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Dual polarized surface plasmon resonance refractive index sensor via decentering propagation-controlled core sensor

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Abstract

Refractive index (RI) is a unique attribute of bio-analytes which highly relies upon their concentrations or the activity/infectivity of the microbes. In this paper, a dual-polarized surface plasmon resonance (SPR) RI sensor based on a decentered propagation-controlled core photonic crystal fiber (PCF) has been studied. Fine-tuned light guidance is realized by scaling down the core air holes. The external surface of the fiber is metalized with a thin gold layer that maximizes the chemical stability by reducing the chances of oxidation. The deposition of the core from the central position reduces the core to analyte distance resulting in efficient coupling as well as greater sensitivity. Finite element method (FEM) based numerical investigation warrants promising sensing performances in wavelength and amplitude interrogation methods. The proposed sensor is viable for the RI range from 1.33 to 1.39, where it demonstrates the highest wavelength sensitivities of 13,700 and 15,400 nm/RIU and highest amplitude sensitivities of 852 RIU-1 and 654 RIU-1 in x-and y-polarized modes, respectively. It also exhibits high sensor resolutions of 7.30 × 10−6 RIU and 6.49 × 10−6 RIU, and high figure of merits of 216 and 256 RIU-1 for x and y-polarized modes, respectively. Along with the liberty of selecting light sources, the highly sensitive nature of the sensor will enable accurate detections of different organic compounds and bio-molecules.

© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

SPR is the collective oscillation of surface plasmon polaritons (SPPs) on any metal-dielectric interface while they are receiving maximum energy from the applied light [1]. Therefore, resonant wavelength is defined by this peak energy transfer point of the optical spectrum where the natural frequency of free surface electrons matches the incident photon frequency. As this resonance is completely reliant upon the refractive index of the concerned light-trapping system, any small change in RI of the surrounding medium of the metal surface affects the resonant wavelength significantly [2]. Due to the extremely sensitive feature of SPR phenomenon, it caught immense attention of sensor engineers and scientists which is apparent by its broad range of applications in the fields of label-free detection and bio-actuation [3]. Biomolecules from the same class possess identical optical characteristics because of the linear correlations between their concentrations and corresponding RIs [4]. Recently, SPR strategy is continuously being integrated in advanced optoelectronic transducers which are successfully employed in environmental monitoring [5], food safety [6], bacteria detection [7] and infectious disease diagnostics [8]. The first illustration of a plasmonic sensor is credited to Kretschmann [9], where he used a prism coupler in conjunction with a thin metal. In 1983, the works of Nylander and Liedberg [10] showed successful employments of SPR for gas sensing. Kretschmann-Raether configuration for phase coupling was very popular in the early stages of SPR biosensing where bulky mechanical components of the sensor limit the options of miniaturization [11,12]. Hence, over time, the manual prism coupling-based sensing approach kept being replaced by the PCF-based RI sensors. Along with cost-effectiveness and simplified mass production facilities, PCF gives high flexibility of design and opens more scopes for remote detection [13,14]. Moreover, PCF does not have complications of eliminating the fiber jacket or additional doping like conventional optical fibers.

When light is transmitted through the PCF, the core of the fiber is consciously designed in a way that an evanescent field originates to interact with the sensing medium. The adjacent placement of unknown analyte to the plasmonic layer helps easy binding of the ligands to the metal surface. The evanescent field penetrates through the cladding region and reaches the sensing layer to supply the required binding energy. Under SPR condition, the received energy of SPPs becomes maximum which mandates a sharp propagation loss peak. At that moment, the real component of the fundamental core guided mode RI and the SPP mode RI are perfectly matched which is called the phase-matching condition [8]. To date, all existing PCF SPR sensors are broadly classified into two categories based on their operational design; internal and external. Internal sensing methods usually involve microfluidic channels with internally coated metal layers or installed nanowire inside the analyte channels. Lately, Wang et. al. [15] designed a wide range sensor with x-polarized and y-polarized mode wavelength sensitivities of 4156.82 nm/RIU and 3703.64 nm/RIU, respectively. A concave-shaped RI sensor, proposed by Pathak and Singh [16] using silver nanowire, was able to show sensitivities of about 9,314 nm/RIU and 1,494 RIU-1 in spectral and amplitude interrogations, respectively. This kind of sensors has a time-consuming refilling procedure after each use and does not possess real-time distributed sensing feasibility. High sensitivity can be achieved in side polished external sensors like D-shaped fiber where the core is located very close to the sensing surface. Liang et. al. [17] investigated a D-polished sensor imposing graphene and zinc oxide layers on the flat side of the PCF that exhibits a peak sensitivity of 6,000 nm/RIU. However, imperfect polishing could cause rough outer surface resulting in faulty operation. On the other hand, optofluidic slot-based structures and externally metalized sensors are largely highlighted PCF SPR sensing strategy since it demonstrates a sophisticated detection tactic with good performance [18]. Recently, a dual-core PCF-based external plasmonic sensor proffers a wavelength sensitivity of 11,200 nm/RIU with a good figure of merit (FOM) of 275 RIU-1 [19].

Chemical stability and large resonant wavelength shifts are the key factors for selecting the plasmonic material of an SPR sensor. Silver (Ag) and copper (Cu) have been reported as good plasmonic metals in terms of sensitivity in many researches [3,6]. However, as they need adhesive layers of less chemically active material such as graphene or titanium dioxide to avoid rapid oxidation, they pose higher fabrication complexities and unnecessarily enlarge the manufacturing cost [19]. On the other hand, gold (Au) is an established stable material as it is less prone to oxidation and also demonstrates decent resonant shifts resulting in promising sensitivity [3]. Herein, we reported an externally Au coated plasmonic sensor based on a 3-rings hexagonally patterned silica PCF. Generally, fabrication of irregularly arranged air holes is considered less efficient as it needs very precise drilling protocol. On the contrary, our sensor can be fabricated by stack and draw method using capillaries of different thicknesses without the need of any drilling. The analyte will be glided over the exterior surface of the fiber to enable fast reuse by simplifying the process of switching analyte [1]. The propagation controlling strategy by reducing core air hole diameters is one of the significant advancements of single-core PCF-based SPR sensing since it mitigates the challenge of guiding the evanescent electric field to the plasmonic layer [20]. Fine-tailoring of light is extremely crucial for PCF SPR sensing technique and many sensors are reported by employing a scaled-down core at the center of the PCF. However, a core located close to the periphery is more responsive to the variation of the analyte RI [21]. This type of fiber core allows to adjust the energy leakage pathways(s) while maintaining a single core. Here we adopted this idea and investigated a decentered propagation-controlled core for the first time. Recently, some optical sensors were designed on the multicore fiber-based approach to achieve desired light tailoring and better sensing performance. In 2021, Shakya and Singh [22] proposed a numerical analysis of a tetra core biosensor yielding maximum wavelength sensitivity of 10,000 nm/RIU in its dominant y-polarized mode. Though multicore fiber distributed sensing systems enable wavelength division multiplexing, thermal loads cause alterations of their super-mode couplings [23]. Mode instability is another frequent problem of these fibers and thus, Otto et al. [24] proposed an improvement in 2014. Two super-modes exist in the dual-core PCF (odd and even modes) due to core spitting and these SPR sensors offer a large number of redundant different order SPP modes. For example, a two-core sensor proposed by Chen et al. [25] exhibited 7 plasmon modes where only 2 (from x and y-pol.) were used for sensing operation. In multicore PCFs, the trade-offs to secure better electromagnetic propagation is difficult, as there are many extra coupling requirements e.g. core-core and core-SPP mode couplings in both even and odd modal analysis. Therefore, we have proposed this type of fiber core that allows to adjust the energy leakage pathways while maintaining a single core.

Here, leveraging the core air hole scaling tactic, we are able to show that centrally displaced mono-core PCF sensors can demonstrate better sensitivity and improved photon-guidance inside the engineered leaky core. High sensitivities in both polarization modes make this sensor a very good candidate in the field of fiber-based biochemical sensing. Fabrication tolerance of pitch variation, air-hole sizes and the width of the gold layer are numerically inspected to achieve the optimal sensing characteristics. Additionally, a relative critical investigation of different variants of our fiber core is discussed to claim the best practicability of the proposed core architecture.

2. Structure design and analysis

Figure 1(a) depicts the cross-sectional view of the proposed sensor. Diameters of one air hole from the first ring and four air holes from the second ring are scaled down using thick-wall capillaries to adjust the transmission-controlled core out of the central position. The stacked arrangement of capillaries is displayed in Fig. 1(b). Another four air holes of the third ring are reduced in diameter to facilitate the SPP excitation by regulating the energy transfer. Two side air holes among those four small holes from the third ring are designed to be the smallest to further enhance the lateral leakage. Thin-wall capillaries with larger inner holes will act as the cladding of the fiber. Cladding layer maintains the extent of light confinement to our desired level by performing modified total internal reflection at the air-silica interface. After stacking the capillaries and drawing the canes, the preform is rotated 90° counter-clockwise for convenient visualization of the electromagnetic mode profiles. The center-to-center distance of two adjacent air holes is defined as the pitch (${\bigwedge}$) of the proposed PCF. We optimized each structural parameter of the sensor individually to ensure the best detection performance and finalized the pitch (${\bigwedge}$) = 1.8µm, large air hole diameters (d) = 1.17µm, core (small) air hole diameters (dc) = 0.415µm, smallest air hole diameters (ds) = 0.250µm, thickness of Au nanolayer (t) = 45nm. Refractive properties of the background material dominate the effective index of the fiber modes. We chose fused silica as the background material of our sensor and Sellmeier equation is used to model its RI which is a function of the transmitted wavelength [17];

$${n^2}(\lambda )= 1 + \frac{{{B_1}{\lambda ^2}}}{{{\lambda ^2} - {C_1}}} + \frac{{{B_2}{\lambda ^2}}}{{{\lambda ^2} - {C_2}}} + \frac{{{B_3}{\lambda ^2}}}{{{\lambda ^2} - {C_3}}}$$
which expresses the RI value of fused silica (n) in terms of operational wavelength (λ) in micrometers and Sellmeier constants Bi = 1,2,3 and Ci = 1,2,3. The approximate magnitudes of these constants are accessible from paper [26]. Since the availability of sufficient free electrons on the metal surface determines the affinity of analyte ligand binding when the energy transaction occurs, the electric property of the metal directly modulates the sensitivity of the sensor. The dielectric constant of Au depends on the incident optical frequency and it can be estimated by the Drude–Lorentz model [27];
$${\varepsilon _{Au}} = {\varepsilon _\infty } - \frac{{\omega _D^2}}{{\omega ({\omega + j{\gamma_D}} )}} - \frac{{\Delta \varepsilon \Omega _L^2}}{{({{\omega^2} - \Omega _L^2} )+ j{\Gamma _L}\omega }}$$
where ɛAu is the dielectric constant of Au, ω is the angular frequency of the transmitted light through the PCF and the existing constants in the modeling equation such as plasma frequency (ωD), damping frequency (γD), oscillator strength ΩL can be obtained from Ref. [28]. To execute the FEM-based investigation, we simulated the structure in commercial software COMSOL Multiphysics 5.5 with an adequately large mesh size (comprising 28,824 sub-domains enclosed by 2,437 boundaries), so that we receive accurate data of the modal losses. We relied on a cylindrical PML and built-in scattering boundary conditions for absorbing the evanescent field that leaves the fiber geometry. In practice, deposition of Au over the exterior surface makes it easier from manufacturing point of view. There are many laboratory options for coating a metal layer over the circular plane of the fiber. However, vapor deposition methods sometimes fail to maintain the uniformity of thickness of the inserted material and sputter deposition may suffer from gaseous contamination [29]. We will prefer using atomic layer deposition (ALD) for our sensor which has the ability to achieve high uniformity of the metal coating [30]. Alternately, nanoparticle layer deposition (NLD) is another well-known less expensive method for avoiding impurity contamination [31].

 figure: Fig. 1.

Fig. 1. Cross-section of (a) the proposed sensor and (b) stacked PCF preform.

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Despite the high performance and user-friendliness, the operational setup of PCF-based SPR biosensors is relatively simpler than any other label-free sensing scheme. As Fig. 2 portrays, initially a broadband light source sends a transverse magnetic (TM) or p-polarized light through the single-mode PCF. Due to decentering core, the coupling between SMF and proposed fiber could increase the loss which will only affect the sensor length. However, the wavelength sensitivity response will remain the same as it depends on the resonant wavelengths. The maximum energy is received by the SPPs at the resonant wavelength which is dependent on the RI of specific liquid streaming over the sensor surface. As the output end of the PCF is probed to a computer-connected photodetector or optical spectra analyzer (OSA), the loss spectrum will be accurately read and fed into the processing unit. The processor then interpolates and fine-tunes the loss curves and compares the sensor response with the pre-trained reference spectrum. Finally, a user-defined decision tree algorithm indicates the RI of the unknown sample on a display.

 figure: Fig. 2.

Fig. 2. Experimental configuration of the detection scheme.

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3. Results and discussions

Electric field distributions of the desired modes exhibit the excitation paths and the leakage intensity of the designed sensor. Within a PCF geometry, the phase coupling and loss coupling are two intertwining phenomena. In case of completely coupled fiber modes under SPR condition, the loss difference between fundamental core-guided mode and defect super mode tends to zero, implying highest possible continuous energy transactions at the resonant point [32,33]. So, to ensure practicable core mode losses strong partial coupling is realized for our PCF. Figures 3(a) and 3(b) are showing the electric field profiles of the fundamental core-guided mode and the SPP mode, respectively for x-polarized light at resonant wavelength for an infiltrated analyte RI 1.37, whereas, Figs. 3(c) and 3(d) are presenting equivalent field distributions of the core-guided mode and the plasmon defect mode respectively in y-polarized mode. Figure 4(a) verifies that the phase-matching condition is satisfied near the resonant wavelengths for RI 1.37 in both polarized modes where we found adequately sharp modal loss peaks. This proves, the maximum excitation mandates the overlapping of the real effective mode indices of the core and the SPP modes at the optical frequency where the sharpest loss is situated. The fiber confinement loss is calculated by the following equation [34];

$$\alpha ({dB/cm} )= 8.686 \times {k_0} \times {\mathop{\rm Im}\nolimits} ({{n_{eff}}} )\times {10^4}$$
Here, λ is the wavelength (in micrometers) of the propagating light and Im(neff) specifies the imaginary effective index.

 figure: Fig. 3.

Fig. 3. Electric field distributions of the core-guided mode and SPP mode for (a, b) x – polarized mode, and (c, d) y-polarized mode at analyte RI 1.37.

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 figure: Fig. 4.

Fig. 4. For test analyte RI 1.37, (a) phase-matching phenomena for x & y-polarizations and (b) birefringence curve of the structure.

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In Fig. 4(a), we found a slight mismatch between two differently polarized loss depths resulting from the induced birefringence of the sensor. The differences in loss magnitudes and resonant wavelengths between two differently polarized modes will allow the cross-checking of the final results which could help to avoid the risk of false-positive response. Furthermore, high birefringence assists the maintenance of the polarization states of the input signal and enhances the overall stability of the optical operation [35]. Birefringence of a geometry is evaluated by the formula below where nx and ny are the real effective indices of x-and y-polarized modes respectively [3];

$$B = |{{n_x} - {n_y}} |.$$

In the birefringence spectrum of RI 1.37 (Fig. 4(b)), a strong birefringent response of 2.2×104 RIU-1 is noted around the resonant wavelength due to the SPR. Later, the sensor illustrated an increased birefringence induction in upper wavelengths (∼3.1×104 RIU-1 at 950nm), forecasting an improved sensitivity in that spectral region. While manufacturing, additional twists introduced in a fibre structure affects the overall sensitivity of any PCF sensor provided that the architecture is heavily polarization-dependent [36]. So, extra caution is highly recommended for configuring the number of twists in our sensor. Again, the real effective RI of SPP mode responds very sensitively to any variation in liquid layer and interacts with core mode’s real effective index accordingly. In other words, the real RI of plasmon mode will match with the real RI of core mode at different optical point within the spectrum for a changed analyte RI. This updated optical resonant wavelength can be found either in forward (red-shift) or backward (blue-shift) direction depending on the type of the PCF. Our sensor demonstrates red-shifts of loss spectra with additional loss depths for every sample RI escalation of 0.01 RIU. The improved sensitivity and the dissimilarities of propagation loss depths are caused by the decreasing gap between index contrasts of the core and the SPP mode owing to the increased analyte RI. Figure 5(a) shows the loss curves for x-polarization and we can see the movement of these curves towards longer wavelength area for analytes applied from RI 1.33 to 1.39. The highest loss depth of 131dB/cm is located at 950nm when the sensing surface is submerged in a sample liquid of RI 1.39. Oppositely, a minimal modal loss is obtained at RI 1.33 where the transferred propagation energy is estimated merely 50dB/cm at 621nm. Figure 5(b) depicts similar results for y-polarized mode at different resonant wavelengths for the same RI range. The lowest loss is depicted by using analyte RI 1.33 and the loss magnitude is 62dB/cm which is sited 2nm right-shifted from the equivalent loss curve found in x-polarization analysis. The magnitudes of peak losses resulted from testing analyte RIs 1.38 and 1.39 are extremely close to each other, implying both of these RIs enforced strong phase couplings with the core. The most distant resonant peaks for two successive RIs are found for RI 1.38 and 1.39 in both polarizations, indicating a great coupling intensified response. The resonant points moved by 137nm and 154nm in the right direction when the RI of the analyte is switched from 1.38 to 1.39 in x and y-polarized modes respectively.

 figure: Fig. 5.

Fig. 5. Loss spectra of (a) x- and (b) y-polarized modes for analyte RI from 1.33 to 1.39. Amplitude sensitivities of (c) x- and (d) y-polarized modes for analyte RI from 1.33 to 1.39.

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The wavelength sensitivity is defined as the spectral shift per RI variation [37];

$${S_\lambda }(nm/RIU) = \frac{{\Delta {\lambda _{peak}}}}{{\Delta {n_a}}}$$
here, Δλpeak is the shift of resonant wavelength and RI change Δna. Hence, the maximum wavelength sensitivities of our sensor are attained 13,700 nm/RIU and 15,400 nm/RIU in x and y-polarized modes, respectively. Table 1 showcases the simulation information and performance parameters for all detectable RIs (1.33-1.39). It evidences that the sensor shows a nonlinear sensing response in terms of performance factors by presenting greater sensitivities for higher RIs. This happens as the ultimate outcome of the reduced RI contrast difference between the core and the SPP modes for higher RIs is less light confinement which results in increased plasmonic coupling at the interface [38].

Tables Icon

Table 1. Performance analysis of the proposed sensor

Our presented sensor shows reasonable average wavelength sensitivities of 4,700 nm/RIU and 4,957 nm/RIU in x & y-polarized modes respectively. The smallest detectable variation in liquid RI is called the sensor resolution of the sensor when we assume the minimum spectral resolution (Δλmin) to be 0.1 nm [3];

$$R({RIU} )= \frac{{\Delta {n_a} \times \Delta {\lambda _{\min }}}}{{\Delta {\lambda _{peak}}}}$$
where, Δna and Δλpeak denote the analyte RI changes and the peak shift of resonant wavelength. Another important sensor parameter, the limit of detection (DL) is the quotient of the maximum resolution and the wavelength sensitivities [39] and the results indicate, the most accurate value for this limit is 4.22×10−10 RIU2/nm for y-polarized light (Table 1). Figures 5(c) and 5(d) exhibit the amplitude sensitivities of the proposed sensor for analytes from 1.33-1.38. In amplitude interrogation, sensitivity is defined as a function of optical wavelength which enables amplitude sensitivity to be computable at any specific frequency without the necessity of wavelength interpolation. Therefore, amplitude interrogation is always regarded as a more cost-efficient performance interrogative approach in comparison to the wavelength interrogation [40]. We have computed the amplitude sensitives of our sensor using the following equation [12];
$${S_A}(\lambda )[{RI{U^{ - 1}}} ]={-} \frac{1}{{\alpha ({\lambda ,{n_a}} )}}\frac{{\partial \alpha ({\lambda ,{n_a}} )}}{{\partial {n_a}}}$$
where, α(λ, na) is the loss depth and ∂α(λ, na) is the difference of loss depths at that corresponding wavelength of two consecutive RIs. Although the sensitivity of a sensor gives an upfront idea about the quality and efficiency of its functionality, aside from it, there are several indicators that are highly expected from a good sensor. High magnitudes of FOMs and sensor lengths, R2 being close to unity in the polynomial fitting, assist the sensing system give extremely precise results. The ratio of spectral sensitivity at a certain RI and the corresponding full-width-half- maxima (FWHM) defines the FOM of the sensor at that RI [39]. The diamond-shaped points of Figs. 6(a) and 6(b) are denoting the FWHM of each RIs in both polarizations whereas, the triangular points are representing the associated FOMs of our proposed sensor. Sensor length is the inverse quantity of the peak modal loss for a given analyte RI [22]. High confinement loss sometimes causes a very weak received signal at the OSA input probe which eventually obstructs the detection viability.

 figure: Fig. 6.

Fig. 6. FOM & FWHM values at different RIs for (a) x-polarized, and (b) y-polarization lights. (c) sensor lengths, and (d) polynomial fitted curve of resonant wavelengths.

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High values of fiber length imply that the receiving end will get a satisfactory signal intensity to process which it can send to the computer system later for extracting the final results. The sensor lengths of the proposed sensor are displayed in Fig. 6(c). When the spectral data reach the computer’s processing unit, the processor requires a predefined fitted curve that tends to the original resonant points. The system works based on the comparison of the received loss curve with the pre-trained data. The proposed sensor demonstrates R2 values of second-order polynomial fitting to be 0.985 and 0.979 in x and y-polarized modes, respectively which are certainly approximating the unity indicating its suitability with the complete detection strategy (see Fig. 6(d)).

4. Core architecture

The proposed sensor’s dual polarization feasibility has been engineered via planning the reduced air hole size in a well-organized pattern that confirms decent performances in both of the polarizations. To assert the polariton excitation dependency of the sensing channels on differently designed cores, we took four different propagation-controlled cores under our critical inspection with analyte RI 1.37 on the sensing surface as depicted in Fig. 7. The structure in Fig. 7(a) consists of the simplest change in our core’s design when we have scaled-up the side (smallest) air holes’ diameters equaling to the core (small) air holes. We can see this suppresses the coupling intensity in the x-polarized mode significantly by shrinking the energy dissipation path in the transverse direction. The loss curve shows a peak transmission loss of mere 35 dB/cm in x-polarization mode for swapping the smallest holes diameters with the core air hole diameters. This peak loss value differs by 85 dB/cm from its correspondent y-polarized peak modal loss value by letting greater dominance to the y-polarization, whereas, for our proposed side air holes size this difference is of sheer 18 dB/cm (see Table 1). The second and third core designs in Fig. 7(b) are aimed to analyze the effects for individually activating only one side of the whole distributed propagation-controlled core as the effective core.

 figure: Fig. 7.

Fig. 7. Effect of different cores on confinement loss and core-mode field distribution.

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For this purpose, core air holes of the previous core structure are replaced by regular air holes up to the middle and the remaining portion is kept untouched. Although this gives us two lattice structures, due to the fact that one is mirrored by the other structure along the y-axis, they depicted similar optical response. The x and y-polarized highest loss responses are obtained 33 dB/cm and 184 dB/cm at resonant wavelengths of 751 nm and 749 nm respectively. Again, the massive loss variation between x and y-polarized modes opposes the highly sensitive dual-polarized functionality. The fourth variant of our investigating cores is designed by totally replacing the smallest air holes and their immediately adjacent small air holes of the structure by regular large air holes (in Fig. 7(c)). This leaves the five small core air holes for acting as the actual core area. This transformation of the core increases the y-polarized confinement loss and takes it beyond our desired loss level where x-polarization shows quite poor loss. The maximum losses are 42 dB/cm and 381 dB/cm for RI 1.37 in x and y-polarized modes respectively. These strongly suggest that, for limiting excessive propagation loss and enabling dual light usability of the sensor, our prescribed design of the core air hole distribution performs the best (see Fig. 1 (a)).

5. Structural tolerance

An optimized thickness of the metal layer is as much crucial as the selection of the plasmonic material. Though the plasma frequency of a material is only related to the relative permittivity of the material, the effective RI concentration is heavily inflected by the thickness of the metal film [12]. Thus, we have critically examined the metal layer thickness in our numerical analysis. In Figs. 8(a) and 8(b), it appears that the loss depth at analyte RI 1.37 decreased with the thickening of the gold layer due to the damping effects. In x-polarized mode, the confinement loss suppresses from 216 dB/cm to 83 dB/cm at RI 1.36 when Au layer thickness changes from 35 nm to 45 nm. Again, it drops down to 45 dB/nm for an Au layer of 55 nm. Similarly, y-polarization modal losses at t = 35 nm, 45 nm and 55 nm are consecutively 165 dB/cm, 101 dB/cm and 37 dB/cm. As larger loss means better analyte engagement at the interface, this decrease of propagation loss affects the amplitude sensitivity of the sensor negatively. The lowest amplitude sensitivities encountered are 280 RIU-1 and 453 RIU-1 for t = 55 nm at RI 1.36 in different polarized modes in Figs. 8(c) and 8(d). Oppositely, a fat Au layer results in a greater concentration of effective index, causing correspondent phase changes of the resonances which imply that the sensor will depict significantly better wavelength sensitivity.

 figure: Fig. 8.

Fig. 8. Loss spectrum with varying gold thickness in (a) x & (b) y-polarized modes. Amplitude sensitivities with varying gold thickness in (c) x & (d) y-polarized modes at RI 1.36.

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For instance, the resonant wavelengths red-shift itself 45 nm and 52 nm for the thick Au nanolayer of 55 nm in x and y-polarized modes, respectively, which are larger than what are found for the other two values of t in our experimentation. For t = 35 nm Au film, the modal losses increase extremely and the wavelength sensitivities decrease, whereas for t = 55 nm Au coating, the corresponding losses drops under their optimal magnitudes and the wavelength sensitivities drop significantly. Hence, based on the above observation, we finally fix an optimized Au thickness of t = 45 nm to maintain good sensitivities in both interrogations. Hence, based on the above observation, we finally fix an optimized Au layer that is 45 nm thick to maintain good sensitivities in both interrogations. It is also noteworthy that the direction of loss variations is suggestive to the changes of the amplitude sensitivities. However, extremely large losses to achieve better amplitude sensitivity are not acceptable for practical limitations (e.g. low input signal strength) [20,41]. Besides, it is verified from the simulation that the spectral sensitivities of our sensor are not depending on other fiber parameters except for the plasmonic layer. Thus, we decided to interrogate the remaining structural parameters based on confinement losses only for convenience, since it will be equivalent to sensitivity-based analysis. The pitch size (${\bigwedge}$) of a sensor can directly moderate the effective core and cladding region and therefore, defining an optimal pitch is mandatory while designing the microstructured holy fiber. The experimental results assure that the hexagonal geometry presents an affordable manufacture tolerance in terms of pitch variation. In Figs. 9(a) and 9(b), we can visualize the loss variations in both polarizations for different values of ${\bigwedge}$, deviated from +10% to -10% from its optimum size when analyte RI 1.37 is under investigation. Here, the fluctuation of losses ranges from 63 dB/cm to 113 dB/cm and from 73 dB/cm to 135 dB/cm for x-and y-polarized lights, respectively. The optimized ${\bigwedge}$ has been selected 1.8 µm for the proposed sensor where moderate losses of 83 dB/cm and 101 dB/cm in x- and y- polarized mode, respectively. Furthermore, the changes in loss levels because of the cladding air hole size are also within a tolerable limit. Figures 9(c) and 9(d) portray, for an increase or a decrease of the optimized larger hole diameters (d = 1.17 µm) of about ±10%, very insignificant differences in loss depths are observed according to the extracted data from the numerical study. Small core air holes and the smallest side air holes influence the x-polarized sensing performance more than the y-polarized sensing performance. For example, if we choose the optimum diameter of core air holes (dc) to be 0.415 µm, for a 10% reduction in its size, x-polarized mode shows an upgraded modal loss of 107 dB/cm at RI 1.37 which is almost 29% higher than its proposed value (see Fig. 10(a)). Whereas, for the same case, y-polarized mode depicts a 6% fall of the confinement loss from the prescribed value in Fig. 10(b).

 figure: Fig. 9.

Fig. 9. Fabrication tolerance effects on pitch size in (a) x -and (b) y-polarized modes at RI 1.37. loss curves for large air hole diameter variations in (c) x & (d) y-polarized modes at RI 1.37.

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 figure: Fig. 10.

Fig. 10. Loss curves for small air hole diameter variations in (a) x-and (b) y-polarized modes at RI 1.37. Fabrication tolerance effects on the smallest side hole size in (c) x -and (d) y-polarized modes at RI 1.37.

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Retrospectively, for a 10% increase of dc from the optimal size, loss at RI 1.37 goes down from 83 dB/cm to 66 dB/ from our preferable loss level in x-polarized mode. Y-polarization modal loss remains unchanged in this particular case. Similar scenario is visible in Fig. 10(c) for the smallest air hole variations where the x-polarized mode losses are 122 dB/cm, 100 dB/cm, 67 dB/cm and 59 dB/cm respectively for ds varied from the optimized value (ds = 0.250 µm) by +10%, +5%, -5% and -10%. Figure 10(d) shows, y-polarized mode yielded a slight degradation of loss by 1∼9 dB/cm for the ±10% variations of the side air hole diameter. Despite more proneness to structural variation of x-polarized mode than y-polarized mode, it can be said that, even taking fabrication defects around ±10% into account, the sensor’s efficiency does not degrade largely. Table 2 includes a performance comparison among some contemporarily reported sensors to help foresee the aptitude of our sensor.

Tables Icon

Table 2. Performance comparison of the proposed SPR sensor with recently reported sensors

6. Conclusion

A dual-polarized PCF-based SPR sensor is presented and numerically analyzed in this paper that performs highly sensitive detection based on the external sensing approach. FEM is employed to conduct the investigation which indicate that the detectability of the sensor is very promising in light of the performance parameters. Our proposed sensor shows the best wavelength sensitivities of 13,700 nm/RIU and 15,400 nm/RIU in x-and y-polarized modes, respectively. The peak amplitude sensitivities are 851 RIU-1 and 654 RIU-1 in those respective polarizations. The sensor also shows the highest FOMs of 216 RIU-1 and 256 RIU-1 in x-and y- polarizations, respectively. As its maximum resolution lies in the range of 10−6 RIU, it will be able to sense extremely microscopic analyte microbes present on its sensing surface. Owing to the highly sensitive nature along with its fascinating detection features, the proposed sensor would be an attractive addition to the existing sensing technology for label-free biochemical sensing and may find potential application in any field related to early diagnosis of cancer cells or microbial infections.

Disclosures

The authors ensure that there are no conflicts of interest.

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

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Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (10)

Fig. 1.
Fig. 1. Cross-section of (a) the proposed sensor and (b) stacked PCF preform.
Fig. 2.
Fig. 2. Experimental configuration of the detection scheme.
Fig. 3.
Fig. 3. Electric field distributions of the core-guided mode and SPP mode for (a, b) x – polarized mode, and (c, d) y-polarized mode at analyte RI 1.37.
Fig. 4.
Fig. 4. For test analyte RI 1.37, (a) phase-matching phenomena for x & y-polarizations and (b) birefringence curve of the structure.
Fig. 5.
Fig. 5. Loss spectra of (a) x- and (b) y-polarized modes for analyte RI from 1.33 to 1.39. Amplitude sensitivities of (c) x- and (d) y-polarized modes for analyte RI from 1.33 to 1.39.
Fig. 6.
Fig. 6. FOM & FWHM values at different RIs for (a) x-polarized, and (b) y-polarization lights. (c) sensor lengths, and (d) polynomial fitted curve of resonant wavelengths.
Fig. 7.
Fig. 7. Effect of different cores on confinement loss and core-mode field distribution.
Fig. 8.
Fig. 8. Loss spectrum with varying gold thickness in (a) x & (b) y-polarized modes. Amplitude sensitivities with varying gold thickness in (c) x & (d) y-polarized modes at RI 1.36.
Fig. 9.
Fig. 9. Fabrication tolerance effects on pitch size in (a) x -and (b) y-polarized modes at RI 1.37. loss curves for large air hole diameter variations in (c) x & (d) y-polarized modes at RI 1.37.
Fig. 10.
Fig. 10. Loss curves for small air hole diameter variations in (a) x-and (b) y-polarized modes at RI 1.37. Fabrication tolerance effects on the smallest side hole size in (c) x -and (d) y-polarized modes at RI 1.37.

Tables (2)

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Table 1. Performance analysis of the proposed sensor

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Table 2. Performance comparison of the proposed SPR sensor with recently reported sensors

Equations (7)

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n 2 ( λ ) = 1 + B 1 λ 2 λ 2 C 1 + B 2 λ 2 λ 2 C 2 + B 3 λ 2 λ 2 C 3
ε A u = ε ω D 2 ω ( ω + j γ D ) Δ ε Ω L 2 ( ω 2 Ω L 2 ) + j Γ L ω
α ( d B / c m ) = 8.686 × k 0 × Im ( n e f f ) × 10 4
B = | n x n y | .
S λ ( n m / R I U ) = Δ λ p e a k Δ n a
R ( R I U ) = Δ n a × Δ λ min Δ λ p e a k
S A ( λ ) [ R I U 1 ] = 1 α ( λ , n a ) α ( λ , n a ) n a
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