Numerical Study of Circularly Slotted Highly Sensitive Plasmonic Biosensor: A Novel Approach

A highly sensitive Photonic Crystal Fiber (PCF) based Surface Plasmon Resonance (SPR) sensor is demonstrated in this paper in the optimized form of circular slotted lattice (CSL) structure. This proposed model performance is numerically scrutinized by using Finite Element Method (FEM) in presence of Perfectly Matched Layer (PML) and Scattering Boundary Condition. Plasmonic material ‘Gold’ which is chemically inert is used in this structure at the outer surface of the slotted area to mitigate fabrication challenge. This model indicates the highest wavelength sensitivity of 16000 nm/RIU using wavelength interrogation, the amplitude sensitivity of 780 RIU −1 by using amplitude interrogation method and the average spectral sensitivity of 6666 nm/RIU, respectively. Besides, this sensor has the potentiality of detecting analytes within Refractive Index (RI) range 1.4 to 1.46 with maximum wavelength resolution of 6.25 × 10 −6 RIU and amplitude resolution of 1.28 × 10 −6 RIU, respectively and the maximum figure of merits of 400 RIU −1 . Moreover, the variation of structural parameters (such as pitch, plasmon layer thickness etc.) and the impact of these changes are also discussed in details. According to the high sensitivity performance, polynomial fit and high Figure of Merit (FOM), this amend structure can be a strong competitor in the field of biosensing.


Introduction
In the study of biosensing and biochemical application the refined physical devices that have a quick respond to the refractive index of surrounding medium is called biosensor.Nowadays, SPR sensor shows incredible performance in the field of biosensing technology.Due to the capability of detecting very small RI and label free sensing properties [1], SPR becomes a suitable platform in biological sample detection, organic chemical sensing, water testing, environmental monitoring, medical diagnosis, antibody-antigen interaction, medical imaging [2][3][4][5][6][7][8][9] and so on.The SPR was first theoretically framed by Zenneck [10] in 1907 who demonstrate that when one medium is made up of lossy dielectric and another medium is lossless then surface electromagnetic wave is produced at the boundary of two medium.The actual development of SPR was progressed by Ritchie [11] in 1957 by giving a numerical demonstration about the presence of the excited phase of the surface plasmon waves at metal dielectric interface.In 1983, Liedberg et al. [12] was first theoretically accomplished SPR sensors by considering the prism coupling technique.On the basis of surface plasmons similar concept is developed by Otto [13] and Kretchmann [14] using the ATR (attenuated total reflection).Though performance of the prismbased sensor is favorable, the remote sensing application limits due to its moving optical and mechanical components [15].Therefore, the cost is high.The bulky configuration also restricts the use of the sensor in https://doi.org/10.1016/j.rinp.2020.103130Received 5 January 2020; Received in revised form 7 April 2020; Accepted 20 April 2020 non-portable manner.
Optical fiber is taken the place of prism to deal with the limitations of the prism coupled sensor.Optical fiber based SPR sensors provide high sensing resolution and wider operating range [16].But due to the narrow acceptance angle [16] the sensor applications are limited.Recently, PCF embraced with SPR have been used in SPR sensing.PCF comes up with a new dimension in sensing due to its atypical characteristics like high confinement, single mode propagation and tunable birefringence [15].PCF allows to scale down the SPR sensor size.In the PCF several air holes are organized in a silica background to make the cladding.Due to the low temperature sensitivity fused silica is used here.Hence, by modifying the geometry of the air holes, the evanescent field can be manipulated [16].SPR effect is created because of the interaction between the plasmonic material and the evanescent field.When TM (transverse magnetic) polarized light incident on the metaldielectric interface, the electron in the plasmonic material is stimulated.Therefore, the free electron creates oscillation.In this way surface plasmon resonance is formed.When the frequency of the incident wave is resembled with the frequency of that oscillating electrons at a certain wavelength then surface plasmon wave (SPW) is produced, which is propagated along the metal-dielectric interface.This wavelength is called as resonance wavelength.At this point a sharp loss peak is seen that is sensitive to the refractive index of the surroundings.By analyzing the shifting of the resonant wavelength, the unknown analyte can be detected.So, while comparing with the fiber-based sensor, it is observed that PCF based SPR sensor gives very high sensitivity with design flexibility.
The choice of plasmonic material is also a major issue in the sensor performance.Most of the works related to the field use gold, copper, silver, niobium, titanium dioxide and aluminium [17].Although Silver as a plasmonic material shows a sharp resonance peak, it is not chemically stable [16] and have oxidization problem.This problem can be removed by using graphene layer.But the deposition of extra graphene layer increases the manufacturing cost and fabrication complexity.Gold as a plasmonic material shows chemical stability and has no oxidization problem [16].It also shows desirable resonance peak.
According to the deposition of plasmon materials, sensors can be classified as internal coating, D-shaped and external coating structure [1].Recently, Rifat et al [18] proposed a sensor with excellent sensing performance in the RI range 1.33 to 1.42.Though it's sensitivity is high, it is very challenging to fabricate in practical due to its selective infiltration and internally metal coating structure.To meet up the fabrication complexity, D-shaped SPR sensor is considered as a better option.Liu et al [19] proposed a D-shape model with spectral sensitivity of 14660 (nm/RIU) in the RI range 1.33 to 1.41.This structure shows a spanking performance and metal deposition in the flat surface is easier than internal metal deposition.Although D-shape have some pretty features, it requires uniform polishing to generate a flat surface.Due to these fabrication intricracies external coating becomes a promising option day by day.Recently, Momota et al [1] proposed a hollow-core circular lattice structure where silver is used as a plasmonic material.Though this structure aids to lessen fabrication difficulties, it shows very low sensitivity in a narrow RI range.Additionally, using silver as a plasmonic material weakens the sensing performance due to its chemical unreliability and oxidation problem [20].Very recently, S. Akter et al in [20] and S. Chakma et al in [21] proposed another externally metal coated SPR sensor where plasmonic material 'Gold' is used.This structure improves the sensing performance but this is not so remarkable in the competitive sensing field.K. Ahmed et al [22] proposed another fabrication friendly highly sensitive SPR sensor with spectral sensitivity of 9000 nm/RIU.Though wavelength sensitivity is satisfactory, its amplitude sensitivity is not so exalted which is cost effective and plain sailing compared to wavelength sensitivity.Another hollow core circularly shaped external coating model is proposed by M. B. Hossain et al. [23] where Silver is used as plasmonic material.This design offers wavelength sensitivity of 21000 nm/RIU but it's detection range and amplitude sensitivity is considerably low.Very recently, another model is proposed by M. A. Mahfuz et al [24] which demonstrates its sensing performance within RI range 1.33 to 1.40.In this model, two different plasmonic materials (Gold, Silver) are used at the outer surface which gives different amplitude sensitivity but wavelength sensitivity of 12,000 nm/RIU for both.Islam, Md Saiful, et al., [25] proposed a sensor which needs the analyte to place around the total fiber core.For this reason, we need more gold coating which is more costly.Also, we can place little amount of analytes.Also, TiO2 is used with gold.And there is a square in the center of the core which carries air holes inside it.So, its fabrication process is very much complex.But in our proposed sensor the amount of gold is reduced by using circular slots, which causes less fabrication cost.Also the can hold more analytes in little place.And the fabrication complexity is reduced.Again Islam, Md Saiful, et al., in [26] proposed a sensor which is a localized SPR sensor.This kind of sensor causes more fabrication complexity.Also, placement of analyte is more tough on this little surface.In our proposed sensor u designed a non-localized SPR sensor which has less fabrication complexity for the circular slots and requirement of less gold.Also, they can hold more analytes.Haider,Firoz,et al.,in [27] proposed a propagation controlled SPR sensor.Here propagation path is created by making some air holes smaller than others which causes more construction complexity of the fiber.Also it can hold little analyte and need more gold coating.But these types of limitations have overcome in our proposed sensor.In [28] proposed a sensor which consists of four large air holes in both left and right, a small air hole in the center, three small air holes in both top and bottom of the fiber.This kind of fabrication technique is very much complex to be applied.Also, the sensor requires more gold which is costly, but can hold less analyte.But considering all the limitations above, our proposed design is very much simple to fabricate, the cost is very less and it can hold much analytes." To repress the reported problems, a circular eight slotted lattice structure is proposed in this paper which is numerically analyzed by FEM.Better to know, this is the latest update slotted structure among the existing models.Here, gold is deposited at the selected slotted areas which make this structure cost effective and alleviates fabrication complexities.Due to its slotted structure, it can hold up more analytes compared to other existing design that ameliorate it's sensing capacity.Also, the number of the slots affect the sensing performance.The more slots around the core, the better light beam can penetrate through the gold thin film.The reason to choose eight slots because the more slots around the core, the better light penetration through plasmonic metal.So obviously 8 slots can give better sensing performance than 2, 4 or 5 slots.But too much slots increase the polishing complexity and cost of this sensor.So, considering the facts, the authors decided to design 8 slots after optimizing the sensing performances using different number of slots in COMSOL Multiphysics software.Sensing performance is explored by wavelength sensitivity, amplitude sensitivity, resolution, linearity and high FOM.Moreover, we comprehensively analyzed the impact of various structural parameters (pitch, gold layer thickness etc.) to calibrate the best performance.

Structural design
Our proposed sensor is made of circular PCF (Photonic Crystal Fiber) with circularly slotted gold layer in the cladding.The design of cross section of the sensor is shown by the given Fig. 1.The fiber contains a ring of eight small air holes around the fiber core.Outside the ring there is another ring of circularly slotted gold thin film layer.We used gold thin film because it is chemically inactive and does not oxidize.Though silver is highly sensitive it is avoided because it is subjected to oxidation.The sensing or detecting analyte is to be placed in the slots.Between each pair of circular slots there is a small air hole.These air holes consist another circular ring of air hole, covering the first ring.Thus, the proposed sensor is structurally symmetric and there is no air hole between the center and a slot so that light can directly be incident on metal surface.For plasmonic material, fused silica (RI 1.4) has been used for its poor temperature sensitivity.
The distance of nearest two air hole center-to-center is known as 'Pitch' which is defined by (∧).The air hole diameter is indicated by (d1) and the diameter of circular slots are symbolized by (ds).The radius of the first air hole ring is identified by (d) and the radius of the ring of circular slots is identified by (r1).The inner radius of the PML layer (Perfectly Matched Layer) is referenced by (r2) and the outer radius by (r), which is the radius of the whole sensor fiber.
Here The distance from the center of the fiber to the centers of the circular slots is 3.24 um.As the eight slots are in equal distance from each other, the two nearest slots form the angle of 360/8 = 45 degree with the fiber center.

Mathematical formulations
The background of fiber core is filled with silica (fused).The effective RI of the silica (fused) is obtained by using Sellmeier equation which is stated by [29,30]: Here, n is a wavelength dependent variable which represents the RI of fused silica.The constants of this equations are: B1 = 0.69616300, B2 = 0.4079426, B3 = 0.8974794, C1 = 0.00467914826, C2 = 0.0135120631, C3 = 97.9340025and the dielectric constant of Au is calculated by the given Drude-Lorentz's formula [31,32], where, Au is gold's permittivity, is high frequency permittivity, ω is the frequency in angular, D is plasma frequency, and The width of spectra according to Lorentz is /2 104.86 THZ, and the oscillation strength is /2 = 650.07THz.Confinement loss is a great indicator of sensors performance.We calculated confinement lose using the equation given by [32,33] (3) Here, Im(n eff ) is the imaginary index mode and ko = 2 / is the wavelength number where is the wavelength at which simulation was operated.
The sensitivity of the sensor can be obtained by using interrogation method wavelength and amplitude.We calculated the sensitivity of wavelength by method of wavelength interrogation using the equation given by [34][35]: Here, peak denotes the peak shifts differences of wavelength and na denotes the analyte refractive index variation.
The amplitude sensitivity is obtained using amplitude interrogation method by the equation given by [36][37][38]: A a a a (5) where, n ( , ) a is the two spectral loss difference.Another important parameter is the sensor resolution which indicates the ability to detect small changes in analyte RI by the sensor.The resolution can be obtained by the equation given by [39]: The FOM (Figure of Merit) which indicates the better detection limit.FOM is defined by [40][41]: where, S is the linear slop of wavelength in resonance and FWHM is Full Width at Half Maxima, for a specific RI.
To analyze the sensitivity of the offered fiber sensor, we applied FEM or Finite Element Method with PML (Perfectly Matched Layer) on the outer of the fiber.To discover its maximum sensitivity, the analyte RI (n a ) was varied from 1.40 to 1.46, Au layer thickness (t ) Au was varied from 30 nm to 50 nm and pitch defined by (∧) was varied from 1.2 to 1.4 µm.For mapping all the air holes, we tried make the size of mesh as smaller as possible.

Results and performance analysis
The proposed SPR works based on the mechanism of the interface of core-clad evanescent field of p-polarized light beam that is fallen on the dielectric metallic surface and release free electron.In that case, the core mode real refractive index (n eff ) and the SPP (Surface Plasmon Polariton) mode equals to each other at a particular wavelength, which generates surface plasmon wave.
The Fig. 2(a) illustrates different mode profiles with core mode and Surface Plasmon Polariton (SPP) mode for different refractive index of analyte and their interactions.The figure exposes that as we increase anlyte RI, the core mode evanescent field gradually spreads towards the metal surface and for further increase in RI, it again confines itself in the core center.For the SPP mode, the light beams initially are scattering in both metal surface and core and gradually penetrates to the metal surface as we increase analyte RI.
The study and analysis have been performed using Finite Element Method with smallest mesh analysis as possible.The proposed fiber (i) shows symmetricity for circular air hole rings and circular ring of slots.So the fundamental mode y-polarized and the fundamental mode xpolarized responses are almost same.In Fig. 2(b) we represented resonant curve, where the core mode (real) and the SPP mode coincides at the wavelength 0.93 µm.This wavelength is known as resonant wavelength.At this wavelength, a sharp peak we observed which defines maximum transfer of energy from core mode to SPP mode.And finding resonance peak at this low wavelength indicates that the proposed sensor is very highly sensitive.
As a first performance parameter, we consider the analysis of confinement loss which varies with the variation of analyte RI by following Eqs.( 3) and ( 4), respectively, which is shown in Fig. 3. Here, we can see that as we increase analyte RI (na), the loss curve experiences red shifts to higher wavelengths.Here, we simulated and verified the results for different RI ranges using COMSOL Multiphysics software by applying PML boundary condition.The simulation results revealed that the proposed sensor shows higher and sharper sensitivities and high detection performance ranging from RI 1.40 to 1.46.The specific applications of this RI sensing range are that our offered sensor can successfully detect the analytes of Carbon Tetrachloride (real RI 1.46), Silicone Oil [nD25] (real RI 1.403), 60% Glucose Solution in Water (real RI 1.4394), Fused Silica (real RI 1.458), Ethylene Tetrafluoroethylene (real RI 1.403), Sugar Solution 50% (real RI 1.42), Polylactic Acid (real RI 1.46) and so on.The analysis found that RIs lower than 1.4 shows very flat and low loss peak which is difficult to detect.And for the RIs larger than 1.46 there are irregular multi-resonance formed in the loss curves which makes the sensing performance unstable.But the sensor can clearly detect and sense the analytes of RI range 1.40-1.46,Therefore, we decided to choose the starting analyte RI range from 1.40 instead of 1.33.While variating the analyte RI from 1.40 to 1.41, 1.41 to 1.42, 1.42 to 1.43, 1.43 to 1.44, 1.44 to 1.45, 1.45 to 1.46, the resonance wavelengths are shifted from 0.65 to 0.68 µm, 0.68 to 0.72 µm, 0.72 to 0.76 µm, 0.76 to 0.84 µm, 0.84 to 0.89 µm, 0.89 to 1.05 µm, respectively, (for t Au = 30 nm, ∧ = 1.4 µm).The highest peak loss was obtained to 80 dB/cm utilizing Eq. ( 3) at wavelength 1.05 µm for analyte RI 1.46.
For, n a = 0.01, min = 0.1 nm, peak = 160 nm, by utilizing Eq. ( 6) the wavelength resolution is obtained 6.25 × 10 6 RIU.That means the designed sensor can detect a little change in analyte RI in 10 6 order.
Thirdly, the amplitude sensitivity of the designed sensor is exposed in Fig. 4. The maximum sensitivity of 780 RIU 1 and resolution of 1.28 × 10 −6 RIU are obtained according to Eqs. ( 5) and ( 6), respectively, which both are found at 0.83 µm, for analyte RI 1.45, t Au = 30 nm, = 1.2 µm.
As a fourth analysis, we optimize the structural parameters, for example gold layer thickness, pitch parameters.Now the point to consider is how the gold thin layer can be placed inside the slots.The gold thin film coating should be uniformly distributed.Chemical Vapor   Deposition Method (CVD) [27] is the best choice for this goal which will minimize the surface roughness of the slots.We also analyzed loss spectra for different Au layer thickness (30 nm-50 nm) for varying analyte RI 1.45 shown graphically in Fig. 5.For Au layer thickness 30 nm, 40 nm, 50 nm the amplitude sensitivity is 780, 448, 210 RIU 1 respectively.Therefore, we can see that for in- creasing thickness the loss curve is redshifted and sensitivity decreases.
We observed that with the increase in pitch value, spectral loss decreases.For the value of pitch = 1.20 µm, 1.30 µm, 1.40 µm the sensitivity is 780, 455, 306 RIU 1 respectively, shown in Fig. 6.
In this section as a fifth parameter, linearity characteristics has been investigated.A good sensor shows either high linearity or high polynomial fit.The proposed sensor shows good polynomial fit shown in Fig. 7 with analyte RI 1.4-1.46.The equation for the polynomial fit and R-square value are shown inside the figure, here y denotes the wavelength at resonance and × denotes the analyte's RI.Because of good polynomial fit the proposed sensor can show high performance in analyte RI detection.
The FOM of the proposed sensor is graphed in Fig. 8 as a sixth parameters.The ring air hole as well as the ring of circular slots are positioned very near the core of the design to produce high birefringence, which yields a high FOM equals to 400 RIU −1 at RI 1.46 according to Eq.The proposed sensor confirms also detection limit.
Apart from the above analysis, our proposed sensor needs low fabrication cost since the gold thin film is coated in small circular slots.For these slots the sensor also can hold much analyte which will improve the sensing performance.
As a final analysis of this work, a comparison among amplitude sensitivity, amplitude resolution, wavelength sensitivity, wavelength resolution and Figure of Merit has been shown in between the existing PCF based SPR bioinstrumentations with the offered design.It can be seen from the Table 1 that the proposed PCF SPR sensor shows improved results in term of detection range.

Conclusion
In this work, a circular slotted SPR based RI sensor is proposed and numerically investigated.Design along with the Performance of the sensor is analyzed using Finite element method or FEM in COMSOL environment.Eight circular slots with gold (Au) layer coating allows the sensor to hold large of analyte.Hence, the sensor exhibits a very high sensing performance.Moreover, use of the gold coating in a selective manner reduce the manufacturing cost.Besides numerical analysis of the sensor shows that the wavelength sensitivity is 16000 nm/RIU using wavelength interrogation, the amplitude sensitivity is 780 RIU −1 by using amplitude interrogation method and the average spectral sensitivity is 6666 nm/RIU, respectively.Additionally, variation in various structural parameters like pitch, gold (Au) layer thickness is also analyzed.Depending on the high performance of the sensor and nobility of the structure, it is anticipated that the sensor can be broadly used in biosensing application.
, ∧ = 1.20 µm, d1 = 0.60 µm, ds = 1.20 µm, d = 1.60 µm, r1 = 3.24 µm, r2 = 4.24 µm.The thickness of Au thin slotted layer is = t Au 30 nm.The RI (refractive index) of the analyte varied from 1.40 to 1.46.These parameters are obtained by numerically analyzing and simulating in COMSOL Multiphysics software varying the parameter values.They are optimized observing their different performances like sensitivity, loss peaks, FOM, linearity etc. for different values of the parameters.

2 D
D is the frequency of damping and weighting factor is .The values of the given parameters are = 5.9673, /= 2113.60 THz, D = 15.92THz, = 1.09 and ω = c 2 / where c is the vacuum's light velocity.