Highly Sensitive Salinity and Temperature Sensor Using Tamm Resonance

In this paper, a Tamm plasmon resonance-based sensor is theoretically studied to calculate the salinity of seawater as well as a temperature sensor based on photonic crystals. The transfer matrix method (TMM) is used to systematically study and analyze the reflected s-polarized electromagnetic waves from the sensing structure. The proposed structure composes of prism/Au/water/(Si/SiO2)N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(\mathrm{S}\mathrm{i}/{\mathrm{S}\mathrm{i}\mathrm{O}}_{2})}^{N}$$\end{document}/Si. The sensitivity, figure-of-merit, quality factor, and detection limit of the sensors are improved by optimizing the thickness of the seawater layer, incident angle, salinity concentration, and temperature. The proposed salinity sensor records a very high sensitivity of 8.5 × 104\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${10}^{4}$$\end{document} nm/RIU and quality factor of 3×103\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3\times {10}^{3}$$\end{document}, and a very low detection limit of 10-7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${10}^{-7}$$\end{document} nm. Besides, the suggested temperature sensor achieves high sensitivity (from 2.8 to 10.8 nm/°C), high-quality factor of 3.5×103\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3.5\times {10}^{3}$$\end{document}, and a very low detection limit of 3×10-7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${3\times 10}^{-7}$$\end{document} nm. These results indicate that the proposed sensor is a strong candidate for salinity and temperature measurements.


Introduction
Water is an essential need for living organisms to stay alive and is one of the most serious global issues facing the world today [1]. The polluted water causes various diseases such as cholera, typhoid, and other water-borne diseases [2]. Salinity is the salts that dissolved in the water and is one of the water contaminations [3]. The phase of salinity measuring is very important to determine the accuracy of water desalination systems. Besides, the temperature and salinity of seawater are very important in the physical oceanography [4].
Recently, more attention has been paid to develop salinity and temperature sensors. In 2009, Possetti et al. [5] proposed an in-fibre Mach-Zehnder interferometer. A theoretical sensitivity for salinity measurements of 46.5 nm/RIU and thermal sensitivity of 53 pm/°C was obtained. In 2014, Kamil et al [6] experimentally demonstrated a method for salinity sensors using tapered single-mode fibre. They reported a sensitivity of 2834.3 nm/RIU. In 2018, a salinity sensor using photonic crystal fibre (PCF) was reported by Vigneswaran et al [3]. This sensor recorded a sensitivity of 5675 nm/RIU. In 2019 [7], Amiri et al. proposed a temperature-salinity tricore PCF sensor with a salinity sensitivity of 5674 nm/RIU, and temperature sensitivity is 4 nm/°C. In 2020, Akter et al. [8] designed a dual-core microstructure PCF as a temperature and salinity sensor. They achieved salinity sensitivity 11,111.11 nm/RIU and temperature sensitivity 1000 pm/°C.
The photonic crystal (PC) is a multi-layer structure with a different dielectric constant in a periodic structure [9][10][11]. PC can be divided according to its periodicity into one dimensional (1D-PC), two dimensional (2D-PC), and three dimensional (3D-PC) [12][13][14][15][16][17][18]. PC manipulates the light propagation through it. When the incident light propagates through the PC, it reflects at each interface. Under a suitable condition, constructive interference between the reflected waves occurs, and the resultant reflected wave destructively interferes with the incident wave. Due to this destructive interference, a forbidden bandgap appears (PBG) [19][20][21].
In 2007, Tamm plasmons (TP) was introduced [22,23]. It is confinement of electromagnetic waves at the interface between 1D-PC and the metallic layer. A TP resonant dip appears inside the PBG. The position of TP dip is very sensitive to the optical properties of the PC and the surrounding [24]. So, the TP structure can be used as a sensor [25].
However, PCF has attracted more attention in most of the previous salinity and temperature studies; it needs a complex manufacturing process and additional equipment to achieve the machining process requirements. Also, the quality of the system depends upon several parameters such as group birefringence, phase, and fringes interference [26,27]. So, we suggest in this manuscript a quite simple and ultra-sensitive one-dimensional photonic crystal structure based on Tamm resonance.
The transfer matrix method (TMM) will be used to systematically study the reflected s-polarized electromagnetic waves from the sensing structure by using MATLAB tools.

Sensor Geometry
The structural parameters of the whole structure (prism/Au/ water/(Si∕SiO 2 ) N /Si) of the sensor are indicated in Fig. 1. It consists of 1D-PC coated with a metallic layer (Au layer). The water layer is presented between the 1D-PC, and the metallic layer that is deposited on the prism face to prevent the metallic layer from floating into the water layer. The TE-polarized light incident with angle 0 from one lateral prism-face to its base reflected out from the other face, and analysed by a photodetector [28].
The water layer can be done experimentally by depositing any suitable layer with the desired dimensions instead. Then, this layer can be easily removed with a strong acid (etching process). Plasma-enhanced chemical vapour deposition (PECVD), spin-coating [29], spray pyrolysis, thermal evaporation, and some other deposition techniques can be used to deposit dielectric ( Si/SiO 2 ) homogeneous films [30][31][32]. Therefore, the convenient and practical qualities to manufacture are taken into account.
The PC is periodically arranged by Si-layer and SiO 2 -layer. The thickness of Si ( d 1 ), SiO 2 ( d 2 ), Au ( d m ), and the water layer ( d w ) are 100 nm, 400 nm, 25 nm, and 700 nm, respectively. The refractive index of the substrate is 3.3.
A significant factor influencing the performance of the proposed sensor is the adjusting of the refractive index of the prism. Leiming et al. reported a SPR sensor and concluded that the highest sensitivity can be achieved using a low refractive index prism [33]. Therefore, the refractive index of the prism in this study will be 1.5.

Numerical Method
The TMM will be used to systematically study the reflected S-polarized electromagnetic waves from the structure by using MATLAB tools. For the s-polarized wave, the transfer matrix (G) of the structure is where G 11 , G 12 , G 21 , and G 22 are the elements of the total matrix of the structure. g m , g 1 , and g 2 are the transfer matrix for the metallic layer (Au), Si , and SiO 2 , respectively as the following: The values of p for the TE wave are given by p i = n i cos i (i = 1, 2andm) , and is the incident angle.
Chebyshev polynomials of the second kind are used to calculate the matrix for N periods [34]. More details can be found in our previous studies [35][36][37]. The reflectance spectra of the proposed structure can be given as [38] where r denotes the reflection coefficient of the structure ( r = (G11+G12ps)pp−(G21+G22ps) (G 11 +G 12 p s )p p +(G 21 +G 22 p s ) ) , p p = n p cosj p (for prism), and p s = n s cosj s (for substrate).
The 1D-PC is designed with two different dielectric layers ( Si and SiO 2 ). The thermal expansion and thermo-optic effects are taken into account to achieve an accurate simulation. The refractive index of Si and SiO 2 as a function of temperature can be calculated as the following: where n 0 is the refractive index of Si ( 3.3 ) and SiO 2 ( 1.46 ) at room temperature, and is the thermo-optic coefficient for Si (1.86 × 10 −4 /°C) and SiO 2 (6.8 × 10 −6 /°C). ΔT is the variation of the temperature. The term ( n 0 ΔT ) indicates the change in the refractive index of the layer with the change of temperature. Also, the thickness of layers changes with the temperature as the following: where d 0 is the room temperature thickness of each layer, is the thermal expansion coefficient of Si (0.5 × 10 −6 /°C) and SiO 2 (2.6 × 10 −6 /°C) [39].
Drude model is used in the calculation of dielectric constant of Au layer ( √ n m ) as the following [40]: where p , , and are plasma frequency, damping frequency, and frequency of the incident light, respectively [24]. As a function of salinity concentration ( C s in %), temperature (T in • C) , and wavelength ( in nm), the index of refraction of seawater is calculated as the following [3,8,41]:

Simulation Results and Discussions
Now, we study the simulation analysis of the incident waves into the proposed sensor and the effect of the metal layer. The structure is composed of prism/Au/water/(Si∕SiO 2 ) N / Si. In Fig. 2, the black and red curves are the reflectance spectra of the prism/water/(Si∕SiO 2 ) N /Si and prism/Au/ water/(Si∕SiO 2 ) N /Si structures, respectively. In the absence of the Au layer, A PBG was expanded from 1514 to 2381 nm, because of the system periodicity. On the contrary of surface plasmon, Tamm resonance has the ability to direct excite at normal incidence by adding an Au layer in front of the 1D-PC. Between the Au surface and 1D-PC, the electromagnetic modes are confined at wavelength 1841 nm (red line in Fig. 2).

Salinity Sensor
In this section, the effect of the change of salinity concentration on the resonant dip position will be studied. As clear in Fig. 3, and according to Eq. 6, the refractive index of water increased with the change of salinity concentration in water. Because the position of the Tamm resonant dip depends on the effective index of refraction of 1D-PC and the surrounding, the dip position is shifted with any increase or decrease in the water refractive index.
It is important to keep in mind that a small change in salinity concentration would cause a resonant dip wavelength ( r ) shift. The darker the reflectivity (zero reflectance), the sharper the dip-position jump [42]. So, even a very small change in the refractive index due to the salinity concentration change can be detected by a sharp dip shift relative to the calibration medium (pure water), as shown in Fig. 4. Fig. 4 shows the reflectance variation versus the incident wavelength for different values of salinity concentration. As the salinity concentration increases from 0 to 50%, the dip position is red-shift to a higher wavelength from 1841.26 to 1849.58 nm with a change in wavelength equal to 8.32 nm.

Effect of the Water Layer Thickness on the Salinity Sensor Performance
As clear in Fig. 5, the Tamm resonance wavelength ( r ) has a large red-shift with the increase of the water layer thickness at a fixed incident angle, Au thin film thickness, and temperature that is due to the increasing of the geometric path of the light wave inside the water layer. Consequently, the coupling between the incident light and water components is enhanced. It is clear from Fig. 5 that the wavelength shifts rapidly improved from 8.32 to 12.68 nm with the increase of water layer thickness from 700 to 6000 nm but slightly increases with further increase in water thickness. So, the water layer thickness of 6000 nm will be the optimum thickness. This result is in agreement with prior experimental and theoretical studies [43][44][45].

Effect of the Incident Angle on the Salinity Sensor
As clear in Fig. 6A, the PBG becomes broader and is blueshifted to lower wavelengths with the increase of the incident angle. Besides, total internal reflection (TIR) occurs with a critical angle ( c ) of 61.6° according to TIR principle: When the angle of wave propagation increases from 0 to 50°, the wavelength shift slightly increases. In contrast, a (9) c = sin −1 n water n prism  Fig. 6B. This jump in the wavelength shift is because the geometrical path of the waves increases with the same behaviour with the increase of the incident angle that causes good confinement through the water molecules [35]. Therefore, the angle of 61.6° will be the optimum angle.

Effect of the Operating Temperature on the Salinity Sensor
As shown in Fig. 7, by increasing the operating temperature from 0 to 15 °C, the wavelength shift decreases from 733.8 to 707.8 nm. Then, the wavelength shift increases from 707.8 to 717.1 nm with the increase of temperature from 15 to 25 °C. For further increase in temperature, the resonance dip goes out from the wavelength range of concern. Although the performance of the salinity sensor at 0 °C is slightly better than the performance at 25 °C, we will consider room temperature (25 °C) as the optimum condition to conserve the energy consumed in the cooling process in our country.
The reflectance spectra of the proposed sensor at the optimum conditions are cleared in Fig. 8. Unlike previous studies of PCF [3,8], and like multilayer photonic crystals [35], the resonant dip is red-shifted to high wavelengths with the salinity increase. by raising the salinity from 0 to 50%, the dip position moves to the right to lower energy radiation having a wavelength shift from 1101.8 to 1817.8 nm.
Now, significant factors like sensitivity (S), quality factor (QF), the figure of merit (FoM), and detection limit (DL) are calculated for the salinity sensor in Table 1. Sensitivity is the ratio between the wavelength shift of the dip and the variation in the water refractive index as the following: FoM depends on both sensitivity and the bandwidth ( FWHM ) of resonant dips as the following: The quality factor is the ratio between the resonant dip position and FWHM as The detection limits denoting the smallest measurable refractive index of salinity concentration change according to The result in Fig. 9 shows that the shift of the resonant dip position in the case of salinity measurements is linearly proportional to the change in the index of refraction of seawater. The green line in Fig. 9 is the linear fitting of the data that indicates a fixed value of sensitivity (8.5 × 10 4 nm/RIU) as the following equation: This linearity of data emphasizes the stability and rationality of the proposed salinity sensor. The proposed sensor recorded a very high sensitivity of 8.5 × 10 4 nm/RIU and quality factor of 3 × 10 3 , and a very low detection limit of a minimum detectable dip position shift is about 3 × 10 −7 nm. These results indicate that the suggested sensor is a strong candidate for salinity measurements than previous studies as clear in Table 3.

Temperature Sensor
In this section, the effect of the temperature variation on the resonant dip position will be studied. As clear in Fig. 10, and according to Eq. 6, the refractive index of water changes with the change of seawater temperature.
At a salinity concentration of 0% and wavelength of 1000 nm, with the increase of the operating temperature from 0 to 100 °C, the refractive index of seawater decreases from 1.3247 to 1.304 ( Δn = 0.0207 ). But, at a salinity concentration of 100% and wavelength of 1000 nm, with the increase of the operating temperature from 0 to 100 °C, the refractive index of seawater decreases from 1.3433 to 1.3282 ( Δn = 0.0151 ). This means that seawater is more sensitive to temperature with a decrease in salinity concentration. Fig. 11 demonstrates the relationship between sensitivity and salinity concentration from 11 to 55%. Below concentration 11%, the resonant dips are blue-shifted and go out from the wavelength range of concern. So, the salinity concentration of 11% will be the optimum salinity for the proposed temperature sensor. The blue line in Fig. 11 is the polynomial fitting of three-degree order like the following:  The plotted reflectance spectra in Fig. 11 illustrate that any change in the operating temperature will be translated into a shift in the resonant dip recorded at the optical analyser. As the operating temperature increases from 0 to 50 °C, the dip position is blue-shifted from 1413.6 to 872.0 nm. For temperatures higher than 50 °C, the resonant dip will overlap with the neighbour dips. So, we will end our study at 50 °C (Fig. 12). Fig. 13 shows the non-linearity (non-fixed sensitivity) of the proposed temperature sensor as in the previous studies [7,8]. The proposer sensor is more sensitive to high temperature (10.8 nm/°C) more than low temperature (2.2 nm/°C). Table 2 demonstrates that the proposed temperature sensor at these conditions recorded a very high sensitivity (15) S T = − 0.3498C 3 s + 42.01C 2 s + −2147C s + 1.208 × 10 5 and quality factor, and a very low detection limit (2 × 10 −7 ). Table 3 introduces a comparison between the proposed salinity-temperature sensor and the previously proposed sensors. The performance of the suggested sensor in terms of sensitivity is better compared with the previous sensors. Besides, this sensor has many advantages because of the low cost, simple structure, very high sensitivity, and flexibility.

Conclusion
In this paper, we proposed a theoretical analysis of salinity and temperature measurements through a 1D-PC platform using Tamm resonance. The seawater layer thickness, the incident angle of electromagnetic wave, the operating   Table 3 Comparison between our proposed salinity-temperature sensor and previously proposed sensors  temperature of the salinity sensor, and salinity concentration in temperature sensor were optimized at 6000 nm, 61.6°, 25 °C, and 11%, respectively. The proposed sensor has a narrower FWHM of about 0.34 nm with ultra-high sensitivity of 8.5 × 10 4 nm/RIU for salinity concentration, and sensitivity from 2.8 to 10.8 nm/°C for the temperature sensor. The linearity between salinity concentration and the Tamm resonant dip enables the proposed structure to detect salinity concentration effectively. Although the relation between the Tamm resonant dip and temperature changes in temperature sensor, it achieved high sensitivity that distinguished it. Fig. 7 clears that the proposed salinity sensor is slightly sensitive in cold countries.
Author Contribution Z.A. Zaky performed numerical simulations, analyzed the data, discussed the results, and wrote the main manuscript text. A.H. Aly analyzed the data, discussed the results, and supervised this work.