1. Introduction

Surface Plasmon Resonance (SPR) based sensors have been gaining increasing attention over the last decade because of their label-free sensing approach, quick response, high accuracy, real-time observation and versatile analyte compatibility [1]. SPR is a resonant oscillation of free electrons between the metallic surface and dielectric that occurs when light is directed at a specific angle of incidence [2]. The light then propagates along the surface of the plasmonic material in the form of resonant oscillation of free electrons. This resonant condition is highly sensitive to the adjacent material of the metal-dielectric interface. Therefore, the SPR phenomenon has been employed in designing various optical sensors based on different structures such as prisms, fiber Bragg gratings, planer waveguides, optical fibers and photonic crystal fibers [1,3]. Photonic crystal fibers (PCF) made of glass with different arrangement of air holes, are being preferred recently for designing SPR sensors because of their miniaturization, tunable geometric parameters and prospect of real-time remote sensing. Furthermore, high design flexibility of PCF facilitates the design of sensors with different ranges of sensing and sensitivities.

Many efforts have been found in the literature demonstrating different designs of PCF based SPR sensors with different performances. These sensors comprise of various shapes of fibers like, circular [2], side-polished [4], H-shaped [5] or micro-channel based [6] PCFs. They also employ different arrangements of air holes for achieving superior performance. Based on the sensing arrangement, all these sensors can be classified into two broad types: internal sensing and external sensing [7]. In the internal sensing approach, the plasmonic layer is placed on the boundary of the dielectric and air hole inside the PCF. Subsequently, the analyte is introduced into the air hole, filling the space where the plasmonic layer is located. Since the analyte alters the distribution of refractive indices inside the fiber, this scheme shows relatively higher sensitivity. However, internal sensing is difficult to practically implement as the deposition of metal layer inside those tiny air holes is challenging and it also ends up increasing propagation loss even at other wavelengths then resonance [8]. Conversely, in the external sensing method, metal layer is directly deposited on the exposed surface of the fiber and analyte is placed around the outer surface of the PCF. Currently, this technique is becoming more popular because of its ease of fabrication and simple detection approach [6,9,10]. For example, a circular sensor with gold deposited on the outer surface has been demonstrated to detect refractive indices (RI) over the range of 1.3356 – 1.43 with a maximum sensitivity of 29500 nm/RIU [9]. An H shaped PCF has been proposed with an RI detection range of 1.33 – 1.49 with a maximum sensitivity of 25900 nm/RIU [5]. A maximum sensitivity of 31000 nm/RIU within the RI range of 1.32 – 1.40 has been reported using a D shaped PCF SPR sensor [10]. Microchannel based RI sensor has been proposed which can detect a range of 1.22 – 1.37 with a maximum sensitivity of 51000 nm/RIU [11]. The highest sensitivity of 116000 nm/RIU has been achieved through a dual core based PCF SPR sensor within the range of 1.29 – 1.39 [6]. Although these sensors demonstrated high sensitivity and improved sensing resolution of refractive indices, their sensing ranges are relatively small for covering a wide variety of practical applications.

A number of studies have also investigated and documented PCF sensors that offer wide detection ranges. Modified D shaped PCF has been reported to be able to detect analytes over a wide range of 1.18 – 1.36 with maximum sensitivity of 20000 nm/RIU [12]. Another sensor was proposed based on D shaped fiber which can detect analytes within a range of 1.15 – 1.36 with a maximum sensitivity of 12600 nm/RIU [4]. An U-grooved selectively coated sensor has the ability to detect broad RI range of 1.29 – 1.40 with a high sensitivity of 12500 nm/RIU [13]. Most of the other wide range PCF SPR sensors in literature are based on internal sensing. A PCF SPR sensor with a detection range of 1.29 – 1.49 had a maximum sensitivity of 4156.82 nm/RIU [14]. Another PCF SPR sensor employing internal sensing had an ultra-wide detection range of 1.0 – 1.43 and a maximum sensitivity of 6300 nm/RIU [15]. Even though these high range sensors, based on either internal or external sensing, provide broad detection range for sensing diverse analytes, they fall far behind when compared to the designs with high sensitivity and high-resolution sensing. For practical applications, it is essential to detect a wide range of refractive indices with good sensitivity and sensing resolution.

In this paper, a photonic crystal fiber-based plasmonic sensor is proposed and numerically analyzed to detect an ultra-wide range of refractive indices with high sensitivity. The fiber has two microchannels on each side, creating four separate plasmonic layers to improve sensing range. Silver is used as a plasmonic material, with a thin layer of TiO$_2$ on top to prevent oxidation. The proposed sensor has an ultra-wide RI detection range of 1.10 – 1.45. The maximum wavelength sensitivity is found to be 24300 nm/RIU with a corresponding resolution of $4.12\times 10^{-6}$ RIU. The maximum figure of merit of the sensor is 120 RIU$^{-1}$. The fiber can also detect RI based on amplitude interrogation with a maximum sensitivity of 172 RIU$^{-1}$. This is the first external-sensing-based PCF sensor with such a wide range and high sensitivity, making it suitable for detecting different chemicals, bio-materials and other sensing applications.

2. Numerical design and modeling

Figure 1 shows the proposed sensor’s cross-sectional view, fiber arrangement for fabrication, and experimental setup. The air holes in the fiber are arranged based on a square lattice with a pitch of 3 $\mathrm{\mu}$m as shown in Fig. 1(b). Relatively small diameter of air holes is used beneath the plasmonic layer to facilitate the coupling of light from the core mode to the plasmonic mode. Also, some air holes are enlarged between the two cores which help to reduce the mutual coupling between them. Additionally, the positions of some air holes of the dual core fiber are also altered slightly for increasing the coupling efficiency between the core and plasmonic layer. As a result, there are air holes of three different diameters denoted by d1, d2 and d3 in Fig. 1(a). The fiber is polished on both sides with a polishing distance (dp) which denotes the distance of the metal layer from center of the core. Silver is deposited on the polished surfaces. A thin layer of titanium oxide is considered on top of silver. It can be observed in literature that, sensors with separate plasmonic layers have a tendency of providing broad sensing range [4,14,15,16]. Two micro channels with diameter of 3 $\mathrm{\mu}$m, are used to create four separate plasmonic layers. Such separate plasmonic layers allow to form resonance at different refractive indices of analytes, ultimately enhancing the sensing range of the sensor. The solid core surrounded by air holes confines the light inside the core. The proposed design can be manufactured using several techniques like, femtosecond laser micromachining [17], focused ion-beam milling [18], chemical etching of the original side-hole [19] and stack and draw method [20]. Figure 1(b) shows the conceivable fiber stack for the fabrication of the proposed fiber based on stack and draw method. According to this method, solid rod and capillaries are stacked together and then drawn at a specific rate to produce the fiber. Different polishing techniques exist for polishing the surface of the fiber accordingly after its fabrication. [10]. Chemical deposition method is applied to deposit silver and titanium oxide (TiO$_2$) on the polished surfaces of the fiber. Figure 1(c) represents the possible experimental setup of the sensor.

 

Fig. 1. (a) Schematic 2-D diagram of proposed SPR sensor, (b) Possible fiber arrangement for fabrication using stack and draw method, and (c) Experimental setup of the sensor.

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The proposed sensor is numerically simulated in COMSOL multiphysics software, a finite element-based mode solver. The whole geometry has been subdivided into 50968 triangles, 3550 edge elements and 88 vertex elements. Maxwell’s equations are solved for each of these elements using finite element method [21]. A perfectly matched layer (PML) is employed to prevent reflection of light from the outer boundary. It mimics an electromagnetic wave propagating towards infinity by absorbing the wave at the boundary. PML is a widely used boundary condition that reduces the computational effort by truncating the open boundary of a simulation environment. The optimized diameters of the air holes are given as d1 = 2.2 $\mathrm{\mu}$m, d2 = 1.0 $\mathrm{\mu}$m, and d3 = 1.75 $\mathrm{\mu}$m. The silver layer has a thickness of 40 nm and the TiO$_2$ layer has a thickness of 10 nm. The distance of the metal surface from the center of core, polishing distance (dp), has been chosen to be 5.5 $\mathrm{\mu}$m. The dielectric constant of the silver is obtained from Drude-Lorentz model [22]. Fused silica (SiO$_2$) is considered as the fiber material. The dielectric constant of silica can be found from the Sellmier’s equation as given below in Eq. (1).

Here $n_{SiO_2}$ represents the refractive index of silica and the operating wavelength is represented by $\lambda$ in $\mathrm{\mu}$m. The corresponding coefficients of Sellmier’s equation are $B_1=\mathrm {0.6961663}$, $B_2=\mathrm {0.4079426}$, $B_3=\mathrm {0.8974794}$, $C_1=\mathrm {4.67914826\ \times }{10}^{-3}\mu m^2$, $C_2=\mathrm {4.67914826\times }{10}^{-3}\mu m^2$, $C_3=\mathrm {97.9340025\times }{10}^{-3}\mu m^2$. The dielectric constant of titanium oxide can be determined using Eq. (2) [8].

3. Result and discussion

Figure 2 illustrates the normalized distribution of electric field intensity of core modes and surface plasmon polariton (SPP) mode for analyte refractive index of 1.32, the dispersion relation of the core mode and SPP mode for analyte refractive index of 1.30, 1.32 and 1.34 and the corresponding variation of confinement loss of core mode. As the design is asymmetric, light from core mode can only couple to SPP if the polarization of the electric field is orthogonal to the metal surface. Figure 2(a) illustrates a typical normalized electric field distribution corresponding to y-polarized TE core mode for analyte RI of 1.32. It shows that the most of the light energy is concentrated inside the core at the wavelengths which are not in resonance. Surface waves can be observed at the metal-dielectric interface in Fig. 2(b). At the resonance condition, as shown in Fig. 2(c), maximum power transfer between the y polarized core guided mode and SPP mode can be observed. This phase matching point can be observed in Fig. 2(d), at the wavelength of 1702 nm, where the real part of the effective mode indices are same for both core mode and SPP mode. Figure 2(d) illustrates the dispersion relation of the core and SPP mode for analyte refractive index of 1.30, 1.32 and 1.34. For better visualization the figure is subdivided into two sections. The first section depicts the variation of effective indices of core modes and spp modes with respect to wavelength and the second section illustrates the variation of confinement loss of the core mode for the same wavelength scale. Surface plasmon resonance is observed only when the effective indices of both core mode and SPP mode are equal or phase matched. Usually, the propagation through the core and thus the core mode index is unaffected by the change in refractive index (RI) of analyte. However, the presence of analyte significantly influences the SPP mode. At a given wavelength, as shown in Fig. 2(d), the SPP mode index is higher for higher value of analyte RI. This could be inferred from the following equation [23],

The confinement loss of the core mode reaches its peak value at such phase matching condition, since part of its guided light energy is transferred to the SPP wave. As previously mentioned, the phase matching point shifts at longer wavelength with the increase in analyte RI. Again, with the increasing wavelength, as shown in Fig. 2(d), the real part of the effective mode index for both core and SPP modes decreases. Thus the phase matching condition occurs at lower value of effective index with the increasing value of analyte RI and vice versa. Since the effective mode index decreases, the peak value of confinement loss increases with the increase in analyte RI. The confinement loss ($\alpha$) has been calculated from Eq. (4) [6].

 

Fig. 2. (a) Typical electric field distributions for the y-polarized TE light corresponding to the core mode of the proposed sensor, (b) surface plasmon polariton (SPP) mode, (c) core mode at phase matching point for analyte RI, $n_a$ of 1.32 and (d) dispersion curves of mode index (core mode and SPP mode) and confinement loss corresponding to $n_a$ of 1.30, 1.32 and 1.34.

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The shift in phase matching point with variation in refractive index can be evaluated from the shift of resonance wavelength. The resonance wavelength is highly sensitive to the adjacent material of plasmonic layer. The estimated confinement loss of the proposed PCF based SPR sensor is presented in Fig. 3 for the analyte RI of 1.10 – 1.45. The resonant wavelength of the sensor experiences a red shift with increasing refractive index of the analytes. The wavelength sensitivity (WS) of the designed sensor can be determined using [11],

 

Fig. 3. Loss spectrum of the SPR sensor for different analytes of refractive indices from 1.10 – 1.45.

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For evaluating the sensor accuracy, resolution(R), which is the smallest detectable variation of the refractive index, can be computed from Eq. (6).

Here $\mathrm {\Delta }{\lambda }_{min}$ is the minimum detectable wavelength variation which is 0.1 nm and $\Delta \mathrm {\lambda }$ peak is the shift in loss resonance peak. To evaluate the noise immunity of the sensor and sharpness of the loss curve figure of merit is widely used performance metric. The figure of merit (FOM) of the sensor can be evaluated from Eq. (7).

Here $S\left (\lambda \right )$ is the wavelength sensitivity of the sensor and FWHM is the full width half maximum of the loss curve.

Figure 4 illustrates the influence of the geometric parameters on the sensor performance by taking an arbitrary analyte with refractive index of 1.36. It can be observed in Fig. 4(a) that, keeping the other structural parameters constant, if the diameter of the air hole d1 increases from 2.0 $\mathrm{\mu}$m to 2.3 $\mathrm{\mu}$m, the confinement loss slightly decreases due to small decrease in mutual coupling between the cores. The resonance wavelength shows a minor red shift. Such small variation indicates that the design is relatively insensitive to small ( 10%) variation of d1, which can be caused by fabrication imperfections. Fig. 4(b) shows the influence of air hole diameter d2 on confinement loss and resonant wavelength. As d2 decreases from 1.2 $\mathrm{\mu}$m to 0.9 $\mathrm{\mu}$m, the evanescent field reaching the plasmonic layer increases, leading to higher confinement loss and a red shift in resonant wavelength. As the coupling efficiency increases, sensitivity and the sharpness of the loss curve also increases with the decrease in d2. However, the loss increases exponentially. Hence, the choice of d2 requires a trade-off between loss and FOM. The optimum diameter for d2 is chosen as 1 $\mathrm{\mu}$m since further decrease in diameter increases the loss significantly.

 

Fig. 4. Variation of confinement loss spectrum due to the variation of diameter of (a) air hole d1, (b) air hole d2, (c) air hole d3 and (d) polishing depth dp, estimated for $n_a$ = 1.36 with a 40 nm thick silver layer and a 10 nm thick TiO$_2$ layer.

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As can be seen in Fig. 4(c), with the increase in air hole diameter d3 from 1.65 $\mathrm{\mu}$m to 1.95 $\mathrm{\mu}$m, the peak loss slightly decreases as mutual coupling between the two cores decreases. The shift in resonance wavelength is also relatively very small as like d1, indicating the design to be less sensitive to the fabrication variation of the d3 air holes. The influence of the variation of polishing depth (dp) is shown in Fig. 4(d). As the distance from the core to the plasmonic medium (dp) is increased from 5.4 $\mathrm{\mu}$m to 5.7 $\mathrm{\mu}$m, the loss of the sensor decreases significantly. However, the FOM also decreases with this increase in dp. As the polishing distance (dp) decreases in Fig. 4(d), more light can reach the metal layer, the sensitivity increases and resonance wavelength faces a blue shift. Hence, the choice of the polishing depth again, as like d2, depends on the trade-off between FOM and loss. The polishing depth has been chosen to be 5.5 $\mathrm{\mu}$m, around which the sensor will have optimum performance considering fabrication induced variations.

In the fabrication process, it is difficult to precisely control the thickness of the silver and TiO$_2$. Figure 5(a) shows the effect of such fabrication tolerance on the sensor performance. As shown in figure, the resonance peak shifts to a shorter wavelength with the increase in thickness of silver from 30 nm to 45 nm, while the loss remains unchanged. However, as the thickness of silver layer increases, the sharpness of the loss curves also increases. The optimum value of the silver layer has been chosen to be 40 nm to ensure the optimum sensitivity within the broad sensing range.

 

Fig. 5. Variation of confinement loss spectrum due to the variation of thickness of (a) Silver ($n_a=1.36$ and TiO$_2$ = 10 nm) and (b) TiO$_2$ ($n_a=1.36$ silver = 40 nm).

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When the thickness of TiO$_2$ is increased from 8 nm to 14 nm, the confinement loss of the sensor increases by a small amount and the resonance peak shows a red shift as depicted in Fig. 5(b). Although the sharpness is increased with increasing thickness, the loss also increases. Therefore, again it requires trade off between FOM and loss of the sensor. However, as can be seen in Fig. 5(b), small variations of the thickness of TiO$_2$ does not have significant impact on sensor performance. The thickness of TiO$_2$ is been chosen to be 10 nm.

The different performance parameters of the proposed sensor for different values of analyte refractive indices are evaluated and listed in Table 1. It can be observed in the table that the proposed SPR sensor exhibits a maximum wavelength sensitivity of 24300 nm/RIU with a corresponding resolution of $4.12\times {10}^{-6}$ RIU. The resolution of the sensor implies that the sensor is able to recognize even the slightest change of the refractive index of analyte at the scale of ${ 10}^{-6}$. The shift of resonant wavelength is the detection criterion in wavelength interrogation method.

Table 1. Performance parameters of the proposed sensor for different values of analyte refractive indices ranging from 1.10 – 1.45.

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Figure 6 illustrates the polynomial fitting of shift of resonant wavelength with respect to variation of refractive indices and the corresponding figure of merit. Figure 6(a) shows the polynomial fitting in which the variation over the whole range has a R${}^{2}$ value of 0.99963. The sensor even shows linear sensing capability within its most of the detection range (1.10 – 1.41) with a R${}^{2}$ value of the fitting line to be 0.9813. The corresponding linear fitting equation can be given as, $y=1916.8\ n_a-815.44.$ The variation of FOM of the proposed sensor with respect to different analyte refractive indices is illustrated in Fig. 6(b). The sensor shows a maximum figure of merit of 120 RIU$^{-1}$ at the RI of 1.44.

 

Fig. 6. (a) Resonance wavelength for different value of analyte refractive indices and (b) Figure of Merit (FOM) of the proposed sensor.

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Variation of amplitude relative to the analyte refractive index gives the amplitude sensitivity ($S_A$), which can be calculated from, [24].

 

Fig. 7. Variation of amplitude sensitivity for different value of analyte refractive indices ranging from 1.10 – 1.45.

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The performance comparison of the proposed design with respect to some recent notable works is listed in Table 2. The proposed design has the widest sensing range among all the other sensors employing external sensing. Also, the proposed sensor has much higher sensitivity compared to other sensors with broad range of refractive index detection capability. The exceptionally wide detection range with the ability to sense low RI analytes make it suitable to detect anesthetic agents like halogenated ether or sevoflurane (1.274-1.276) [25], different types of aerogels (1.05-1.27) [26], fluorine-containing organics such as HFC-152a (1.1142-1.2336) [27], cancerous cells (1.38-1.401) [28], pharmaceutical drugs, detection and analysis of pathogens, detection of food agents, cooling agents and so on [4,29].

Table 2. Performance comparison of the proposed sensor with existing literature.

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4. Conclusion

An ultra-wide range dual-core photonic crystal fiber (PCF) based surface plasmon resonance (SPR) sensor was designed and numerically investigated in this work. The fiber consists of solid core with one ring of circular air holes acting as the cladding. The fiber had polished surfaces on both sides and plasmonic layer of silver was employed onto the flat outer surface of the fiber. Two microchannels were employed on each side of the fiber and thus the sensor forms four separate plasmonic layers on its external surface to achieve a wide detection range. A thin layer of titanium oxide (TiO2) was considered on top of the silver to prevent its oxidation problem. The numerical investigation was conducted using the finite element method (FEM)-based mode solver in COMSOL Multiphysics. The proposed sensor can sense over an ultra-wide range of refractive index (RI) from 1.10 – 1.45 . The maximum wavelength sensitivity of the sensor was 24300 nm/RI and the corresponding resolution was $ 4.12\times {10}^{-6}$RIU. The sensor showed a maximum figure of merit of 120 RIU$^{-1}$ at the analyte RI of 1.44. The sensor could also support the inexpensive amplitude interrogation approach with a maximum amplitude sensitivity of 172 RIU$^{-1}$. Due to an ultra-wide detection range, high sensitivity as well as its easy fabrication, the proposed sensor can be considered as a suitable candidate for multipurpose RI measurement in the field of biomaterial detection, chemical sensing, pharmaceutical drugs and other analytes detection.