Numerical Investigation of Simultaneous Refractive index Sensor using 1D multichannel photonic crystal device

We present a multichannel sensor for the simultaneous monitoring of three different samples. established from a one-dimensional photonic crystal, this device is formed by an alternating layer of silicon dioxide (SiO2) and titanium dioxide (TiO2) with three defect layers containing the samples to be monitored. Numerical studies claim that three transmission peaks appear in the bandgap, these transmission peaks are caused by the three samples inltrated in the defect layers. In real-time detection purposes, it is possible to exploit these transmission peaks. In addition, peak frequencies have the advantage of being susceptible to sample concentrations. With this photonic structure, a sensitivity of 800 nm per unit of refractive index (RIU) is reached.


Introduction
Sensor is a device which senses the physical, biological and chemical changes in parameters such as refractive index [1][2][3][4], temperature [5], pressure [6], pH [7], gas [8], magnetic uid [9] and so on. Sensors based on optics have a lot of attention in detecting the small changes in temperature, pressure, chemical composition etc., due to their high sensitivity [10]. The designs of optical devices based on the periodic structures have been developed recently. Photonic Crystal (PC) is a periodic structure with different dielectric constant which controls the light guiding properties and the existence of the photonic band gap (PBG) is an interesting property of PC. It prohibits the propagation of electromagnetic waves inside the PC. It can control the guiding of photons in PC. It can also control the localization of light and spontaneous emission. The periodic structure of PC is broken entirely by introducing the defects which allows controlling and manipulating the light. PC based optical devices such as lters, logic gates, sensors [11] were reported earlier.
The various devices such as sensors, splitters and multiplexers based on the PC material are designed and fabricated in recent years. These sensors are also emerging in the eld of healthcare, defence, security, aerospace, environment and food quality control [12,13] based on the principle of photonics.
The applications of PC sensors are also extended to identify DNA, protein cell, bacteria [14] and are highly e cient. Different blood components such as glucose and haemoglobin are detected and simulated in a PC ring resonator and the effect of parameters are investigated. These blood constituents are analysed by using the photonic sensing technology [15]. The propagation of electromagnetic waves is affected while passing the PC structure with this blood components, the permittivity of the biological molecules is greater than those of air and water.
The functional materials of magnetic uids have been investigated due to their special magnetic properties based on the combination of solid magnetic particles and the uidity of the liquid [16]. By adjusting the strength of the critical magnetic eld [17], the refractive index of magnetic uids can be changed. A sensor based on magnetic eld and temperature in a magnetic eld which is in ltrated into the PC cavity is investigated by Zhao et al. [18]. In refractive index mechanism, the characteristics of the transmission spectra will be changed due to their change in the refractive index of the biological molecule which is bind to the active sensing surface. The detection of analytes such as blood glucose [19], cancer cell [20], and blood plasma [21] are reported earlier by PC cavity technique. The sensor is able to sense three different analytes with their refractive indices simultaneously which have some cavities and are investigated with three cavities by author [22]. In the present work, three different analytes such as haemoglobin, urine and magnetic uid are sensed with multiple cavities simultaneously by using the PC device.

Methods
The aim of the research is to design a multichannel sensor based model which can monitor different samples simultaneously. The geometric model is shown in Fig. 1. It is of the form AB N Def1 BA M Def2 AB M Def3 BA N , where M and N denote the numbers of AB bilayers placed on either side of the defect layer, Def I (I = 1, 2 or 3). A photonic structure cell is formed by two dielectric layers (layer A and layer B). In the xy plane are located the layers of the PC, the z axis is perpendicular to the interfaces of the layers. We assume that the layers are in nite along the x and y directions, while the photonic structure is nite along the z direction ( Several techniques are used in the study of the propagation of electromagnetic waves in periodic structures, among these methods there is the transfer matrix method and the Green function method.
These two methods allow us to determine the dispersion relation, the transmission and re ection coe cients [23]. Velasco et al. and El Boudouti et al. have established a remarkable relationship between transfer matrices and Green's functions. This combination allows the study of the physical properties of any composite system. In this paper, we use the interface response theory of continuous media, a simple presentation of the Green function [24][25][26]. This technique is the most suitable for the treatment of composite systems containing several interfaces [27,28].

Results And Discussion
We consider a one-dimensional photonic structure of nite size AB N Def1 BA M Def2 AB M Def3 BA N , as depicted in Fig. 1. The analytes to be sensed are introduced into the cavities (Def1, Def2, and Def3). A spectrometer detects the light emitted by the source after its transmission from the photonic crystal. Fig. 2 shows the one-dimensional structure which is used to calculate the transmission spectra. The periodic layers from each part of the three defects layers, Def1, Def2, and Def3, are made of two materials, A and B. It is assumed that the layers A of thickness d A to be silicon dioxide SiO 2 . The layers B of thickness d B are titanium dioxide TiO 2 . The period of perfect structure is d=d A +d B . The choice of these dielectrics is justi ed by the very wide use of these two materials SiO2 and TiO2 [29] as substrates for photonic structures of detection. the PC is enveloped by air. The three defects layers, Def1, Def2, and Def3, will be lled by three different analytes. In our study, we will change the lengths of the defect layers.
We consider a normal incidence of light on the left surface of the PC. Incident light is linearly polarized: In order to use the con guration of Fig. 1 for simultaneous detection of three analyte samples, the usual approach is to de ne special characteristics like transmission peaks in the transmission spectrum. We will show that, at normal incidence, the resonances corresponding to the three defects can occur in the transmission spectrum only with a good choice of the thickness of these three layers defects. Then we discuss the occurrence of resonances modes according to thickness d Def , and after we study the change of the refractive index, with the aim of having the three defects modes corresponding to the three defect layers inside the photonic structure band gap.
In this section, we analyze numerically the transmission spectrum as a function of the defect layers thickness, and as a function of the sample concentrations. In this article, we limit our study to the rst PBG of spectra. For the numerical calculations we choose the following parameters of the PC: the PC's period d = 1360 nm, and the dielectric layer thicknesses d A =952 nm and d B =408 nm. The thickness of the dielectric defect layers is equal to d Def = 1713.6 nm. The refractive indices for the photonic crystal constituents are equal to n A =1.45 (for SiO 2 ), n B =2.46 (for TiO 2 ).
We display the transmittances according to the frequency for a regular PC (black lines) and a defective PC (blue lines) in Fig. 3. we assume that the incidence of the electromagnetic wave towards the photonic structure is normal. It is shown that for these three thickness values of the defect layers, the defect modes occur inside the transmission spectrum PBGs. From the study of Fig. 3, it can be noted that when d Def = 272 nm, two defect modes appear in the band gap (blue curves), localized at f = 5.8060 e + 13 Hz, and f = 6.2847 e + 13 Hz in the infrared (IR) regions, when d Def = 843.2 nm, one defect mode appears in the band gap (blue curves), localized at f = 7.1384 e + 13 Hz, and when d Def = 1713.6 nm, three defect modes appear in the band gap (blue curves), localized at f = 5.9009 e + 13 Hz, f = 6.4060 e + 13 Hz, and f = 6.7402 e + 13 Hz.
These ndings clearly show that the thickness of the defect layers changes the defect modes properties within the IR regions.
We deduced that the change of three layers of the perfect photonic crystal with other layers, induces the appearance of peaks inside the forbidden bands. Consequently, the choice of d Def (or the ratio d Def / d), is a determining indicator in the occurrence, the tunability, the sensibility and the controlling of the peaks within the forbidden band of the PC. It implies that, for detection purposes, the parameters of the photonic crystal should be well de ned in order to have isolated peaks in the forbidden band. This is closely related to the optimization of an e cient sensor with high sensitivity and wide measurement spectrum.
In order to better understand the existence and the comportment of the defect modes as a function of d Def , we studied the progress of the reduced frequencies of the transmission according to the length d Def , in the PC with three defects. Figure 4 shows the results, the black dotted lines denote the maximum transmission. However, the primrose yellow zones represent the PBG. It can be seen that with this super lattice we have two band gaps, the rst one is between 50 THz -75 THz, and the second one is between 179 THz − 198 THz, branches appear automatically inside the band gap. the frequencies of these branches rely upon the length d Def .
if we look at the rst bandgap (50thz -75thz), when 100 nm < d Def <400 nm, two defects modes occur in the band gap, when 700 nm < d Def <1100 nm, only one defect mode appear in the band gap, and when 1700nm < d Def <2100 nm three defects modes appears in the band gap.As a summary, one can say that in order to bring up the three defect modes corresponding to the three defects introduced into the photonic structure, the value of the thickness of the defect layers must be between 1700 nm and Table 1 Keeping defect 2 (hemoglobin), and defect 3 (urine) refractive indices constant and changing the refractive index of the defect 1 (magnetic uid). We apply the above-mentioned analysis to a practical case, by setting the parameters of the photonic sensor to D = 1360 nm such as d A =952 nm, d B =408 nm, and d Def = 1713.6 nm. With these sensor settings, the operating wavelength of the device will be close upon the infrared (IR) spectrum. In this spectral domain, the sensor sensibility determined by S = Δλ/Δn is evaluated to be 800 nm/RIU. Figure 6 represents the relationship between the resonant frequency and the refractive index for the three samples lling the cavities, Ferric magnetic uid (Fig. 6a), Hemoglobin (Fig. 6b), and urine ( Fig. 6c)  Finally, it can be concluded that the proposed sensor exhibits better performance compare to recent published articles. The proposed sensor gains the maximum sensitivity of 800 nm/RIU; FoM of 420000 (RIU − 1 ) and exhibits better outcomes compare to articles [15,19,21,22,27,30]. In addition, it can be highlighted that the sensitivity response of proposed model can be enhanced by varying the size of the defect layer in the model. This system could be applied for monitoring in the biomedical sensor for detection of dangerous biological molecules in any magnetic uid, hemoglobin and/or urine concentration. This work is carried out through the simulation process. In future, we will try to fabricate the model and compare the outcomes with real time results.

Conclusion
We have investigated the possibility of using a one-dimensional photonic structure as multichannel sensor. We show that this structure composed by alternating layers of silicon dioxide (SiO 2 ) and titanium dioxide (TiO 2 ) can be employed as a highly sensitive sensor to monitor the concentration of three different samples when it is enlightened in normal incidence. We have shown that the width of the defect layer must be correctly adjusted to form a structure allowing to have the three defect modes su ciently isolated in the transmission spectrum. This sensor offers high sensitivity, 800 nm per refractive index unit (RIU). where layer A and layer B, respectively represent the layers of silicon dioxide (SiO2) and titanium dioxide (TiO2), and the defect represents the analytes to be detected. Structure of the calculation. A and B represent, respectively, the layers of silicon dioxide (SiO2) and of titanium dioxide (TiO2) and the defect represents the analytes to be detected.

Figure 6
Transmission curves of the crystal shown in Fig. 1 with the rst cavity lled by the magnetic uid (89.9Oe of concentration), the second cavity lled with Hemoglobin (10g / l of concentration), and the third cavity lled with urine (15 mg / dl of concentration) for dDef = 272 nm (a), dDef = 843.2 nm (b) and dDef = 1713.6 (c) at normal incidence.