We consider a one-dimensional photonic structure of finite size ABN Def1 BAM Def2 ABM Def3 BAN, 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 dA to be silicon dioxide SiO2. The layers B of thickness dB are titanium dioxide TiO2. The period of perfect structure is d=dA+dB. The choice of these dielectrics is justified 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 filled 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: TE-polarizations.
In order to use the configuration of Fig. 1 for simultaneous detection of three analyte samples, the usual approach is to define 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 dDef, 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 first 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 dA=952 nm and dB=408 nm. The thickness of the dielectric defect layers is equal to dDef = 1713.6 nm. The refractive indices for the photonic crystal constituents are equal to nA=1.45 (for SiO2), nB=2.46 (for TiO2).
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 dDef = 272 nm, two defect modes appear in the band gap (blue curves), localized at f = 5.8060 e+ 13Hz, and f = 6.2847 e+ 13Hz in the infrared (IR) regions, when dDef = 843.2 nm, one defect mode appears in the band gap (blue curves), localized at f = 7.1384 e+ 13Hz, and when dDef = 1713.6 nm, three defect modes appear in the band gap (blue curves), localized at f = 5.9009 e+ 13Hz, f = 6.4060 e+ 13Hz, and f = 6.7402 e+ 13Hz. These findings 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 dDef (or the ratio dDef / 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 defined in order to have isolated peaks in the forbidden band. This is closely related to the optimization of an efficient 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 dDef, we studied the progress of the reduced frequencies of the transmission according to the length dDef, 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 first 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 dDef.
if we look at the first bandgap (50thz – 75thz), when 100 nm < dDef <400 nm, two defects modes occur in the band gap, when 700 nm < dDef <1100 nm, only one defect mode appear in the band gap, and when 1700nm < dDef <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 2100 nm to design a sensor, we must form a structure with which the transmission coefficient has well-defined characteristics as well as a very high sensitivity to infiltrating samples.
We introduce the defect layer1, defect layer2 and defect layer 3 to monitor the concentration of magnetic fluid, hemoglobin and salt in urine. We are varying the concentration of each sample and will analyse the behaviour of the defect modes corresponding to each defect layer.
We report the evolution of the transmission curves in Fig. 5. When the refractive index of the magnetic fluid which is infiltrated in the defect layer 1 is increased, we notice a displacement of the peak characterizing this defect layer towards the lowest frequencies; we also noticed that there is a reduction in the transmission of the defect peak. When we increase the refractive index of the hemoglobin in the defect layer 2, we notice a displacement of the peak characterizing this defect layer towards the lowest frequencies, so the transmission of the defect peak decreases when the refractive index increases. When we increase the refractive index of the urine which is infiltrated into the defect layer 3, we always notice a displacement of the peak characterizing this defect layer towards the lowest frequencies, but here the transmission of the defect peak increases with the increase in the refractive index. These results are summarized in Tables 1, 2, and 3 along with the quality factors of the defect peaks.
Table 1
Keeping defect 2 (hemoglobin), and defect 3 (urine) refractive indices constant and changing the refractive index of the defect 1 (magnetic fluid).
DDef(nm) | Defects1 peak frequency | Q-factor | Oe | Refractive Index |
1713.6 nm | 5.9012 e+ 13 | 3471 | 89.9 | 1.4635 |
5.9006 e+ 13 | 3105 | 120.3 | 1.4645 |
5.9002 e+ 13 | 2935 | 150.0 | 1.4654 |
5.8997 e+ 13 | 2783 | 180.4 | 1.4662 |
Table 2
Keeping defect 1 (magnetic fluid), and defect 3 (urine) refractive indices constant and changing the refractive index of the defect 2 (hemoglobin).
DDef(nm) | Defects2 peak frequency | Q-factor | Concentration(g/l) | Refractive Index |
1713.6 nm | 6.4056 e+ 13 | 2128 | 10 | 1.341299324 |
6.4011 e+ 13 | 2140 | 20 | 1.360719324 |
6.3922 e+ 13 | 2145 | 30 | 1.399559324 |
6.3836 e+ 13 | 2263 | 40 | 1.438399324 |
Table 3
Keeping defect 1 (Magnetic fluid), and defect 2 (hemoglobin) refractive indices constant and changing the refractive index of the defect 3 (urine).
DDef(nm) | Defects3 peak frequency | Q-factor | Concentration(mg/dl) | Refractive Index |
1713.6 nm | 6.7401 e+ 13 | 2339 | 0–15 | 1.336 |
6.7361 e+ 13 | 2217 | 2.5 | 1.339 |
6.7323 e+ 13 | 2090 | 5 | 1.342 |
We apply the above-mentioned analysis to a practical case, by setting the parameters of the photonic sensor to D = 1360 nm such as dA=952 nm, dB=408 nm, and dDef = 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 filling the cavities, Ferric magnetic fluid (Fig. 6a), Hemoglobin (Fig. 6b), and urine (Fig. 6c) with various concentrations. From the figure, we have a linear relationship between frequency and IR, where the slope represents the sensibility of 800 nm/RIU. A 30.4 Oe change in the concentration of the magnetic fluid, a 0.2 g / l change in the hemoglobin concentration and a 0.015 mg change in the urine concentration may be detectable. The figure of merit, FoM = S / Δλ can also determine the detection performance of photonic structures. The formula of the figure of merit mentions that the narrow resonances improve the detection because they allow a precise determination of the shift of the resonance according to the surrounding medium [30]. The value of the figure of merit FoM of this structure is calculated as 420000 (RIU− 1).
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 fluid, 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.