A highly sensitive quadruple D-shaped open channel photonic crystal fiber plasmonic sensor: A comparative study on materials effect

A highly sensitive dual-polarized ’ X ’ oriented quadruple D-shaped open channel photonic crystal fiber (PCF) based surface plasmon resonance (SPR) sensor for various analyte detection is proposed in this paper. Gold is taken as a plasmonic material for its stability and compatibility. Silicon nitride (Si 3 N 4 ) and titanium oxide (TiO 2 ) has been used separately as an adhesive layer of gold to elevate the sustainability of the evanescent field. This paper shows a comparative study and inspects the effect of sensing performance between Si 3 N 4 and TiO 2 as an adhesive layer of gold. Numerical investigations have been followed up using the finite element method (FEM). For practical feasibility, analyte and plasmonic materials have been placed at the outer surface of the sensor. After watchful investigation, the maximum wavelength sensitivities of 21,000 nm/RIU (Refractive Index Unit) and 18,000 nm/RIU have been found for the y-polarization when using TiO 2 and Si 3 N 4, respectively. The highest amplitude sensitivities are of 914RIU (cid:0) 1 and 625RIU (cid:0) 1 for TiO 2 and Si 3 N 4, respectively. Furthermore, minimum wavelength resolutions of 4.76 × 10 (cid:0) 6 RIU and 5.55 × 10 (cid:0) 6 RIU have been observed in y-polarization for TiO 2 and Si 3 N 4, respectively. The sensor evinces a maximum figure of merit (FOM) of 236RIU (cid:0) 1 for TiO 2. This sensor has the analyte sensing range of 1.31 – 1.38RI (Refractive Index) for TiO 2 and 1.32 – 1.39RI for Si 3 N 4 . The sensor also delivers low confinement loss for Si 3 N 4 and TiO 2, which certifies viability in fabricating the design. Recognizing this sensor ’ s wavelength sensitivity, amplitude sensitivity, and sensing RI range, it could be a promising candidate for detecting different liquid analytes with excellent accuracy.


Introduction
SPR is an occurrence that happens if propagated light strikes a metal film at the surface interface with a matched frequency of the incoming photons and the surface electrons.SPR detects collective oscillations of free electrons in which the light is propagated into a metal film known as plasmonic metal.Those free electrons are known as surface plasmons.Any minuscule variation in refractive index (RI) close to the surrounding of the plasmonic metal causes a significant change in the effective mode index of the core.The effective RI of the surface plasmon polariton (SPP) mode is also altered, which brings a shift in the resonant wavelength that can be detected later on.The discovery of this phenomenon has been first introduced by R.M Wood [1].However, Bo Leidberg is known for introducing the SPR sensor at first in 1983 [2].In recent times, SPR sensors have drawn our attention for their tremendous ability to detect environmental pollutants [3], chemicals [4], bio-chemicals [5], medicines [5], cancers [6], gases [7], temperatures [8] and even pressure [9].
For the objectivity of SPR sensors, collaboration with PCF has attained noteworthy recognition due to fast response, freedom in design and adjustment, less weight, controllable sensing range.PCF has advanced facilities over conventional optical fiber such as flexibility, compatibility, liberty in designing the geometry, and lightweight [10,11].Differently shaped and various structures of PCF have been found in the last few years such as hexagonal internally metal-coated [12], D-shaped structures [13], square lattice airhole arrangements [14], external metal-coated [15], and nanowire-based [16].These PCFs figuratively come in the following two classes: internal and external.The plasmonic metal layer is coated inside an airhole with the analyte and outside of the fiber with an analyte channel in the exterior section for internal and external sensing respectively.Gold and silver are most common as plasmonic metals for their stability and compatibility [17].Gold is more stable and gives a higher rise in peak shifts.Gold is also less sensitive to temperature and humid issues than silver [18].So, most of the SPR-PCF sensors have been conducted with gold as plasmonic metal.However, internally sensing PCFs are difficult to fabricate as it requires analyte filling in a small airhole as well as coating plasmonic metal within a small area in the core region of the PCF [19].Moreover, adhesive plasmonic layer like titanium oxide (TiO 2 ) has been reported in several SPR-PCF related works to have better interaction of surface plasmons with the attaching metal layer [20,21].The evanescent field propagates along with the metal surface and hits the plasmonic metal, and vitalizes electron oscillations on the metal.These play a role in the formation of surface plasmon waves (SPW).An abrupt loss peak is noticed when the SPWs propagate in the dielectric interface [22].The external sensing mechanism is always desirable for the feasibility of the sensor.Hossen et al. proposed an external sensing mechanism-based gold-coated PCF-SPR based sensor which had a wavelength sensitivity (WS) of 6000 nm/RIU and amplitude sensitivity (AS) of 442.11RIU − 1 [15].Another dual-polarized spiral PCF was reported with a maximum WS of 4300 nm/RIU and AS of 420.4RIU − 1 [22].Another bimetallic coated PCF was found with WS of 23,000 nm/RIU, but the AS was not discussed in the paper [23].D-shaped channel-based PCF-SPR sensors usually show relatively high sensitivity as compared to other external sensing-based PCF sensors.Chen et al. came forward with a D-shaped PCF having a WS of 11,055 nm/RIU [24].Another D-shaped square lattice airholes-based PCF was reported which had the WS of 20,000 nm/RIU and AS of 1054RIU − 1 [25].Several papers have been found that used TiO 2 as an adhesive layer of gold and all of them showed a very good WS and AS.However, very few works are found that come forward with a comparative analysis of sensing performance among different plasmonic materials.Also, very few works are found that used other adhesive layers of gold rather than TiO 2 .One study was found that delivered a comparative analysis on sensing performance among plasmonic materials but WS and AS were not high enough [26].
Our proposed PCF sensor comes forward with a newly approached geometric structure having 'X' oriented quadruple D-shaped channels.This paper inspects and shows a comparative study on sensing performance between TiO 2 and Si 3 N 4 (silicon nitride) as additional plasmonic  material of gold.Si 3 N 4 has not been used as plasmonic material so often before in SPR-PCF based sensors.We have investigated and performed two separate simulations using Au-TiO 2 and Au-Si 3 N 4 combinations as plasmonic materials in our sensor.The sensor evinces two orthogonal x and y-polarization modes which ensure greater capability in receiving the incoming light.The sensor shows good WS of 21,000 nm/RIU and 18,000 nm/RIU for Au-TiO 2 and Au-Si 3 N 4 combinations respectively in y-polarization.The AS of 914RIU − 1 and 624RIU − 1 is found for Au-TiO 2 and Au-Si 3 N 4 combinations respectively in y-polarization.This paper also concentrates on wavelength resolution, the figure of merit and fabrication tolerance.Sensing range of 1.31-1.38RIand 1.32-1.39RIhas been observed for Au-TiO 2 and Au-Si 3 N 4 combinations respectively which ensures good capability in detecting various bio-chemicals, medical diagnostics and other liquid analytes.

Modelling and numerical analysis
The diagrammatic cross-sectional depiction for our proposed sensor is portrayed in Fig. 1(a) and 1(b).This structure has quadruple D-slotted channels in four corners of the sensor with five different types of airholes marked as d 1 , d 2 , d 3 , d 4 , and d 5 .Airholes have been organized incrementally from inwards to outwards to have better confinement of the field in the core.Four identical airholes marked as d 5 have been placed just under the four D-shaped channels to reduce the attachment between core guided mode and SPP mode.These air holes also help to lessen the confinement loss effectively.Four air holes with two different sizes marked as d 1 and d 2 have been placed near the center of the sensor to make an asymmetric core for raising the birefringence slightly.Four air holes with the largest diameter denoted as d 4 have been put on the outermost section of the sensor to increase the chance of confinement of light in the core region.Gold is used as the plasmonic metal for its stability and compatibility with the adhesive layers.TiO 2 and Si 3 N 4 have been utilized separately as two different adhesive layers.We have introduced these two adhesive layers to make a comparative study on sensing performance.We also need these adhesive layers to help gold for raising the sensing performance as well as to increase the attachment with the base fiber material.
One of the aims of this paper is to differentiate and analyze the sensing performance and response between TiO 2 and Si 3 N 4 as an adhesive layer of gold because both having good optical and physical properties.After watchful investigation, ideal airhole parameters are found, which are d 1 = 1.5μm , d 2 = 1.55μm, d 5 = 1.35μm , d 3 = 1.75μm , d 4 = 2.5μm.When Au-TiO 2 is used as the plasmonic material combination, we have kept the thickness of gold and TiO 2 at 80 nm and 10 nm, respectively.The distance between two airholes (d 3 ) is defined as Λ 1, and the distance from center to d 1 airholes is marked as Λ 2 .Λ 1 and Λ 2 are kept at 2.5μ m and 3μ m respectively.The D-shaped channel radius is kept at 1.5μm.Au-Si 3 N 4 has also been used as one of the plasmonic material combinations.The optimum thicknesses of gold and Si 3 N 4 are then kept at 65 nm and 25 nm, respectively.Si 3 N 4 is placed in between the gold layer and analyte; on the contrary, when TiO 2 is used, it is placed in between silica and gold.
Fused silica has good optical transparency with high-temperature tolerance.It also has a very appreciable mechanical strength.Because of having a very low absorption loss in the 1.5μm wavelength region, we have selected fused silica as the background material.The RI of fused silica can be calculated as follows [27]: where η si is the wavelength-dependent RI of silica with a valid wavelength region of 0.22 to 3.71μm.B i andC i where i = 1, 2, 3 are the Sellmeier constants for silica [25].Gold is used as a plasmonic metal for its stability as a chemical element.The dielectric constant of gold can be calculated by the Drude-Lorentz model [28]: where ∊ ∞ is the permittivity at high frequency, ω D is the plasma frequency, Δ∊ is the weighting factor, γ D is the damping frequency and Γ L and Ω L are the spectral width and oscillator strength of Lorentz oscillators, respectively.Values of all these parameters have been taken from [22].TiO 2 is one of the adhesive layers that has been used in this paper.It helps gold to have a strong attachment with silica as well as to boost up the sensing performance.The RI of TiO 2 is stated as [20]: where n TiO2 denotes the RI of TiO 2 which is wavelength dependent.
In another simulation, Si 3 N 4 has been used as an adhesive layer on the gold film.Si 3 N 4 has a high RI, which helps to increase the limitations of light.It balances the depth of penetration of the evanescent field to control the resonance.So Si 3 N 4 is another good candidate that can be used as an adhesive layer.Note that, we have used Si 3 N 4 in the upper area of the D-channel to have direct interaction with the analyte.The RI of Si 3 N 4 can be obtained from the Sellmeier equation as follows [29]: where C 1 , C 2 , D 1 andD 2 are the Sellmeier constants for silicon nitride [29].
The whole simulation has been employed in Comsol Multiphysics v5.5.The total sensor radius is kept at 11.6μm with a non-physical PML employed at the outermost layer of the fiber having a thickness of 1.4μm, which is around 10% of the total radius.PML acts like a boundary condition that absorbs surface radiations.The physical and optical properties of PML should be the same as the background material of the fiber to avoid noteworthy changes in sensing performance.However, fabricating the lattice design is manageable by utilizing the existing technologies.The sensor offers differently sized circular air holes and four identical D-shaped open channels coated with gold, TiO 2, and Si 3 N 4 .The Stack-and-draw technique potentially fabricates annular air holes.Chemical vapor deposition (CVD), wheel polishing, or highpressure chemical deposition can be utilized for coating the thin layers of gold, TiO 2 and Si 3 N 4 [12].The pulse laser technique can be used to fabricate the D-shaped open channels [25].For the pragmatic realization of the lattice design, a general experimental set-up idea should be discussed which is depicted in Fig. 1(c).A broadband or supercontinuum light source can be utilized to pass the light into a polarizer and a polarizer controller to have a linearly polarized light.This light then can enter into a single-mode fiber (SMF) which will be therefore coupled with our PCF via splicing technique.SMF provides the opportunity to receive the light and take it into the PCF.On the other hand, there will be chemicals to be sensed which are required to pass through a mass flow controller (MFC).MFC secures and controls the flow of those chemicals and lets them enter into the in-let.Interaction between ligand and different analytes effectively changes the mode index of the SPP mode resulting in a blue or redshift in the response curve.This can be observed by an optical spectrum analyzer (OSA).OSA can be utilized to sense waveforms via a computer.

Simulations and results
The simulation operation has been carried out utilizing the finite element method (FEM) as a numerical tool in COMSOL Multiphysics.Reflected light at the boundary is absorbed by the circular PML.For evaluating the performance analysis, a physics-controlled mesh sequence with extra fine element size has been applied.The complete mesh consists of 67,718 domain elements and 4652 boundary elements.Average element quality of 0.8579, element area ratio of 2.69 × 10 − 4 and mesh area of 422.6μ m have been found from the simulation tool.Triangular mesh elements divide the total of the geometry.The largest and the lowest mesh element sizes are 1.55 × 10 − 6 and 6.96 × 10 − 9, respectively.The maximum growth rate is a parameter that allows element sizes to grow from smaller regions to higher ones.For the most quixotic scenario, its value should be close to unity.From our simulations, its value has been set to 1.3.The ratio of the boundary element size to the curvature radius is 0.3.The temperature and pressure have been set to room temperature, 293.15K and 1 atm, respectively, for running the simulations.The confinement loss (CL) is stated as [28] where k 0 = 2π λ which is the free space wave number and λ being the effective wavelength and Im(n eff ) being the imaginary portion of effective index.
The evanescent field is responsible for exciting the SPWs.The coinciding of the frequency and the momentum of the core field with the incident light induces a coupling between the evanescent field and the surface plasmons under resonance conditions.The selection of the plasmonic material along with the spatial arrangement of the PCFs can successfully manipulate the occurrence of the resonance condition.The impact of the shape of the fiber can result in the shifting of the resonant λ towards shorter and longer wavelengths.Under phase-matching conditions, the effective indices of the core and SPP mode coincide with one another to give a steep peak point of the loss at definite indices of the analyte, caused by the maximum modal power transfer between the two modes.
The EM field profiles of the core guided mode and the SPP mode in x and y-polarizations for both Au-Si 3 N 4 and Au-TiO 2 combination for 1.36RI are portrayed in Fig. 2. Fig. 2(a, b, e, and f) exhibit the core guided modes in x-pol.and y-pol.both for Au-Si 3 N 4 (a, b) and Au-TIO 2 (e, f), respectively.It confirms that the core mode is guided through the center region of the sensor.Fig. 2(c, d, g, and h) show the respective SPP modes for Au-Si 3 N 4 (c, d) and Au-TIO 2 (g, h) in x and y-polarizations.Greater penetration of the evanescent field and energy flow to the metaldielectric interface will enhance stronger resonance peaks, a prominent advantage for easy detection.
The effective index of the core, as well as the SPP mode steadily decline with the increase of λ.The dispersion relation represented in Fig. 3(a) enunciates that the crossing of the two modes has formed an incomplete coupling.However, Fig. 3(b) shows the crossing of the core mode and SPP mode as well as the loss curve where phase matching occurs at the wavelength of 1.98μ m for an analyte index of 1.36.This condition paves the way for the evanescent field to better interlink with the surface plasmons.From Fig. 3, it is clear that the resonance wavelength is obtained when the crossing of the refractive index of the core mode and the surface plasmon polariton mode has taken place.As the refractive index of the modes is directly proportional to the propagation constants of the modes, the occurrence of the crossing ensures the phasematching condition; that is, the phases of the modes are matched when the propagation constants of the two modes are exactly equal to each other.The matching of the propagation constants signifies that the momentum and the frequency of the incoming light and the surface plasmonic waves (SPW) have also coincided.The SPWs show momentum and frequencies in close proximity to the momentum and frequency for incoming light of the near-infrared and mid-infrared region, for which the crossing takes place in this spectrum during the occurrence of resonance.Once the crossing is ensured, maximum power transfer from the incident light to the plasmonic waves occurs at those resonant wavelengths.The change of analyte index alters the phase-matching condition to a different resonant wavelength, as illustrated in Fig. 4. The sensitivity with respect to λ, which is known as wavelength sensitivity, has the following form [21]: in which peak wavelength shifts is represented by Δλ, Δn a being the difference between two consecutive RIs.The maximum S λ derived from the design is 21,000 nm/RIU and 18,000 nm/RIU for analyte RI of 1.37 and 1.38 for Au-TiO 2 and Au-Si 3 N 4 respectively.However, Tables 1 and  2 deliver detailed information about peak loss, resonant wavelength and wavelength sensitivity for both Au-Si 3 N 4 and Au-TiO 2 combinations.
Amplitude sensitivity is another important optical property for judging the sensor performance [12]: δα(λ, n a ) δn a (7) where the α(λ, n a ) is the loss corresponding to a given analyte index n a corresponding to the refractive index difference δn a of two consecutive loss spectra.The design expresses good S A since the Gaussian curves display good propagation loss differences with respect to analyte changes.Due to its high amplitude sensitivity, the proposed sensor shows the promise to be practically implemented in detecting biochemical and chemical analytes as amplitude interrogation is a costeffective method to practically realize.modes at 1.38RI respectively for Au-Si 3 N 4 .Additionally, Fig. 5(c, d) shows AS spectra when using Au-TiO 2 for the same.Maximum AS of 854.6RIU − 1 and 914RIU − 1 is noticed in x and y-pol.respectively for 1.37RI.The peaks of the AS curve continuously increase with the increment in wavelength.It is because of the continuous increment of loss peaks in the longer wavelength that the loss difference between two consecutive RI increases.In the context of maximum AS, it is concluded that the Au-TiO 2 combination has higher amplitude sensitivity than Au-Si 3 N 4 .

Study on plasmonic material variation
Fig. 6(a, c) depicts the loss curves for different thicknesses of gold for Au-Si 3 N 4 and Au-TiO 2 combinations for 1.37RI and 1.36RI, respectively in y polarization.The damping loss of the sensor increases with the increment of the gold thickness, which reduces the propagation of the evanescent field in the cladding region.This is compensated by a lower confinement loss.From Fig. 6(a, c), it is revealed that the graphs show a blue shift in curves with a reduction in confinement loss peak as we go on increasing the thickness of the gold.Fig. 6(b, d) illustrates the loss spectra for different thicknesses of Si 3 N 4 and TiO 2 layer for 1.37RI and 1.36RI in y-pol.respectively.Fig. 6(b) shows a slight blue shift in loss curves with a decrement in confinement loss peak as we continue to increase the thickness of Si3N4.Fig. 6(d) reveals a redshift in loss curves with an increment in loss peak as we go on increasing the thickness of TiO2.The continuous increment in the thickness of the TiO2 layer also results in shifting the resonant wavelengths towards longer wavelengths.
From Fig. 6(e, f), the effect of thickness alterations for a larger range is observed on the resonant wavelengths and the corresponding peak losses for both the adhesive layers keeping the analyte refractive index unaltered.It is noticeable that, with the adhesive layer increment, the effects on resonant wavelength and peak loss for Si 3 N 4 and TiO 2 are reciprocal to each other.From a pragmatic point of view, the fabrication feasibility starts to get critical for growing lesser and lesser metal layer thickness below 10 nm.But for a higher thickness of Si 3 N 4 , Fig. 6(e) delineates that the resonant wavelength shows blueshifts, and the peak losses become very low.The lowering of the peak loss indicates that a thicker Si 3 N 4 adhesive layer damps the plasmonic oscillations for which the energy transfer from the incident light wave to the SPWs decreases.When the analyte refractive index is lower, then the peak losses already remain low (close to 4 dB/cm).If we keep the thickness value higher, then the peak losses will go down even lower than that.Negligible losses imply that there is almost no drop in the output light intensity.This will cause detection hindrance.Hence, our suggestion is to keep the thickness at an optimum value, around 25 nm.For TiO 2 , it is observable that increasing thickness causes redshift of the resonant wavelength, and the peak loss values become greater.A greater peak loss suggests that a thicker TiO 2 layer enhances the coupling effect.Higher loss values are an impediment to getting viable output optical signals.This limits the sensing length of the sensor as well.Hence, we suggest keeping the TiO 2 layer thickness at an optimum value, around 10 nm.

Comparative study on loss spectra between TiO 2 and Si 3 N 4
We have calculated the loss values for TiO 2 and Si 3 N 4 as adhesive layers for analytes RI 1.35 and 1.36 and plotted loss spectra for running a comparative analysis as presented in Fig. 7.It is visible that the loss values at resonant wavelengths of Si 3 N 4 are less than that of TiO 2 for both 1.35RI and 1.36RI.We also notice that the resonant wavelengths for Si 3 N 4 are lower than that of TiO 2 .The peak losses are greater for TiO 2 because when the maximum binding condition occurs at the interface, the RI of the plasmonic material surface generally increases more.Therefore, more evanescent waves pass through the cladding region and increase the leakage loss than that of Si 3 N 4 .At maximum binding conditions, the RI of the Au-TiO 2 surface is significantly higher than the RI of the Au-Si3N4 surface.Wavelength sensitivities for TiO2 and Si3N4 as adhesive layers for 1.35RI are 9500 nm/RIU and 6800 nm/RIU, respectively.From the figure, it is prominent that the peak loss transition between analyte RI 1.35-1.36for TiO2 adhesive layer is greater than that for the Si3N4 adhesive layer, which results in the greater WS value for TiO2.

Comparative study on fabrication tolerance
The loss curve and the resonant wavelength of our proposed sensor are sensitive to structural variations.It is considered to have ±1% or ±2% variations from the ideal parameters [20].Fig. 8(a, b, and c) come forward with an analysis of loss spectra with ±5% varying of d 2 , d 3, and d 5 respectively in y-pol.from the ideal values for both Si 3 N 4 and TiO 2 as adhesive layers of gold for 1.36RI.The loss curves show a slight red and blue shift for +5% and − 5% varying of d 2, respectively from the ideal value of 1.55μm in Fig. 8(a).The effective mode index of the core mode and the SPP mode changes with the increment and decrement of d 2 which in turn changes the phase-matching condition.Therefore, it results in red or blue shifts.The resonant wavelength and the loss peak shift are higher for TiO 2 than that of Si 3 N 4, which reveals that TiO 2 is more sensitive to structural variations as an adhesive layer of gold.Fig. 8 (b) shows that the loss peak significantly and slightly decreases with the increment of d 3 for TiO 2 and Si 3 N 4, respectively.d 3 airholes directly obstruct the coupling between the core and the SPP mode resulting in a decrement in loss peak as we carry on increasing the diameter.
Fig. 8(c) illustrates the loss spectra for both adhesive layers with a ±5% varying of d 5 in y-polarization for 1.36RI.From the figure, it is confirmed that the peak loss noticeably increases with the decrement of d 5 for both TiO 2 and Si 3 N 4 .d 5 airholes are placed just under the Dshaped channels that directly impede the coupling.Reducing d 5 ensures greater coupling between core and SPP mode resulting in a higher loss peak.We have seen a modest higher peak loss transition for TiO 2 than that of Si 3 N 4 because of Au-TiO 2 combination having a larger effective index than that of the Au-Si 3 N 4 combination.As the Au-TiO 2 has a larger effective index, light passes through the plasmonic material surface more than that of the Au-Si 3 N 4 resulting in a higher loss peak.It also  reveals that there is no shift in resonant wavelength of loss curves as there are negligible changes in effective mode indices for core and SPP mode.Fig. 8(d) comes up with the analysis of loss spectra for a ±5% variation of the pitch (Λ 2 ) for both TiO 2 and Si 3 N 4 .Decreasing the pitch secures a smaller core area which increases the confinement loss.It is evident from the figure that peak loss transition is higher for TiO 2 than that of Si 3 N 4 because of the same reason discussed earlier.

Sensor evaluation
Wavelength resolution is one of the crucial sensing parameters which shows how a minute change in RI can be detected by the sensor.A lower value of wavelength resolution gives rise to a better capability of detecting minute RI change.Wavelength resolution can be calculated as follows [20]: where Δλ peak is the peak wavelength difference and Δn a is the variation of analyte index.Δλ minimum is generally assumed to be 0.1.However, our proposed PCF shows minimum resolution of 4.76 × 10 − 6 RIU and 5.55 × 10 − 6 RIU in y-pol.for Au-TiO 2 and Au-Si 3 N 4 combination, respectively.
Another crucial parameter that is worth mentioning for evaluating better sensing capacity is the figure of merit (FOM).The high FOM is an indication of superior sensing capabilities.The FOM of SPR sensors can be defined as follows [28]: where S λ is the wavelength sensitivity and FWHM is the full width at half the maximum of the gaussian loss curve.The highest FOM of 236 RIU − 1 and 153.8 RIU − 1 is observed in y-pol.for Au-TiO 2 and Au-Si 3 N 4 combination, respectively.The figures of Fig. 9 show the polynomial fitting curves and properties of resonant wavelengths vs analyte RI in y-polarization for both Au-Si 3 N 4 (Fig. 9a) and Au-TiO 2 (Fig. 9b) combinations.The sensing range for analyte RI is  maximum transition in resonant wavelength is 180 nm between 1.38 and 1.39 RI.For the Au-TiO 2 combination, the highest resonant wavelength value is 2.320 µm at 1.38RI, and the maximum transition in resonant wavelength is 210 nm between 1.37 and 1.38 RI.So, it is evident that the WS value is greater for the Au-TiO 2 combination.The more the Adjusted R 2 value will be close to 1, and the root mean square (RMS) error will be close to 0, the more perfect the curve fitting will be, and for both combinations, we notice that the Adjusted R 2 values are almost one and the root mean square errors are almost 0. Here, fifth (5th) order polynomial fitting characteristics are executed and plotted to obtain the most accurate fitting.Table 3 comes forward with a comparison between our proposed sensor and most recently published PCF-SPR sensors where the maximum WS, AS, and sensing RI range are compared.

Concomitant D-Shape open ring design analysis and fabrication feasibility
D-shape lattice designs have stood out to be the most efficacious amongst all kinds of PCF SPR optical sensors considering good wavelength sensitivity, amplitude sensitivity, FOM, stable optical mode responses, and broader sensing range.A D-shaped SPR sensor has been first introduced as a novel design with a maximum WS = 11055 nm/RIU in 2018 [24].However, its AS and FOM have not been evaluated as the design did not present itself with sharp Gaussian peaks.Later on, Dshaped designs with modified PCF arrangements have been studied to improve its sensing performance [25,32,34].Recently, more studies have been published with D-shaped open ring analysis.A dual open Dchannel design shows the highest WS = 5000 nm/RIU, highest AS = 396RIU − 1, and FOM = 47 RIU − 1 [36].Another dual open D-channel design shows the highest WS = 13,500 nm/RIU using gold with different doping materials [26].With an open D-channel arrangement, an SPR sensor shows a maximum WS = 17,000 nm/RIU, but the AS has been significantly improved [37].The most recent work on SPR sensor presents itself with 4 D-shape open channels, which is similar to ours [38].However, the PCF arrangement differs from ours.This design is comparatively more complex [39].All these works have been evaluated via simulation and numerical analysis.Our work comes forward with a lattice design with a satisfactory sensing performance with sharp Gaussian responses.This work evaluates for the first time a comparative sensor analysis between the most effective adhesive layers for the plasmonic metal gold, TiO 2, and Si 3 N 4 for open D-channels.In terms of the pragmatic development of an SPR sensor, gold deteriorates very quickly when there is frequent liquid analyte contact.An adhesive layer solves the issue.Not any adhesive layer is suited for the task.The layer has to be such that the sensing potential provided by the plasmonic metal does not deteriorate, rather the adhesive layer can enhance the sensing response up to a certain extent.
The number of works dedicated to practically realizing SPR PCF optical sensors with complete experimental analysis is quite low.With the advancement of technology, functional SPR sensors are being on the verge of full development.Fabrication technology nowadays has the potential to manufacture the lattice designs of the most recently proposed sensor models.The stack and draw technique is the most popular fabrication scheme for designing any PCF arrangements [40].Our PCF arrangement uses a square lattice design with varying diameters moving from one ring to the other.This design is fairly supported by the stack and draw mechanism.Femtosecond lasers can form the open microchannels on the four sides of the lattice design [41].Focused ion beam milling is another effective way to go about introducing deep open channels into the design [42].For metal layer deposition, chemical vapor deposition (CVD) and atomic layer deposition (ALD) turn out to be the most effective means for growing metallic nano-layers [43,44].

Conclusion
We have presented a dual-polarized quadruple D-shaped open channel PCF-SPR sensor in this paper.The sensor has a unique design with four identical D-shaped channels in four corners of the structure.Gold has been used as a plasmonic material owing to its stability and compatibility.We have employed TiO 2 and Si 3 N 4 in the sensor alternatively, executing two separate investigations to build up a comparative study between both the materials as adhesive layers and to examine the distinct effects they bring on the sensing performance.While using the Au-TiO 2 combination, maximum wavelength sensitivity, amplitude sensitivity, resolution, and FOM have been found 21,000 nm/RIU, 914RIU − 1 ,4.76 × 10 − 6 RIU, and 236 RIU − 1 in y-polarization, respectively, with a sensing range of 1.31-1.38RI.The sensor has shown moderated confinement loss on average, which ensures simplicity in fabricating the design.When the Au-Si 3 N 4 combination is used as plasmonic materials, we have found lower confinement loss, wavelength sensitivity, and amplitude sensitivity, but the sensing range has slightly increased than Au-TiO 2 .For this sensor, TiO 2 and Si 3 N 4 both have shown promising results as an adhesive layer of gold.

Fig. 1 .
Fig. 1.(a) Geometry for Au-Si 3 N 4 combination, (b) Geometry for Au-TiO 2 combination, and (c) illustration of the experimental setup of the proposed sensor.

Fig. 4 (
a, b) illustrates gaussian loss curves for a range of 1.32 to 1.39RI for Au-Si 3 N 4 in x and y-pol.respectively.Fig.4(b) portrays that the maximum loss peak is 86.11 dB/cm at 2.2μ m wavelengths.Fig.4(c, d) shows the loss curves for a range of 1.31 to 1.38RI of the analytes for Au-TiO 2 combination in x and y-pol.respectively.It can be seen from Fig.4(d) that the maximum loss peak is 142.9 dB/cm at 2.32μ m.The resonant wavelength redshifts towards a higher wavelength.The loss peak also increases with the increment in wavelength.Redshifts in the loss curve occur for the continuous decrement of the effective mode index of the analyte as we go on increasing the wavelength.Because of the reduction in the mode index of the analyte, greater evanescent waves want to penetrate to the cladding.So, the peak loss becomes sharper and broader in the longer wavelengths resulting in an increment in loss peaks as well as in resonant wavelengths.Maximum resonant wavelength shifts of 180 nm and 210 nm are obtained from Fig.4(b, d) for analyte RI of 1.39 and 1.38 for Au-Si 3 N 4 and Au-TiO 2 respectively.

Fig. 5 (Fig. 2 .
Fig. 2. Electric field profile of the core modes (a, b and e, f) in x-pol.and y-pol.for Au-Si 3 N 4 and Au-TiO 2 combination respectively and SPP modes (c, d and g, h) in x-pol.and y-pol.for Au-Si 3 N 4 and Au-TiO 2 combination, respectively.

Fig. 3 .Fig. 4 .
Fig. 3. Dispersion relations of plasmon polariton mode, fundamental core mode, and loss spectra in y polarization of (a) Au-Si 3 N 4 combination for 1.37RI and (b) of Au-TiO 2 combination for 1.36RI.

Fig. 6 .
Fig. 6.Loss spectra of Au-Si 3 N 4 combination for variations in gold thickness (a), Si 3 N 4 thickness (b) for 1.37RI and Loss spectra of Au-TiO 2 combination for variations in gold thickness (c), TiO 2 thickness (d) for 1.36RI (e) Resonant λ and peak loss changes for Si 3 N 4 thickness variations and (f) Resonant λ and peak loss changes for TiO 2 thickness variations.

Table 1
Performance analysis of the proposed sensor for AU-TIO 2.

Table 2
performance analysis of the proposed sensor for AU-SI3N4.
1.32-1.39for the Au-Si 3 N 4 and 1.31-1.38 for the Au-TiO 2 combination.The highest resonant wavelength value for Au-Si 3 N 4 combination is 2.20 µm at 1.39 RI, and the