Wide range refractive index sensor using a birefringent optical fiber

In this article, an efficient high birefringent D-shaped photonic crystal fiber (HB-D-PCF) plasmonic refractive index sensor is reported. It is able to work over a long low refractive index analyte range from 1.29 to 1.36. This modified simple structured hexagonal PCF has high birefringence in the near-infrared region. A thin gold film protected by a titanium dioxide (TiO2) layer is deposited on the D-surface of the PCF which acts as surface plasmon active layer. The sensor consists of an analyte channel on the top of the fiber. The performance of the HB-D-PCF is analyzed based on finite element method. Both wavelength and amplitude interrogation techniques are applied to study the sensing performance of the optimized sensor. Numerical results show wavelength and amplitude sensitivity of 9245 nm/RIU and 1312 RIU−1 respectively with high resolution. Owing to the high sensitivity, long range sensing ability as well as spectral stability the designed HB-D-PCF SPR sensor is a potential candidate for water pollution control, glucose concentration testing, biochemical analyte detection as well as portable device fabrication.


Introduction
In the current century, demand for portable, lightweight, long-range, highly sensitive sensors are in peak due to the faster technical development. To satisfy this need intense research work is being performed in the field of photonic crystal fiber (PCF) incorporated optical sensors. PCFs are advantageous over other waveguides due to its great structural flexibility, advantageous optical properties as well as light manipulating capability (De and Singh 2019a;Maji and Chaudhuri 2014;Russell 2003). Based on these charming properties many PCF sensors are reported which are well responding in the field of physical and analyte sensing (De et al. 2019;Pinto and Lopez-Amo 2012). On the other hand, surface plasmon resonance (SPR) is a unique optical phenomenon. In which free electrons at metal-dielectric interface got oscillated by the p-polarized light. Also, maximum energy transfer takes place from the fiber guided mode to the surface plasmon mode when frequency of both these modes are same. This is the resonance frequency which significantly got shifted with changing environment (Islam et al. 2019;Rifat et al. 2016c). So, when this delicate SPR phenomenon is combined with the PCF then the response of these sensors improvised several times in comparison to the non-SPR PCF sensors (Dora Juan 2017). Though PCF is not the first optical element with which plasmonic metals were combined. Firstly invented bulky and less responding prism-based SPR sensors (Raether 1968) were left behind by the optical fiber using SPR sensors. With time, structural and material selection limitation of the standard optical fiber becomes the barrier in its sensitivity enhancement. Then SPR based PCF sensors take the optical sensing technology to a new height (Dora Juan 2017) in the last decade.
For the fabrication of SPR based PCF sensor both internal and external sensing approaches have been applied (Akowuah et al. 2012;Dora Juan 2017). In the case of internal sensing approach air holes of PCF are selectively coated with plasmonic metal as well as filled with analyte (Akowuah et al. 2012). But for external sensing approach both plasmonic metal coating and analyte are situated at the outer surface of PCF (Rifat et al. 2016a). If a comparison is drawn in between these two techniques external sensing is more suitable for real-time applications and mass production of PCF-SPR sensors. As, plasmonic metal layer deposition and its thickness control, analyte filling, probe reuse are more accessible in this case (Dora Juan 2017). Many external plasmonic layers incorporated PCF sensors are reported till date, like, D-shape sensor , slotted sensor (Akowuah et al. 2012), flat fiber sensor (Rifat et al. 2016d), micro channel consisting sensors (Liu et al. 2017b) etc. It is prominently noticeable that most of these sensors have high sensitivity and spectral stability in the RI range of 1.40-1.46 due to the less RI discrepancy between the analyte and background material which is silica in most of the cases. But when the analyte RI is far less than the background material then confinement of propagating mode is less affected by the external analyte change resulting in inadequate response to the surrounding changes (Dora Juan 2017). To date, several PCF-SPR low RI sensors are reported. In 2017 Liu et al. reported two open-ring channels consisting PCF based SPR sensor (Liu et al. 2017b) which has a sensitivity of 5500 nm/RIU in the RI range 1.23-1.29. Though this sensor is responding well toward the analyte change but double-side polishing of the PCF is a troublesome job as well as it makes the probe more fragile. Also, this sensor is operating in the mid-infrared range. Optical sources in this range are not easily available. Next year, Dash et al. proposed a micro channel consisting PCF based SPR sensor (Dash et al. 2018) of sensitivity 5000 nm/RIU in the RI range 1.32-1.34. Though this structure is less fragile in nature but both sensitivity as well as responding analyte range are limited. After that Islam et al. proposed two plasmonic strips consisting birefringent PCF based plasmonic sensor (Islam et al. 2019) which has a sensitivity of 111000 nm/RIU in the RI range 1.33-1.43. Though previously mentioned sensor is showing very high sensitivity but its spectral stability is inferior. For real-time applicability of a sensor not only high sensitivity but also its spectral stability matters. Very recently, Wang et al. reported a polarization independent PCF using SPR sensor (Wang et al. 2019b) in 1.20-1.33 RI range with sensitivity 7738 nm/RIU. Though it has good sensitivity but its internal structure is very complicated. Also, there are multiple SPR peaks due to the higher order mode coupling. It may create problem during suspected analyte detection.
From a vast literature survey we have concluded that though a large number of D-shaped fiber senor have reported till today. But a simple structured, long ranged, biocompatible sensor is still in need. Considering this fact, based on external sensing approach a HB-D-PCF SPR sensor is designed and analyzed for a long low RI analyte region. The D-surface of this fiber probe is coated with active gold and titanium-di-oxide (TiO 2 ) layers. Using the commercial COMSOL Multiphysics software (FEM), for different active layer thickness coupling conditions and loss spectrum are numerically investigated to achieve the optimized sensor structure. Also, performance of the optimized structure is studied thoroughly based on the wavelength and amplitude interrogation techniques. Mostly incomplete coupling is observed between the fundamental core mode and fundamental SPP mode in the analyte RI range 1.29-1.36. For this sensor maximum wavelength and amplitude sensitivity are found to be 9245 nm/RIU and 1312 RIU −1 respectively with high resolution. The advantage of the proposed HB-D-PCF is that it shows high birefringence in the nearinfrared region. This helps in manipulating the core guiding light toward the D surface, as a result more interaction with the analyte. Also, due to its moderate propagation loss it is suitable in fabricating a practically realizable sensing probe. As the sensor is operating in near-infrared region, the penetration depth of the evanescent wave and its interaction with the analyte are more in comparison to the visible region.

Structure design and numerical modeling
The schematic of the designed HB-D-PCF sensor and its 3D view are depicted in Fig. 1a, b. Air holes are distributed in a hexagonal manner in the cladding region of the PCF. Also, there are two large elliptical air holes around the core. These elliptical holes are promoting the birefringence of the fiber. For this structure, distance between Fig. 1 a Schematic of the proposed HB-D-PCF; b 3D view of the HB-D-PCF sensor two successive air holes i.e. pitch, circular air hole diameter and eccentricity of the elliptical air holes are 2.00 µm, 1.10 µm and 0.25 respectively. The area of each elliptical hole is 3.14µm 2 . This HB-D-PCF is made of silica and all holes are filled with air. Optimization of the previously mentioned structural parameters can be found in detail in our another publication (De and Singh 2019b). In this work we used the same PCF with modification for further study. This PCF can be considered as a strong competitor of the commercially available PCF PM-1550 by Thorlabs. Many sensors and interferometers are reported based on this PM-1550 PCF. Similarly, our designed PCF can also be used for fabricating versatile PCF sensors. Incorporation of the plasmonic metal layer on the polished surface of this HB-D-PCF and its application as a low RI analyte sensor is one of them. In our designed HB-D-PCF plasmonic sensor the basic fiber is polished and then the polished surface is coated with thin gold and titanium dioxide (TiO 2 ) layers respectively. On top of these active layers suspected analyte is placed. Polishing depth from the surface of the fiber, gold layer thickness and TiO 2 layer thickness are denoted by h, T g and T t respectively. Gold is a well-known chemically stable plasmonic metal. For this structure, high RI transparent TiO 2 layer protects the gold layer from corrosion as well as enhances the coupling between the evanescent waves of core guided light and external analyte. To realize this HB-D-PCF sensing probe practically, it is suggested to incorporate a thin (≤ 5 nm) TiO 2 layer between the fiber (silica) and gold layer. This ultra-thin TiO 2 layer is incorporated as an adhesive layer in spite of weaker adhesion in comparison to commonly used Cr and Ti coating (Aouani et al. 2009) because of its advantageous spectral tenability over previously mentioned materials (Jiao et al. 2009). In our calculation, it is incorporated as a part of the upper TiO 2 tuning layer to reduce the computational time. Moreover, the TiO 2 layer brings down the operating wavelength as well as SPR frequency in the near-infrared region. It is advantageous in several aspects e.g. infrared light has deeper penetration of SPW evanescent tail as a result sensitivity enhancement and wider availability of infrared sources and detectors (Ziblat et al. 2006). For this HB-D-PCF analyte RI is varied from 1.29 to 1.36. Also, the sensor structure is optimized based on polishing depth and layer thickness which are discussed in Sect. 5.1. RI of air is 1. Material dispersion of silica is considered throughout the simulation using the Sellmeier equation (De and Singh 2019a). The complex dielectric constant of gold is taken into account in this simulation as per Johnson and Christy data (Johnson and Christy 1972). The dispersion relation of TiO 2 is taken into account as per Mishra et al. (Mishra and Mishra 2015), Here, λ is the wavelength of core guided mode. FEM based numerical simulation is used to analyze the sensor under study. Also, an anisotropic perfectly match layer is placed around the fiber to reduce radiation loss. During numerical analysis cross-section of the sensor is discretized into small triangular element. Then Maxwell's em equations are applied at each element. Combining all these solutions global matrix is formed and finally effective refractive indices (n eff ) of different modes are computed. During this simulation 26,503 domain elements, 2289 boundary elements and 175,387 degrees of freedoms are solved. (1)

Fabrication prospects
The designed HB-D-PCF is practically realizable in dimension. This hexagonal fiber can be fabricated using developed stack and draw technique (Russell 2003) and laser drilling technique (Becker et al. 2013). The fused preform technique can be applied to realize the elliptical air holes (Falkenstein et al. 2004). Also, lase drilling technique (Becker et al. 2013) and 3D printing technique (Rosales et al. 2020) can be applied to build the preform. Then using this preform fiber can be fabricated by developed stack and draw technique. The D-surface of this structure can be achieved by careful polishing of the fiber surface Dora Juan 2017). For this HB-D-PCF sensor, gold and TiO 2 layers are externally coated. So, this structure is free from internal or selective coating complexity. The gold and TiO 2 layers can be deposited on the D-surface by applying the sputtering technique (Armelao et al. 2005) and chemical method (Pathak et al. 2016) respectively. Additionally, few microliter analyte is needed to pour on the top of the sensing probe. Figure 2 depicts a recommended experimental setup. Free space coupling (Heng et al. 2016) or recently developed connector technique (Morishima et al. 2018) can be applied to launch light at the probe and then routed to the OSA (optical spectrum analyzer) (Wu et al. 2017). Considering all these aspects and currently available fiber technology, we authors are hopeful regarding the real-time applicability of this sensor. It should be kept in mind that polishing of the PCF should be performed very carefully to avoid the damage of the probe. Also, after the fabrication the probe should be attached with a rigid platform to avoid the deterioration of the sensor performance.

Working principle of the proposed SPR sensor and dispersion relation
For this probe, light is propagating along z-direction and all modal analysis are performed at the x-y plane (Fig. 1a). The working principle of this HB-D-PCF is governed by coupled mode theory (CMT). As per this theory core guided mode and SPP mode gets coupled at a particular frequency when their effective refractive indices (n eff ) are matched. It is also known as the phase matching point (Dora Juan 2017). Here, it is worthy of mentioning that throughout all analysis y polarized fundamental core mode is considered because this mode breaks the symmetry of the structure as the plasmonic layer is situated in the y-direction. As a result better interaction takes place between evanescent wave of y polarized core mode and analyte in comparison to the x polarized mode in the infrared region ; Dora Juan 2017). For this sensor, energy coupling takes place from the core mode to the fundamental surface plasmon polarization (SPP) mode and maximum loss appears in the core mode at the resonance wavelength. This loss spectra is highly dependent on structural parameters, active layers thickness and the surrounding environment. Confinement loss of both core guided mode and SPP mode can be formulated as, here, Im(n eff ) is the imaginary part of effective RI (Gangwar and Singh 2017). Figure 3 shows the dispersion repletion of core mode and SPP mode for the optimized structure at n a = 1.33. In Fig. 3 Re(n eff ) of core mode, Re(n eff ) of SPP mode and loss of core mode variation with changing wavelength are denoted by solid green line, solid red line and blue line with circle respectively. It can be observed from Fig. 3 that at 1.415 µm propagating wavelength Re(n eff ) of core mode and SPP mode are matched and coupling takes place between them. At this particular wavelength loss of the core mode is maximum and it is known as SPR wavelength. Figure 4 represents the electrical field distribution of core and SPP modes for n a = 1.33. Figure 4a, b are the core and SPP mode at 1.380 µm wavelength (away from coupling) and Fig. 4c is the coupled mode at 1.415 µm wavelength. It can be visualized that at coupling wavelength electric field is prominently present both in core and SPP mode. The SPR wavelength suffers a significant shift with the changing environment. So, wavelength sensitivity can be calculated by tracking the SPR wavelength shift as follows, here, Δλ peak is the SPR wavelength shift for Δn a , analyte RI change.
Not only the strength of coupling but also the coupling nature between core and SPP mode can be explained well based on CMT (Fan et al. 2015;Ma et al. 2013). Following this theory two coupled modes can be presented as follows, (2) α(dB∕cm) = 8.686 × 2π λ Im n eff × 10 4 (3) S (nm/RIU) = Δ peak Δn a (4) here, β 1 and β 2 are propagation constants, E 1 = A exp(iβz) and E 2 = B exp(iβz) are fields associated with the core and SPP mode. z and Ҡ are the propagation length and coupling strength respectively. By substituting E 1 and E 2 in the solution of Eqs. (4) and (5), it can be written as, here β ave = (β 1 + β 2 )/2 and δ = (β 1 − β 2 )/2. β 1 , β 2 and δ all are complex quantities with δ = δ γ + iδ i . When, δ i ˃ Ҡ, β + and β − have same real part and different imaginary part. In this case an incomplete coupling takes place. On the other hand, complete coupling takes place in a converse case. Figure 5 depicts the incomplete coupling at n a = 1.33 for the designed HB-D-PCF. The coupling nature over the entire analyte range will be discussed in Sect. 5.2.

Influence of structural parameters on loss spectrum and optimization
The PCF shows high birefringence throughout the near-infrared region (as shown in Fig. 6 (De and Singh 2019a)) and it suffers increment with increasing wavelength. It has birefringence of 3.93 × 10 -3 at 1.55 µm wavelength. The presence of broader passage along y-direction is the reason behind more modal spreading as well as high birefringence (De and Singh 2019a). The effect of polishing depth and active layers thickness on loss spectrum are investigated in detail to design an optimal performing HB-D-PCF sensor, and (6) Fig. 4 electric field distribution of a core guided mode, b SPP mode and c coupled mode findings are depicted in Fig. 7. During this process parameters are optimized one at a time.
With changing parameters losses of core guided modes are calculated using Eq. (2). For a SPR sensor, thickness of the plasmonic metal layer is a crucial parameter. Because SPP wave as well as modal coupling are strongly dependent on this layer thickness. Figure 7a shows the variation of loss spectra for different polishing depths when T g = T t = 40 nm. For increasing h from 3.94 µm to 4.39 µm with an iteration of 0.15 µm, SPR wavelength suffers blue shift (indicated with blue arrow) from 1.269 µm to 1.165 µm with varying loss peak. In the beginning, loss started to increase with increasing polishing depth because deeper polishing allows more interaction between core mode and external analyte. In this case loss is maximum for h = 4.24 µm with sharp loss peak. But when the fiber is polished more then there is a coupling tendency between core mode and first order SPP mode (blue dash-dot line). As a result, loss peak of fundamental mode decreases and sensitivity becomes less. Also, very deep polishing makes the fiber fragile and coupled modes desultory. So, h = 4.24 µm is chosen to get a well-responding sensing probe. It can also be observed that response of the probe is highly sensitive to the polishing depth. So, special care should be taken during fabrication. Figure 7b shows loss spectra of core mode for varying T g with h = 4.24 µm and T t = 40 nm. For increasing T g from 35 to 55 nm with an iteration of 5 nm, SPR wavelength suffers red shift (indicated with red arrow) from 1.160 µm to 1.274 µm. One fact is noticeable in Fig. 7b that resonance loss is maximum for 40 nm thick gold layer with a most sharp peak among all. It can be explained as, for a well responding SPR sensing probe the plasmonic layer has an optimum thickness. When the plasmonic layer is too thin then it is not able to accommodate a sufficient number of SPP modes due to high mechanical damping. contrarily when the plasmonic layer is too thick core mode is unable to interact with external analyte properly or penetration depth is limited i.e. plasmonic damping (De and Singh 2020). So, the optimum gold layer thickness is chosen as 40 nm for this HB-D-PCF sensor.
Then the effect of T t on fundamental core mode loss is studied in detail with h = 4.24 µm and T g = 40 nm as shown in Fig. 7c. For increasing T t from 35 to 60 nm with an iteration of 5 nm, SPR wavelength suffers red shift (indicated with red arrow) from 1.140 to 1.576 µm with loss increment at the beginning. For T t = 50 nm, loss curve is very sharp with highest loss. Also, higher order resonance loss peak is much lower than the fundamental core loss peak. It can be noticed that with increase T t resonance loss peak started to increase until Fig. 7 a Loss spectrum of the designed HB-D-PCF sensor with changing h at n a = 1.33. b T g and c T t at n a = 1.33 the other higher order loss peak appears prominently. The reason behind this is the TiO 2 layer enhances the mode coupling as well as light analyte interaction. But wider T t screens core guided light from analyte. So, T t = 50 nm is chosen as optimized TiO 2 layer thickness.

Performance analysis
The loss spectrum of the optimized HB-D-PCF SPR sensor having structural parameters h = 4.24 µm, T g = 40 nm and T t = 50 nm are depicted in Fig. 8a. The proposed sensor is performing best in the analyte RI (n a ) range 1.29 to 1.36. For an analyte having RI below this range modes become desultory. Also, for an analyte above this RI range wavelength response is poor. It can be observed from Fig. 8a that SPR wavelength suffers a red shift from 1.220 to 1.672 with increasing n a (indicated with red arrow). The reason behind this is that n eff of core mode and SPP mode are close to RI of silica fiber and n a respectively. So, increment in n a causes red shift of the phase matching point as well as SPR wavelength (De and Singh 2020). It is also noticeable in Fig. 8a that loss peak goes through a circle of rising and fall in that particular range. In the beginning, loss suffers increment with increasing n a and then comes to a maximum of 239 dB/cm at 1.415 µm wavelength for n a = 1.33. After that, loss stars to decrease with increasing n a . This is because of the strongest coupling between core mode and SPP mode at n a = 1.33 which is also observable in Fig. 10. Throughout the studied RI range loss is moderate for this sensor which is another attractive feature for its practical implementation. The performance of the optimized HB-D-PCF SPR sensor is summarized in Table 1. SPR wavelength shift with changing n a is depicted in Fig. 8b. By applying wavelength interrogation technique on this cure wavelength sensitivity can be calculated using Eq. (3). The highest sensitivity of this sensor is found to be 9245 nm/RIU. These observed data points are fitted very well with second-degree polynomial equations with R 2 value 0.9998. The relation between SPR peak and n a can be presented as follows, Figure of merits (FOM) (Fan et al. 2015) of this sensor can be calculated as follows, (7) λ peak = 81.0511 − 126.6890n a + 50.2362n 2 a Fig. 8 a Loss spectrum for various analytes, b SPR wavelength variation with changing analyte with varying n a full width at half maximums (FWHM) are presented in Table 1. For this HB-D-PCF SPR sensor FOM can reach up to 342 at n a = 1.33 which is reasonably high. In this designed fiber, asymmetry is induced around the core by incorporating two elliptical air holes next to the core. Due to this a broader passage way is created along y direction in comparison to x direction. Here, more interaction takes place between fiber guided light and analyte because active layers (Au and TiO 2 ) are situated on polished surface along y direction. As a result sensitivity got enhanced (Dash and Jha 2014).
Also the amplitude interrogation technique is applied to investigate the sensitivity of the proposed sensor. This technique is economically beneficial because of the use of a single source. When propagating light suffers loss of α(λ, n a ) due to the propagation through a probe length L, its amplitude sensitivity can be defined as (Dash and Jha 2014;Rifat et al. 2015), Figure 9 depicts amplitude sensitivity of the proposed sensor in the RI ranging from 1.30 to 1.36. Again red shift is noticeable in this case with increasing n a (denoted by red arrow). The reason for this shift is previously mentioned. Maximum S A is found to be 1312RIU −1 with n a = 1.33. Also, the coupling characteristics between core mode and SPP mode is presented in Fig. 10. It shows incomplete coupling throughout the studied RI range. So, this HB-D-PCF SPR sensor is advantageous in detecting bio analytes (Merwe 2000).
Resolution shows the minimum detection ability of a sensor which can be calculated using following equation (Rifat et al. 2016d), In case wavelength interrogation method, R of the HB-D-PCF sensor is 1.08 × 10 -5 RIU when Δλ min = 0.1 nm and for amplitude interrogation method it is 7.62 × 10 -6 RIU for 1% , n a n a (10) R = Δn a × Δ min Δ peak RIU

Conclusion
An optimized SPR sensor is proposed based on a high birefringent PCF. Its sensing performance as well as coupling nature are investigated in RI range 1.29-1.36 using wavelength and amplitude interrogation techniques. This HB-D-PCF SPR sensor exhibits maximum wavelength and amplitude sensitivity of 9245 nm/RIU and 1312 RIU −1 respectively. It is able to detect RI change up to the order of 10 -6 . Also it shows a high FOM of 342. This moderately lossy SPR sensor is practically realizable using developed stack and draw Our work method and can be a good competitor of commercially available fiber using D-PCF sensors. Long range sensing ability of this complexity free structure is its key advantage over many D-shaped plasmonic PCF sensors. The promising features of the proposed sensor make it a suitable candidate for integrating with the lab-on-a-fiber technology, developing fiber interferometer as well as fabricating portable biochemical sensing devices.