Introduction

Surface plasmon resonance (SPR) refers to an electromagnetic phenomenon, which is generated by the combination of free electron oscillations and a transverse magnetic polarized electromagnetic wave on the surface between dielectric medium and metal film [1, 2]. Due to outstanding features such as label-free monitoring, high sensitivity, and real-time detection, as well as owning multifarious applications such as environmental monitoring, medical diagnostics and food safety, polarization filters, and absorbers, SPR has achieved unprecedented progress in the realm of sensors [2,3,4]. Kretschman proposed a configuration of SPR sensors based on prism coupling [2, 3, 5]. Bulky apparatus, heavy weight, inability of remote detection, and inflexibility were major inefficiencies of this configuration, which are refined by the advent of photonic crystal fiber SPR sensors by Jorgenson where gold was used to create the SPR phenomenon [2,3,4,5]. Owning outstanding characteristics such as tunable effective refractive index in the fiber core, controllable birefringence, and superior light confining capabilities, PCF-SPR sensors have drawn a great deal of attention [2, 4]. SPR-based sensors, according to PCF’s properties, use several sensing configurations mainly including internal and external metal coating-based sensing approaches. In internal sensing, the analyte is infiltrated in the selective micro-meter-sized air holes [6, 7]. Rifat et al. proposed a SPR-PCF sensor in which a large air-hole beside the core for efficient light coupling between the cores and SPR modes is introduced [8]. In addition, this large air hole will facilitate material coating and effective analyte flow. Conversely, the external metal coating–based sensing method is commonly used; not only does it provide more flexibility, but also it is easier compared to covering the inner air holes as well [8, 9]. To date, various externally coated SPR-based PCF sensors, which can include D-shaped structures, have been reported. A dual-polarized spiral photonic crystal fiber based on surface plasmon resonance was proposed in ref. [9]. They showed wavelength sensitivity of 4600 \(\frac{nm}{RIU}\) and amplitude sensitivity of 420.4 \({RIU}^{-1}\) in the y-polarized mode. In the x-polarized mode, the maximum wavelength sensitivity is 4300 \(\frac{nm}{RIU}\) and the amplitude sensitivity is 371.5 \({RIU}^{-1}\). A dual-core PCF sensor using gold as a plasmonic material with high value of amplitude sensitivity but lower value of wavelength sensitivity was reported by Paul et al. [10]. In 2020, Han et al. designed a large detection-range plasmonic sensor based on an H-shaped PCF with maximum wavelength sensitivity of 25,900 \(\frac{nm}{RIU}\) [11]. Recently, SPR-based PCF sensors have encountered two main problems. First, due to micro-sized air holes, metal coating and analyte filling are challenging procedures [8, 9, 11, 12]. The second problem is about low RI or high RI PCF-SPR sensors are due to their narrow RI range of detection [6, 11]. This problem can be solved by using the total internal refraction and the crystal geometrical engineering.

Opening-up micro-structured optical fibers (MOF), such as D-shaped or exposed-core MOF-SPR sensors [13,14,15], are the promising approaches to facilitate the infiltration problem. An opening-up dual-core microstructure optical fiber–based plasmonic sensor with a large detection range and linear sensitivity was proposed in [14] and showed the maximal sensitivity of 4900 \(\frac{nm}{RIU}\) when the RI of the analyte is close to that of the fiber background material. To overcome the problems aforementioned, in this paper we propose an opening-up plasmonic sensor based on dual-core PCF which can be operated in the range from 1.42 to 1.46. For improving sensing performance, a large hole between two cores in the opening-up slot is introduced. The opening-up section as a sensing channel is coated with gold film where a thin titanium dioxide (\({TiO}_{2}\)) layer is placed between gold and analyte in only this hole part. Next, with imposing changes in the surface of this part including applying grated gold film and sandwiching a thin layer of \({TiO}_{2}\) between fiber surface and gold, we investigate the effect of these structure variations on sensing performance. Recently, an investigation revealed that the gold layer coated on the fiber can be flaked off from the fiber [6]. \({TiO}_{2}\) accompanied by a gold layer can conquer the adhesion problem of gold to fiber [16]. Regarding sensitivity, this sensor shows a high sensitivity value better than that in [14]. The opening-up part is directly filled with analyte and supports possibility for real-time sensing.

Design and Numerical Method

Figure 1(a) shows the schematic representation of our proposed sensor, comprising an open slot which is coated by a gold layer. This part acts as a sensing channel and can be directly in contact with the analyte. In addition, to improve the sensing performance, we introduce a large hole with diameter of \({2r}_{c}\) between two cores in the sensing channel. This is because evanescent waves can enhance the resonance effect, which may improve the sensitivity significantly. This dual-core SPR-PCF sensor has been designed by arranging the air holes in a hexagonal lattice with pitch size \(\Lambda\). For introducing two solid cores, two air holes in the second ring of the hexagonal lattice are removed. The air holes with radius \(r\) work as a low refractive index cladding, enabling mode guidance in the fiber core. Furthermore, we applied a shift by a distance \({d}x\) in the center of four selected air holes which is situated near the large hole from their original position. Shifting holes lead to achievement of an optimum structure which is needed to get high sensitivity. With the purpose of increasing the plasmon excitation, a thin layer of \({TiO}_{2}\) with the thickness of \({t}_{{TiO}_{2}}\) is deposited on gold.

Fig. 1
figure 1

Cross-section view of the DC-PCF-SPR sensor magnifying of central large hole a with \(Au\) and \({TiO}_{2}\) thin layers between \(Au\) and analyte b with \(Au\) nano-continued grating layer and thin \({TiO}_{2}\) layer between fiber material and \(Au\)

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Our sensor is modeled using the following parameters: \(\Lambda =2.26 \ {\mu m}\), \(r=0.4 \ {\mu m}\), \({d}x=0.3 \ {\mu m}\), \({r}_{c}=1.85 \ {\mu m}\), \({t}_{Au}=40 \ {nm}\), \({t}_{{TiO}_{2}}=7 \ {nm}\), \(w=1 \ {\mu m}\), \({h}_{1}=7.5 \ {\mu m}\), \({h}_{2}=4.75 \ {\mu m}\). From the fabrication point of view, considering the similar design, the open-slot part can be made by femtosecond laser micromachining [17], focused ion-beam milling [18], or chemical etching of the original side-hole PCF [19] or can be directly drawn by creating an opening at the preform stage of the fiber fabrication [20]. The gold grating was introduced to modulate the resonance wavelength and enhance the RI sensitivity. Again considering similar designs, there are some methods for the creation of metallic grating such as electron beam etching technology [21], high-pressure microfluidic chemical deposition [22], two-photon direct laser writing technique [23], and electron beam etching technology [24]. The refractive indices of background material and air-holes are supposed to be 1.45 and 1, respectively, and gold permittivity is modeled from Johnson and Christy data [25]. The RI of \({TiO}_{2}\) is calculated by the following [26]:

$${n}_{{TiO}_{2}}^{2}=5.913+\frac{0.2441}{{\lambda }^{2}-0.0803},$$
(1)

where \(\lambda\) is in micrometers.

A perfectly matched layer (PML) is applied as a scattering boundary condition. The FDTD method is employed to investigate the sensor performance. Figure 1(b) shows the same structure associated with some changes in the surface of the proposed sensor. Indeed, grated \({Au}\) is used as a plasmonic material in the large-hole part and the \({TiO}_{2}\) thin layer is deposited between fiber and gold due to adhesion assistance. The optimized parameters are as follows: segmented \({Au}\) film thickness \({d}_{1}=25 \ {nm}\) and continuous \({Au}\) film thickness \({d}_{2}=15 \ {nm}\), total segment number \(N=28\), \({t}_{{TiO}_{2}}=5 \ {nm}\). Other geometric parameters are the same as mentioned before.

The key factor to analyzing the performance of PCF-SPR sensors is calculation of the confinement loss of the fundamental core mode. The imaginary part of the effective refractive index (\({n}_{eff}\)) is used to determine the confinement loss and can be expressed as the following [27]:

$${\alpha }_{c}\left(\frac{dB}{cm}\right)=8.686\times \frac{2\pi }{\lambda \left({\mu m}\right)}Im\left({n}_{eff}\right)\times {10}^{4},$$
(2)

where \(\lambda\) is the operating wavelength. The proposed sensor has two guiding modes (a) x-polarization and (b) y-polarization. In the dual-core PCF-SPR sensors, for x-polarization and y-polarization, the odd and even modes are excited simultaneously. But here the confinement loss of the odd mode for y-polarization is the largest, which means that the SPR mode couples with the odd mode for y-polarization more strongly than the other polarization. Hence, we focus on the odd core mode for y-polarization in the following numerical analysis.

Results and Discussion

Different structural parameters such as radius of central large hole (\({r}_{c}\)), width of slot (\(w\)), distance between center and end of slot (\({h}_{2}\)), and position of the neighboring holes of the central hole (\(\mathrm{d}x\)) are examined, and optimum parameters are selected throughout this work. Performance of the proposed sensor is numerically carried out by the FDTD method in the wavelength range of 0.975–1.7 \(\mu m\), and fundamental core mode, SPR mode, and dispersion relation are investigated for the proposed sensor. The first part of the results is associated with the configuration of Fig. 1(a). The electric field profile of the odd fundamental core, SPR, and coupled core-SPR modes at the resonance wavelength are depicted in Fig. 2a–c, respectively. Obviously, in the resonance condition most of the energy is confined in solid core regions, and only a small part of energy penetrates to the metal film surface (see Fig. 2c). This penetration causes a peak in the loss spectrum which can be analyzed by the dispersion relationship between the fundamental core mode and the SPR mode as it is shown in Fig. 2d. In fact, coupling between the core and plasmonic modes occurs when the propagation constant and wave vector of two modes become equal. This condition is known as phase matching.

Fig. 2
figure 2

Electric field distribution of the a y-polarized odd core mode, b odd SPP mode, c resonance condition, and d dispersion relation of core mode (green), SPR mode (blue), and loss spectrum (red) of core mode for \({n}_{a}=1.43,\) \({t}_{{TiO}_{2}}=7 \ nm,\) \({t}_{Au}=40 \ nm\) 

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As it is clear from this figure, the real part of \({n}_{eff}\) of both modes coincides at the wavelength of 1.4589 \(\mu m\), called resonance wavelength where corresponding loss is 89.97 \(\frac{dB}{cm}\).

The real part of the effective index of the plasmonic mode is highly dependent on the small variation of analyte RI. When the RI of analyte is changed, it leads to the resonance wavelength shifts. Using the mentioned optimized parameters, the loss curves of the proposed dual-core SPR-PCF sensor for different RI of analyte ranging from 1.42 to 1.46 in the absence of \({TiO}_{2}\) layer are plotted and shown in Fig. 3.

Fig. 3
figure 3

Loss curves as a function of operating wavelength of the proposed sensor for different analytes without \({TiO}_{2}\) configuration \(\left({t}_{{TiO}_{2}}=0 \ nm\right),\) \({t}_{Au}=40 \ nm\)

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As it is clearly shown in Fig. 3, with increasing \({n}_{a}\) up to 1.45, a red shift of resonance wavelengths is found, and the loss spectra noticeably increase. But, when \({n}_{a}\) changes from 1.45 to 1.46, the resonance wavelength shifts towards a longer wavelength, while loss decreases. In fact, when the refractive index changes from 1.45 to 1.46, a significant decrease in the effective refractive index occurs as the wavelength increases, which cause a reduction in RI contrast between core and SPP modes. The coupling between these modes is weakened which leads to loss decrement. Next, we have examined the loss curves of the proposed sensor by introducing an extra overlayer of \({TiO}_{2}\). Interestingly, it can be observed that by applying the \({TiO}_{2}\) layer, a monotonic increasing trend in resonance wavelength and its intensity is achieved, as it is shown in Fig. 4.

Fig. 4
figure 4

Loss curves as a function of operating wavelength of the proposed sensor for different analytes for \({t}_{{TiO}_{2}}=7 \ nm,\) \({t}_{Au}=40 \ nm\) 

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With increasing RI of analyte \({n}_{\mathrm{a}}\), the peak of loss shifts toward a longer wavelength and confinement loss increases as well.

It is convenient to investigate the sensor performance from the loss curve by using the wavelength and amplitude interrogation methods. The ratio of peak wavelength change to refractive index is known as the wavelength sensitivity, and it is computed as below [28]:

$${s}_{\lambda }=\frac{{\partial \lambda }_{peak}}{{\partial n}_{a}} \left[\frac{nm}{RIU}\right].$$
(3)

Also, the amplitude sensitivity can be evaluated by the following equation [28]:

$${S}_{A}=-\frac{1}{\alpha \left(\lambda ,{n}_{a}\right)}\times \frac{\partial \alpha \left(\lambda, {n}_{a}\right)}{\partial {n}_{a}}\left[{RIU}^{-1}\right],$$
(4)

where \(\alpha \left(\lambda ,{n}_{a}\right)\) is the confinement loss at different RI. With these definitions, the proposed sensor shows wavelength sensitivities of 15,167, 6894, 3158, and 2179 \(\frac{nm}{RIU}\), respectively, when the analyte’s RI changes from 1.42 to 1.46 with a step of 0.01. The maximum wavelength sensitivity is 15,167 \(\frac{nm}{RIU}\) which is higher than that previously proposed in [14] which is a similar work, and also it is higher than the maximum wavelength sensitivity of the proposed sensor in the absence of \({TiO}_{2}\) (13,024 \(\frac{nm}{RIU}\)). Furthermore, the amplitude sensitivities obtained are 207.19, 62.55, 35.40, and 22.91 \({RIU}^{-1}\), correspondingly.

Generally, geometric parameters have a dominant effect on the sensor performance. The effects of the change of \(Au\) and \({TiO}_{2}\) thickness on loss spectra are depicted in Figs. 5 and 6, respectively. As it is seen from Fig. 5a with increasing gold thickness from 30 to 50 \({nm}\), loss increases, and wavelength redshifts for the RI analyte of 1.43, while due to the different phase matching conditions (for two different analytes), the ascending trend is absent for the case of \({n}_{\mathrm{a}}=1.42\). Figure 5b shows the amplitude sensitivity; the maximum \({S}_{\mathrm{A}}\) of 411.1 \({RIU}^{-1}\) is obtained for \({t}_{Au}=40 \ {nm}\) with \({n}_{a}\) varying from 1.42 to 1.43. These results are summarized in Table 1 which included both wavelength and amplitude sensitivity for the proposed sensor with various thicknesses of gold. Considering wavelength and amplitude sensitivity, \({t}_{Au}=40 \ {nm}\) is chosen as optimum thickness of \(Au\) in our calculations.

Fig. 5
figure 5

a Loss variation for different thicknesses of gold layer of the proposed sensor and b amplitude sensitivity for different thicknesses of gold layer with \({t}_{{TiO}_{2}}=7 \ nm\)

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Fig. 6
figure 6

Loss curves for thickness variation of \({TiO}_{2}\) for \({n}_{a}=1.43,\) \({t}_{Au}=40 \ nm\)

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Table 1 Effect of gold thickness on \({S}_{w}\) and \({S}_{A}\) 
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By this value of \({t}_{\mathrm{Au}}\), the effect of different \(TiO_{2}\) thicknesses on loss curves is illustrated in Fig. 6 where wavelength sensitivity can be calculated by its data.

The obtained \({S}_{\mathrm{W}}\) for given \(TiO_{2}\) thicknesses are 13,024, 12,538, 15,167, and 14,157 \(\frac{nm}{RIU}\), respectively, in which \({t}_{{TiO}_{2}}=7 \ {nm}\) shows better sensitivity. Titanium dioxide has not only diminished the adhesion problem but because of its high refractive index, it strongly attracts the field from the core mode, and causes strong coupling between core and plasmonic mode [29].

Besides of sensitivity, another factor for analyzing sensor performance is figure of merit (FOM) which can be defined as the ratio of sensitivity to full width at half maximum (FWHM) as [30]:

$${FOM}\left({{RIU}}^{-1}\right)=\frac{{sensitivity }\left(\frac{{nm}}{{RIU}}\right)}{{FWHM}\left({nm}\right)}.$$
(5)

Now then, the sensitivities and FOM of the proposed sensor are investigated for the wide range of analyte RI which are summarized in Table 2.

Table 2 Performance analysis of the proposed sensor by varying the dielectric RI
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The proposed sensor shows the best performance in RI range of 1.42–1.43 with respect to wavelength and amplitude sensitivities and FOM. By increasing \({n}_{a}\), these sensing factors decrease monotonically.

The resolution of the sensor is also essential to determine the detection capability of the offered sensor and can be computed by [30]:

$$R\left({RIU}\right)=\Delta {n}_{a}\times \Delta {\lambda }_{min}/\Delta {\lambda }_{peak},$$
(6)

where \(\Delta {\lambda }_{min}\) is assumed to be 0.1 \({nm}\). The maximum resolution of the proposed sensor is obtained as high as \(6.6\times {10}^{-6}\). Therefore, the smallest change in analyte RI in order of \({10}^{-6}\) can be detected with a high degree of accuracy.

The last part of this work is devoted to the effect of grating on the surface of structure corresponding to the second configuration, as shown in Fig. 1(b). A similar calculation is done for this configuration in the presence of grating for various structural parameters such as segment number, segmented metal film thickness, and thickness of the continuum part of the metal layer. A typical SPR mode profile for the grated dual-core PCF-SPR sensor is presented in Fig. 7. Simultaneously localized SPR and propagated SPR in the neighborhood of the segment part are clearly observed.

Fig. 7
figure 7

Electric field distribution of the SPR mode for grated structure for \({n}_{a}=1.43\)

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The wavelength sensitivity, amplitude sensitivity, and figure of merit for the grated structure are computed and tabulated for different thicknesses of \({TiO}_{2}\) and also in the absence of the \({TiO}_{2}\) layer. Evidently, as shown in Table 3, in all cases of the presence of the extra \({TiO}_{2}\) layer, the proposed sensor shows better results in comparison with the bare one, the absence of the \({TiO}_{2}\) layer. Thus, \({TiO}_{2}\) has the definite effect on improving sensor detection sensitivity. It is seen that the maximum values of \({S}_{W}\), \({S}_{A}\), and \(\mathrm{FOM}\) belong to grating configuration associated with \(5 \ {nm}\) of \({TiO}_{2}\) thickness. Therefore, we continue our simulation with \(5 \ {nm}\) thickness of \({TiO}_{2}\)

Table 3 Performance analysis of the proposed sensor for grating configuration by varying \({TiO}_{2}\) thicknesses
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The sensing parameters for different analyte refractive indexes of the grated structure with \({t}_{{TiO}_{2}}=5 \ {nm}\), \({t}_{Au}=40 \ {nm}\), and segment number of 28 are shown in Table 4. It can be concluded from this table that \({S}_{W}\), \({S}_{A}\), and FOM reach their maximum value when RI varies between 1.43 and 1.44.

Table 4 Performance analysis of the proposed sensor for grating configuration by varying the dielectric RI
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Figure 8 shows the effect of N, segment number, on the wavelength sensitivity with and without the \({TiO}_{2}\) layer. Also in Table 5, the effects of this parameter on the other sensing factors are shown.

Fig. 8
figure 8

Wavelength sensitivity of the core mode for different N for \({n}_{a}=1.43\)

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Table 5 Effect of \(Au\) grated with \(5 \ nm\) thickness of \({TiO}_{2}\) on \({S}_{w}\), \({S}_{A}\), \(FOM\), and average sensitivity for different N
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This figure depicted that the existence of the \({TiO}_{2}\) layer has a considerable role on \({S}_{w}\) behavior. In fact, in the absence of \({TiO}_{2}\), when N increases, sensitivity varies in a zigzag form where it has a smooth behavior with a single peak value in the presence of \({TiO}_{2}\). The peak value in both cases occurs in \(N=28\). It is worth mentioning that the same calculation for N values smaller than 20 is done which gives sensitivities lower than the obtained peak value. Consequently, the sensitivity can be effectively tuned by the segment number. We consider \(N=28\) as an optimized segment number.

From Table 5, it is observed that when N varies from 20 to 38, the maximum obtained wavelength, amplitude sensitivity, FOM, and average sensitivity are 13,295 \(\frac{nm}{RIU}\), 511.4 \({RIU}^{-1}\), 166.18 \({RIU}^{-1}\), and 8455.6 \(\frac{nm}{RIU}\) in the presence of the \({TiO}_{2}\) layer. The corresponding values decrease to 12,397 \(\frac{nm}{RIU}\), 302.9 \({RIU}^{-1}\), 130.5 \({RIU}^{-1}\), and 8193 \(\frac{nm}{RIU}\) in the absence of \({TiO}_{2}\). It is worth noting that these maximum values allocate to \(N=28\).

Considering the optimized values of \({t}_{Au}=40 \ {nm}\), \({t}_{{TiO}_{2}}=5 \ {nm}\), and \(N=28,\) the effect of \({d}_{1}\) and \({d}_{2}\) on the sensor performance is considered simultaneously, with the condition of \({d}_{1}+{d}_{2}=40 \ {nm}, \left({d}_{1}+{d}_{2}={t}_{Au}\right)\). Results are shown in Fig. 9 which shows the loss spectra for different arrangements of \({d}_{1}\) and \({d}_{2}\). For arrangements of \({d}_{1}=30 \ {nm}\) and \({d}_{2}=10 \ {nm}\) when \({n}_{a}\) changes from 1.42 to 1.45, the wavelength sensitivities are 7432, 10,467, 5805, and 3205 \(\frac{nm}{RIU}\), while the corresponding values are 6379, 12,397, and 5805 \(\frac{nm}{RIU}\) for the arrangement of \({d}_{1}=25 \ {nm}\) and \({d}_{2}=15 \ {nm}\).

Fig. 9
figure 9

Loss spectra as a function of different arrangements of \({d}_{1}\) and \({d}_{2}\)

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As a result, when \({d}_{1}=25 \ {nm}\) and \({d}_{2}=15 \ {nm}\), the maximum wavelength sensitivity is higher than that when the sensor is set with \({d}_{1}=30 \ {nm}\) and \({d}_{2}=10 \ {nm}\).

Conclusion

In summary, two different configurations of highly sensitive opening-up dual-core photonic crystal fiber sensors based on surface plasmon resonance have been introduced and numerical analyses have been performed by using the FDTD method. The opening-up structure not only simplifies analyte infiltration and gold coating but also offers the capacity for real-time sensing. The results reveal that the odd mode for y-polarization coupled with odd SPR mode more strongly due to its largest confinement loss in two structures. Additionally, a comparison was made in each configuration in the presence of \({TiO}_{2}\) and in the absence of \({TiO}_{2}\) in terms of the sensitivity and FOM. As regards applying the \({TiO}_{2}\) layer improving the sensitivity by about 16% for the first configuration and about 7% for the second configuration, it was observed that the dual-core SPR-PCF sensor with a \({TiO}_{2}\) thin layer without grating structure shows the highest sensing performance. Surprisingly, this sensor has the capability to detect higher or lower RI than the RI of the background material. Owning to the highly sensitive response, the proposed sensor can be considered ideal for refractive index detection.