In this section, the sensitivity of the THz sensor is estimated from its sensing performance for analytes with different indexes of refractive profiles, and the results are presented. The sensing performance of the sensor is estimated using the analyte whose thickness, ‘ta’ is placed above the conducting layer as shown in Fig. 10. The different filler materials such as minerals, diatomaceous earth and talc are considered analytes in this research. These fillers when added with the polymers will reduce the cost of the materials [33]. The analyte is varied based on their unique refractive index value which varies from n = 1(air) to n = 2.67 (lead oxide). The dielectric constant (ɛr) is computed from the refractive index (n) which is known in prior. The thickness of the analyte, ta is fixed to be 1 µm.
The absorption characteristics of the designed metamaterial THz sensor for various refractive indices are depicted in Fig. 11. It is inferred that the increase in refractive index causes a redshift in the resonant frequency. The perturbation theory and the equivalent medium theory [32] are used in computing this redshift in frequency. The shift in resonant frequency is estimated using the fields in the sensor with respect to the change in dielectric constant using the Eq. (3).
$$\frac{\varDelta \omega }{{\omega }_{0}}=\frac{{\int }_{{v}_{0}}\left(\varDelta \varepsilon {\left\stackrel{}{{E}_{0}}\right}^{2}+\varDelta \mu {\left\stackrel{}{{H}_{0}}\right}^{2}\right)dv}{{\int }_{{v}_{0}}\left(\varepsilon {\left\stackrel{}{{E}_{0}}\right}^{2}+\mu {\left\stackrel{}{{H}_{0}}\right}^{2}\right)dv}= \frac{{\int }_{{v}_{0}}\left(\varDelta \varepsilon {\left\stackrel{}{{E}_{0}}\right}^{2}\right)dv}{{\int }_{{v}_{0}}\left(\varepsilon {\left\stackrel{}{{E}_{0}}\right}^{2}\right)dv}$$
3
where E0 and H0 are the electric and magnetic field in the sensor without analyte respectively, Δɛ and Δµ are the change in permittivity and permeability respectively. The equivalent medium theory is used to estimate the effective dielectric constant when the sensor is loaded by Eq. (4) [32].
ɛeff= ɛsub+αɛair+(1α)ɛr (4)
The sensor performance is estimated using three different parameters viz. sensitivity (S), quality (Q) factor, and FWHM. Sensitivity is defined as the ratio of change in frequency (Δf) to the change in refractive index (Δn). Thus, the average sensitivity is estimated to be 1.37 THz/Refractive Index Unit (RIU) for refractive indices considered between n = 1 to n = 2.67. The absorptivity of 99.9% is also maintained for all the refractive indices up to 2.67 as shown in Table II. It is observed that the proposed sensor is highly sensitive for n = 1.41 with the sensitivity of 1.47 THz/RIU, whereas the THz sensor shows the least sensitivity for n = 2.67 with the sensitivity of 1.30 THz/RIU. The other parameters such as FWHM and Q factor are estimated and tabulated in Table II. Q factor is defined as the ratio of resonant frequency (fr) to FWHM. The Q factor of 4.47 is obtained for the refractive index n = 1. From the table, it is inferred that, as the refractive index increases, the Q factor is reduced. The capacitance of the sensor estimates the Q factor. However, when the sensor is loaded with the analyte, the capacitance of the sensor is said to be an effective capacitance (Ceff). Thus, the effective capacitance is the total sum of the capacitance due to the sensor and the analyte (Csensor) [12]. The capacitance of the sensor Csensor is varied based on the change in the refractive index of the analyte, Therefore, the Ceff of the sensor varies. Thus, the quality factor of the THz sensor is affected due to the change in effective capacitance using the expression Q = 1/ωCR. Hence, the Q factor and the capacitance of the sensor are inversely proportional to each other. Therefore, the increase in the refractive index of the load increases the effective capacitance in turn reduces the Q factor, and thus, the resonant frequency of the THz sensor is reduced.
TABLE II CHARACTERISTICS OF ABSORPTION FOR DIFFERENT REFRACTIVE INDEX PROFILE
RI

A (%)

S (THz/RIU)

Δf (THz)

FWHM (THz)

Q

1

99.9





1.6

4.47

1.41

99.7

1.47

0.60

1.65

3.97

1.73

99.9

1.37

1.00

1.55

3.97

2.00

99.3

1.36

1.36

1.6

3.67

2.23

99.5

1.46

1.65

1.5

3.67

2.44

99.6

1.33

1.92

1.5

3.49

2.67

98.6

1.30

2.14

1.35

3.71

Furthermore, the sensor performance for different thicknesses of the sample is analyzed and plotted in Fig. 12. The sample thickness is varied from 1 µm to 10 µm with a fixed refractive index n = 1.41. It is inferred from the figure that, as the thickness of the sample increases, the redshift in the frequency of 0.1 THz. Thus, the variation in the thickness of the analyte shows the average deviation of 59 GHz/µm. Similarly, the increase in thickness of the analyte reduces the absorptivity to 96%. The best curve fit is found using the R2 value. The dependent variable (S) and independent variable (n) are related using the value of R2. The value of R2 is estimated for the linear curve is 0.9995 whereas, for the exponential fit, the R2 value is 0.8719. Therefore, the linear curve fit is expressed using the equation S = 1.2644n1.1747 (as shown in Fig. 13), where n is the refractive index of the analyte and S is the sensitivity of the sensor in THz/RIU.
The performance of other refractive indexbased THz sensors reported in the literature is compared with the proposed THz sensor, which is presented in Table III. It is inferred from the table, that the proposed THz sensor is miniaturized compared to the works presented in the literature [15–17] by 23%, 76%, and 74% respectively. The proposed THz sensor exhibits high sensitivity compared to the references [13], [15–17]. The estimated sensitivity is 56% greater than the sensitivity in the reference [13], compensating with the effective size of the sensor which is larger by 65%.
TABLE III COMPARISON OF PROPOSED SENSOR PERFORMANCE WITH OTHER RELEVANT WORKS
Ref.

Effective size (λeff × λeff)

Geometrical Size (µm x µm)

% Miniaturization
(refer λeff)

f
(THz)

Sensitivity (GHz/RIU)

[13]

0.391 × 0.391

36 × 36



2.249

300

[15]

0.763 × 0.763

140 × 140

23

1.52

430

[16]

1.368 × 1.368

500 × 500

76

0.557

128

[17]

1.317 × 1.317

300 × 300

74

0.22, 0.48, 0.72, 0.76

139.2

This work

0.67 × 0.67

15 × 15



7.16

1370

The following are the important features of the designed highly sensitive THz sensor: 
1. The effective footprint of the proposed metamaterial THz sensor is 0.67 λ eff x 0.67 λeff which is lesser by 23%, 76%, and 74% of the structures proposed in [15–17] respectively. Thus, the proposed design is ultraminiaturized.
2. Maximum absorption of 99.9% is obtained at 7.16 THz in a free space environment.
3. A high sensitivity of 1.47 THz/RIU for the refractive index of 1.41 at 7.16 THz is offered by the proposed THz sensor, which is highest by 612% on average when compared to the works proposed in [13], [15–17].
4. It offers insensitive polarization characteristics and stable angular characteristics with less than 0.24% deviation upto the incident angle of 60˚.
5. The increase in thickness of the analyte is also analyzed and the average deviation of 59 GHz/µm is observed.