Introduction

Given its unique optical properties and its ability to solve the diffraction limit, the influence of surface plasmon resonance (SPR) on the interface between plasmonic materials and dielectrics has attracted considerable interest among researchers [1,2,3]. The characteristic for the SPR is the coherent oscillation of electrons on the surface of plasma materials, generating localized SPR and propagating surface plasmon (SPP) forms of SPR [4,5,6]. These phenomena are integral at the design of nanophotonic devices, particularly in sensing and detection applications [7,8,9].

Photonic crystal fibers (PCFs) utilize air holes to lower the fiber-cladding's effective refractive index (RI), enabling total internal reflection within waveguide. The lattice pattern of air holes endows PCFs with a wide range of optical behaviors that are not achievable with conventional optical fibers [10,11,12]. In particular, PCFs can manipulate light in various ways, including guiding specific modes, enabling broadband transmission, exhibiting modal birefringence, and facilitating nonlinear optical effects [13, 14].

Incorporating SPR and SPP effects into PCFs enhances their performance in sensing applications. SPR-PCF sensors, achieved of coating metal layers or nanoparticles on the PCF surface, exhibit remarkable sensitivity to changes are expected in RI near the fiber surface. This sensitivity enables label-free detection, real-time monitoring, and compatibility with diverse analytes, making them highly versatile in various sensing scenarios. In recent years, there has been a growing interest in SPR-PCF-based sensors because of their ability to control the coupling energy between the fiber and the surrounding medium under test [15]. For instance, Dandapat et al. demonstrated the biomolecule sensing capacity of such sensors by the calculating the adlayer/surface sensitivity [16, 17]. The integration of plasmonic materials with PCF technology to construct SPR-PCF-based sensors offers significant advantages, including design and compact dimensions [18,19,20,21]. This combination allows for tailored sensor designs that can be adapted to specific application requirements while maintaining compact form factors suitable for various deployment scenarios.

The mechanism of the SPR-PCF sensor is based on the principle of SPR coupled with the testing medium. As light propagates through the PCF, it interacts with the air holes in fiber cladding. Metal coatings or nanoparticles placed onto the PCF surface selectively enhance the evanescent field near the fiber surface. The sensor operates through evanescent electromagnetic (EM) interaction with plasmonic nanometals. When the sensor is exposed to an analyte with an RI close to the metal's dielectric constant, SPRs are excited at the metal–dielectric interface, leading to changes in PCF's optical properties, such as shifts in resonance wavelengths or intensity variations. By monitoring these changes, the SPR-PCF sensor can detect and quantify RI variations in the surrounding medium with high sensitivity and specificity [22, 23]. Electromagnetic waves penetrate the fiber cladding region, generating evanescent electromagnetic waves that excite the free electrons on the surface of nanometals, producing SPP waves at the metal–dielectric interface [24,25,26,27,28]. At resonance wavelength, the effective RI part of the core-guided mode and the SPP mode perfectly match phase, resulting in sharp confinement loss (CL) peaks, which can detect unknown samples/analytes [29,30,31].

Increasing the number of air holes in the PCF cladding lowers its equivalent RI, while decreasing the number of air holes increases the equivalent RI of the cladding area. The properties of PCF are closely dependent on the number and arrangement of air holes in the fiber cladding. The number of circular air holes used in the SPR-PCF sensor directly affects the CL experienced by the guided modes within the fiber. Increasing the number of air holes typically leads to higher CL because of the increased interaction between the guided modes and the surrounding air holes. This increase in CL can affect the sensor's overall performance by the influence of transmission properties and sensitivity to changes in RI. Therefore, careful optimization of the number and arrangement of air holes is essential to balance the trade-off between CL and sensor performance in SPR-PCF sensors.

Various design strategies have been proposed in recent years using the different values of arrangements and amounts of air holes placed in PCF cladding. Li et al. [32] introduced a D-shaped PCF sensor employing 43 circular air holes and one elliptical air hole in the fiber cladding, achieving an average RI sensitivity of 12,167 nm/RIU within the range of 1.26 to 1.32. Majeed et al. [33] developed a dual open microchannel SPR-PCF RI sensor using 60 rectangular air holes in the PCF, achieving a sensitivity of 33,000 nm/RIU in the RI range of 1.37 to 1.43 and a maximum resolution of 5.56 × 10−6 RIU. Chang et al. [34] designed an SPR-PCF sensor with 36 air holes, achieving a CL of 442 dB/cm for y-polarized mode. Rifat et al. [35] proposed a plasmonic PCF sensor with 37 air holes, obtaining a maximum sensitivity of 3,000 nm/RIU in the RI range of 1.46 to 1.49. Although SPR-PCF sensors demonstrate high RI sensitivity, their structures involve numerous air holes (more than 36), increasing fabrication complexity and production costs.

In this study, we introduce a simplified sensor structure with a PCF surface coated with an Au layer and only four half-circular circular air holes, which can detect analytes externally. We inspect the sensitivity of this device using the COMSOL Multiphysics software based on the finite element method (FEM). Our investigation reveals that structural parameters, such as the air hole size and thickness of the plasmonic material (Au), significantly influence the full width at half maximum (FWHM) and the CL amplitude. Md. Saiful Islam et al. [36] designed a biosensor using a configuration with four truncated air holes, while our work utilizes a structure with four perfectly circular air holes in the fiber cladding. It is crucial to highlight several key distinctions between our study and the work of ref. [36]. First, in their study, four air holes are incorporated into the fiber cladding, but their edges are partially truncated, which complicates the fabrication process of the SPR PCF. This complication arises because the truncated edges lack a surface for the Au film to adhere to, making it difficult to form air holes in the fiber cladding. Additionally, this may potentially affect precision. In contrast, our research employs a configuration with four complete air holes in the fiber cladding, facilitating the coating of the Au film on the outer layer and reducing fabrication challenges. Second, while both studies employ a PCF design with minimal air hole density in the cladding region, our research focuses specifically on investigating the sensitivity to SPR for sensing applications. We provide a comprehensive exploration of SPR sensing performance and provide information on potential applications, thus extending the scope beyond mere design similarity. Third, our numerical investigation delves into detailed electromagnetic behavior, encompassing analysis of field distributions, mode profiles, and sensitivity enhancements. This in-depth analysis contributes to a better understanding of the underlying mechanisms governing SPR sensing in PCF structures with minimal air hole density, thus adding depth to the field of study. Furthermore, while the work by ref. [36] provides flexibility in providing valuable information on exposed core localized SPR biosensors; our study expands the research landscape by focusing on a different PCF configuration. By emphasizing the significance of minimal air hole density for achieving high sensitivity in SPR sensing applications, we contribute to advancing the field. In summary, our research offers a thorough investigation into the SPR sensing performance of a simple PCF design with minimal air hole density. We believe that our study provides valuable insight and lays the groundwork for further advancements in plasmonic photonic crystal fiber sensors.

The novelty of our proposed SPR-PCF sensor lies in its superior sensing performance, characterized by higher sensitivity and better resolution, achieved with the fewest air holes in the fiber cladding. To the best of our knowledge, our sensor design incorporates the most minor air holes compared to reported articles in the literature. Our results establish an experimental foundation and provide theoretical insights for the development of high-sensitivity SPR-PCF sensors, demonstrating that our designed structure exhibits superior sensing performance with higher sensitivity and better resolution while utilizing the least number of air holes in the fiber cladding.

Simulation Models and Principles

Large-diameter circular air holes are more uncomplicated to process in the fabrication of PCFs than small-diameter air holes. Additionally, circular air holes are more accessible to manufacture than elliptical air holes in fabrication. For simplicity in fabricating the fiber structure and considering cost, we opt for a configuration with four larger circular air holes in the PCF cladding, as illustrated in Fig. 1. This figure presents a schematic diagram of the designed SPR-PCF-based sensor. To improve birefringence [37,38,39], we employed two sizes of circular air holes in the fiber cladding, denoted by radii r1 and r2,. Their coordinates are (± d1, 0) along the x-axis for the larger holes and (0, ± d2) along the y-axis for the smaller ones. Furthermore, four uncoated curves with a radius of r3, are placed at the fiber boundary (± d3 ± (d2 + r2 + h)). The reason to not coat the Au film on the surface of the four half-circular curves was to maintain the open windows, which facilitated the coupling effect between the fiber core mode and the analyte under testing [40].

Fig. 1
figure 1

Schematic diagram of the designed SPR PCF-based sensor with structure parameters

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A gold (Au) film coats the flat surfaces of the top and bottom surfaces and the fiber's outer surface, enhancing the SPR-PCF sensor's detection capability. The analyte (thickness 0.5 µm) under test surrounds the entire fiber structure and consists of liquids with different refractive indices in the range of n = 1.30–1.385, where n represents RI. Changes in RI (Δn) result in variations in resonance wavelength (Δλres), enabling the detection of changes in RI. Numerical simulations were conducted using COMSOL Multiphysics, with scattering boundary conditions and perfectly matched layer boundary conditions added in the external computational domain to absorb reflections at the boundaries. A finer mesh of 17,576 domain elements and 1,574 boundary elements was used.

A fused silica material with a diameter of 6 µm diameter serves as a representation of the core and cladding regions. The RI of this material is determined using the Sellmeier equation [41]:

$${n}^{2}\left(\lambda \right)= 1+\frac{{B}_{1}{\lambda }^{2}}{{\lambda }^{2}-{C}_{1}}+\frac{{B}_{2}{\lambda }^{2}}{{\lambda }^{2}-{C}_{2}}+\frac{{B}_{3}{\lambda }^{2}}{{\lambda }^{2}-{C}_{3}}$$
(1)

In Eq. (1), n and λ denote RI and wavelength (in units of µm). B1 = 0.696163, B2 = 0.4079426, B3 = 0.987479400, C1 = 0.0046791486, C2 = 0.0135120631, and C3 = 97.9340025 are constant values of the Sellmeier equation.

We chose Au as the plasmonic material due to its chemical stability in aqueous environments and its significant change in the resonant wavelength (λpeak) compared to other emerging nanometals. The permittivity of Au can be obtained using the Drude-Lorentz model, which is available directly from the COMSOL Multiphysics material library.

The sensor performance formulas can be expressed in Table 1.

Table 1 Formulas of sensor performance
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Results and Discussions

Based on the FEM simulations, the structural parameters are provided in Table 2.

Table 2 The structural parameters for the designed structure
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Figure 2 shows the real part of the RI for the core-guided mode (represented by the blue line) the SPP mode (represented by the red line), and the CL spectrum (depicted by the black curve). Using the geometric parameters listed in Table 2, the RI of the surrounding analyte is set to nana = 1.37.

Fig. 2
figure 2

a Real part of the RI for the core-guided mode (represented by the blue line), the SPP mode (represented by the red line), and b the CL spectrum (depicted by the black curve)

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In Fig. 2, the optical properties of the effective RI and CL for the x- and y-polarizations exhibit considerable similarity. The peak wavelength (λpeak) is observed when the effective RI curve coincides with a high-order SPP mode. Under these conditions, energy is transferred from the guided core mode to the SPP mode, resulting in a CL peak at λpeak = 657 nm for nana = 1.37.

Figure 3(a)–(c) depict the electric field distributions of the SPP and core-guided modes at the resonance wavelength (λpeak) of 657 nm for the x- and y- polarizations. The illustrations clearly show the effective confinement of electric fields on the Au surface for the SPP mode and within the fiber core for the core-guided mode. Figure 3(a) shows that the SPR effect of the SPP mode is more pronounced on the four cutting edge surfaces than on the flat top and bottom surfaces of the Au film. This enhanced effect is attributed to the ability of surface plasmon resonance to intensify at sharp edges and corners. Therefore, this phenomenon facilitates the energy transition from the core region to the Au film.

Fig. 3
figure 3

E-field distributions at λpeak = 657 nm: a SPP mode, b core mode for x-polarization, and c core mode for y-polarization

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Crucial factors in the SPR-PCF sensor, which includes geometric parameters such as t, r1, r2, r3 and h, influence the sensitivity of the designed structure. In subsequent simulations, we systematically inspect the geometric parameters shown in Table 1. Additionally, simulation results for the y-polarization are presented, as the results for both x- and y-polarizations are comparable in the proposed SPR-PCF. Furthermore, the variations in d1, d2, and d3 have minimal impact on the simulation results; therefore, these values remain consistent, as listed in Table 2.

The value of t plays a crucial role in influencing the CL of the designed sensor. Variations in t strongly affect the change in the peak wavelength (λpeak), providing a means to measure the interaction of the surface-coated testing medium with the external Au. FEM simulations (not presented here for simplicity) indicate a negligible CL peak due to the absence of the SPP effect when the outer surface of the SPR-PCF is not coated (i.e. t = 0 nm), rendering it nonfunctional for sensing purposes. However, as t increases from 10 to 50 nm (related to the skin of Au), significant changes in the expected sensor response [45, 46].

Figure 4 illustrates the CL spectra for different t that range from t = 10 nm to t = 50 nm. The other structural parameters, namely r1, r2, r3, d1, d2, d3 and h, are set to 0.8, 0.7, 0.4, 1.8, 1.5, 2.25 μm, and 75 nm respectively. When t is 10 nm, the CL peak occurs at λpeak = 510 nm, indicating a relatively low CL value compared to other values of t and a wide FWHM. This is attributed to a limited energy transfer from the fiber core region to the Au surface when t is relatively thin.

Fig. 4
figure 4

CL spectra for various Au thicknesses, t = (10, 15, 20, 25, 30, 40, 45, 50) nm

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As t increases from 15, 20, 25, 30, 40 to 45 nm, the CL peak significantly redshifts, and the value of CL increases, with λpeak shifting to 545 nm, 600 nm, 657 nm, 785 nm, 800 nm, and finally 810 nm, respectively. The corresponding CL values are 722.04, 1632.20, 2520.80, 4731.60, 5600.00, and 5700.92 dB/cm, respectively. This result suggests that the SPR effect can be adequately induced at a suitable Au thickness within this t range. The coupling effect between the fiber and Au films is enhanced, reaching its maximum value at t = 45 nm with λpeak = 810 nm. However, when t increases to 50 nm, the coupling effect weakens due to the shielding of EM waves from the surface of the Au film, resulting in a decrease in the CL peak. Therefore, as t changes from 40 to 50 nm, the CL peak decreases from 5700.92 dB/cm to 815.28 dB/cm.

Figure 4 shows that it is the most crucial factor affecting the optical performance of the SPR-PCF. This can be explained by the matching impedance between the core and cladding regions of the fiber and the Au surface, as well as the SPR resonance conditions. When the resonance conditions of the fiber are met, variations in t lead to changes in impedance. Meanwhile, as the resonance conditions of the fiber change with t, λpeak should increase to maintain impedance between the surface of the PCF and the Au film.

Based on the CL spectrum curves obtained from Fig. 4, Au thicknesses in the range of t = (15, 20, 25, 30, 40, 45) nm can effectively serve as an SPR sensor, allowing manipulation of the desired peak wavelength depending on the t value. However, the CL spectrum curves for t = (15, 20, 25) nm exhibit a lower CL peak wavelength and a higher FWHM, while those for t = (30, 40, 45) nm show a higher CL peak wavelength and a narrower FWHM. This indicates that the optimal range of t can be selected from t = (30, 40, 45) nm. We selected t = 30 nm as the optimal value to conserve Au material and consider the cost of the material.

The dimensions of the circular air holes and the half-curve at the flat planes play a crucial role in influencing the CL value, as they can alter the effective refractive index in the fiber cladding region. According to the FEM simulations, the dimensions of the air holes (r1, r2) and the half-curve (r3) significantly affect the coupling effect to transfer energy between the core-guided mode and the surface plasmon polariton (SPP) mode.

Figures 5, 6, and 7 illustrate the CL versus wavelength for r1, r2 and r3 ranging from 0.76 µm to 0.89 µm, 0.67 µm to 0.75 µm (withn increase of 0.1 µm), and 175 nm to 525 nm (with an increase of 25 nm), respectively. The other structural parameters, namely d1, d2, d3, and t, h, are set to 0.8, 0.7, 0.4, 1.8, 1.5, 2.25 μm, 25 nm, and 75 nm, respectively. Furthermore, r3 = 0 nm indicates flat planes without a half-curve in the top and bottom cases.

Fig. 5
figure 5

CL spectra vary r1 in the range of 0.76 µm ≤ r1 ≤ 0.89 µm with an increase of 0.1 µm

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Fig. 6
figure 6

CL spectra of r2 in the range of 0.67 µm ≤ r2 ≤ 0.75 µm

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Fig. 7
figure 7

CL spectra of r3 = 0 nm and 175 nm ≤ r3 ≤ 525 µm with an increment of 25 nm of the proposed SPR-PCF structure

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Figure 5 presents CL spectra that vary r1 in the range of 0.76 µm to 0.89 µm with an increase of 0.1 µm. CL peaks exhibit slight redshifts from λpeak = 655 nm to 659 nm as r1 increases from 0.76 µm to 0.89 µm, and the corresponding CL values decrease from 3077 dB/cm to 1311.00 dB/cm. The decrease in CL values with increasing r1 is attributed to the larger air hole size, which reduces the effective RI in the fiber cladding, thus mitigating the coupling effect between the PCF and the external Au coating film.

It should be noted that the CL spectrum curves cannot exhibit a suitable SPR shape if r1 is more significant than 0.89 µm or less than 0.76 µm based on FEM simulations (not shown here for simplicity). Therefore, the suitable range of r1 can be selected as 0.76 µm ≤ r1 ≤ 0.89 µm.

The size of r2 can affect birefringence due to the different effective RI caused by the varying air sizes in the x- and y-directions, while maintaining the value of r1. Figure 6 shows the CL spectra of r2 ranging from 0.67 µm to 0.75 µm with an increase of 0.1 µm. Figure 6 shows that the CL peak undergoes a redshift and exhibits a higher value as r2 increases within the range of 0.67 µm to 0.75 µm. These r2 values apply to the designed device, indicating that we can manipulate the desired operating wavelength by adjusting r2. The CL peaks show significant redshifts from λpeak = 648 nm to 669 nm as r2 varies from 0.67 µm to 0.75 µm, with the corresponding CL values increasing from 1845 dB/cm to 4190.00 dB/cm. The increase in CL values with increasing r2 is attributed to the larger air hole size, which enhances the coupling effect between the fiber core and the external Au coating film, particularly under y-polarized light. In this scenario, we selected r2 = 0.73 µm as the appropriate value, as it is acceptable CL (4340 dB/cm) and FWHM (15 nm).

The size of r3 also significantly influences the CL value due to four half-curves (with a radius r3) in the flat planes at the top and bottom, forming a dielectric window without Au coating. This results in different coupling effects between the two flat Au coating ends and the four air holes in the fiber cladding. Figure 7 illustrates the CL spectra for r3 = 0 nm and the range of 175 nm ≤ r3 ≤ 525 nm (with an increase of 25 nm) for the proposed SPR-PCF structure. In Fig. 7, the black line represents the case (r3 = 0 nm) without half curves on the surface of the upper and lower planes, which exhibits a low CL and a larger FWHM compared to the other cases with r3 curves on the upper and bottom planar surfaces. This result is due to the reduced coupling effect between the PCF and the analyte when the half-curves are positioned at the top and bottom flat planes. For the other cases with half-curves in the flat planes of the top and bottom, the CL peaks undergo a blueshift from λpeak = 694 nm to λpeak = 642 nm as r3 varies from 175 to 525 nm, with CL values ranging from 1395 dB/cm to 2960 dB/cm. The range of r3 from 250 to 450 nm experiences higher CL values and a smaller FWHM (less than 20 nm) because this suitable range of r3 speeds drives the EM wave away from the PCF to the Au film surface. We selected r3 = 400 nm for the subsequent simulation based on an acceptable CL value (2520 dB/cm) and a smaller FWHM (13 nm).

The value of h significantly influences the CL value due to the gap between the air holes and the flat Au coating planes, which affects the coupling effect between the PCF ends and the air holes. Subsequently, we examine the various numbers of h. The other structural parameters, namely r1, r2, r3, d1, d2, d3, and t, are set to 0.8, 0.7, 0.4, 1.8, 1.5, 2.25 μm, and 25 nm, respectively. As depicted in Fig. 8, the CL spectrum experiences a redshift with increasing h in the 20–160 nm range. When h is in the range of 20 to 80 nm, it has a slight redshift from λpeak = 657 nm to λpeak = 658 nm, and the CL amplitude increases from 1713 dB/cm to 3257 dB/cm, decreasing to 2532 dB/cm when h = 160 nm. The FWHM enlarges with increasing h, which can be attributed to the reduced coupling effect between the surface plasmon polariton (SPP) mode of the Au coating plane and the core-guided mode of the air holes. The length of the Au-coated flat planes decreases with increasing h. These Au-coated flat surfaces speed up the coupling effect between the PCF and the analytes, and the gold-coated flat length depends on h. According to the CL spectra, the available h-range can be chosen as 40–120 nm. We select h = 80 nm for subsequent simulations because it has a higher CL value and a smaller FWHM (10 nm).

Fig. 8
figure 8

CL spectra for 20 nm ≤ h ≤ 160 nm with an increment of 20 nm

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Application of the RI Sensor

Finally, we examine the application of the designed RI sensor. Table 3 shows the optimal structural values based on Figs. 5, 6, 7, and 8.

Table 3 Optimal structural values of the designed structure
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We inspect the RI of the analyte, nana = 1.30, 1.31, 1.32, 1.33, 1.34, 1.35, 1.36, 1.37, 1.375, 1.38, 1.385, as the surrounding medium under test. Figure 9(a) and (b) present CL spectra for different RI values of the analytes (nana). Figure 9(a) shows results for nana ranging from 1.30 to 1.35 in increments of 0.01, while Fig. 9(b) shows results for nana = 1.36, 1.37, 1.375, 1.38, and 1.385. The CL amplitude is observed to increase with increasing nana, reaching a maximum value ranging from 202 dB/cm to 3655 when the nana varies from 1.30 to 1.375. Subsequently, CL decreases from 3655 dB/cm to 1600 dB/cm as the nana varies from 1.375 to 1.385. These CL values are proportional to Im(neff) based on Eq. (2). The maximum CL amplitude occurring at nana = 1.375 is attributed to the favorable resonance condition at this wavelength, which facilitates the coupling between the surface plasmon polariton (SPP) mode and the core-guided mode. The maximum nana value of 1.385 is selected in the proposed SPR PCF because no valid CL peak is observed when the nana ≥ 1.385. In other words, for RI values of the target analyte ≥ 1.385, the λpeak was not obtained, indicating that the proposed PCF cannot function as an SPR sensor when the nana ≥ 1.385.

Fig. 9
figure 9

CL spectra for different RI of analytes (nana), (a) nana = 1.30, 1.31, 1.32, 1.33, 1.34 and 1.35, (b) nana = 1.36, 1.37, 1.375, 1.38, and 1.385, respectively

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As shown in Fig. 9(a) and (b), with an increase in nana, all curves show a redshift. When the nana values are lower, the CL peak undergoes a shift; for example, when the nana changes from 1.30 to 1.36 with an increment of 0.01, the CL peak changes from 202 dB/cm to 1146 dB/cm. However, according to Eq. (2), as Im(neff) increases, the higher the value of nana, the faster the position change of the CL peak; for example, when nana increases from 1.37 to 1.375, the CL peak changes from 3655 dB/cm to 1660 dB/cm, and then when nana increases from 1.375 to 1.385, the CL decreases from 2295 dB/cm to 3655 dB/cm. It should be noted that when nana ≥ 1.36, the CL spectrum exhibits a noticeable redshift.

Figure 10 illustrates the λpeak and CL spectra for different nana values within the range of 1.30 to 1.385. The sensitivity S can be determined by Eq. (2). As shown in Fig. 10, the S are SAB = 11,000 nm/RIU, SBC = 4,800 nm/RIU, SCD = 3,600 nm/RIU, SDE = 3,500 nm/RIU, SEF = 2,100 nm/RIU in the wavelength range of 500 to 770 nm, respectively, SFG = 1,700 nm/RIU, SGH = 1,300 nm/RIU, SHI = 1,200 nm / RIU SIJ = 1,000 nm/RIU, and SJK = 600 nm/RIU. For the SAB case, the calculated figure of merit (FOM, defined by SAB/FWHM) can obtain FOM = 220 1/RIU. The maximum theoretical resolution (MTR) of RI is expressed by Eq. (4). Δnana and Δλpeak in SAB as shown in Fig. 10 are Δnana = 0.005 and Δλpeak = 55 nm, respectively. Assuming Δλmin = 0.1 nm, the achievable MTR is 9.09 × 10–6 RIU.

Fig. 10
figure 10

λpeak (nm) and CL spectra for different analytes (nana) with a range of 1.30–1.385

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Table 4 presents the relevant data extracted from Fig. 10. This includes the nana, CL (dB/cm), λpeak (nm), L (cm), S (nm / RIU) and R, corresponding to variations in refractive indices within the range of 1.30–1.385. Sensitivity increases with increasing nana, whereas length and resolution decrease with decreasing nana.

Table 4 The nana, CL (dB/cm), λpeak (nm), L (cm), S (nm / RIU) and R for RIs ranges from 1.30 to 1.385
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Table 5 compares a summary of the sensing performance, including the RI range, the number of air holes, the maximum S, L, and R, between the designed sensor and the previously published ones. It demonstrates that our designed structure exhibits excellent sensing performance with high sensitivity and better resolution while utilizing the minor air holes in the fiber cladding.

Table 5 Comparison of performance analysis between the designed structure and the previously reported sensors
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Conclusions

In conclusion, we have presented a simplified SPR-PCF sensor structure consisting of only four circular air holes coated with an Au layer on both polished and external PCF surfaces. Our proposed sensor demonstrates the capability to detect analytes externally. Through a comprehensive evaluation using the FEM in the COMSOL Multiphysics software, we have thoroughly assessed the sensing performance of this device and characterized its behavior. Our investigation has highlighted the significant influence of structural parameters such as t, r1, r2, r3 and h on key sensor metrics including FWHM and CL amplitude. Optimizing these parameters, our proposed SPR-PCF sensor achieves a remarkable wavelength sensitivity of 11,000 nm/RIU, with a detection resolution of 9.09 × 10–6 RIU, observed for an analyte refractive index (RI) of 1.395. This level of sensitivity makes our device well suited for detecting highly active chemical and biological liquid samples. Furthermore, our sensor design stands out for its minimalistic approach, which incorporates the least number of air holes compared to articles reported in the literature. This simplicity streamlines fabrication processes and reduces costs, making our sensor a practical and cost-effective solution for high-sensitivity SPR-PCF sensing applications. Our study generally advances the SPR-PCF sensor technology by providing valuable theoretical insights. Our results underscore the superior sensing performance of our proposed SPR-PCF sensor, characterized by higher sensitivity and better resolution, achieved using the least air holes in the fiber cladding.