1. Introduction

Surface Plasmon Resonance is well suited with up to the minute sensing technology due to the ability of specific, accurate, real-time, and label-free detection [1]. To date, SPR sensors have been recommended on a large scale in bio-engineering, environmental observation, gas detection, antigen-antibody collaboration, virus detection, and medical diagnostics because of their non-invasive nature [2–5]. Moreover, the increasing demand for biosensors as well as the advancement of optical devices also facilitates the practical realization of the SPR sensor. Several operating platforms like Prism, optical fiber, and Photonic Crystal Fiber (PCF) are investigated for originating Surface Plasmon Resonance phenomena.

In 1957, Ritchie has given the first concept of Surface plasmons (SPs) [6]. Earlier, Surface Plasmon Resonance (SPR) sensors were investigated under a prism-based platform, introduced by Otto [7], which was upgraded by Kretschmann [8] in 1968. In the kretschmann setup, the sensing performance is robust but due to the requirement of moving optical and mechanical components, the sensor configuration has become bulky. Therefore, the application of the prism coupled sensor limits for remote sensing [2]. Thus, to prevail over the drawbacks of prism-based sensors, conventional fiber-based sensors were adopted. Though fiber-based sensors show the capability of remote sensing, it suffers from low sensitivity and narrow acceptance angle due to their single structure [9]. PCF examines a new dimension in SPR sensing by controlling the sensor properties as well as dealing with the problems associated with the traditional fiber-based sensor. Moreover, PCF based SPR sensors allow the design freedom and compactness by introducing an array of air holes. Besides, propagation can be controlled by modifying the PCF parameters like the diameter of air hole, Pitch, metal film thickness, etc. During the fabrication process, all the parameters can be modified by pressurizing on PCF's holes [10]. Thus, light coupling from the core to the cladding can be controlled which is the major concern of PCF-SPR sensors. Thereby, the sensor performance can be improved by maintaining strong coupling within the Surface Plasmon Polariton (SPP) mode and core guided mode.

In order to create SPR effect, various plasmonic materials (silver, copper, aluminum, gold, niobium) have been investigated by the researchers. Silver (Ag) exhibits smaller optical damping with a sharp resonance peak and has no interband transition [11]. However, oxidization in an aqueous medium restricts the usage of silver in a broader sense [12]. An extra layer of graphene on Silver (Ag) can resolve the problem but this bimetallic profile arises more complication in the manufacturing process owing to the maintenance of uniform thickness of the metal layer [15]. Moreover, such a structure increases the manufacturing cost. Though aluminum possesses high electron density, attributes like higher damping loss, interband transition, oxidization in aqueous solvent turns it inefficient [12]. This day, most of the plasmonic sensor has been realized with gold (Au) as it has several advantages over the other plasmonic material like stability under aquatic environment, biocompatibility, chemical inactivity and ease of materialization [11].

This thin metallic film can be placed over the internal or external surface of Photonic Crystal Fiber (PCF). When the metallic layer is placed on the outer surface of the PCF, it is known as externally metal coated and when the metallic layer is placed into the inner surface of the PCF, it is known as internally metal-coated PCF. Few internally coated plasmonic sensors are reported in Refs. [13,14]. These sensors offer good sensitivity but in practice, it is very difficult to uniformly fabricate the micron-scale air-holes internally. Externally metal-coated sensors can eradicate this complexity. Rifat et al. [15] proposed a single-core externally coated design with the maximum WS of 4000nm/RIU and AS of 478 RIU⁻¹ in a very narrow detection range (1.33 to 1.37). Momota et al. [16] suggested another model with the WS of 4,200 nm/RIU and the AS of 300 which is very low compared to the present work. Very recently, Liu et al. [17] proposed a d-shape plasmonic sensor with a maximum WS of 15,000 nm/RIU and AS of 442.47 RIU⁻¹. Though this sensor offers good sensitivity, it is very challenging to make a flat surface. All these reported sensors are single-core. Nowadays, multi-core models become very popular due to its out-standing sensing performances and fabrication functionality. Paul et al. [18] suggested a dual-core plasmonic sensor with the maximum WS of 5,800 nm/RIU and 11,500 nm/RIU for x and y-polarized modes respectively. It also offers the maximum AS of 554.9 and 636.5 for x and y-polarized mode respectively. A dual-core plasmonic sensor with two open channels is presented by Akter et al. [19] which shows the maximum WS of 5,000 nm/RIU and AS of 396 that is very low compared to others. Recently, Shafkat et al. [20] proposed a dual-core photonic crystal fiber plasmonic sensor where the maximum spectral sensitivity is 10,700 nm/RIU and the maximum AS is 1770. An H-shape dual-core model is proposed by Li et al. [21] which shows the maximum WS of 12,600 nm/RIU and a very low amplitude sensitivity of 34.64. Moreover, an additional layer of Graphene is deposited over the silver layer to prevent the oxidation issue. This additional layer creates fabrication complexity. Very recently, Mahfuz et al. [22] proposed another dual-core externally coated model with a good WS of 28,000 nm/RIU and AS of 6829. In this structure, an additional titanium oxide (TiO2) layer is used over the gold (Au) layer which makes the fabrication process complex.

In this paper, we proposed a four open-channel dual-core plasmonic sensor with outstanding sensing performances. Here we used gold as a plasmonic material which is externally deposited in the selected slotted portion of the structure. So, less amount of gold is required which makes this structure more economical. Moreover, these channels radii are adjustable according to the amount of analytes. Various structural parameters like air-hole, pitch, plasmonic layer thickness are varied and investigated to obtain the best result. Finally, fabrication tolerances are scrutinized up to 2% to prove the performance accuracy. By considering the performance excellency, fabrication functionality, and economic factor this proposed sensor can be a suitable option for the sensing applications.

2. Design method and theoretical background

The cross-sectional transverse view and the stacked preform of the proposed PCF sensor are given in Fig.1ab. The sensor structure consists of three rings formed with air holes, containing a smaller air hole at the center. Two air holes in the second ring have been cancelled out to create birefringence effect. Four air holes in the first ring have been intentionally made small so that light can easily penetrate from the center and be confined in the cores. In addition, four air holes in the third ring have been cancelled to make four circular slots where gold is to be coated. Four slots have been taken to keep the slots closest to the cores so that light can easily stimulate the electrons of the gold coating. If we take more than four slots, the distances from the cores to the slots will increase. Hence, we will have to omit more air holes between the core region and slots. Eventually, the light confinement in the core region will be lost which is not desirable at all. Because the light beams then will be more scattered and fewer light beams will hit the metal surface. The first and second rings are formed by constructing the air holes 30° apart and for the third ring, the air holes are placed 20° apart from each other in an anti-clockwise rotation. The fabrication process of the proposed sensor can be completed introducing with solid rods and the capillaries, as illustrated in Fig. 1(b).

 

Fig. 1. (a) Cross sectional view, and (b) Stack preform of the proposed PCF-SPR sensor in xy plane, with Λ = 2 µm, d_c = 0.6 µm, d_s = 0.4 µm, d_l = r = 1.19 µm and t_g = 30 nm.

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The center to center distance between two nearest air holes is mentioned as pitch, which is denoted by (Λ). The center air hole diameter is denoted as d_c, and the diameter of the smaller and larger air holes are marked as d_s and d_l respectively. The radius of the circular slots is denoted as r. The gold layer thickness is t_g. For our proposed sensor, the optimized values are: Λ = 2 µm, d_c = 0.6 µm, d_s = 0.4 µm, d_l = r = 1.19 µm and t_g = 30 nm. The radius of the first ring is Λ, and the second and third rings are 2Λ and 3Λ respectively whereas the distance between circular slot’s center and the fiber center is 2.4Λ. The fiber core diameter is 12r. The radius of the analyte layer and the PML layer are 4Λ and 5Λ respectively. All the parameters are optimized by a large number of simulations in COMSOL Multiphysics software.

Fused silica has been chosen as the material at the background of the proposed sensor, for its low temperature sensitivity. Gold has been used as the plasmonic material to prevent oxidization problem. The fabrication process of this PCF is done by stack and draw method which is very clean, flexible and cost-effective. Fig. 1(b) represents the stack preform view of the proposed sensor where large, small and no air-hole regions are preformatted as thin capillary, thicker capillary and solid rods respectively. To obtain uniformed gold layer thickness on the slotted region Chemical Vapor Deposition (CVD) technique is employed which offers minimal roughness.

The refractive index (RI) of fused silica can be obtained using the Sellmeier’s equation [23]:

Where n is the complex refractive index (wavelength-dependent) of fused silica and λ is the wavelength in µm unit. B₁, B₂, B₃, C₁, C₂, and C₃ are known as the Sellmeier constants. The values of these constants for the fused silica are: 0.69616300, 0.407942600, 0.897479400, 0.00467914826, 0.0135120631 and 97.9340025 respectively.

To obtain the dielectric constant of gold, we used the Drude-Lorentz model which is characterized by the given equation [24]:

Where ɛ_Au refers to the permittivity of gold and ɛ_∞ is denoted as the permittivity of gold at higher frequency which is valued by 5.9673, ω is known as the angular frequency and is calculated by ω = 2πc/λ. Where c is the light velocity in space, ω_D is referred to as plasma frequency, γ_D indicates the damping frequency. Here, it is known that ω_D /2π = 2113.6 THz, γ_D /2π = 15.92 THz and the weighting factor is Δɛ = 1.09. Now, Г_L /2π = 104.86 THz and Ω_L /2π = 650.07 THz are respectively the Lorentz oscillators’ spectral width and oscillator’s strength.

The confinement loss is the main parameter to be calculated to analyze all the performance parameters, which is obtained by the equation as follows [25]:

Here, Im(n_eff) is used as the indication of the imaginary refractive index where ko = 2π/λ is the number of wavelength and λ denotes the wavelength at which the analysis has to be performed. The little change in analyte RI has great impact on the real part of n_eff,. results in the shift of the resonance wavelengths.

The wavelength sensitivity is obtained using the following equation, by the method of wavelength interrogation [26]:

Here, Δλ_peak is the indicator of the difference of wavelength for the two nearest peak shifts. Δn_a is the variation of analyte refractive index (RIU).

The amplitude sensitivity is obtained from the following Eqn. (6), by the method of amplitude interrogation [24]:

Here, ∂(λ, n_a) is the difference of two nearest spectral losses.

Another important performance parameter is resolution of the sensor, which indicates the sensor’s ability of how small changes in analayte RI can the sensor detect, which is obtained by the equation as follows [1]:

The FOM is the last performance parameter which indicates the better the detection limit. FOM definition is given by the equation in the following [23]:

Where, S is the resonance wavelengths’ linear slope for two nearest RI and FWHM is the Full Width at Half Maxima for the first RI which are counted for linear slope.

3. Simulation and detailed performance analysis

The basic working mechanism of the dual core SPR sensor is the coinciding of the core-clad evanescent field when the Transverse Magnetically (TM) polarized beams of light are incident on the thin metal surface. The sensor performance is analyzed numerically by using Finite Element Method along with Perfectly Matched Layer applying scattering boundary conditions. Modal analysis has been carried out keeping the smallest mesh as possible. To analyze the sensor performance, we considered the following analysis:

3.1 Dispersion relationship between core guided and SPP mode

The dispersion occurs in the sensor when the light beams being TM polarized, become penetrated through the core and incident on the metal dielectric surface releasing free moving electrons. At a particular wavelength, the incident light beams’ the frequency and the metal surface free electrons’ frequency coincides with each other. At this time there is a huge energy transmission loss which indicates the highest energy transfer from core to cladding. This phenomenon is known as resonance and this particular wavelength is defined as resonance wavelength. At this wavelength we observe a huge sharp peak in the confinement loss curve of the sensor. The wavelength where the core guided mode real part and the SPP mode real part intersects together indicates the resonance wavelength. The core guided mode (x and y polarized) and SPP mode electric field distribution are represented in Fig. 2(a), and Fig. 2(b) represents the dispersion relation of the proposed dual core sensor. From the Fig. 2(b) we can see that the resonance wavelength (RW) for RI 1.38 is at 0.63 µm.

 

Fig. 2. (a) Electric field distribution thermal view of the proposed SPR sensor: (i) x polarized core guided mode, (ii) y polarized core guided mode, (iii) SPP mode, where RI = 1.38, tg = 30 nm, Λ = 2 µm. (b) Dispersion relationship between core guided mode and SPP guided mode, where, RI = 1.38, tg = 30 nm, Λ = 2 µm.

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Also, it is obvious that the proposed sensor exhibits higher resonance loss peak in y polarized fundamental core mode rather than x polarized fundamental core mode. Therefore, the y polarized fundamental core mode and SPP mode has been considered for further analysis.

3.2 Response to analyte variation

We analyzed the response of the sensor while varying the refractive index (RI) of the analyte. Figure 3(a) shows the different confinement loss (CL) curves for varying analyte’s RI from 1.33 to 1.45. From the figure we can observe that the increase in the RI of the analyte, the curves experience red-shifts. Accordingly, the confinement loss peak increases because of the lower contrast of the core-clad refractive index. The sensor’s maximum wavelength sensitivity is obtained 38,000 nm/RIU for RI 1.44 with a resolution of 2.63 ${\times} $ 10⁻⁶ RIU, using Eqn. (4) and Eqn. (6) respectively. The resolution shows that the sensor can detect the RI of unknown analyte of minimum 10⁻⁶ order. The amplitude sensitivity curve is shown in Fig. 3(b). The sensor’s maximum amplitude sensitivity is obtained 1286 RIU⁻¹ for RI 1.42, using Eqn. (5). The lowest resonance depth was obtained for RI 1.33 which indicates the lowest energy transmission from the core mode to SPP mode. The detailed performances are included in Table 1 at the bottom of performance analysis section.

 

Fig. 3. (a) Spectral loss curves, (b) Sensitivity curves and (c) Normalized 2D color mapping of CL intensity of the proposed SPR sensor, for analyte variation 1.33-1.45 RI, Λ = 2 µm and t_g = 30 nm.

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Fig. 3(c) represents the normalized 2D CL intensity color map for analyte variation from 1.33 RI to 1.45 RI. From the mapping we observe that the intensity increases for increasing analyte’s RI, due to the increase of coupling efficiency between fundamental core guided mode and SPP mode. The intensity is minimum for 1.33 RI and maximum for 1.45 RI.

3.3. Pitch variation

The pitch variation test is shown in Fig. 4 for RI 1.37 and 1.38 with pitch variation from 1.9 µm to 2.1 µm. From Fig. 4(a), as the pitch is increased, the difference of effective refractive index (n_eff) between core and cladding is also increased. As a result, the loss peak is visibly decreased. If we decrease the pitch, the core becomes narrower and light beams of large wavelengths cannot pass through the narrow core. So we obtain loss peak near smaller wavelengths. As we increase the pitch, eventually increase the core space, light beams from larger wavelength passes through the core. Therefore, we obtain loss peak at larger wavelengths for increased pitch. The lowest loss 27 dB/cm is obtained for 2.1 µm and 1.38 RI. And the maximum loss is found 40dB/cm for 1.9 µm and 1.38 RI. The highest wavelength sensitivity has been achieved 2000 nm/RIU for both 1.9 µm and 2.1 µm, 1.37 RI. The pitch variation sensitivity curve is illustrated in Fig. 4(b). The maximum amplitude sensitivity is 124 RIU⁻¹.

 

Fig. 4. (a) Loss spectrum and (b) Amplitude sensitivity curve, for pitch variation 1.9 to 2.1 µm, RI 1.37 and 1.38, tg = 30 nm

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3.4 Thickness variation

Variation of the dielectric gold thin film thickness is shown in Fig. 5, for variation of thickness from 30 nm to 50 nm. From Fig. 5(a) we find that when the thickness is increased, the confinement loss peak decreases. It indicates that the increasing of the thickness results to less energy transmission from core to metal surface. Again, the higher thickness creates the n_eff of SPP mode more bound in Au layer. The results in the loss curves are red shifts. The amplitude sensitivity curves are shown in Fig. 5(b). As the thickness increases, sensitivity of the sensor also increases. The highest sensitivity is obtained 123 RIU⁻¹ for 40 nm.

 

Fig. 5. (a) Spectral loss curves and (b) Amplitude sensitivity curves, for thickness variation 30 nm - 50 nm with Λ = 2 µm.

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3.5 Fabrication tolerance

We also tested the tolerance of the sensor by varying the parameters for + 2% and -2% of their optimum values. Fabrication tolerance indicates a sensor's stability against any intended or unintended little variation of the fabricating parameters. We tested the tolerance for pitch variation and thickness variation which are represented in Fig. 6. From the Figs. we see that varying the parameters in + 2% and -2% of them leads to little shifts of the resonance peaks. As a result, any deviation of the parameters will cause little effects in the performance of the sensor. That clearly indicates high tolerance and stability of the sensor.

 

Fig. 6. Fabrication tolerance due to: (a) Pitch variation and, (b) Thickness variation, for Λ = 2 µm, tg = 30 nm

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3.6 Polynomial curve fitting characteristics

The proposed sensor shows the polynomial curve fitting characteristics of the resonance wavelength (RW) with respect to refractive index (RI) which is shown in Fig. 7. From the Fig. 7 we say that the RW points are highly adjusted to third order polynomial curve by showing the R- square value of 0.9965. The third order polynomial equation is-

Where, y indicates the wavelength at resonance point and x indicates the RI of the analyte.

 

Fig. 7. Polynomial fitting of different resonance wavelengths for RI 1.33 to 1.45, Λ = 2 µm, tg = 30 nm

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3.7 Figure of merit (FOM)

A good sensor performance also shows a high Figure of Merit (FOM). The FOM of the proposed dual core sensor is shown in Fig. 8. As the RI of the analyte increases, the loss curve becomes sharper. This type of change indicates the decreasing FWHM which results the FOM to increase. From the figure we obtain the maximum FOM is 760 RIU⁻¹, which really indicates a greater FOM. This also indicates the ability of high detection range. The detailed FOMs are shown in Table 1.

 

Fig. 8. FOM curve of the proposed dual core sensor for analyte RI 1.33 to 1.44.

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Table 1. Detailed Performance table of the proposed dual core sensor

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Table 1 shows the detailed performance of the proposed sensor for each individual RI in terms of confinement loss, wavelength sensitivity (WS), amplitude sensitivity (AS) and FOM.

Apart from those parameters, our proposed dual core sensor also exposed lower fabrication cost as the gold is inert in small slots in circular shapes. So we need less gold coating and it can hold much analytes inside the slots.

To prove the compatibility of our proposed sensor, we also added a table with comparison of some recent works in Table 2. This also shows that our proposed sensor can proudly stand as a perfect candidate in the field of optical bio sensing.

Table 2. A comparison table with the existing sensor

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3.8 Experimental validation

The experimental process is ongoing to our lab experiment and it is intended to add in futher research work. The proposed experimental method is shown in Fig. 9 [27].

 

Fig. 9. Experimental setup of the proposed sensor

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3.9 Comparative study

Lastly, we have arranged information in a tabular form that shows a comparative study among different performances of the raised SPR sensor with other existing sensors from the literature [31], [13], [32], [18] and [33] which are referred to in Table 2.

The establishment of Table 2, was made by considering the amplitude sensitivity (AS), wavelength sensitivity (WS), wavelength resolution (WR) and FOM. From the table, it is revealed that our raised OC-DC-PCF sensor has attained the numerical sensitivity of amplitude and sensitivity of wavelength are 1286 RIU⁻¹ and 38000 nm/RIU respectively, which are intensively larger values than the previously proposed PCF sensor and the wavelength sensitivity of 38,000 nm/RIU that exhibits the highest value in the existing literature. For larger wavelength sensitivity, the sensor can become a successful applicant for remote biological, biomedical and biochemical analyte detection.

4. Conclusion

To summarize, an extremely sensitive realistic DC-PCF based plasmonic biosensor is investigated under amplitude interrogation (AI) and wavelength interrogation (WI) method. The suggested structure maintains a robust coupling between the core guided and plasmon mode as visualized in intensity profile, thus improving the sensor behavior. The design parameters are optimized using COMSOL Multiphysics software under finite element method to ameliorate the sensor performance, that provides highest wavelength and amplitude sensitivity of 38,000 nm/RIU and 1,286 RIU⁻¹ with a maximum sensor resolution of 2.63 ${\times} $ 10⁻⁶ RIU. Chemically inactive gold is put in the slotted portion in order to make the sensor more economical. Moreover, the four slotted section can contain a high volume of samples that is beneficial for proper analyte detection and can easily be realized in practice. Fabrication tolerance of the suggested sensor is analyzed up to 2% and no major change appears in the sensor response. Therefore, as a result of being economically and practically feasible with high sensitivity, this sensor has a plethora of applications in the area of biological and biochemical detection.