2.1.

Optical Fiber

The coupling device is considered a multimode optical fiber (of core diameter $D$ ), whose wavelength-dependent refractive index $\left(n_c\right)$ is represented in terms of the Sellmeier expression, as follows¹⁰:

2.2.

Metal Layer

As shown in Fig. 1, a small portion (of length $L$ ) of fiber cladding is removed and is coated with a thin Ag layer of thickness $d$ . According to the free-electron Drude model, the wavelength-dependent complex dielectric function $\left({\epsilon }_m\right)$ of Ag can be written as:

2.3.

Buffer Layer

The Ag layer in Fig. 1 is followed by a buffer layer of thickness in the vicinity of $1\text{to}15\mathrm{nm}$ with refractive index of 1.45 (Ref. 11). Preferably, this buffer layer should be in the form of a biochemical layer for two important reasons. First, it prevents the blood sample from being in direct contact with the Ag layer, which may contaminate the blood sample, thereby affecting sensor’s performance. The contamination due to the presence of the Ag layer may arise due to the fact that silver is prone to oxidation problems when used in liquid environments. If inappropriately exposed to liquids, Ag may form a thin $\left(2\text{to}3\mathrm{nm}\right)$ oxide layer on its surface. Such an oxide layer may lead to errors in SPR measurements, and for this reason, the Ag layer must be protected against such oxidation issues. Therefore, one may choose a biochemical layer that can act as a protective layer to keep the Ag layer from being oxidized. Second, the structural compatibility of the blood sample with such a biochemical layer is another added advantage. Structural compatibility lies in the fact that due to having both chemical and biological characteristics, a single biochemical layer may provide stable bonding at the two interfaces (one with the Ag layer and another with the blood sample) to prevent any structural anomaly at those interfaces (e.g., polyethyleneglycol may be able to satisfy the preceding conditions). Our previous studies show that for silica fiber, the biochemical layer should have a thickness in the vicinity of $1\text{to}15\mathrm{nm}$ in order to achieve highly sensitive SPR measurements.¹¹ Therefore, for the present study, we assumed this biochemical layer to be $15\mathrm{nm}$ thick.

2.4.

Blood Sample Layer

The final layer in the present SPR sensor is a very thin layer of blood sample. In general, there is no limit to the thickness of the outermost (i.e., sensing) layer for SPR-based measurements. We carried out our calculations for blood layer thickness of $1\mathrm{nm}\text{to}1\mu \mathrm{m}$ and there was no change in the SPR curves for three blood groups due to high optical activity of the SPW (in terms of its large penetration depth into the blood sample layer). Therefore, a very small amount of blood sample is required with the proposed scheme.

2.5.

Transmitted Power Calculations

First, the transfer matrix method is used to calculate the reflectivity $\left(R_p\right)$ of the present SPR sensor design (Sec. 5). Then, the following form of angular distribution for collimated (i.e., all guided rays) launching of light in optical fiber is followed:¹¹

3.1.

Occurrence of SPR and Stability against Thermal Variation

In order to set the optimized design parameters, the foremost task is to analyze the possibility of occurrence of SPR with the present blood-group sensing scheme. Figure 3 shows the spectral variation of $K_{\mathit{SPW}}$ for three blood groups (O, A, and B) along with $K_{\mathit{EW}}$ for fused silica fiber. The curves correspond to room temperature (i.e., $25°\mathrm{C})$ . As is shown in Fig. 3, the $K_{\mathit{SPW}}$ curves for the three blood groups intersect the $K_{\mathit{EW}}$ curve at three different wavelengths $\left({\lambda }_{\mathit{SPR}}\right)$ , marked by a solid vertical line at each intersection point (i.e., $642.59\mathrm{nm}$ for A, $651.05\mathrm{nm}$ for B, and $658.57\mathrm{nm}$ for O blood groups). This suggests that light can be coupled to SPW to enable SPR-based detection of blood groups with the present fiber sensor scheme. The overall $\delta {\lambda }_{\mathit{SPR}}$ is $15.98\mathrm{nm}$ , which is sufficiently large to distinguish among the three blood groups. Furthermore, we have also studied the effect of temperature variation on the preceding result by taking the thermo-optic effect in fused silica and Ag layer into account.¹² The corresponding dotted vertical lines show that at $50°\mathrm{C}$ , ${\lambda }_{\mathit{SPR}}$ values shift to the slightly shorter side (i.e., $642.36\mathrm{nm}$ for A, $650.85\mathrm{nm}$ for B, and $658.32\mathrm{nm}$ for O blood groups). However, between $25°\mathrm{C}$ and $50°\mathrm{C}$ , the change in ${\lambda }_{\mathit{SPR}}$ is linear, small, and almost identical for all three blood groups, which suggests that there is a negligible effect of temperature variation on blood-group detection under the present fiber-optic SPR sensor scheme.

Fig. 3

Simulated results related to the fulfillment of plasmon resonance condition for three blood groups at $25°\mathrm{C}$ and $50°\mathrm{C}$ .

3.2.

Optimization of Design Parameters: Master Plot

The next task is to optimize the design parameters related to optical fiber (i.e., $L$ and $D$ ) and Ag layer (i.e., $d$ ) in order to ensure large $\delta {\lambda }_{\mathit{SPR}}$ and small FWHM of SPR curves. From Eq. 7, it is clear that both $D$ as well as $L$ affect only the number of reflections, therefore, it is more appropriate to try to optimize the ratio $(L∕D)$ . Figure 4 depicts a master plot showing the effect of $L∕D$ on performance parameters: overall $\delta {\lambda }_{\mathit{SPR}}$ and average FWHM. The value of $L∕D$ is varied from 10 to 200. The master plot also contains the corresponding plots for two values (i.e., $30\mathrm{nm}$ and $60\mathrm{nm}$ ) of $d$ . Apparently, as $L∕D$ increases, the overall $\delta {\lambda }_{\mathit{SPR}}$ decreases, whereas average FWHM increases for any value of $d$ . This means that with an increase in $L∕D$ , the sensor’s performance deteriorates, which may be explained in terms of SPR-curve broadening. Each reflection a ray undergoes at the fiber–metal interface causes a certain fraction of optical power to dissipate into the sensing region due to the coupling of the evanescent wave with SPW. This further implies that larger the number of reflections, the more the decay in power $\left(P_{\mathit{trans}}\right)$ transmitted at the fiber’s output end due to greater dissipation of power. This decay results in the downfall of SPR curve and, therefore, increases its FWHM. Since number of reflections increases with an increase in $L∕D$ , FWHM increases with $L∕D$ . Moreover, since energy-flow inside the fiber takes place in form of different discrete guided modes, which one of the modes gets coupled to SPW will depend on the precise amount of energy transferred. Further, since a mode is characterized by its angle $\left(\theta \right)$ , $K_{\mathit{EW}}$ corresponding to the coupled mode also is affected, which in effect causes the ${\lambda }_{\mathit{SPR}}$ to shift to some other value to ensure the fulfillment of the resonance condition [see Eq. 1]. Furthermore, since the amount of energy transfer significantly depends on $L$ and $D$ in terms of number of reflections, these two parameters ultimately affect the resonance condition also. More precisely, the resonance condition is satisfied at different wavelengths depending on what value of $L∕D$ is taken.

Fig. 4

Simulated master plot in order to optimize the design values of fiber core diameter $\left(D\right)$ , sensing region length $\left(L\right)$ , and silver layer thickness $\left(d\right)$ .

The master plot also shows that the sensor’s performance gets better with an increase in $d$ . The reason is the variation in interaction between SPW and the fiber mode with a change in $d$ . The thicker the Ag layer, the smaller the interaction between SPW and the fiber mode. A small interaction causes less absorption of light power, and the SPR curve shifts upward. The upshift results in narrowing of the SPR curve, and hence FWHM decreases. This variation of interaction between SPW and fiber mode also affects the resonance condition (as described earlier), and the overall $\delta {\lambda }_{\mathit{SPR}}$ increases for a thicker Ag layer.

3.3.

Demonstration of Fiber-Optic SPR Sensing for Blood-Group Detection

Following the optimization of design parameters, Fig. 5 depicts the three SPR curves for three different blood groups (O, A, and B). The curves have been plotted at $25°\mathrm{C}$ for $L∕D=10$ and $d=50\mathrm{nm}$ . According to Fig. 5, the ${\lambda }_{\mathit{SPR}}$ values for the A, B, and O groups are $620.30\mathrm{nm}$ , $629.51\mathrm{nm}$ , and $633.58\mathrm{nm}$ , respectively. The preceding ${\lambda }_{\mathit{SPR}}$ values are fairly separated from one another, exhibiting an overall $\delta {\lambda }_{\mathit{SPR}}$ of $13.28\mathrm{nm}$ for three blood groups. The overall $\delta {\lambda }_{\mathit{SPR}}$ becomes slightly smaller than was shown in Fig. 3 because of all-guided ray launching, which affects the angular distribution of the rays, and hence affects the resonance condition. Keeping in mind that a spectral shift of as small as $0.01\mathrm{nm}$ is commonly detectable these days, the preceding results indicate that blood-group detection with a fiber-optic SPR sensor can be conveniently carried out with high sensitivity.

Fig. 5

Simulated SPR curves for three blood groups plotted with $L∕D=10$ , and $d=50\mathrm{nm}$ at $25°\mathrm{C}$ .

Further, the sensed refractive indices of the A, B, and O groups at their corresponding ${\lambda }_{\mathit{SPR}}$ values (i.e., $620.30\mathrm{nm}$ , $629.51\mathrm{nm}$ , and $633.58\mathrm{nm}$ , respectively) are 1.3768, 1.3788, and $1.3796\mathrm{RIU}$ , respectively (Fig. 2). Thus, sensed refractive indices corresponding to the three blood groups are separated by $0.0028\mathrm{RIU}$ . This means that an overall $\delta {\lambda }_{\mathit{SPR}}$ of $13.28\mathrm{nm}$ corresponds to an overall refractive index change of $0.0028\mathrm{RIU}$ . Therefore, assuming a standard spectral resolution limit of $0.01\mathrm{nm}$ , the theoretical detection limit with the proposed sensor design is of the order of ${10}^{-4}\mathrm{RIU}$ .

Furthermore, the FWHM values for A, B, and O blood groups are $44.23\mathrm{nm}$ , $38.03\mathrm{nm}$ , and $35.04\mathrm{nm}$ , respectively—i.e., an average FWHM of $39.10\mathrm{nm}$ . The preceding FWHM values are in a fairly reasonable range compared to general SPR curves obtained in theoretical and experimental results.