Modeling and analysis of D–shaped plasmonic refractive index and temperature sensor using photonic crystal fiber

In this study, a D–type photonic crystal fiber (PCF) based surface plasmon resonance (SPR) sensor is proposed for measurement of both refractive index (RI) and temperature. The RI sensing part is constructed by deposition of a silver layer on the plane of the D–type structure, and the temperature sensing part is formed by filling the silver nanowire and the liquid analyte into an elliptical hole in the PCF. The proposed design then can be used for temperature and analyte RI sensing through the coupling between the core guided modes and the surface plasmon modes around the nano silver rod and layer. We study the coupling characteristic and sensing performance of the sensor. The numerical results show that the maximal sensitivity in terms of RI units (RIU) is 6.9 μm/RIU in the range of 1.33–1.38, and the maximal temperature sensitivity is 3 nm /°C in the range of 27–67 °C.


Introduction
The SPR is the coupling of electromagnetic (EM) waves and free electron density oscillations on the metal-dielectric interface. Owing to the high sensitivity to the metal surface RI variations, it has been utilized in several sensing apparatus, including optical waveguides, PCFs and conventional fibers (Klantsataya et al. 2016;Rifat et al. 2017;Zhao et al. 2018). The PCF-SPR sensors show privileged features such as appropriate phase matching, high integration and flexible design that make them attractive for application. To attain SPR sensing in PCFs, a thin metal film is deposited on the inner walls of the PCF holes and a proper analyte is then filled. The resonance peak in the loss spectra of the transmitted light occurs as the real part of the effective refractive index of the core mode (n eff ) is equal to that of the SPR mode at a specific wavelength. As the analyte RI changes, the propagation constant of the relevant mode changes too and affects the SPR spectrum.
Because the SPR spectrum is very sensitive to the variations in the medium RI surrounding the metal surface, any parameter that affects the medium RI can be detected by monitoring changes in the SPR spectrum. As a consequence, the RI of the filling liquid (as the temperature sensing material) and so the n eff of the PCF design will be temperature dependent. Hence, PCF-SPR temperature sensor can be fabricated. It is necessary to say that the diameter of air holes in PCF-SPR sensors is usually in the order of a few microns. Thus, the metal deposition operation in these holes is so hard to perform in practical issues. Furthermore, either in RI or in temperature PCF-SPR sensor devices, the variation in SPR spectrum is eventually affected by RI of the medium around the metal surface. Determination of the factor (analyte RI or temperature) that causes changes is difficult from the SPR spectrum. Hence, it is hard to achieve a simultaneous analyte RI and temperature sensing in a PCF-based SPR sensor. One solution to overcome the difficulties of metal coating is to use D-type or exposed-core PCFs (Luan et al. 2018. Meanwhile, simultaneous detection of RI and temperature will be realized by creating vertical sensing channels in the D-shaped or exposed-core PCF-SPR sensor . A review of the literature shows a growing development of PCF-SPR sensors during the recent years. Hameed et al. (2016) have reported a novel highly sensitive SPR-based liquid crystal (LC) PCF temperature sensor. By optimization of the geometrical structural parameters, they achieved the high sensitivity of 10 nm /°C. An et al. (2017a, b) proposed a D-shaped PCF-SPR RI sensor and studied the related performance. The maximum sensitivity of 10,493 nm∕RIU was obtained with a very high resolution of 9.53 × 10 − 6 RIU. Islam et al. (2020) have offered the external sensing approach of a PCF-SPR sensor with excellent sensitivity. The circular air cavities in the blueprint were disposed in a strategical order to enhance the performance as a sensor as well as to make it fabrication feasible. The Finite Element Method was utilized to optimize all the fiber parameters. After the optimization of all the fiber parameters, they derived maximum amplitude sensitivity and wavelength sensitivity of 5060 RIU − 1 and 41,500 nm/RIU, respectively, with a maximum sensor resolution 2.41 × 10 − 6 for wavelength and 1.98 × 10 − 6 for amplitude. Azab et al. (2017) have proposed a novel design of compact SPR multifunctional biosensor based on LC PCF. The reported multifunctional sensor offers high sensitivity of 5 nm /°C and 3700 nm/RIU for temperature and analyte refractive index sensing, respectively.
In this study, a D-shape PCF-SPR sensor for measuring RI and temperature is designed. The main goal is to achieve high sensitivity and fabrication feasibility. The RI sensing portion is constructed by coating the metallic Ag film on the polished surface plane of the Dshape PCF and the temperature sensing part is formed by filling the Ag nanowire into the hole of the PCF filled with benzene as the temperature sensing analyte. The proposed design has a silver nanorod that is placed on the bottom of a large elliptical hole. In this regard, Luan et al. (Lee 2012) have successfully fabricated a PCF with silver nanorods that are attached to the inner surface of the desired capillaries by using capillary force and air pressure. This hole can be filled by benzene under capillary forces as reported by Huang et al. (2004). Ag layer always shows a high sensitivity and sharper resonance peak in comparison to Au layer which results in to detection accuracy (Pathak and Singh 2020). However, due to strong oxidization tendency of Ag in air, the proposed setup is more appropriate for the ambient without oxidizing agents. In the recent decades, the metallic nanowire has caught tremendous attention of scientists as an excellent plasmonic medium for sensor applications (Pathak and Singh 2020;Pathak et al. 2019). The two mentioned sensing segments can excite two independent peaks with orthogonal polarizations, which can be utilized to discern RI or temperature changes. In the simulation process, the impedance boundary condition is considered and the finite element method (FEM) is employed to study the PCF-SPR properties and sensing performance. The FEM divides the proposed sensor into homogeneous subspaces which are triangular in shape. The neighboring subspaces promote solving Maxwell's equations using FEM. This FEM also helps obtaining the mode field pattern and effective index with more accurate results. Furthermore, the number of domain elements and boundary elements are 26,220 and 1759 respectively. In the designed sensor, the metallic Ag layer is deposited on the D-plane as the RI sensing part, exposing it directly to the analyte. Also, the air holes are decorated as triangular lattice. The lattice constant or pitch of the PCF (Λ) is considered 4 μm. The fiber radius (r) is equal to 7 Λ and the distance between the center of fiber and the boundary polished surface is h = 1.1 Λ. The thickness of Ag layer (t Ag ) is 42 nm and the radius of Ag nanowire (r Ag ) is 200 nm. With optimization of air holes we can confine efficiently the maximum portion of the light in the fiber core. The air holes with optimized diameter of d 1 = 0.8 Λ and d 2 = d 1 -1.5 μm are used to attain well coupling between surface plasmon polariton (SPP) mode and core guided mode. To reduce the interference of different polarization, elliptic air holes have been optimized on both sides of the fiber core. The major and minor axis of the ellipses is considered as a = 0.8 Λ and b = a/3, respectively. One elliptic hole is filled with Ag nanowire and benzene (as sensing medium) to construct the temperature sensing portion. The fused silica is taken as the background material with RI = 1.45. The RI of benzene used is dependent on both temperature and wavelength changes as follows (Luan et al. 2014)
The modes will couple, when their n eff are equal. Fundamentally, at the point of intersection, the frequency of the guided photons through the core and the frequency of the surface electrons of the plasmonic metal are matched and maximum power is transferred from the core guided fundamental mode to the SPP mode due to perfectly phase matching. Hence, confinement loss of the core guided fundamental mode is found maximum at a particular value of RI of analyte. To investigate the coupling properties of the designed sensor, we display the n eff curve and E-field distributions along with the loss spectra of the pertinent modes in Fig. 2. In an optical fiber, the modal-field distribution is generally either oscillatory or evanescent in the transverse direction. If the modal-field distribution is oscillatory in the core and evanescent in the cladding, the mode is confined in the core as the modal-field distribution rapidly decays in the cladding. These modes are identified as core-guided modes. On the other hand, the SPPs are known as non-radiative optical modes related to plasma oscillations of free electrons resonantly excited at a metal surface and propagate along the surface with evanescent electromagnetic fields. The sensing mechanism depends principally on the coupling between the SPP modes around a metal surface and the core-guided modes inside a near medium. The coupling takes place when the real part of the effective indices of a core mode and SPP mode are equal. Therefore, matching occurs and maximum power transfer happens from the core-guided mode to the SPP mode and resonance is achieved. The confinement loss of the sensor can be characterized by using the following formula (Hao and Nordlander 2007) The metal nanorods can stimulate a limited number of discrete SPP modes on their surface (Nagasaki et al. 2011). As can be seen from the figure, the x-polarized SPP mode of Ag nanorod can couple to the x-polarized core mode at a particular wavelength. On the other hand, the coated Ag film on the D-plane can merely stimulate the y-polarized SPP mode which can couple to the y-polarized core mode at the resonance wavelength only. This behavior can be obviously seen by the E-field distributions in the figure. Clearly, the x-and y-polarized core modes are well confined in the core zone. The curve of confinement loss has an explicit absorption peak at the wavelength corresponding to the intersection points in the real part of the n eff of the SPP mode, which confirms the phase matching coupling in which extreme energy can be propagated from the core mode to the SPP modes of Ag nanorod and thin film along the x-polarized and y-polarized directions, respectively.

Fig. 2
Real part of n eff for x and y-polarized core and SPP modes along with the loss spectra for the x and y-polarized core modes. The corresponding electric field distributions are also shown. The red arrows display the polarization direction of E-field

Results and discussion
As the analyte RI (n Anl .) or temperature sensing medium RI (n Tem .) changes, the corresponding intersections (phase matching points) changes accordingly, resulting in the shift of the resonance peaks of x-and y-polarized to different wavelengths.

RI sensing analysis
The variation of the confinement loss curve of y-polarized resonance peak is illustrated in Fig. 3 at different n Anl . As the n Anl enhances, the resonance peak (λ Peak ) shifts to longer wavelengths, and the intensity of the resonance peak gradually rises. The λ Peak increases from 0.56 to 0.76 μm as n Anl changing from 1.33 to 1.38. This implies that the sensor can provide higher sensitivity at higher n Anl of the detection range. The sensitivity of the sensor of the RI unit (RIU) can be defined as (Chen et al. 2021) S n (µm/RIU ) = ∆λ peak ∆n Anl.
where ∆λ peak denotes the shift of y-polarized peak. As displayed in the inset of Fig. 3, the maximal S n is 6.9 μm/RIU in the range 1.33-1.38. The higher n Anl may lower the limit of the core mode, and hence enhances the evanescent E-field in the sensing area, which results in a higher sensitivity. Nevertheless, as the n Anl exceeding 1.41 (not shown), the higher order SPP modes are excited, that lead to more noise in the loss spectra of the core modes. Therefore, the sensor is not appropriate to sense the n Anl beyond 1.41. The detection limit is an important figure-of-merit (FOM) to characterize the sensor performance, and is defined by the smallest detectable change in RI. This parameter is stated as (Danlard and Akowuah 2020) where FWHM denotes the full-width at half maximum of resonant peak. The calculated FOM varies from 0.28 to 0.98 RIU − 1 as RI increased from 1.33 to 1.38. Both the increase in sensitivity and decrease in FWHM with RI contribute to an improved detection limit with increasing RI.

Temperature sensing analysis
A temperature sensor works on the basis of the change of RI of the temperature sensitive material (Benzene in this study) with the change in temperature. Hence, the λ Peak shifts with the temperature variation. The detection range (27-67 °C) is chosen based on the boiling and melting point of the benzene. Figure 4a shows the change of RI of the analyte at the D-surface of the sensor with temperature in the measurement range from 27 to 67 °C. From the figure, it can be seen that temperature changes resulting very little change in the RI of analyte at the D-surface. So, the effect of temperature change in benzene has ignorable and trivial effect on the RI of the other analyte. Fig. 4 (a) Refractive index change with temperature of the analyte at the D-surface and (b) Dependence of the confinement loss curve of the x-polarized on the analyte temperature. Inset represents the peak wavelengths (λ Peak ) and temperature sensitivities (S T ) for x-polarized core modes at different temperatures Fig. 3 Dependence of the confinement loss curve of the y-polarized on the analyte RI (n Anl .). Inset represents the peak wavelengths (λ Peak ) and RI sensitivities (S n ) for y-polarized core modes at different n Anl The variation of the confinement loss curve of x-polarized resonance peak is depicted in Fig. 4b at different temperatures. As the temperature increases, the λ Peak moves toward longer wavelengths and the intensity of the λ Peak increases. The λ Peak increases from 0.95 to 1.02 μm as the temperature changing from 27 to 67 °C. The temperature sensitivity can be calculated by (Chen et al. 2021) The average S T of the proposed dual-function sensor is 2 nm/°C between 27 and 67 °C and the maximum S T is 3 nm/°C in the whole range of temperature. This value is very higher than the reported values for the Mach-Zehnder interferometer NFN structure (∼0.014 nm/°C) (Bai et al. 2014), modal interferometer PCF (∼92.6 pm/°C) (Zhao et al. 2015), liquid-sealed PCF (∼166 pm/°C) (Qiu et al. 2012), and surface long-period grating (LPG) D-shaped PCF (∼0.3 nm/°C) (Kim et al. 2011). It is necessary to say that the achievement here is merely valid for temperatures in which the sensing material remains liquid state. Moreover, for the temperature sensing channel, due to concerns related to homogeneous thermal distribution inside the elliptical hole that may affect the sensing performance, further calibration is needed during the measurement.

Amplitude analysis
To detect the analyte, sensor is operated in the range of wavelength according to wavelength interrogation technique, and spectral manipulation is needed. Since no spectral manipulation is required, it is more cost effective to utilize the amplitude interrogation technique (AIT) to investigate the performance of the sensor. The amplitude sensitivity can be calculated by (An et al. 2017a, b) Where α, Δα and Δn Anl . stand for loss, loss difference and variation of the analyte RI, respectively. The amplitude sensitivity is calculated based on AIT and shown in Fig. 5. As seen from Fig. 5a, the amplitude sensitivity of the proposed RI D-shaped sensor is 185.54, 283.16, 371.13, 474.87, and 642.50 RIU − 1 at wavelength of 0. 566,0.609,0.667,0.694,and 0.788 μm,respectively. Similarly,from Fig. 5b, the amplitude sensitivities of 256.58, 270.78, 286.17, and 301.72 RIU − 1 are observed at temperature regions of 27-37 °C, 37-47 °C, 47-57 °C, and 57-67 °C, respectively. As it is seen, the maximum amplitude sensitivity for RI channel is 642.50 RIU − 1 at 788 nm and the corresponding value for temperature sensing channel is 301.72 RIU − 1 at 1032 nm. These values are higher than the reported values in Ref (Chen et al. 2021).
Generally, a slight variation of ± 1% can happen in the optimized structural parameters during the. fabrication (Pathak et al. 2021). To verify the achieved performance of the proposed sensor, we have studied the modeled structural parameter with the fabrication tolerance of ± 2%. Figure 6 shows typically the effect of r Ag and t Ag on the amplitude sensitivity for n Anl .=1.36-1.37 and T = 47-57 °C with the variation of ± 2% from their optimum value. As it can be clearly observed, the resonance peak shifts very slightly over ± 2% variation of r Ag and t Ag from their optimum value. Also, the maximum amplitude sensitivity is increased/ decreased by 1.73 RIU − 1 /1.82 RIU − 1 due to ± 2% variation of r Ag . The corresponding values for ± 2% variation of t Ag are 2.21 RIU − 1 /1.47 RIU − 1 . Accordingly, 2% variation in r Ag and t Ag will not affect the sensitivity of the proposed sensor during the fabrication process.

Fabrication possibility
Compared with the ordinary optical fibers, the fabrication process of the nanostructured PCF sensor is more sophisticated. Some conventional and well known routes are sol-gel (Romanova and Matyushkin 2017), chemical vapor deposition (Haque et al. 2019), wheel polishing method (Zhang et al. 2007), atomic layer deposition , stackand-3D printing, injection modeling, and capillary stacking techniques (Sardar et al. 2021). Utilizing the drilling technique, a computer-controlled mill has been employed to drill air holes in the solid rode and solid tube, and draws them to the inner and outer air structure fibers, respectively . For instance, an Au-MgF 2 -deposited nanostructure is concisely explained experimentally in Ref. (Bartkowiak 2018) by changing the layer size and parameters. As well, in the case of fabrication, some SPR-PCF sensors with Ag-Tio 2coated (Noman et al. 2020), Au-coated (Cao et al. 2018), and MgF 2 /TiO 2 -coated optical filter (Silva et al. 2020) are experimentally presented The suggested sensor can be used as a biosensor because the operating analyte range is 1.33 to 1.38. A notable number of biological analytes' RIs lie in the range of 1.33 to 1.38, for instance, tuberculosis cells sensing (1.345-1.349) (Ramanujam et al. 2020), pregnancy testing (1.335-1.343) (Mitu et al. 2021), cancer cell detection (1.36-1.38) (Jabin et al. 2019), alcohol sensing (1.333-1.3611), different blood components sensing (1.33-1.40) , etc. Hence, the wide range of analytes and high sensing performance of the suggested sensor make it a promising candidate in the large number of SPR-PCF biosensor applications.

Conclusions
In this study, we propose a SPR sensor based on a D-shaped PCF that contains two sensing channels for simultaneous RI and temperature sensing. The sensing performance of the designed sensor is investigated using wavelength and amplitude interrogations. The maximum wavelength RI and temperature sensitivities are 6.9 μm/RIU and 3 μm /°C, and the corresponding amplitude sensitivities are 642.50 RIU − 1 and 301.72 RIU − 1 . The interference challenge between the x-and y-polarization of RI and temperature channels is solved wholly by utilizing the D-shaped PCF with ellipse air holes. Therefore, no cross-sensitivity will happen. Furthermore, the coupling between the core mode and the SPP modes excited by the Ag film and the Ag nanorod is discussed and analyzed.