Salinity Sensor Based on 1D Photonic Crystals by Tamm Resonance with Different Geometrical Shapes

In this paper, we demonstrate a novel salinity sensor based on Tamm-plasmon-polariton (TPP), comprising different shapes of Bragg reflector (ordinary, texturing, and sawtooth) and metallic layer. The finite element method is used to study the considered structure and sensing performance by using the COMSOL multiphysics simulation procedure. Here, we study the effect of surface morphology on the sensitivity; firstly, in the case of one-dimensional photonic crystal-centered defect, it harms the sensitivity; secondly, texturing and sawtooth in the case of Tamm resonance increases the sensitivity, as for texturing the surface, the sensitivity quality factor (Q) = 236 and figure of merit (FOM) = 170. For sawtooth surfaces, Q = 272.4, and FOM = 199. The consequences of structural parameters on the efficiency of sensing are studied, and new procedures are proposed to enhance TPP-based sensors. A simple and functional alternative to conventional salinity sensors may be the proposed solution.


Introduction
Photonic crystals (PCs) are an artificial structure arrangement in high-low dielectric materials in periodicity to govern the propagation of electromagnetic waves (EMWs) through structures [1][2][3]. PCs are classified into three categories according to the number of dimension periodicity. As a consequence, it can be one-dimensional (1D), twodimensional (2D), and three-dimensional (3D). Recently, photonic crystals (PCs) received great attention due to their unique properties in optical applications such as optical fiber [4], Bragg mirrors, optical and temperature sensors [5][6][7][8][9][10], waveguides, solar energy applications [11][12][13], light-emitting diodes (LEDs) [14], optical switches, and solar water desalination [15,16]. From this point of view, 1D PCs attract much more attention in manufacturing owing to their low cost and ease of fabrication comparable to 2D PCs and 3D PCs. The properties of 1D PCs considerably depend on the optical parameters of the individual constructing layers. The most significant parameters for 1D PCs are the refractive index (n) and extension coefficient (k) of the used materials in addition to the number of periods (N) [17]. The photonic bandgap (PBG) is an essential feature of PCs; electromagnetic modes cannot spread in the photonic bandgap region. As a consequence, electromagnetic waves cannot pass through these PBGs [18,19]. Thus, by controlling the dielectric contrast between the used materials, we can appoint the structure to be suitable for our application. So, 1D PCs have been growing day by day owing to their promising properties and flexibility to use as we need [20][21][22].
In recent decades, sensors are considered as one of the most used applications of photonic crystals owing to their ability to distinguish the different materials, whereby due to the change in the analyte refractive index, the detection procedure mainly depends on the shift of the resonance peak in the transmission or reflection range. Practically, for the saline water, the change in the refractive index is owing to the variation of salt concentration. Sensitivity, quality factor, and the figure of merit are the parameters that determine the sensor efficiency. Owing to their high sensitivity, optical sensors with surface plasmon resonance (SPR) have seen tremendous growth in environmental and chemical monitoring [23,24]. Nearly all current SPR-based sensors, however, employ metal and dielectric hybrid systems with nanostructures appropriately considered, requiring an expensive and complicated fabrication process [25]. Therefore, as a result of these shortcomings, a portion of the devotion is diverted to planar scenarios for cost-effective strategies. Unfortunately, planar architectures' poor optical efficiency in light trapping remains one of their major defects. As a result, some well-thought-out planar structures appear [26,27]. Tamm Plasmon resonance (TPR), proposed by Kavokin et al. [28], is gaining popularity [29]. With a satisfactory light-trapping property, it can provide an alternative to the planar structure.
The electromagnetic modes at the interface of a metal and a one-dimensional distributed-Bragg-reflector are referred to as Tamm-plasmon-polariton (TPP) (DBR) [30]. TPP is offering promising methods for avoiding the shortcoming of SPR-based geometries [31,32]. Because of the photonic bandgap (PBG) in the DBR and high electromagnetic attenuation in metals, TPP modes are confined to the interface. In other words, the normal part of the wave vector of propagating wave in the periodic region (Bloch wave vector) falls inside the photonic stop-band of DBR structure which brings about the direction of electromagnetic wave alongside the interface. Interestingly, the TPP modes have exceptional control over the mode volume by preferentially operating at the desired wavelength in the DBR's PBG [33]. The flexibility in modifying the dispersion properties of the TPP modes is therefore significantly greater than that of the SPP modes. The dispersion curve that often lies above the light-line of a high-index component of DBR is the most attractive characteristic of TPP modes. This feature facilitates direct freespace excitation of TPP modes at normal as well as angular incidence [34]. PBG exists for both the electric component (TE) and magnetic component (TM) polarization. Thus, TPP modes could be motivated for both TE and TM polarization states. Owing to these unique properties, TPP modes provide a promising platform in photonic applications for potential applications such as integrated photonic devices and highly sensitive optical sensors [35,36].
The motivation and novelty of this paper is the coupling between the TPP resonance and different morphology of 1D PCs as we change the shape of the surface (ordinary, texturing, and sawtooth) of each layer in the Bragg reflector structure as we will discuss in "Modeling and simulation". Thus, the different structures of texturing and sawtooth have a good ability to localize and distinguish the different defect modes in the PBG regions. Then, we will examine the sensor performance by calculating many parameters such as the sensitivity (S), the figure of merits (FOMs), and the quality factor (Q).

Modeling and Simulation
In this section, the modeling and theoretical analysis of our proposed structure are studied by COMSOL multiphysics based on the finite element method (FEM). For more accurate results, the meshing size must be ten times smaller than the lowest incident wavelength [37,38]. Here, our design is one-dimensional photonic crystals with different surface shapes as in Fig. 1. In Fig. 1, a periodic structure represents one-dimensional photonic crystals with refractive indexes n 1 and n 2 respectively, also with thicknesses d 1 and d 2 as we have shown. Since we take a periodic boundary condition in Fig. 1 Schematic structure of different constructions of 1D-binary PCs; the thicknesses of the materials are denoted by d 1 and d 2 , respectively, and the corresponding refractive indices are separately indicated by n 1 and n 2 , N is the number of periods, n o is the refractive index of the air, and n s is the refractive index of the substrate layer. a A schematic diagram of an ordinary 1D-binary PCs structure. b A Schematic diagram of the texturing 1D-binary PCs structure with the width and height of the texturing are donated by W and H, respectively. c A schematic diagram of the sawtooth 1D-binary PC structure with the width and height of the texturing are donated by W and H, respectively every two sides of the structures and the two ports as port 1 is the incident electromagnetic wave, and port2 is the transmitted electromagnetic wave as shown in Fig. 1.
Firstly, we design the considered structures of onedimensional PCs with a defect layer from saline water in the center of the structure and determine the sensitivity as in the following section. The optical constants of the water such as refractive index depend on the following parameters, the salinity S (%), the temperature of the seawater (T), and the probing wavelength (λ) in nm as in Eq. (1) [39][40][41]: where S, , T, and n are the salinity (%), the incident wavelength in nm, the temperature of the seawater (°C), and the refractive index of the seawater represented in refractive index units (RIU), respectively. Thus, the refractive index of the saline water is varying from 1.3326 to1.3505 as a function of the change in salinity level from 0 to100% at room temperature, according to the last equation.
Then in this part, we offer a novel methodology by FEM to modeling one-dimensional Tamm resonance modes with different structures and surface morphology as we see below, which includes all the relevant physics and proposes a simpler method to study trends of fluid sensors or especially salinity sensor in the desalination process. As in Fig. 2, also this structure could be fabricated by the electron ion beam lithography method as it is used to fabricate one-dimensional photonic crystals [42,43].
Finally, the efficiency and performance of any sensor type are determined by the values of the many parameters like the sensitivity (S), the FOM, and therefore the quality factor (Q). (1) These parameters are often obtained using the subsequent expressions [44]: where Δ , Δn , and r are the differences in wavelengths, change in refractive index, and the central wavelength, respectively. And FWHM is the full-wave at half maximum.

Results and Discussions
Our results and discussions here are displayed through two parts corresponding to the different structures of onedimensional photonic crystals. In the first part, we study the effect of surface morphology on the defected onedimensional photonic crystal of the ordinary 1D PCs, texturing 1D PCs, and sawtooth 1D PCs as in Fig. 1, by adding a central defect layer from saline water, and we calculate the sensitivity of the considered structure. Then, in the second part, we study also the effect of surface Schematic structure of the one-dimensional Tamm resonance sensor which consists of one-dimensional PCs, water layer, and metallic layer as shown. The thicknesses of the 1D PC materials are denoted by d 1 and d 2 , respectively, and the corresponding refractive indices are separately indicated by n 1 and n 2 , and N is the number of periods. n o , n s are the refractive indices of the air and substrate layer, respectively; n a , d a are the refractive index and thickness of the saline water layer; and finally, n m , d m are the refractive index and thickness of the metallic layer morphology of Tamm-plasmon-polariton (TPP) resonance structure by adding a metallic layer to the last structures of the Bragg reflector. Moreover, we calculate the sensitivity of the sensor and its properties to determine the optimum parameters for our device.

Defected One-Dimensional Photonic Crystal
We are beginning with one-dimensional photonic crystals which we discussed previously as in Fig. 1a in "Modeling and simulation". Here, the transmission spectrum curve is formed using FEM, as shown in Fig. 3. In Fig. 3A, this structure is composed of multilayer having the form (AB) N , where A is silicon ( Si ) and B is silicon dioxide ( Sio 2 ) with thicknesses 40 nm and 20 nm, respectively, for different periods (N) as shown. It is observed that there is a photonic band gap formed in the visible region (286-390) nm for each number of periods equal to 10 and 15. Moreover, the increasing of the number of periods causes the sharpness of the photonic band gap edges and the resonance peaks. In Fig. 3B, we added a defect layer from saline water in the center of the structure with a thickness equal to 60 nm; thus, we noticed that we have a defect peak at a wavelength equal to 308 nm; also, the number of resonance peaks and transmittance is changed, wherein the number of resonance peaks is decreased by adding a defect layer as shown, and the transmittance is also decreased. But we are not able to discriminate between the different refractive index of saline water so that we zoom on the wavelength range (303-313) nm as in Fig. 3C. That is why, to calculate the properties of this sensor, the sensitivity(S) = 57.1 nm∕RIU , Q = 123.36, and figure of merit(FOM) = 22.84RIU −1 :

Defected Texturing 1D PCs
Here, we change the morphology of one-dimensional photonic crystal layers as in Fig. 1b which we discussed previously in "Modeling and simulation". Thus, the transmission spectrum curve is formed using FEM, as shown in Fig. 4; in Fig. 4A, this structure is composed of multilayer texturing surface having the form (AB) N , where A is silicon ( Si ) and B is silicon dioxide ( Sio 2 ) with thicknesses donated by 40 nm and 20 nm, respectively, for different periods (N) as shown, and the width and height of the textured are 20 nm and 10 nm respectively. Here, this structure formed a photonic band gap in Fig. 4 as in the ordinary 1D PCs (Fig. 3) because the dimensions of the textured unit cell (W, H) are small compared to the incident wavelengths; therefore, it slightly differs from the ordinary 1D PCs in the resonance peaks as a result of the surface morphology. In Fig. 4B, we added a defect layer from saline water in the center of the structure with a thickness equal to 40 nm; thus, we noticed that we have a defect peak at a wavelength equal to 287 nm but we are not able to discriminate between the different refractive index of saline water so we zoom on the wavelength range (282-292) nm as in Fig. 4C. Here, we have a redshift  Fig. 5. In other words, by increasing the analyte layer, the sensitivity is decreased. Therefore, the effect of analyte thickness in this case is the inversion of its effect in the ordinary defected 1D-PCs.

Defected Sawtooth 1D PCs
In this subsection, we change the morphology of onedimensional photonic crystal layer surface as in Fig. 1c which we discussed previously in "Modeling and simulation". Thus, the transmission spectrum curve of the considered structure is shown in Fig. 6; in Fig. 6A, this structure is composed of multilayer texturing surface having the form (AB) N , where A is silicon ( Si ) and B is silicon dioxide ( Sio 2 ) with thicknesses donated by 35 nm and 40 nm, respectively, for different periods (N) as shown, and the width and height of the sawtooth are 10 nm and 15 nm, respectively. In Fig. 6B, we added a defect layer from saline water in the center of the structure with a thickness equal to 30 nm; thus, we noticed that we have a defect peak at the PBG, and then we differentiate between the different refractive index as in Fig. 6C, Finally, we calculate the sensor parameters,S = 61.45nm∕RIU, Q = 134, and FOM = 26.7 RIU −1 . In Fig. 7, we have the localization of electric field in the top of the sawtooth. Because the saw tooth structure gives at least two chances for the photons to incident on the structure, it decreases the reflectance of the structure and increases the transmittance, and localization of the E-field in this interface of the structure.

1D DBR PC Tamm Resonance
In this subsection, we present the simulated results of Tamm resonance which is considered as 1D distributed Bragg reflector (DBR) PC with a defect and metallic layer as in Fig. 2. The 1D distributed Bragg reflector is designed from two dielectric materials that repeated for N periods. Here, the dielectric first layer is set to be aluminum dioxide (Al 2 O 3 ) with a refractive index of 1.86 and thickness of 90 nm. The other layer of dielectric material is titanium dioxide (TiO 2 ) with a refractive index of 2.5, and the thickness of this layer is chosen to be 80 nm. As in Fig. 8, we have a photonic bandgap in the range of wavelengths from 675 to 850 nm. Thus, we set the number of periods to be 10 to justify the defect resonance peak in this range of PBG. Then, by adding an analyte layer from saline water with a refractive index (1.3326-1.3505) as we discussed previously in "Modeling and Simulation" with a thickness equal to 4000 nm and a metallic layer from gold with a thickness of 500 nm. Therefore, we will optimize parameters of the structure in Fig. 2 such as the number of periods, the We are beginning with the optimization of the thickness of the analyte layer as in Fig. 9. Here, in Fig. 9, the thickness of saline water is a variable from 1000 to 4000 nm. Thus, we noticed that by increasing the saline water thickness, the number of defect resonance peak which appears in the photonic bandgap region increases. So, we can consider that increasing the defect layer thickness is adding another layer of water to the structure, and the new defect water layer caused a new defect peak in the PBG as we see in the figure. Thus, increasing the defect layer thickness produces a new defect resonance peak. We have a redshift of the resonance defect peak owing to the increase in the refractive index of the saline water. In addition, we determine the efficiency and performance of the sensor by calculating values of many parameters such as the sensitivity (S), the quality factor (Q), and the figure of merits (FOM) as we discussed previously in "Modeling and Simulation". Therefore, the sensitivity of the structure also increases by a remarkable ratio as a result of increasing the saline water defect layer thickness. We choose the high

Reflection
Here, in Fig. 10, we optimize the number of periods for distributed Bragg reflector with Tamm resonance structure. We notice that an increase in the number of periods caused an increase in the sharpness of the resonance peaks, and the number of resonance defect peaks remains constant. Therefore, by calculating the sensor parameters, we find that the sensitivity has a small change by increasing the number of periods, but the other parameters such as quality factor and figure of merits change by a remarkable ratio as we have shown below: At Wherein, by increasing the thickness of saline water to be 6000 nm and N equal to 10, we have S = 559.7 nm∕RIU , Q = 2882, and FOM = 1998 RIU −1 .

1D Texture DBR PC Tamm Resonance
In this subsection, we present the simulated results of 1D texturedistributed Bragg reflector (DBR) PC Tamm resonance which is considered as the coupling between the 1D texture DBR PC with a defect and Tamm resonance structure. We presented the optimization procedure of this structure, beginning with the number of period optimization as in Fig. 11.
Here, by increasing the number of periods, the PBG edges become sharper than the others, but we have the sensitivity decrease by increasing the number of periods as we have shown in contrast with the ordinary 1D DBR PC Tamm resonance, so, we prefer to use a structure with a small number of periods. In addition, we have a redshift owing to the increase in the refractive index of the saline water: At Then, we optimize the thickness of the analyte layer to get the high sensitivity at the number of period 5; we change the thickness of the saline water layer from 4000 to 6000 nm as in Fig. 12; we noticed that by increasing the thickness of saline water, the number of defect resonance peaks is increased as we have shown, that is, for the same reason as we discussed previously at "1DDBR PC Tamm resonance" subsection.
We can conclude these results in the following: At d w = 4000nm , S = 536nm∕RIU Q = 182 and FOM = 128 RIU −1 .

1D Sawtooth DBR PC Tamm Resonance
In this subsection, we present the simulated results of 1D sawtooth DBR PC Tamm resonance which is considered as the coupling between the 1D sawtooth DBR-PCs with a defect and Tamm resonance structure. We presented the optimization procedure of this structure, beginning with the number of period optimization as in Fig. 13. Here, the

S=436 nm/RIU N=5
Reflection sharpness of the resonance peaks increased as the number of periods increased, whereas the number of resonance defect peaks remained constant. Therefore, by increasing the number of periods, the sensitivity of the structure is decreased as we have shown in Fig. 13; therefore, we chose the number of periods to be 5 for its higher sensitivity than the others.
Then, in Fig. 14, we study the effect of saline water thickness on the reflection spectrum, wherein we can calculate the sensitivity of the structure. From the calculation, we found that the sensitivity is increased by increasing the saline water thickness as follows: At Also, as in Fig. 15, we have a localization of electric field on the saline water layer as we have shown, wherein it assists in discrimination between the different refractive index of saline water which corresponds to the salinity level. Therefore, increasing the saline water thickness causes increase in the sensitivity.
From Table 1, we summarize this part of the results and calculations about the Tamm resonance salinity sensor. Thus, we have found a remarkable enhancement on the sensor parameters like sensitivity (S), quality factor (Q), and figure of merit (FOM), by changing the morphology of the layer surface. Here, we noticed that the sensitivity changed from 559.7 nm∕RIU (ordinary Tamm resonance) to 612.3 nm∕RIU (sawtooth Tamm resonance) at the thickness of saline water equal to 6000 nm. Although the dimension of the sawtooth (W, H) is small with respect to the incident wavelength, it is expected that the sensitivity could be enhanced by a remarkable value in the case of large dimension of the sawtooth. Finally, we can say that the sawtooth Tamm resonance structure and texturing Tamm resonance structure are good candidates for salinity sensor application. Also, changing the morphology of the layer surface of PCs is a promising point to research.

Conclusion
Finally, from the last results, we found that a change in the surface morphology could affect strongly on the sensitivity, and we have two cases corresponding to the last results; firstly, change in the surface morphology in one-dimensionalcentered defect PCs is caused by the decrease in sensitivity of the structure. Secondly, change in the morphology (textured and sawtooth) in the case of Tamm resonance with a defect caused an increase in the sensitivity of the considered structure by a remarkable ratio. Here, we noticed that the sensitivity changed from 559.7 nm∕RIU (ordinary Tamm resonance) to 612.3 nm∕RIU (sawtooth Tamm resonance) at the thickness of saline water equal to 6000 nm. Thus, change in the morphology of the layer surface of PCs is a promising point to research owing to its ability to photon tapping.
Author Contribution (1) The authors made substantial contributions to conception and design, and/or acquisition of data, and/or analysis and interpretation of data; (2) the authors participated in drafting the article or revising it critically for important intellectual content; and (3) the authors gave final approval of the version to be submitted. All the authors contributed equally.
Funding The Deanship of Scientific Research at King Khalid University, Saudi Arabia, funded this work through the Research Group Program under grant no. R.G.P 2/127/42.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.
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The authors declare no competing interests.