Performance Enhancement of Gold Coated D-shaped PCF Sensor using Monolayer MoS2

In this paper, we theoretically propose a surface plasmon resonance (SPR) - based D - shaped photonic crystal fiber (PCF) sensor with gold coating and an overlayer of molybdenum disulfide (MoS 2 ) 2D material. We design the PCF sensor using the square lattice arrangement of airholes for sensing the analytes of refractive index ranging from 1.33 to 1.42, which includes most of the bio - samples. Further, we optimize the proposed sensor in terms of two different air hole radii, pitch distance, thickness of the gold layer, and 2D material. The details numerical results corroborate that the sensor exhibits a wavelength sensitivity of 20,200 nm/RIU without coating of MoS 2 layer. However, it does exhibit an enhanced wavelength sensitivity of 22,800 nm/RIU with a high spectral resolution of 4.38 × 10 - 6 RIU when a monolayer of MoS 2 is coated onto the gold layer. In addition to wavelength sensitivity, we also compute the amplitude sensitivity and is 752 RIU - 1 with a resolution of 1.34×10 - 6 RIU. Besides, we carry out the tolerance studies to ensure the robustness of the proposed sensor. Finally, we also analyze the linearity of the sensor through the R 2 value and the same is 0.9688. Thus, the proposed D - shaped MoS 2 coated PCF sensor may find potential application in the detection of chemical and biological samples.


Introduction
In the past two decades, super-sensitive detection of chemical and biological samples has been made feasible with the invention of PCF sensors.PCF has an advantage over conventional optical fiber due to its light manipulation capabilities, as it encompasses the freedom of structural engineering [1].From the day of the invention of PCF in the year 1996 by Philip Russell, many PCF sensor models have been investigated by exploiting the various structural parameters [2].The different proposed models include external metal layer coating [3], internal metal coating [4], and side polished fiber [5].Internal metal coating and analyte filling are highlly challenging and and the process is also not economically viable.In a side polished fiber, as the plasmonic material lies closer to the core, the interaction between core mode and surface plasmon mode can be enhanced by polishing the PCF to a certain polishing depth.More control over the excitation is possible by tuning the polishing depth [6].Along with different models, various lattice geometries of air holes have been explored such as square [7], hexagonal [8] and circular [9] arrangements, etc.
There are many fiber sensors that work based on the various principles such as evanescent wave and surface plasmon, etc. PCF sensors work by exploiting the principle of surface plasmon resonance [10].Surface plasmon is a weakly propagating wave excited by an incident transverse magnetically polarized electromagnetic field.The resonant absorption that occurs between the p-polarized incident light and the p-polarized surface plasmon wave is SPR.SPR takes place when the incident light interacts with the plasmonic metal layer and it enhances the resonance of free electrons over the metal-dielectric interface.As this localized surface plasmon wave is very sensitive to the change in the surrounding refractive index (RI), it plays an important role in measuring the resonance wavelength shift [11].Yet, the SPR optical sensors based on metal-coated prism-based Kretschman and Otto configurations are bulky and require sophisticated optomechanical components.This limitation curbs the use of SPR sensors in a wide range.To overcome such limitations, PCF SPR sensor which has a flexible and tunable structural configuration has been proposed [12].The flexibility, costeffectiveness, high sensitivity, portability, real-time detection capability, remote sensing and label-free sensing of the SPR based PCF sensor makes it a promising candidate for sensing.Hence, nowadays, PCF based biosensors are widely used in the drug industry, liquid/gas detection, food quality measurement, biomedical and biochemical applications [13].
To enhance the detection capability and sensitivity of SPR based PCF sensors, various novel materials and hybrid structures have been explored in recent years [14,15].For example, various plasmonic metal coatings like gold (Au), silver (Ag), indium tin oxide (ITO), etc have been integrated with 2D materials for enhanced sensing of the samples [16,17].Due to high chemical stability and corrosion resistance over other metals, Au is substantially used as a plasmonic material.However, the only drawback is it exhibits less biomolecular adsorption.This pitfall can be resolved by coating additional 2D material over the Au metal.Coating 2D materials over the metal surface as a biomolecular recognition layer helps to devise a highly sensitive sensor as it supports enhanced biomolecule absorption [18].Very recently, coating of an additional layer of 2D material, namely, titanium carbide (Ti3C2Tx) over Au layer on top of the D-shaped surface plasmon PCF biosensor has been reported [19].Here, it is observed that coating Ti3C2Tx along with Au increases the sensitivity 6.5 times when compared to that of without Ti3C2Tx coating.In 2018, Wu et.al proposed an Al/ Ti3C2Tx coated SPR biosensor and proved the boost in sensitivity by 46.3% after coating it with Ti3C2Tx [20].MXENE materials like Ti3C2Tx are unstable and get oxidized easily.To delay the oxidation process, additional synthesis steps should be followed [21].This shortcoming makes the MXENE material less alluring.2D transition metal dichalcogenides like MoS2 are very stable and they become promising materials in sensing applications due to their large surface area, hydrophobic surface, large tunable band gap [22,23], high optical absorption efficiency [24], etc.A large bandgap of the 2D MoS2 can be obtained using monolayer MoS2 nanosheets (thickness ~ 0.65 nm).Controlled large-scale synthesis of monolayer to fewlayer MoS2 nanosheets is possible by chemical vapor deposition (CVD) technique [25,26].In 2019, Shivam Singh et.al proposed a multilayer Au/ MoS2/ Graphene PCF sensor with a sensitivity of 14,933.34nm/RIU.The experimental realization of multilayer coating has been made possible in recent days with the development made in precise coating technology [18].
In this manuscript, we propose a simple D-shaped SPR based PCF sensor with a square lattice airhole arrangement coated with hybrid metal (Au)/ 2D material (MoS2) for sensing RI of a wide range from 1.33 to 1.42.To propose the compact PCF sensor, minimum number of airholes has been impregnated in the PCF structure.The side polished structure is adapted to ease the excitation in the plasmonic layer.Air holes of 3 different radii have been chosen where the air holes in the top face of the core region have less radius compared to all other air holes.This will considerably allow more light from the core region to propagate and excite the surface plasmons.Two air holes in the bottom of the core region have a relatively large radius compared to the other air holes to support the tight light confinement.Along with the coating of Au, an overlayer of 2D material of MoS2 has been coated onto the Au layer.This work confirms the enhancement of sensitivity on coating MoS2 nanosheet of monolayer thickness.This study also emphasizes the importance of the selective thickness of MoS2 being coated onto the metal surface.Figure 1 depicts the cross-section view of the D-shaped SPR based PCF sensor.Here, the top portion that is impregnated with air holes have been removed by polishing it to D-shape.The model encapsulates air holes of 3 different radii with square lattice arrangement.The front row of air holes on the top face of the PCF structure has a radius of 0.8 μm (R1).This reduced radius of the air holes ensures more light propagation from the core mode to the surface plasmon mode.The two middle air holes located in the bottom surface of the PCF have a larger radius of 1.5 μm (R2).The other air holes have the same radius of 1 μm (R3).The distance between the two adjacent air holes, which is the pitch (Λ), is set as 4 μm.The polished surface is coated with Au metal of thickness (tAu) 45 nm.As an overlayer, a single layer MoS2 nanosheet of thickness (  2 ) 0.65 nm is coated on top of the Au metal.The analyte chamber is placed upon the MoS2 nanosheet for external sensing.The sensing performance of the proposed sensor has been studied for a wide range of RIs from 1.33 to 1.42.Here, finite element method is used for designing PCF by using COMSOL software.The PCF is overlaid with a phase matching layer (PML) of thickness 1 μm as a radiation absorber.
Gold is selected as a plasmonic material as it exhibits high resonance wavelength shift, less sensitive to humidity and temperature and also it is a chemically stable element [28].The relative permittivity of gold is acquired from Drude-Lorentz model [29].
Here,  ∞ = 5.9673 is the permittivity of Au at higher frequency,  is the angular frequency,   2 ⁄ = 2113.6THz is the plasma frequency,   2 = 15.92 ⁄ THz is the damping frequency and ∆ (=1.09) is the weighing factor.The Lorentz oscillator strength and spectral width are represented by   2 ⁄ = 650.07THz and   2 ⁄ = 104.86THz, respectively.
Where,  0 = -27.239, 1 = -0.60969, 2 = 0.0056183, Experimental fabrication of the proposed PCF model can be done through highly controlled stack and draw method using a pre-modelled silica preform.As this simple model incorporates less number of airholes, stacking process is easy when compared to the other proposed models.Then it is polished to obtain a D-shaped structure.

Optimization of structural parameters of proposed sensor
After designing the geometry of the proposed PCF sensor, the structure has to be evaluated by optimizing all the structural parameters.The optimization process is done through the conventional brute-force method [11].Here, one parameter is varied at a time by keeping all the other parameters as constants.Figure 2 shows the phase-matching plot incorporating the dispersion relation of the core mode (red curve) and surface plasmon mode (blue curve) along with the confinement loss spectra (black curve).It is obtained by using the structural parameters: na = 1.41, tAu = 40 nm, R1 = 1 μm, R2 = 1.5 μm, R3 = 1 μm, Λ = 4 μm.The refractive index of core mode and surface plasmon mode decreases by increasing the wavelength.The maximum coupling between these modes occurs at 930 nm wavelength which is apparent from the intersection point of the core mode and surface plasmon mode as shown in the Figure 2.This intersection point is the resonance point.As the modes obey phase-matching condition, the amount of energy transfer between them gets enhanced.At this point, the confinement loss is maximum and the same is estimated to be 2 dB/cm.The confinement loss is calculated using the following equation [30].
= 8.686 ×  0 × (   ) × 10 4 (/) (6) Here,  0 is the wave number and (   ) is the imaginary part of effective refractive index.The phase matching point gets shifted when there is a change in external RI.This makes the resonance wavelength to fluctuate with respect to the change in RI.By considering the optimization of the PCF structural parameters, gold layer thickness, two different air hole radii, pitch and thickness of 2D material coating have been varied.To study the sensor performance, we consider the refractive index of the analyte ranging from 1.33 to 1.42.But, for optimization, we consider only the RIs of 1.40, 1.41 and 1.42.Figure 3 illustrates the change in the confinement loss curve for x-polarization with respect to the incident wavelength for various thicknesses of gold layer from 40 nm to 50 nm with a step size of 5 nm.The performance of the SPR sensor crucially relies on the thickness of the coated metal layer.While varying the thickness of the gold layer, the other parameters are kept constant.Here, we observe that the confinement loss decreases with the increase in thickness.This is due to the fact there is a decrease in the coupling efficiency between the fundamental mode and surface plasmon mode when thickness is increased.Also, the resonant wavelength is red-shifted.The maximum peak shifts are 168, 192 and 220 nm for the corresponding thicknesses of 40, 45 and 50 nm, respectively.The peak shift for the 50 nm thickness is maximum when compared to the other thicknesses.However, the loss spectrum gets flattened after the wavelength of 1.2 μm.Thus, 45 nm is optimized as a final gold layer thickness considering its peak resonant shift and its full-width half maximum. Figure 4 shows the variation of confinement loss for different front-row air hole radii, R1 on the top face of the PCF.The radius of the front row air holes is varied from 1 μm to 0.8 μm.These airholes with smaller radius relaxes the tight confinement of light inside the solid core region and allows further to penetrate towards the plasmonic metal layer.This will enhance the interaction of the light with the plasmonic layer.It can be noted from Figure 4 that the confinement loss peak increases by decreasing the radius of the airhole.For the analyte values of 1.40, 1.41 and 1.42, the maximum peak resonant wavelength shifts are 192, 197 and 202 nm for the respective air hole radii of 1 μm, 0.9 μm and 0.8 μm.Thus, by considering the maximum confinement loss characteristics and peak resonant shift, the top face air hole radius is optimized to be 0.8 μm. Figure 5 depicts the confinement loss characteristics for the two middle airholes, R2 located at the bottom surface of the PCF.We choose the three different of RIs of analyte, 1.40, 1.41 and 1.42 for the analysis.Here, we vary the radii of the airholes from 1.25 to 1.75 μm with a step size of 0.25 μm.As shown in the Figure 5, when the radius of the larger airhole increases, the peak loss increases.This is due to the fact that the core region gets shifted more towards the plasmonic layer.Hence, efficient interaction of light with the metal layer takes place.It is also observed that the peaks are red-shifted with the corresponding increase in the radius of the air holes.For the airhole radii of 1.25 μm, 1.5 μm and 1.75 μm, the respective wavelength shift is found to be 188, 192, and 195 nm.Though the shift for 1.75 μm is more compared to the other radii, there is a fabrication difficulty as the two larger air holes have a very small separation between them.Therefore, the larger airhole radius has been optimized to be 1.5 μm.The next optimizing parameter is the pitch which is varied from 4 to 3.6 μm with a step size of 0.2 μm.As portrayed in the Figure 6, when the pitch between the adjacent airholes decreases, the loss peak decreases and it gets blue-shifted.For the pitch values of 4 μm, 3.8 μm and 3.6 μm, the maximum resonant wavelength shift is found to be 192, 207 and 233 nm, respectively.Even though the shift is more for the 3.6 and 3.8 μm pitch values, the 4 μm peak is well defined and also the full-width half maximum (FWHM) of this peak is less when compared to the 3.6 μm and 3.8 μm pitch values.Therefore, 4 μm is recorded as an optimized pitch parameter.The final optimizing parameter is the MoS2 layer.In this sensor, we coat a 2D material (MoS2) over the surface of the Au layer.MoS2 coating acts like a biomolecular recognition layer for increasing biomolecular absorption as it functionalizes the Au surface.Figure 7 portrays the comparative loss peak difference between the uncoated PCF, monolayer MoS2 (0.65 nm) coated PCF, and bilayer MoS2 (1.3 nm) coated PCF for the analytes of RIs 1.40, 1.41 and 1.42.The maximum resonant peak shifts of 228 and 264 nm take place for the monolayer and bilayer MoS2, respectively.We find that the confinement loss increases as the number of MoS2 layer increases.Though the peak shift is more for bilayer MoS2, the loss peak is not well defined as in the case of monolayer MoS2.Also, the peak is broadened for bilayer MoS2 which increases the FWHM that is responsible for the selectivity of the sensor.Hence, monolayer MoS2 is the optimized coating thickness for our proposed model.

Investigation of the Proposed D-shaped PCF Sensor Performance
Having optimized the structural parameters of the proposed sensor, the next step is to investigate the performance of the sensor by determining the sensitivity.In order to understand the significance of MoS2 coating, we compare the sensing performance of the sensor with and without MoS2 coating.Figures 8 and 9 describe the variation of the loss spectra against wavelength for various values of RI of the analyte from 1.33 to 1.42 with and without MoS2 coating.We carry out the analysis only for the RIs that show well defined peaks devoid of distortion.We investigate the sensing performance of the proposed sensor for the above optimized parameters of tAu = 45 nm, R1 = 0.8 μm, R2 = 1.5 μm, R3 = 1 μm, Λ = 4 μm,   2 = 0.65 nm.From Figure 8, it clear that the RI increases the peak resonance shifts to a longer wavelength.The sensitivity analysis is done through the wavelength interrogation method by studying the shift in wavelength by using the following sensitivity equation [31]. ). (7) Here,   is the variation in resonant wavelength, and   is the change in analyte RI which is 0.01 in this case.It can be observed from Figure 8 that the wavelength shift for the analyte of RI 1.41 to 1.42 is 228 nm with MoS2 coating.But, for a model without MoS2 coating, the maximum resonant wavelength shift appears to be only 202 nm which is 26 nm lesser than the model with a MoS2 layer.MoS2 is a transition metal dichalcogenide material where the plane of metal atom (Mo) is bonded with two planes of chalcogenide atoms (S).MoS2 can efficiently absorb various biomolecules due to its large surface to volume ratio and it also have high charge carrier mobility.The increase in sensitivity of MoS2 coated sensor is because of the strong coupling that occurs at the metal-2D material.Such coupling enhances the confinement of the electric field on the top surface of the D-shaped PCF [22].Also, the resolution of the proposed sensor is calculated using the following equation and it is found to be 4.38 × 10 -6 RIU for a spectrometer resolution of 0.1 nm.Furthermore, we also compute the amplitude sensitivity of the proposed sesnor using the following equation [32].

𝑅(𝑅𝐼𝑈) = ∆𝑛
Here, (,   ) denotes the confinement loss, ∂(,   ) is the difference in confinement loss peak and ∂  is the difference between the closer analyte RI.From Figure 10, the amplitude sensitivity is found to be 752 RIU -1 and the maximum resolution the device is 1.34×10 -6 RIU.Linearity of a sensor is an important factor as produces consistent predictable response to changes in input over a defined range.Hence, the linearity of the proposed sensor model is calculated and the same is depicted in Figure 11.It represents the variation of resonant wavelength against the analyte refractive index range from 1.33 to 1.42.The polynomial fitting of the curve gives the R 2 value of 0.9688 which is closer to 1.The larger linearity depicts the precision of the proposed sensor.Hence, the proposed structure is adaptable to practical sensing applications.To determine the sensing performance of the proposed sensor, along with the sensitivity (  ), FWHM, signal-to-noise ratio (SNR), detection limit ( n), and figure of merit (FOM) are the crucial factors.Therefore, along with the sensitivity, the abovementioned parameters have also been analyzed for the proposed sensor [5].
Here,   is the difference in peak loss of the sucessive analyte,   is the full width half maximum of the loss peak.Table 1 encapsulates the sensitivity, SNR, detection limit and FOM data of the proposed sensor for the analytes ranging from 1.33 to 1.42.Our proposed sensor shows high SNR which is an important factor to eliminate false positive response.Moreover, FOM of the proposed sensor is found to be 304 for the analyte of 1.41.High sensitivity and FOM are necessary for the fine resolution of the change in refractive index.

Fabrication Tolerance of the Proposed D-shaped PCF Sensor
From the experimental point of view, the proposed D-shaped PCF sensor model with the optimized parameters can be fabricated using the stack and draw method.Even with the development of advanced fabrication technology, there is always a probability of unavoidable error, which, in turn, may change the parameters from the optimized values.So, it is necessary to study the tolerance level of the proposed sensor probe.Hence, in this section, we analyze the fabrication tolerance of ± 2% from the optimized value.To examine the fabrication tolerance, we consider the analyte of RI 1.40.
Figure 12 shows the ± 2% (why not 5%) tolerance of gold layer thickness.As shown in the Figure 12, the peak experiences a blue shift and the peak loss increases when the thickness is varied from 45 nm to 44.1 nm.The shift in peak takes place from 894 nm to 890 nm which is a 4 nm variation and the loss value increases from 3.59 dB/cm to 3.80 dB/cm.Further, with the increase in gold layer thickness from 45 nm to 45.9 nm, the peak undergoes a red shift and the peak loss decreases.Here, the peak shift takes place from 894 nm to 899 nm which is a 5 nm variation and loss value decreases from 3.59 dB/cm to 3.40 dB/cm.As the resonant peak variation is incremental for the change in thickness of the gold layer, it is admissible upon fabrication.As can be seen in the Figure 13, there is no change in resonant wavelength.However, the loss decreases with the increase in the radius of the airhole.
Fabrication tolerance for ± 2% variation of two middle airholes located at the bottom of PCF is given in figure 14.From Figure 14, it is evident that there is no change in resonant wavelength for the ± 2% variation and the peak loss increases little for the increase in the airhole radius.Therefore, for the ± 2% variation in airhole radii, the proposed model is highly robustness.Finally, the fabrication tolerance of pitch value is analyzed for ± 2% variation and it is depicted in Figure 15.When the pitch is increased from 4 μm to 4.08 μm, the resonant wavelength experiences a blue shift from 894 nm to 892 nm with a change of 2 nm.However, the resonant wavelength undergoes redshift from 894 nm to 897 nm with a change of 3 nm when the pitch is decreased from 4 μm to 3.92 μm.Also, the loss increases a little amount with the increase in pitch value.As the change is negligible, it does not have much impact on the sensor performance.Consequently, the fabrication tolerance analysis clearly shows that the proposed sensor is highly robust agains the variations of the structural parameters.The sensing performance of our proposed MoS2 coated D-shaped PCF model is compared with the other previously proposed works and it is given in the Table 2.It can be deduced from the Table 2 that the proposed sensor shows a better performance for a wide range of wavelength than the previously reported sensors.

Conclusion
In this work, we have theoretically proposed a D-shaped PCF sensor with an overlayer coating of MoS2 over Au metal layer.We have optimized the structural parameters of the PCF to obtain high sensitivity and robustness of the proposed sensor.Further, the sensitivity of MoS2 coated and MoS2 uncoated sensors has been compared.Here, we have found that for the analyte refractive index range of 1.33 to 1.42, the MoS2 coated sensor exhibits a high sensitivity of 22,800 nm/RIU with a high spectral resolution of 4.38 × 10 -6 RIU and the MoS2 uncoated sensor exhibits a sensitivity of 20,200 nm/RIU.Hence, it is proved that the coated 2D material enhances the overall sensitivity of the proposed structure.This is due to the large surface adsorption efficiency and wide range band gap tunability of MoS2 coating.In addition, we have also computed the amplitude sensitivity and the same is 752 RIU -1 with a corresponding resolution of 1.34×10 -6 RIU.As the hunt for sensor models with broad detection range and high sensitivity prevails, the proposed model could pose as a potential candidate.

Figure. 1 .
Figure. 1. Cross-sectional view of the proposed D-shaped SPR based PCF sensor.

Figure. 2 .
Figure. 2. Dispersion relation of core mode, surface plasmon mode and loss spectra for RI of analyte 1.41.

Figure 3 .
Figure 3. Confinement loss characteristics for different gold layer thickness by varying analyte RIs.

Figure. 11 .
Figure.11.Numerical fitting result of resonant wavelength as a function of analyte RIs ranging from 1.33 to 1.42  =

Figure. 12 .
Figure.12. Fabrication tolerance analysis for ± 2% variation of tAu Figure 13 portrays the fabrication tolerance for ± 2% variation in the radius of the airholes on the top face of the PCF.As can be seen in the Figure13, there is no change in resonant wavelength.However, the loss decreases with the increase in the radius of the airhole.
Table. 1. Sensing performance of the proposed model for analyte range from 1.33 to 1.42.