac{\Delta\;Resonance\;frequency }{\Delta\;n}\;GHz/RIU$$
(10)

The sensor sensitivity and quality factor of each case are calculated and introduced in Table 1. It may be seen that the suggested biosensor achieves an average sensitivity of 556.325 GHz/RIU with simple design. The performance of the reported biosensor is shown in Table 2 compared to previous designs. It may be seen that the current sensor sensitivity is higher than the other metamaterial structures with simple design. Although, the metamaterial sensor reported by Zhengzheng [52] has higher sensitivity than our design, however, it has complex design which will be challenge for fabrication. Therefore, the reported metamaterial sensor has high sensitivity with simple design for fabrication.

The proposed sensor can be manufactured using state-of-the-art technology. First, the background gold layer with a thickness of up to 200 nm can be deposited onto a GaAs or silicon wafer through e-beam evaporation [41]. Next, the liquid polyimide will be deposited onto the top surface of the gold layer by spin- coating. Then, it will be heated to 110 °C for 6 min on a hot plate [53]. The next step is to cure it for 5 h in a 275 °C oven in a nitrogen medium to form dielectric layers with thicknesses of 0.5 µm to 8 µm. An additional layer of gold is formed on the upper surface of polyimide through e-beam evaporation. In addition, photoresist layers can deposited on the upper dielectric layers with spin coating, and the patterns will be converted from photomasks to photoresists through UV irradiation and will be developed within the framework of AZ300 MIR. Photolithography can also be used to obtain metallic patches.

Conclusion

We proposed and analyzed novel metamaterial biosensor for Hb concentration detection and for early cancer detection with high sensitivity. Full vectorial finite element method is used to simulate the studied designs. The reported biosensor can detect the analyte refractive index change with high linear sensitivity. High sensor sensitivity of 1.08 GHz/g/dL is achieved at 1.1 THz with a narrow resonant peak and high Q-factor of 13.2 for Hb concentration detection. Further, an average sensitivity of 556.325 GHz/RIU is achieved for cancer early detection for basal cell, breast cell, Jurkat cell and Cervical cell which is greater than those presented in the literature with simple design. Moreover, the proposed sensor can be fabricated using current technologies that have already been employed in the fabrication of similar designs.