1. Introduction

Due to biophotonics advancement, small sophisticated devices exist for various biochemical and biosensing applications [1]. These sensing devices are called sensors. In biosensing, analytes with different $RI$ values are investigated in terms of various sensing parameters [2]. $PCF$ can be used in designing a biosensor based on the variation of $RI$. Various techniques for $RI$ sensing are developed to date, among which the $SPR$ phenomenon is mostly used for optical sensing-related applications [3]. This technique is used in the field of food quality monitoring [4], environmental monitoring [5], biomedical diagnostics [6], etc. $PCF$ has revolutionized photonic sensing as it can easily control the flow of light by the change in the structural parameters. $PCF$ is equipped with unique features like controlled birefringence, high nonlinearity, single-mode behavior, and other dispersion-related advancements [7].

In literature gold ($Au$) [8], silver ($Ag$) [9], aluminium ($Al$) [10], graphene [11], titanium dioxide ($Ti{O_2})$ [12], etc., are extensively used as a plasmonic material for designing a biosensor. Different plasmonic materials possess other properties and advantages like $Ag$ offer sharp resonance peak but suffer from the problem of quick oxidation. Thus a thin layer of graphene is placed over the $Ag$ to prevent it from early oxidation [9]. Among plasmonic materials, $Au$ is considered as a useful plasmonic material as it is stable and chemically inert [8]. Nowadays, researchers are exploring the combination of two or more plasmonic materials for sensitive plasmonic sensing. The combination of$\; Ag$ with graphene is examined in [9], $Au$ with $T{a_2}{O_5}\; $in [13], etc. Thus in this research work, a combination of $Au$ with $Ti{O_2}$ for sensitive plasmonic sensing is explored. $Ti{O_2}$ layer is mainly used to provide necessary adhesion between the $Au$ layer and the fiber [14].

Hasan et al. [15] designed an anisotropic biosensor using $PCF$. They have created a spiral airhole arrangement for their sensor. $Au$ is used as a plasmonic material in their designed sensor. Their sensor has presented $WS$ of $4600\; nm/RIU$ and $4300\; nm/RIU$ for $x - pol.$ and $y - \; pol.$ respectively. They have obtained a maximum $AS$ of $371.5\; RI{U^{ - 1}}$ and $420.4\; RI{U^{ - 1}}$ for $x - pol.$ and $y - \; pol$, $\; $respectively. Momota et al. [16] proposed a $PCF\; SPR$ sensor for chemical sensing applications. They used $Ag$ as a plasmonic material in their proposed design. Their sensor offered $WS$ of $4200\; nm/RIU$, $AS$ of $300\; RI{U^{ - 1}}$ and $SR$ of $2.38 \times {10^{ - 5}}\; RIU$ respectively. Wei et al. [17] presented a $PCF\; SPR$ sensor with $Au$ coating as the plasmonic material. They have investigated a single $LA$ having a $RI$ value of $1.42\; RIU$ from their proposed design. Their sensor has obtained a full $WS$ of $10488.5\; nm/RIU$ and $8230.7\; nm/RIU$ for $x - \; pol$. and $y - pol.$ respectively. They have obtained $FOM\; $of $949.8$ $RI{U^{ - 1}}\; $and $791.4\; RI{U^{ - 1}}\; $for $x - pol.$ and $y - \; pol.$ respectively. Mollah et al. [18] designed a dual-polarized $PCF\; SPR$ sensor. They have obtained $WS$ of $11000\; nm/RIU$, $AS$ of $1532\; RI{U^{ - 1}}$ and $SR\; $of $9.09 \times {10^{ - 6}}\; RIU$ for $x - pol.$ and $y - \; pol.\; $respectively. Ayyanar et al. [19] presented a $PCF\; SPR$ sensor for cancer detection. They have obtained $WS$ of $7916\; nm/RIU\; $and $10625\; nm/RIU$ for $x - $ and $y - \; pol.\; $respectively for cervical cancer cells, $WS$ of $5714.28\; nm/RIU$ and $7857.14\; nm/RIU$ for $x - $ and $y - \; pol.\; $respectively for breast cancer cells and $WS$ of $4500\; nm/RIU$ and $6000\; nm/RIU$ for $x - $ and $y - \; pol.\; $respectively for basal cells. In [15], $LA$ having $RI\; $varying from $1.33$ to $1.38\; RIU$ with a step size of $0.01$ are explored. In [16], researchers have designed a $PCF\; SPR$ sensor to detect $LA$ with $RI$ in the range of $1.33\; $to $1.37\; RIU$ with a step size of $0.01$. In [20], $LA$ having $RI$ varying from $1.32$ to $1.38\; RIU$ with a step size of $0.01$ are investigated. In [21], $LA$ having $RI$ ranging from $1.20\; $to $1.33\; RIU$ are explored, $PCF\; SPR\; $sensor for $RI\; $varying from $1.27\; $to $1.32\; RIU$ is presented in [22].

Table 1 presents a comparison of techniques used to design $SPR$ based sensors along with their merits and shortcomings.

Table 1. Comparison of various $SPR$ based sensing methodologies

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Thus it can be observed that among all the techniques developed to date using $SPR$ phenomenon, $PCF$ based $SPR$ sensors have shown tremendous advantages over existing $SPR$ approaches. Accordingly, it has been observed that several $PCF\; SPR$ sensor designs are proposed for detecting a wide and narrow range of analytes. Therefore, it is impressive to monitor a $PCF\; SPR$ sensor’s performance for the narrow $RI\; $range. Thus, an exhaustive study on an ultra-sensitive $PCF\; SPR$ biosensor’s performance for an intermediate RI range varying from $1.340$ to $1.380\; RIU$, having a miniature stepsize of $0.005$, is presented in this research work.

The sensing ability of the proposed biosensor is investigated through the Finite Element Method ($FEM$) and circular Perfectly Matched Layer ($PML$) condition. Geometrical parameters are advanced to obtain acceptable sensing parameters. The purpose of this investigation is to investigate $WS$, $AS$, $SR$, full-wave half maximum ($FWHM$), and $FOM$ for $LA\; $in the $RI\; $range of $1.340\; $to $1.380\; RIU$.

Fabrication tolerance for the proposed sensor is investigated with a ${\pm} 5\%$ variation in the geometrical parameters. Real-time spectroscopy analysis of the $LA$ having $RI$ values of $1.340\; RIU$, $1.360\; RIU$, and $1.380\; RIU$ are performed to analyze the transmission, absorbance, and their relation with the $RI.\; $Thus, the proposed sensor’s structural simplicity and competent characteristics enhance its practical fabrication possibility for various optical sensing applications.

The organization of the article is split into the following sections. Section 2 explains the use of the $FEM$ for anisotropic $PML$ condition. Section 3 presents the designing details of the presented $PCF\; SPR$ biosensor. Section 4 presents the spectroscopy analysis of the $LA$ having $RI$ value of $1.340\; RIU$, $1.360\; RIU$, and $1.380\; RIU$, respectively. Details of the performance analysis of the proposed biosensor are presented in section 5. In section 6, results of the variations in the proposed biosensor’s geometrical parameters are presented. Finally, section 7 offers final remarks on the performed research work.

2. Analysis of finite element method for anisotropic perfectly matched layer

The $FEM$ applies to both waveguides and $PCF$. Through this method, propagation characteristics of modes are investigated. Fiber cross-sections are divided into homogeneous subspaces in $PCF$, where Maxwell Equations are solved. These subspaces are mostly triangles in geometry and approximate circular-shaped structures [28]. Thus a complete vector formulation is required for the fibers with arbitrary air fillings and different $RI$. Therefore a full vector $FEM$ based on an anisotropic $PML$, calculates numbers of modes in a single run without any iterative procedure [28]. The $FEM$ is applied to the $PCF\; $to investigate the modes’ propagation property using Maxwell Equations [28]. The Maxwell equation for a waveguide having an arbitrary cross-section is expressed by Eq. (1) [28].

Matrixes represented by Eq. (4) and Eq. (5) are inserted in Eq. (1) to obtain the modified Maxwell Equation represented by Eq. (6) [28].

The constants ${s_x}$, ${s_y}$ and ${s_z}$ are the scaling parameters having complex values. These parameters have assigned value $\alpha $. The leaky mode analysis is performed by assuming $({\alpha = 1 - {\alpha_j}} )$. Thus an appropriate ${\alpha _j}$ can be selected for the adsorption or no adsorption scenario from the $PML$ layer. A parabolic profile assumed for the ${\alpha _j}$ is represented by Eq. (7) [28].

3. Structural designing of the proposed sensor

To date, different configurations of $PCF\; SPR$ structures are proposed like D shaped [30], internal metal-coated [31], external metal-coated [32], nanowire-based [33] and slotted based [34]. In internal metal and nanowire-based coating, air holes are selectively filled with $LA$, and the metal layer surrounds the core. This approach is challenging from a fabrication prespective [31]. In slotted-based and D-shaped $PCF$, despite metal coating is applied at the outer end, precise surface polishing is required, which again creates a complication during the practical fabrication of the $PCF$ [30]. Thus external metal deposition ($EMD$) approach is quite reliable and less challenging from the fabrication point of view [32]. This metal deposition approach is preferred over other deposition approaches and is also used extensively for real-time biosensing applications [35]. $PCF\; SPR$ sensing is a competitive and promising sensing technology, however at the device development front, they are again at an early stage. Most researchers have presented theoretical and computation models, demonstration, and proof of concept related to $PCF\; SPR$ sensors. The real time implementation of these theoretical models is still limited because of fabrication challenges [36]. Thus in this research work, a $PCF\; SPR$ sensor model based on $EMD$ technique is presented which enhances its chances of practical fabrication in future.

The schematic diagram of the proposed plasmonic biosensor in the two-dimensional ($2D$) $x - \; y$ plane is presented in Fig. 1(a). The air holes are arranged in two different configurations within the $PCF$ structure. The first air hole lattice consists of big air holes having dimension ${d_2}$ and is organized in the hexagonal dimensional pattern. These air holes are arranged in ${60^0}$ degree anti-progressive rotation pattern. The second air hole lattice consists of small air holes of dimension ${d_1}$ and organized in an octagonal dimensional pattern. These air holes are arranged in ${30^0}$ degree anti-progressive rotation pattern. The center-to-center distance between two consecutive air holes is called pitch (${\Lambda } $), which is selected as ${\Lambda } = 2\,\mathrm{\mu}m$. The dimensions of the small air holes and big air holes are ${d_1} = 0.2 \times {\Lambda } $ and ${d_2} = 0.5 \times {\Lambda } $ respectively. The combination of $Au$ and $TiO_2$ used as the plasmonic material for the presented sensor design. The thickness of these materials are considered as ${t_{Au}}\, = \; \,40\; nm\; $and ${t_{Ti{O_2}}}\, = \; \,80\; nm,$ respectively. The $LA$ sensing layer’s width is kept $1\; \mu m,$ and the thickness of $PML$ layer is held as $2\; \mu m$. Hence the optimum parameters for the proposed sensor design are tabulated in Table 2.

 

Fig. 1. (a) x- y plane representation of the proposed biosensor (2D) (b) Stacked preform of the presented sensor

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Table 2. Optimum sensor parameters

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The mutilated preform of the presented biosensor is shown in Fig. 1(b). All the dependable (solid) rods, thin-wall capillary, $PML$, and thicker wall capillary are stacked. Hence the $PCF$ structure can be assembled using the Stack and Draw process [37]. After the $PCF$ is manufactured, $Au\; $and $Ti{O_2}$ layers are deposited on the $PCF$ using the chemical vapor deposition ($CVD$) [38] technique, as discussed in [39]. It is also essential to consider that big air holes represented by 1 to 6$\; $are omitted to develop a hexagonal lattice of big air holes. Thus a simple structure of the $PCF$ is designed using the $EMD$ technique for enhancing its practical fabrication possibility.

Figure 2 represents the experimental $LA$ sensing set up with an optical spectrum analyzer ($OSA$) connected to study the wavelength shift. The IN and OUT ports contain $LA$ reserves whose $RI$ needs to be detected. The red and blue shifts in the resonance wavelength ($RW$) corresponding to the reference wavelength of the $LA$ are analyzed using an $OSA$. Thus by analyzing these wavelengths, unknown $LA$ can be detected accurately. The sensing ability of the setup can further be improved by adding a polarization controller.

 

Fig. 2. Pictorial representation of the liquid analyte sensing setup

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The background material used in the presented sensor is fused silica. The $RI$ of the fused silica is obtained using the Sellmeir equation represented by Eq. (8) [33].

$Ti{O_2}$ is considered as a good plasmonic material because when it is used along with $Au$ it provides necessary adhesion. When $Au$ is used as plasmonic material alone, it gets flaked off quickly because of the extreme pressure. The use of $Ti{O_2}$ with $Au$ provide enhanced stability to the sensor design. Beside $Ti{O_2}$ is also having a higher $RI$ value, thus acting as good transition material [25]. A relatively thick layer of $Ti{O_2}$ is attached over the $Au$ layer to provide necessary adhesion. The $RI$ of $Ti{O_2}$ is expressed by Eq. (10) [40].

The optical field distribution for the $x - \; pol.$ and $y{-}\; pol.$ is shown in Fig. 3. In $PCF\; SPR$ interaction, surface plasmon polariton ($SPP$) and leaky core mode get interfaced with each other at a specific wavelength. This wavelength is known as resonance wavelength ($RW$). The effective mode index’s fundamental part becomes precisely identical with the real part of $SPP\; $mode at resonance condition. $SPP$ mode is susceptible to the $RI\; $of the $LA$. When the $LA$ $RI$ is changed, a shift in the $RW\; $occurs from a higher to lower wavelength or vice versa. Hence the $LA$ is detected accurately.

Figure 3(a) and Fig. 3(c) represent the core mode for $x - \; pol.$ and $y - \; pol.$, respectively. $SPP$ mode formation for $x - \; pol.$ and $y - \; pol.$ is shown in Fig. 3(b) and Fig. 3(d), respectively.

 

Fig. 3. Core mode and plasmonic ($SPP$) mode representation for $LA$ having $RI$ value of $1.360\; RIU$

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The dispersion relationship developed between the $SPP$ mode, core mode, and the confinement loss ($CL$) for $LA$ having $RI$ of $1.360\; RIU$ for $x - \; pol.$ and $y - \; pol.$ is represented in Fig. 4(a) and Fig. 4(b), respectively. At the resonance condition, it is seen that electric field strength is good, along with both polarization modes. Concerning $x - \; pol.$, the $CL$ reported for the $LA$ having $RI$ $1.360\; RIU$ is $106.4\; dB/cm$ at the $RW$ of $1270\; nm.\; $Similarly, for $y - \; pol.$ the $CL$ reported for the analyte having $RI$ $1.360\; RIU$ is $108.8\; dB/cm$ at the $RW$ of $1240\; nm.$ At these $RW$, the phase matching between the $SPP$ mode and core mode is done correctly. Thus the peak power gets conveyed from the core mode to $SPP\; $mode, and the resonance condition is achieved.

 

Fig. 4. Relationship of dispersion between core guided mode and $SPP$ mode for$\; LA\; $having $RI$ value of $1.360\; RIU$ (a)$\; x - \; pol.\; $(b) $y - \; pol.$

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4. Experimental analysis of analytes for modeling a biosensor

Spectroscopy analysis of $LA$ presents information about that transmission and absorbance from the analyte samples and their impact on the $RI$ of the analyte. The spectroscopy analysis of the $LA$ suggests the result that due to $RI\; $change of just $0.02$ (i.e., $RI\; 1.340$-$1.360\; RIU$=$1.360$-$1.380\; RIU$=$0.02$) how transmission and absorbance get affected. Thus an ultrasensitive $PCF\; SPR\; RI$ sensor is designed in this work for regular monitoring of the $LA$ having $RI\; 1.340\; RIU$ to $RI\; 1.380\; RIU$. In this section, we lay the conditions for modeling a biosensor. Three $LA$ samples having a $RI$ value of $1.340\; RIU$, $1.360\; RIU$, and $1.380\; RIU$ are analyzed. A spectroscopy setup is developed and presented in this section, through which transmission and adsorption from these $LA$ are investigated. The objective of this investigation is to justify a need for the $PCF\; SPR$ biosensor, which presents ultra-sensitive behavior even to a minute change in the $RI.$ The transmission (%) and absorbance ($AU$) are the two critical parameters associated with the spectroscopy analysis of the $LA$. Fig. 5 presents the pictorial representation of the$\; LA$ analysis process inspired by the Beer lambert law [41].

According to Fig. 5, it can be seen that light traveling within the optical fiber is entering the sample compartment with intensity $({I_{in}}$). This intensity of light get reduced to $({I_{out}}$) when the light leaves the sample compartment. Thus mathematically, an amount of light is absorbed by the sample solution, which can be expressed as ${I_{absorbed}} = |{{I_{in}} - {I_{out}}} |$. Thus when the light of equal intensity passes through an $LA$ having $RI\; $value of $1.340\; RIU$, $1.360\; RIU$, and $1.380\; RIU$, the behavior of light will be entirely different for all three samples. This can also be understood that for a less concentrated solution having $RI$ value of $1.340\; RIU$, light transmission will be more, and the absorbance of light will be less. Similarly, for a more concentrated solution having $RI$ value of $1.380\; RIU$, light transmission will be relatively more minor, and absorbance will be more.

 

Fig. 5. Pictorial view of the spectroscopy analysis of the $LA$

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If the amount of light entering the analyte has an intensity ${I_{in}}$ and a light leaving the analyte is having an intensity ${I_{out}}$. Then the ratio of both of these lights is called transmission, [42], which is a unitless quantity. The transmission of light from a $LA$ is expressed by Eq. (11).

Transmission in percentage is expressed by Eq. (12) [43].

As discussed earlier that an amount of light is lost in between entering and leaving the analyte. This light is assumed to be absorbed by the $LA$ and is known as the absorbance of the analyte. It is represented by Eq. (13) [44].

The absorbance is also proportional to the path length of the sample holder, which is represented by Eq. (14) [45]. Its unit is $AU\; $and known as arbitrary unit.

Figure 6 represents the developed experimental setup for analyzing the $RI$ of the sample solutions. Three $LA$ investigated in this practical work are expired transformer oil ($RI\; 1.340\; RIU$) [46], ethyl alcohol ($RI\; 1.360\; RIU$) [47], and propyl alcohol ($RI\; 1.380\; RIU$) [48].

 

Fig. 6. Developed sensing setup to analyze transmission and absorbance from analytes samples

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The $LA\; $solutions are analyzed for their transmission and absorbance, and later the transmission (%) and absorbance ($AU$) from these sample solutions will be obtained. This analysis provides information about the behavior of $Tx\; (\%)$ and $Ab\; ({AU} )$ corresponding to different $RI$ values.

In this experiment, the $Tx\; (\%)$ corresponding to three different analytes, i.e., expire transformer oil ($ETO$), ethyl alcohol ($EA$), and propyl alcohol ($PA$) is obtained in the wavelength range of $200\; nm$ to $1200\; nm.\; $All three analytes have shown their unique behavior towards the halogen light.

In Fig. 7(a), the spectral behavior of the $ETO$ is represented in the black color. It offers $Tx\; (\%)$ of $30.67$, $64.80$, and $61.88,$ correspondings to the wavelength of $664.2\; nm$, $844.6\; nm,$ and $923.8\; nm$ respectively. The spectral behavior of the $EA\; $is represented in the red color. It shows $Tx\; (\%)$ of $39.16$, $75.38$, $72.18,$ and $60.87$ correspondings to the wavelength of $509.6\; nm$, $729.9\; nm$, $897.5\; nm,$ and $968.7\; nm$ respectively. Finally, the spectral behavior of the $PA$ is represented in the blue color. It shows $Tx\; (\%)$ of $57.08$, $61.03$, $57.71$, and $53.52$ correspondings to a wavelength of $617.4\; nm$, $734.7\; nm$, $898.7\; nm,$ and $979.1\; nm$ respectively. Figure 7(b) represents the spectral behavior of the analytes transmission (%) in the wavelength range of $800\; nm$ to $1000\; nm$.

 

Fig. 7. Transmission (%) for the $ETO$, $EA$, and $PA$ (a) Wavelength range of $200\; nm$ to $1200\; nm$ (b) Wavelength range of $800\; nm$ to $1000\; nm$

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Figure 8(a) represents the spectral behavior of the absorbance caused due to the three $LA.$ The spectral behavior of the $ETO$ is described in the red color. It shows $Ab\; ({AU} )$ of $0.138\; AU$, $0.118\; AU$, and $0.152\; AU$ at $579.2\; nm$, $848\; nm$, and $936.1\; nm$ respectively. The spectral behavior of the $EA$ is represented in the blue color. It shows $Ab\; ({AU} )$ of $0.176\; AU$ and $0.171\; AU$ at $888.8\; nm$ and $7967.6\; nm$ respectively.

 

Fig. 8. Absorbance ($AU$) for the $ETO$, $EA$, and $PA$ (a) Wavelength range of $200\; nm$ to $1200\; nm$ (b) Wavelength range of $800\; nm$ to $1000\; nm$

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Finally, the spectral behavior of the $PA$ is represented in the green color, which shows the $Ab\; ({AU} )$ of $0.206\; AU$, $0.212\; AU$ and $0.227\; AU$ at $709.1\; nm$, $879.2\; nm$ and $987.9\; nm$ respectively. Figure 8(b) represents the spectral behavior of the absorbance for the $LA$ in the wavelength range of $800\; nm$ to $1000\; nm$.

Table 3 presents the summarized information about the transmission (%) and absorbance ($AU$) obtained from the $ETO$, $EA$, and $PA$. This comparison is performed in the wavelength range of 9$00\; nm$ to $1000\; nm$ to determine the change in the $Tx\; \%$ and $Ab\; ({AU} )$.

Table 3. Transmission and absorbance for $ETO$, $EA$ and${\; }PA$

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Figure 9(a) represents that for $RI\; 1.340\; RIU$ highest amount of $Tx\; \%$ is obtained, followed by $Tx\; \%$ of$\; RI\; 1.360\; RIU$ and $Tx\; \%$ of $RI\; 1.380\; RIU$. Thus it is concluded that with the increase in the $RI$ of the $LA$, a decline in the $Tx\; \%\; $would occur.

 

Fig. 9. (a) Comparison of transmission (%) for $ETO$, $EA$ and $PA$ from 900$\; nm$ to $1000\; nm$ (b) Comparison of absorbance ($AU$) for $ETO$, $EA$ and $PA$ from 900$\; nm$ to $1000\; nm$

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Similarly, Fig. 9(b) represents that for $RI\; 1.340\; RIU$ lowest amount of $Ab\; ({AU} )$ is obtained, which increases with the increase in the value of the $RI\; 1.360\; RIU$ and $RI\; 1.380\; RIU$ respectively. Thus it concluded that with the rise in the $RI\; $of $LA$, an increase in the $Ab\; ({AU} )$ would occur.

Therefore, it is concluded that transmission and absorbance are inversely proportional to each other, and with the rise in $RI$ of $LA$, transmission and absorbance get directly affected. Thus the behavior of more such $LA$ can be detected from the proposed device, and an ultrasensitive $PCF\; SPR$ biosensor is an ideal device to detect such changes.

5. Performance analysis of the presented plasmonic biosensor for LA sensing

The proposed sensor performance is evaluated based on conventional sensing parameters like $WS$, $AS$, $SR$, $FOM$, etc. It has been observed that in many cases, that strong coupling is developed only across one polarization. Thus performance investigation is performed only across a single polarization mode. The proposed sensor design has obtained strong coupling across both polarization modes due to the symmetrical arrangement of air holes. According to the coupled-mode theory of light propagation, light travel in horizontal and vertical directions when traveling within a fiber [49].

Thus, the presented sensor’s performance is investigated for both $x - pol.$ and $y - \; pol.$ in this study. The numerical analysis is presented by optimizing the geometrical parameters of the sensor, like the thickness of plasmonic materials ${t_{Au}}$ and ${t_{TiO2}}$, pitch size, dimensions of big air holes, and measurements of small air holes.

5.1 Wavelength Sensitivity ($WS$) ($nm/RIU$)

Figure 10 represents the $CL\; $($dB/cm$) as the wavelength function for different $LA$. The $CL$ is expressed by Eq. (15) [5].

 

Fig. 10. Variation in confinement loss against change in wavelength (a) $x - \; pol.$ (b) $y - \; pol.$

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The deviation in the $RW$ is from $975\; nm$, $1025\; nm$, $1100\; nm$, $1160\; nm$, $1210\; nm$, $1270\; nm$, $1360\; nm$, $1450\; nm$, and $1550\; nm$ for $LA$ having $RI$ $1.340$, $1.345$, $1.350$, $1.355$, $1.360$, $1.365$, $1.370$, $1.375$ and $1.380\; RIU$ respectively for $x - \; pol$. Therefore the shift occurred in the $RW$ between the $RI$ is $50\; nm$, $75\; nm$, $60\; nm$, $50\; nm$, $60\; nm$, $90\; nm$, $90\; nm$ and $100\; nm$ for $LA$ having $RI$ $1.340$, $1.345$, $1.350$, $1.355$, $1.360$, $1.365$, $1.370$ and $1.375\; RIU$ respectively.

The$\; RW\; $for the $y - pol.$ has deviated from $990\; nm$, $1050\; nm$, $1120\; nm$, $1190\; nm$, $1240\; nm$, $1300\; nm$, $1370\; nm$, $1450\; nm$, and $1540\; nm$ for $LA$ having $RI$ $1.340$, $1.345$, $1.350$, $1.355$, $1.360$, $1.365$, $1.370$, $1.375$ and $1.380\; RIU$ respectively. Therefore the shift occurred in the $RW$ between the $RI$ is $60\; nm$, $70\; nm$, $70\; nm$, $50\; nm$, $60\; nm$, $70\; nm$, $80\; nm$ and $90\; nm$ for $LA$ having $RI$ $1.340$, $1.345$, $1.350$, $1.355$, $1.360$, $1.365$, $1.370$ and $1.375\; RIU$ respectively.

The $WS$ $(nm/RIU)\; $is measured by the wavelength interrogation method and is expressed by Eq. (16) [11].

Using, Eq. (16), $WS$ is calculated as$\; 10000\; nm/RIU$, $15000\; nm/RIU$, $12000\; nm/RIU$, $10000\; nm/RIU$, $12000\; nm/RIU$, $18000\; nm/RIU$, $18000\; nm/RIU$ and $20000\; nm/RIU$ for $LA$ having $RI\; 1.340$, $1.345$, $1.350$, $1.355$, $1.360$, $1.365$, $1.370$ and $1.375\; RIU$ respectively considering $x - pol.$

$WS$ for $y - {\; }pol.$ is calculated as $12000{\; }nm/RIU$, 14$000{\; }nm/RIU$, $14000{\; }nm/RIU$, $10000{\; }nm/RIU$, $12000{\; }nm/RIU$, $14000{\; }nm/RIU$, $16000{\; }nm/RIU$ and $18000{\; }nm/RIU$ for${\; }LA$ having $RI{\; }1.340$, $1.345$, $1.350$, $1.355$, $1.360$, $1.365$, $1.370$ and $1.375{\; }RIU$ respectively.

Thus the average $WS$ is $14375\; nm/RIU$ for $x - \; pol.$ and $13750\; nm/RIU$ for $y - \; pol.$, respectively.

5.2 Amplitude sensitivity (AS) (1/RIU)

Figure 11 represents $AS$ as the function of the wavelength. It is calculated using the amplitude interrogation method and is expressed by Eq. (17) [50].

More precisely, the $AS$ is changed from $720.5\; RI{U^{ - 1}}$, $850.4\; RI{U^{ - 1}}$, $937.6\; RI{U^{ - 1}}$, $1058\; RI{U^{ - 1}}$, $\; 1193\; RI{U^{ - 1}}$, $1490\; RI{U^{ - 1}}$, $\; 1802\; RI{U^{ - 1}}$ and $2158\; RI{U^{ - 1}}$ corresponding to $x - \; pol.$ for $LA$ having $RI\; 1.340$, $1.345$, $1.350$, $1.355$, $1.360$, $1.365$, $1.370$, and $1.375\; RIU$ respectively, shown in Fig. 11(a).

 

Fig. 11. Variation in amplitude sensitivity against change in wavelength (a) $x - \; pol.$ (b) $y - \; pol.$

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$AS$ for $y - {\; }pol.{\; }$is changed from $413.3{\; }RI{U^{ - 1}}$, ${\; }608.4{\; }RI{U^{ - 1}}$, ${\; }799.8{\; }RI{U^{ - 1}}$, $1017{\; }RI{U^{ - 1}}$, ${\; }1294{\; }RI{U^{ - 1}}$, $1675{\; }RI{U^{ - 1}}$, $2217{\; }RI{U^{ - 1}}$ and $3167{\; }RI{U^{ - 1}}$ for $LA$ having $RI$ $1.340$, $1.345$, $1.350$, $1.355$, $1.360$, $1.365$, $1.370$, and $1.375{\; }RIU$ respectively, represented in Fig. 11(b).

Therefore from the proposed sensor configuration, a maximum $AS$ of $2158\; RI{U^{ - 1}}$ and $3167\; RI{U^{ - 1}}$ is obtained for $x - \; pol.$ and $y - \; pol.$, respectively.

5.3 Sensor resolution (SR) (RIU)

It is considered a determining parameter through which the ability of the sensor to reveal a slight change in $LA$ $RI$ can be analyzed. It is calculated with the assistance of Eq. (18) [40].

5.4 Figure of merit (FOM) and full wave half maximum (FWHM)

A Figure of merit ($FOM$) is considered a critical parameter to check the detection ability of the sensor. $FOM$ is expressed by Eq. (19) [51].

5.5 Fitting characteristics of a resonance wavelength with refractive index

Linear polynomial fitting of the $RW$ with $RI\; $is vital from the point of sensor optimization. Polynomial fitting of the $RW$ with the $RI$ for the $degree\; (1 )$ and $degree\; (2 )$ is shown in Fig. 12. Linear polynomial fitting of $degree\; (1 )$ and $degree\; (2 )$ for $x - \; pol.$ is shown in Fig. 12(a-b), respectively. Similarly, the linear polynomial fitting of $degree\; (1 )$ and $degree\; (2 )\; $for$\; y - \; pol.$ is shown in Fig. 12(c-d), respectively. The fitting parameters like small scale error ($SSE$), R-square, adjusted R-square, and root mean square error ($RMSE$) along with the developed linear and quadratic relationships are tabulated in Table 4. It is evident from Table 4 that R-square has obtained maximum values for the degree (2) concerning $x - \; pol.$ and $y - \; pol.$, respectively. It is also noted that the R-square value for all four cases is close to unity with indicates excellent fitting to sensor response

 

Fig. 12. Polynomial fitting of the $RW\; $with $RI$ of $LA$ (a) $x - \; pol.$ ($Degree\; 1$) (b) $x - \; pol.$ ($Degree\; 2$) (c) $y - \; pol.$ ($Degree\; 1$) (d) $y - \; pol.\; $($Degree\; 2$)

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Table 4. Fitting parameters between refractive index and resonant wavelength

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Table 5 presents the detailed information of the various parameters obtained from the designed biosensor for different values of $RI.$

Table 5. Sensing parameters for the proposed biosensor for different values of the refractive index

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6. Effect on sensing parameters by changing the geometrical parameters of the proposed sensor

6.1 Increasing the $Au$ and $Ti{O_2}$ layer thickness by 50 nm and 90 nm, respectively

In this section, the results of the change in $CL$, $WS\; $and $AS$ are presented by increasing the $Au$ and $Ti{O_2}$ layer thickness. The thickness of the $Au$ layer is increased from $40\; nm\; $to $50\; nm,$ similarly the thickness of the $Ti{O_2}$ layer is increased from $80\; nm\; $to $90\; nm$, respectively. The thickness of both materials is increased together, and the analysis is performed on this configuration. It is important to note that the rest geometrical parameters remain the same as optimum parameters. Figure 13 represents the $CL$ spectrum for the proposed biosensor. It can be observed that the $RI$ of $LA$ is directly proportional to the $CL$. The $CL$ spectrum against wavelength ($nm$) for $x - \; pol.$ and $y - pol.$ are shown in Fig. 13(a) and Fig. 13(b), respectively.

 

Fig. 13. Variation in confinement loss versus wavelength by increasing the $Au$ and $Ti{O_2}\; $layer thickness (a) $x - \; pol.$ (b) $y - \; pol.$

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From, Fig. 13(a) and Fig. 13(b), it is observed that $CL$ has changed from $53.73\; dB/cm$ to $151.9\; dB\; /cm$ for $x - \; pol.$ and $54.66\; dB/cm$ to $154.3\; dB/cm$ for $y - \; pol.\; $respectively which is less than the peak $CL$ at optimum layer thickness.

From Fig. 13(a), the deviation in the $RW$ is observed from $1220\; nm$, $1260\; nm$, $1320\; nm$, $1380\; nm$, $1460\; nm$, $1540\; nm$, $1620\; nm$, $1710\; nm$, and $1800\; nm$ for $LA$ having $RI$ $1.340$, $1.345$, $1.350$, $1.355$, $1.360$, $1.365$, $1.370$, $1.375$ and $1.380\; RIU$ respectively for $x - \; pol.$ Therefore, the shift in the $RW$ is 40 nm, 60 nm, 60 nm, 80 nm, 80 nm, 80 nm, 90 nm and 90 nm for LA having RI 1.340 $1.345$, $1.350$, $1.355$, $1.360$, $1.365$, $1.370$ and $1.375\; RIU$ respectively.

From Fig. 13(b), the deviation in the $RW$ is observed from $1200\; nm$, $1240\; nm$, $1280\; nm$, $1340\; nm$, $1400\; nm$, $1480\; nm$, $1570\; nm$, $1660\; nm$, and $1760\; nm$ for $LA$ having $RI$ $1.340$, $1.345$, $1.350$, $1.355$, $1.360$, $1.365$, $1.370$, $1.375$ and $1.380\; RIU$ respectively for $y - \; pol.$ Therefore the shift occurred in the $RW$ between the $RI$ is $40\; nm$, $40\; nm$, $60\; nm$, $60\; nm$, $80\; nm$, 9$0\; nm$, $90\; nm$ and $100\; nm$ for $LA$ having $RI$ $1.340$, $1.345$, $1.350$, $1.355$, $1.360$, $1.365$, $1.370$ and $1.375\; RIU$ respectively.

Using Eq. (16), $WS$ is obtained as$\; 8000\; nm/RIU$, $12000\; nm/RIU$, $12000\; nm/RIU$, $16000\; nm/RIU$, 16$000\; nm/RIU$, $16000\; nm/RIU$, $18000\; nm/RIU$ and $18000\; nm/RIU$ for $LA$ having $RI$ $1.340$, $1.345$, $1.350$, $1.355$, $1.360$, $1.365$, $1.370$ and $1.375\; RIU$ respectively for $x - pol.$

$WS$ for $y - {\; }pol.$ is $8000{\; }nm/RIU$, $8000{\; }nm/RIU$, $12000{\; }nm/RIU$, $12000{\; }nm/RIU$, $16000{\; }nm/RIU$, $18000{\; }nm/RIU$, $18000{\; }nm/RIU$ and $20000{\; }nm/RIU$ for $LA{\; }$having $RI$ $1.340$, $1.345$, $1.350$, $1.355$, $1.360$, $1.365$, $1.370$ and $1.375{\; }RIU$ respectively.

Thus the average $WS$ be $14500\; nm/RIU$ and $14000\; nm/RIU$ for $x - pol.$ and $y - \; pol.$, respectively.

Also, the $AS$ is changed from $821.9{\; }RI{U^{ - 1}}$ to $2086.5{\; }RI{U^{ - 1}}$ for $x - \; pol.$ and $827{\; }RI{U^{ - 1}}$ to $2717{\; }RI{U^{ - 1}}$ for $y - \; pol.$, respectively.

More precisely, the $AS$ is changed from $821.9\; RI{U^{ - 1}}$, $854.2\; RI{U^{ - 1}}$, $911.2\; RI{U^{ - 1}}$, $993.6\; RI{U^{ - 1}}$, $1114\; RI{U^{ - 1}}$, $1294\; RI{U^{ - 1}}$, $1582\; RI{U^{ - 1}}$ and $2086\; RI{U^{ - 1}}$ corresponding to $x - \; pol.$ for $LA$ having $RI$ $1.340$, $1.345$, $1.350$, $1.355$, $1.360$, $1.365$, $1.370$, and $1.375\; RIU$ respectively, shown in Fig. 14(a). $AS$ is changed from $827\; RI{U^{ - 1}}$, $867.5\; RI{U^{ - 1}}$, $979.1\; RI{U^{ - 1}}$, $1020\; RI{U^{ - 1}}$, $1308\; RI{U^{ - 1}}$, $1577\; RI{U^{ - 1}}$, $1991\; RI{U^{ - 1}}$ and $2717\; RI{U^{ - 1}}$ for $LA$ having $RI\; 1.340$, $1.345$, $1.350$, $1.355$, $1.360$, $1.365$, $1.370$, and $1.375\; RIU$ respectively, for $y - \; pol.$, as shown in Fig. 14(b).

 

Fig. 14. Variation in amplitude sensitivity against change in wavelength by increasing the $Au\; $and $Ti{O_2}\; $layer thickness (a) $x - \; pol.$ (b) $y - \; pol.$

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Therefore from the proposed sensor configuration, a maximum $AS$ of $2086\; RI{U^{ - 1}}$ and $2717\; RI{U^{ - 1}}$ is obtained for $x - \; pol.$ and $y - \; pol.$, respectively.

Thus from this investigation, it has been observed that the overall $WS$ increases, whereas the $CL$ and $AS$ decrease when the combined thickness of the plasmonic material is increased. This change in the sensing behavior is observed because when the thickness of the plasmonic material is increased. It resists the evanescent field’s penetration, resulting in a reduction in the strength of $SPW$ [53].

6.2 Analysis of variation in ${d_1}$, ${d_{2}}$ and $ \wedge $ by ${\pm} 5{\%}$

In this section, variations in the sensing parameters are analyzed by varying the geometrical parameters. Researchers used to demonstrate the ability of their designed sensor by changing the geometrical parameter dimensions. Reeve et al. [53] showed the performance of their designed sensor with ${\pm} 1\%$ fabrication tolerance. Later with the advancement in the field of $PCF\; SPR$ sensing researcher began to test their sensors with ${\pm} 2\%$ fabrication tolerance [33], ${\pm} 3\%$ fabrication tolerance [54], ${\pm} 4\%$ fabrication tolerance [55], etc. The fabrication tolerance of the proposed sensor is tested for ${\pm} 5\%$ variation in the geometrical parameters. Later the geometrical dimension of a particular structural parameter is varied by ${\pm} 1\%$, ${\pm} 2\%$, ${\pm} 4\%$, etc., keeping other structural parameters unchanged. Then the effect on sensing parameters like $CL$, $WS$, and $AS$ is monitored for these variations in the structural parameters. The sensing parameters reported after variations are compared with the optimum sensing parameters, and thus the change in the parameter value is obtained.

Firstly, the diameter ${d_1}$ of the presented sensor is varied by ${\pm} 5\%.$ Fig. 15(a) shows the $CL$ spectrum for the $x - \; pol.$ By reducing ${d_1}$ by $- 5\%$, $CL$ is decreased by $0.4\; dB/cm$ and $2.8\; dB/cm$ for $LA$ having $RI\; 1.380\; RIU\; $and $RI\; 1.375\; RIU$, respectively. By increasing ${d_1}$ by $+ 5\%$, $CL\; $is increased by $10.6\; dB/cm\; $and $3.7\; dB/cm$ for $LA\; $having $RI\; 1.380\; RIU$ and $RI\; 1.375\; RIU$, respectively. Figure 15(b) shows the $CL$ spectrum for the $y - \; pol.$ By reducing the ${d_1}$ by $- 5\%$, $CL\; $has decreased by $0.7\; dB/cm\; $and $3.1\; dB/cm\; $for $LA$, having $RI\; 1.380\; RIU\; $and $RI\; 1.375\; RIU$, respectively. By increasing the ${d_1}$ by $+ 5\%$, $CL\; $is increased by $11.1\; dB/cm$ and $4.1\; dB/cm$ for $LA$ having $RI\; 1.380\; RIU\; $and $RI\; 1.375\; RIU$, respectively. Figure 15(c) shows $AS\; $spectrum for the $x - \; pol.$ The $AS$ is increased by $704\; RI{U^{ - 1}}$ for $- 5\%{\; }{d_1}$ and decreased by $1093\; RI{U^{ - 1}}$ for $+ \,\; 5\%$ ${d_1}\; $for $LA$ having $RI\; 1.375\; RIU$, respectively. Figure 15(d) shows $AS$ spectrum for the $y - \; pol$. The $AS$ is increased by $907\; RI{U^{ - 1}}$ for $- 5\%{\; }{d_1}$ and reduced by $860\; RI{U^{ - 1}}$ for $+ 5\%\; {d_1}$ corresponding to $LA\; $having $RI\; 1.375\; RIU$, respectively. Therefore no change in the $WS$ is recorded for $x - \; pol.$ and $y - \; pol.$ respectively. Whereas $CL$ has shown less sensitive behavior and $AS$ have shown more sensitive behavior corresponding to a slight change in geometrical parameters ${d_1}$.

 

Fig. 15. Variation in confinement loss against wavelength by varying ${d_1}$ by ${\pm} 5\%$ (a) $x - \; pol.$ (b) $y - \; pol.$; Variation in amplitude sensitivity against wavelength (c) $x - \; pol.$ (d) $y - \; pol.$

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Secondly, the dimension ${d_{2}}\; $of the big air, holes are varied, and its effect on the $CL$ and $AS$ is analyzed. Figure 16(a) shows the $CL$ spectrum for the $x - \; pol.\; $By reducing ${d_{2}}$ by $- 5\%$, $CL$ is decreased by $18.1\; dB/cm$ and $18.3\; dB/cm$ for $LA$ having $RI\; 1.380\; RIU\; $and $RI\; 1.375\; RIU$, respectively. By increasing ${d_{2}}$ by $+ 5\%$, $CL$ is increased by $36.6\; dB/cm\; $and $22.5\; dB/cm$ for $LA\; $having $RI\; 1.380\; RIU$ and $RI\; 1.375\; RIU$, respectively. Figure 16(b) shows the $CL$ spectrum for the $y - \; pol.$ By reducing the ${d_{2}}$ by $- 5\%$, $CL$ has decreased by $18.4\; dB/cm\; $and $18.6\; dB/cm\; $for $LA$ having $RI\; 1.380\; RIU\; $and $RI\; 1.375\; RIU$, respectively. By increasing the ${d_{2}}$ by $+ 5\%$, $CL\; $is increased by $36.8\; dB/cm$ and $22.5\; dB/cm$ for $LA$ having $RI\; 1.380\; RIU\; $and $RI\; 1.375\; RIU$, respectively. Figure 16(c) shows $AS\; $spectrum for the $x - \; pol.\; $The $AS$ is increased by$\; 1463\; RI{U^{ - 1}}$ for $- 5\%{\; }{d_{2}}$ and decreased by $1072\; RI{U^{ - 1}}$ for $+ \,\; 5\%$ ${d_1}\; $for $LA$ having $RI\; 1.375\; RIU$, respectively. Figure 16(d) shows $AS$ spectrum for the $y - \; pol.$ The $AS$ is increased by $1394\; RI{U^{ - 1}}$ for $- 5\%{\; }{d_{2}}$ and reduced by $1504\; RI{U^{ - 1}}$ for $+ 5\%\; {d_{2}}$ corresponding to $LA$ having $RI\; 1.375\; RIU$, respectively. Therefore no change in the $WS$ is recorded for both $x - \; pol.$ and $y - \; pol.$, respectively. Here $CL$ has shown more sensitive behavior as compared to change in structural parameter ${d_1}\; $and $AS$ have shown sensitive behavior towards a slight change in geometrical parameters ${d_{2}}$.

 

Fig. 16. Variation in confinement loss against wavelength by varying ${d_{2}}$ by ${\pm} \,\; 5\%$ (a) $x - \; pol.$ (b) $y - \; pol.$; Amplitude sensitivity versus wavelength (c) $x - \; pol.$ (d) $y - \; pol$.

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Finally, the pitch (${\Lambda } $) is varied for the proposed sensor, and its effect on the $CL$ and $AS$ is analyzed. Figure 17(a) shows the $CL$ spectrum for the $x - \; pol.$ By reducing ${\Lambda } $ by $- 5\%$, $CL\; $is decreased by $13.8\; dB/cm$ and $15.2\; dB/cm$ for $LA$ having $RI\; 1.380\; RIU\; $and $RI\; 1.375\; RIU$, respectively. By increasing ${\Lambda } $ by $+ 5\%$, $CL$ is increased by $29.9\; dB/cm\; $and $17.1\; dB/cm$ for $LA$ having $RI\; 1.380\; RIU$ and $RI\; 1.375\; RIU$, respectively. Figure 17(b) shows the $CL$ spectrum for the $y - \; pol.$ Reducing the ${\Lambda } \; $by $- 5\%$, $CL$ has decreased by $13.5\; dB/cm\; $and $2.8\; dB/cm\; $for $LA$ having $RI\; 1.380\; RIU\; $and $RI\; 1.375\; RIU$, respectively. By increasing the ${\Lambda } $ by $+ 5\%$, $CL$ is increased by $2.8\; dB/cm$ and $16.7\; dB/cm$ for $LA$ having $RI\; 1.380\; RIU\; $and $RI\; 1.375\; RIU$, respectively. Figure 17(c) shows $AS\; $spectrum for the $x - \; pol.$ The $AS$ is increased by $558\; RI{U^{ - 1}}$ for $- 5\%{\; }{\Lambda } \; $and decreased by $1072\; RI{U^{ - 1}}$ for $+ \,\; 5\%$ ${\Lambda } \; $for $LA$ having $RI\; 1.375\; RIU$, respectively. Figure 17(d) shows $AS$ spectrum for the $y - \; pol.$ The $AS$ is increased by $3352\; RI{U^{ - 1}}$ for $- 5\%{\; }{\Lambda } $ and reduced by $839\; RI{U^{ - 1}}$ for $+ 5\%\; {\Lambda } $ for $LA$ having $RI\; 1.375\; RIU$, respectively. Finally, here also no change in the $WS\; $is recorded for both $x - \; pol.$ and$\; y - \; pol.$ respectively. Whereas $CL$ and $AS$ have shown sensitive variation corresponding to a slight change in the ${\Lambda } $ dimension.

 

Fig. 17. Variation in confinement loss against wavelength by varying ${\Lambda}$ by ${\pm} 5\%$ (a) $x - \; pol.$ (b) $y - \; pol.$; Amplitude sensitivity versus wavelength (c) $x - \; pol.$ (d) $y - \; pol.$

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Table 6 compares the proposed biosensor’s sensing parameters with other dual-polarized sensors developed to date. The comparison is performed based on sensing parameters like $WS$, $AS$, $SR$, $FWHM$, and $FOM$. The proposed sensor has obtained a $WS$ of $20000\; nm/RIU\; $and $18000\; nm/RIU$ for $x - pol.$ and $y - \; pol.$, respectively, which is better than the $WS$ of other sensors. The $AS$ obtained from the proposed sensor for both polarization modes is higher than the earlier reported sensors. The $SR$ obtained from the proposed sensor is better than the $SR$ of other reported sensors. None of the earlier reported sensors have presented the $FWHM\; $parameter for their sensor design. The $FOM$ is directly indicated by Refs. [20] and [17] without providing information about $FWHM$. Thus the proposed plasmonic biosensor is suitable for sensing $LA$ with a moderate range of the $RI$. The proposed sensor also presents better and complete sensing parameters for $x - pol.$ and$\; y - \; pol.$ than the existing sensors.

Table 6. Performance comparison of the presented sensor with earlier reported sensors

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7. Conclusion

A sensitive and anisotropic plasmonic biosensor is presented in this article for testing of $LA$ having $RI$ $1.340\; RIU$ -$1.380\; RIU$. The sensing capability of the proposed sensor is investigated using the $FEM$ method. The geometrical parameters of the sensor are optimized for achieving maximum sensitivity. The maximum wavelength sensitivity of $20000\; nm/RIU$ and $18000\; nm/RIU$ is obtained for $x - \; pol.$ and $y - pol.$, respectively. The maximum amplitude sensitivity of $2158\; RIU{\; ^{ - 1}}$ and$\; 3167\; RIU{\; ^{ - 1}}$ is obtained for $x - pol.$ and $y - \; pol.$, respectively. Moreover, maximum sensor resolution of $5.00 \times {10^{ - 6}}$ $RIU\; $and $5.55 \times {10^{ - 6}}{\; }RIU\; $is obtained for $x - pol.$ and $y - \; pol.\; $respectively. A linear relationship between the resonant wavelength and $RI$ produces a maximum value of $R$-Square, i.e., $0.9972$ for $x - pol.$ and $0.9978$ for $y - \; pol.$ corresponding to a degree (2). The figure of merit obtained from the proposed sensor is $93.45\; RIU{\; ^{ - 1}}$ for $x - pol.$ and $105.88\; RIU{\; ^{ - 1}}$ for $y - \; pol.$ All the sensing parameters are obtained for the $LA$ having $RI\; 1.375\; RIU$. The spectroscopy analysis of the $LA\; $with $RI\; 1.340\; RIU$, $RI\; 1.360\; RIU$, and $RI\; 1.380\; RIU$ produce interesting outcomes that, with the increase in $RI$ of $LA$, transmission (%) gets decreased, and the absorbance ($AU$) get increased. Thus, due to structural simplicity, fabrication feasibility, and compassionate performance, the presented biosensor can be considered a suitable candidate for detecting various $LA$ for a moderate $RI$ range.