This section of the manuscript deals with the results and discussion of the proposed work. The basic idea of our design is based on the existence of a resonant mode inside the PBG due to the break in the periodicity of the structure. The defect layer region is filled by various alcohol solutions of different concentrations under investigation separately, which results in the change in the refractive index of various alcohol samples as per the details mentioned in
Table 1. This change in the refractive index of various alcohol samples causes the change in the position and intensity of the defect mode inside the PBG. In our proposed design, the numeric values of metal nanoparticles are taken as
Hz,
[
25,
26],
Hz,
a = 20 nm,
which are impeded in MgF
2 of
[
29]. The thickness of layers A, B and C are taken as
d1 = 68.3 nm,
d2 = 45.9 nm and
dc = 125 nm, respectively. The period number has been fixed to 5. The refractive index of the substrate is taken as
. The proposed bio-alcohol sensor is composed of ten alternating layers of material nanocomposites and GaAs with an air cavity at the center.
The proposed structures can be realized by using a dip coating fabrication technique in addition to a sol-gel method because the spin coating process can allow the fabrication of a periodic layered structure composed of many materials including nanoparticles and polymer solutions. To initiate the spin coating process, a precursor solution is to be dropped over the flat substrate, then the solvent is evaporated from the substrate by conducting the spin process. Before spinning the next layer, we use an annealing procedure to solidify the earlier deposited layer on the substrate. The aforementioned process will be repeated till we obtain a stack of the required number of layers. The thickness of each film of the multilayer periodic stack can be controlled with the variation of either rotation speed or cast solution concentration. Since the sol-gel technique does not require any complex installations associated with technology, this minimizes the fabrication cost of the photonic structure.
After fabrication, the proposed structure is examined by using an angle-dependent spectroscopic elliposmetric method. This method helps to analyze the thickness and material dispersion in nanocomposite and GAaS material layers by using the software Complete EASE. The optical response of the proposed bio-alcohol sensor loaded with the water sample containing different organic materials is recorded by using the Kretschmann configuration. In this process, we have to connect the proposed structure and USB4000 spectrometer through the optical fiber via a microscope objective.
Now, the wavelength-dependent nature of the real and imaginary part of the refractive index of silver has been discussed with the help of
Figure 2a. This figure has been plotted with the help of Equation (2) in accordance with the Drude model. It shows the wavelength-dependent dispersive properties of the real and imaginary part of the refractive index of silver. It shows that in the visible region of the electromagnetic spectrum, the real part of the refractive index of silver is very small and varies little with respect to wavelength. On the other hand, the imaginary part of the refractive index of silver gradually increases and becomes significant with respective increases in the wavelength, as evident in
Figure 2a. It shows that as wavelength increases from visible to infrared, the imaginary part of the refractive index of silver also increases from 0 to 14. It indicates the enhancement in losses associated with silver if we go from the visible to the infrared region. Next, we examine the change in the refractive index (
nc) of water samples containing different acetone concentrations (
c) as per the experimentally obtained data of
Table 1, with the help of Abbe’s refractometer at a temperature of 30° and a wavelength of 589 nm. For this purpose, we have taken experimental data from reference [
30] and applied cubic curve fitting to obtain the following relation (11), which elaborates the refractive index of water mixtures dependent on acetone concentration. The results are plotted in
Figure 2b.
Figure 2b shows the refractive index of the water mixture increases linearly with increase in the acetone concentration and nicely fitted over the experimental data of
Table 1.
Now, we investigate the optical transmittance of the proposed design by loading the defect layer region one by one with different water samples containing the organic materials methanol, acetone, ethanol, propanol, butanol, pentanol, chloroform and phenol, each of a concentration
c = 30%, and observe the corresponding change in the central wavelength and intensity of the respective defect modes inside the PBG of the proposed design with the help of
Figure 3. It has been observed that, due to changes in the water samples containing methanol, acetone, ethanol, propanol, butanol, pentanol, chloroform and phenol, the central wavelength of the respective defect modes shifts to 529.1 nm, 532.3 nm, 535 nm, 537.6 nm, 541.3 nm, 543.3 nm, 549.3 nm and 565.5 nm inside the PBG with respect to the central wavelength of the defect mode corresponding to the pure water sample at 529.9 nm. The change in the central wavelength of the defect mode is due to change in the refractive index of the water samples containing pure water, methanol, acetone, ethanol, propanol, butanol, pentanol, chloroform and phenol in accordance with
Table 2. The refractive index values of water samples containing methanol, acetone, ethanol, propanol, butanol, pentanol, chloroform and phenol, each of a concentration
c = 30%, are 1.33, 1.3256, 1.3602, 1.3750, 1.3968, 1.4087, 1.444 and 1.542 respectively. The intensity of each defect mode is about 99%, as is evident from
Figure 3a,b. The shifting of these defect modes corresponding to water samples containing different organic materials towards the higher-wavelength side inside the PBG is in accordance with the standing wave formulation of laser cavities [
31]:
where
is the optical path difference,
is an integer,
is the wavelength of incident light,
is the effective refractive index of the proposed bio-alcohol sensor and
is the geometrical path difference. The increase in the refractive index of water samples containing different organic materials results in the shifting of the defect mode towards the longer-wavelength side to keep the optical path difference fixed.
3.1. Effect of Increasing the Thickness of Defect Layer Region at θ = 0°
Now we have given our efforts to study the effect of increasing the thickness of the defect layer region from 45 nm to 165 nm in steps of 40 nm on the resonant peak inside the PBG corresponding to water samples containing different organic materials of a fixed concentration of 30%, which varies from methanol to phenol in accordance with
Table 2. The transmission spectra of the proposed structure with four different defect layer thicknesses
dc = 65 nm, 85 nm, 125 nm and 165 nm are plotted in
Figure 4a–d, respectively with the angle,
θ = 0°. The increase in the thickness of the defect layer region also increases the path by which it has to travel by electromagnetic waves inside the defect layer, which results in the strong interaction between the water sample under investigation and light. We have noticed from
Figure 4a–d that the increase in the thickness of the defect layer also improvers the intensity as well as the full width half maximum (FWHM) of the defect mode corresponding to each water sample. At
dc = 65 nm, the defect modes corresponding to the water sample containing methanol and phenol are located between the range 422.3 nm to 431.3 nm. The intensity of the defect modes is around 88%, and their FWHM is quite large. As we increase the thickness of the cavity region from 65 nm to 165 nm, we observe that their intensity starts to improve and reaches unity at
dc = 165 nm. The increase in the thickness also reduces the FWHM of each defect mode, which is desirable for high-performance biosensors. At
dc = 165 nm, the defect modes relocate their positions between 587.9 nm and 628.6 nm inside the PBG corresponding to the water samples containing methanol and phenol, respectively, as shown in
Figure 4d. Thus, the defect layer’s thickness is one of the important parameters in designing any efficient biosensor, which also improves the sharpness of the tunneling peak inside the PBG.
3.2. Effect of Increasing the Incident Angle with dc = 125 nm
Next, we study the effect of changes in the angle of incidence corresponding to the TE polarization case on the transmission properties of the proposed structure at a fixed cavity thickness
dc = 125 nm. All the other structural parameters have remained fixed as discussed above. The transmittance of the proposed bio-alcohol sensor loaded with water samples containing different organic materials included in this study corresponding to incidence angles 0°, 20°, 40° and 60° have been plotted in
Figure 5a–d, respectively.
Figure 5 shows that as the angle of incidence increases from 0° to 60° in steps of 20°, the defect modes associated with different organic samples start to move towards the lower-wavelength side with respect to the defect mode corresponding to the pure water sample due to the blue shifting of the PBG. The angle-dependent movement of these defect modes associated with water samples containing different organic materials along with the PBG can be easily explained on the basis of Bragg–Snell’s law [
32,
33] as
where
is the wavelength of the incident light,
is the order of diffraction,
is representing interplanar distance,
is the effective refractive index and
is the angle of the incident light. It can be easily understood from Equation (13) that the increase in the incident angle is compensated by the lowering of the central wavelength of the defect mode in order to maintain equality. Besides the movement of the defect mode dependent upon the incident angle, we have also noticed the gradual decrease in the intensity of defect modes with increases in the incident angles. At extremely higher angles, the decrease in the intensity of the defect modes is more prominent. Additionally, we have also observed the gradual reduction in the FWHM of each defect mode with an increase in the angle of incidence, which is always desirable for any high=performance biosensor.
3.4. Defining the Parameters for Evaluation of the Performance of the Proposed Bio-Alcohol Sensor
In order to evaluate the performance of the proposed bio-alcohol sensor, we have calculated the most common parameters, which in turn examine the working performance of any biosensing structure. First, we have calculated the numeric value of sensitivity (
S) for our design with the help of the following equation [
34].
where,
,
,
and
are the wavelength and refractive index of pure water.
Next, we have calculated the quality factor (
Q) value of our proposed design. One of the most essential requirements is to obtain accuracy in the measurements of biosensors. The higher value of the
Q factor is always expected for any biosensing design to obtain accurate findings. The
Q factor is defined [
35] as
where
is the central wavelength of the defect mode and
is the
FWHM of the defect mode.
The ability of any biosensor to sense the minute change in the position of the defect mode inside the PBG is associated with the figure of merit (
FoM). It is inversely proportion to the FWHM of the defect mode and directly proportion to S according to the relation as under [
36]
The detection limit (
DL), which describes the smallest detectable change in the index of refraction of the sample under examination, can be calculated by [
37]
Finally, we have calculated the damping ratio (
), which is a dimensionless parameter. It describes how an oscillation in a system decays after a disturbance and is given by [
37]
In order to analyze the dependence of the sensitivity of the proposed 1D bio-alcohol sensor as a function of the thickness of the defect layer region, we have plotted a sensitivity versus defect layer thickness diagram when the cavity region is loaded with the water sample containing phenol of a concentration of 30% at
θ = 80°.
Figure 7 shows that the variation between the changes in the sensitivity of the proposed bio-alcohol sensor from 113 nm/RIU to 405.66 nm/RIU is due to a change in the thickness of the defect layer region from 85 nm to 230 nm, respectively. We have also applied linear curve fitting on the simulated data to obtain the curve fitting equation
. The blue solid line curve in
Figure 6 represents linear curve fitting between
S and
dc. Here,
is the root mean square value between the simulated and linear fitting data. It indicates that the sensitivity increases linearly with increases in the thickness of the defect layer region.
3.5. Analysis of Bio-Alcohol Sensor for Achieving Optimum Performance
The analysis of the proposed design has been carried out by means of calculating the numeric values of parameters
S,
Q,
FoM,
DL and
as defined in
Section 3.4 above. Keeping in mind the importance of selecting the thickness of the cavity region as well as the angle of incidence as discussed in
Section 3.1 and
Section 3.2, respectively, to achieve our goal, we have tried two combinations to explore the optimum performance of the proposed design. First, we have fixed the angle of incidence at 70° and varied
dc = 125 nm and 165 nm to obtain the numeric values of the parameters
S,
Q,
FoM,
DL and
. The results are summarized in
Table 3 and
Table 4, corresponding to
dc = 125 nm and
dc = 165 nm, respectively, at
θ = 70°. Here, we have chosen
f = 2 × 10
−5 to optimize absorption, as discussed in
Section 3.3. All the other parameters of the structure remain the same as discussed earlier.
Table 3 shows that the sensitivity of the design varies between 206.896 nm/RIU to 227.27 nm/RIU, corresponding to the water sample containing acetone and methanol, respectively, of a concentration of 30%. The order of the
Q,
FoM and
values of the proposed design with
dc = 125 nm at
θ = 70° are 10
2 to 10
3, 10
2 and 10
−4, respectively. Now, attempts have been made to improve the numeric values of these parameters. For this purpose, we have increased the dc to 165 nm, keeping
θ = 70°. The numeric values of the parameters
S,
Q,
FoM and
of the design with the modified value of
dc = 165 nm are summarized in
Table 4 below.
We have seen from
Table 4 that by increasing the thickness of the cavity region from 125 nm to 165 nm and keeping
θ = 70°, one can easily improve the performance of the biosensor. Therefore, optimizing the thickness of the cavity region is a very essential requirement to design high-performance biosensing structures.
Next, we have further increased the thickness of the cavity region to 230 nm and varied the angle of incidence from 70° to 80° to study the performance of the proposed structure when it is loaded with water samples containing methanol, acetone, ethanol, propanol, butanol, pentanol, chloroform and phenol, each of a concentration of 30% with respect to the pure water sample. The numeric values of the parameters
S,
Q,
FoM and
of the design with
dc = 230 nm corresponding to
θ = 70° to
θ = 80° are summarized in
Table 5 and
Table 6, respectively.
It can be seen from
Table 5 that as we increase the thickness from 165 nm to 230 nm and keep the angle of incidence fixed at 70°, the sensitivity of the proposed structure is tremendously enhanced. It varies between a maximum of 454.545 nm/RIU, corresponding to the water sample with methanol, to a minimum of 369.339 nm/RIU, corresponding to the water sample with phenol. Here, it should be noted that all calculations have been performed with respect to water. The other parameters of the design are also improved significantly. Finally, we have tried to improve the performance further by means of externally tuning the incident angle. For this reason, we have increased the angle of incidence to 80° and kept
dc = 230 nm. The corresponding results are presented in
Table 6 below.
From the data of
Table 6, we can conclude that the sensitivity of the structure reaches its maximum under this combination and varies between a maximum of 500 nm/RIU and a minimum of 405.66 nm/RIU, corresponding to water samples containing methanol and phenol, each of a concentration of 30%, respectively. The order of the quality factor is 10
3, which is large and signifies the accuracy of the measurements. The
FoM of the design is also of the order 10
3, which is as large as expected and indicates the ability of the design to sense the minute change in the position of the defect mode due to changes in the sample. The order of the damping ratio is very low, and hence the oscillations produced in the system due to changes in the water sample die out quickly. According to the current results, the average value of the detection limit is about 1 × 10
−5 RIU, which is per our desire. The transmittance spectra of the proposed structure have been plotted in
Figure 8 under optimum conditions as discussed above. It shows that, under optimum conditions, the defect modes corresponding to different water samples are found between 520 nm to 620 nm inside the PBG of the design. These defect modes are distinguishable and smooth. Though under optimum conditions the intensity of these defect modes reduces to 65%, this value is enough to be detected by transducers to produce measurable electric signals. There is one more common observation: as the refractive index of the water sample increases, the separation between consecutive defect modes also increases.
The comparison between the performance of the proposed bio-alcohol sensor and a previously reported similar kind of biosensors has been presented in
Table 7. It shows that the sensitivity of our biosensor is better in contrast to the findings of previously reported biosensors. Moreover, the proposed bio-alcohol sensor has lots of additional advantages such as low cost, simpler design, high sensitivity, extremely low detection limit and easier fabrication and handling.