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Optimized Cancer Cells Sensor Based on 1D Photonic Crystal Vertical Slot Structure

This paper reports the investigation of a one-dimensional (1D) photonic crystal (PhC) sensor with improved performance for detecting different categories of cancer cells. The sensing region consists of a vertical slot (VS) introduced inside the periodic Bragg mirror. The structure operating principle is based on the change of the refractive index (RI) of the analyte incorporated in the VS, which leads to the shift in the resonant wavelength peak. The sensing properties have been numerically simulated and analyzed using the transfer matrix method (TMM). The study shows that the optimization process of the structure tends to enhance sensitivity. From the result of the numerical simulation, it is found that the final optimized sensor exhibits the higher sensitivity of 3201 nm/RIU than other similar devices. We believe that the obtained results will be valuable for designing highly sensitive PhC sensors.


INTRODUCTION
The major cause of mortality worldwide is cancer diseases. Cancer can arise from the uncontrolled growth of cells in different parts of the body, so there are more than 100 various types of cancer diseases. The early detection of cancers increases the chances of treating and curing them before they have spread. Therefore, the development of accurate, reliable, and rapid sensors is necessary. The optical biosensor can be utilized for detecting cancerous cells in the early stage.
In recent years, photonic crystals (PhCs) have received great attention in sensing and monitoring applications owing to their advantages of high sensitivity, rapidity, and easy integration. The most important optical characteristic in cancer is refractive index, which mainly determines the difference between normal and malignant cells [1]. The contrast between the refractive indices of the cancerous and normal cells is the principle of photonic biosensors [2][3][4][5][6][7]. PhCs are artificial optical structures formed by periodic arrays of different materials in one, two, or three dimensions [8,9]. This periodicity provides a range of frequencies, where the propagation of the electromagnetic waves is forbidden named photonic bandgap (PBG). Making defects in the PhC structure permits modes in the PBG region. The position of the transmission peak is controlled by the change of the refractive index or the shape of the defect. Owing to their interesting feature, PCs have been used in various applications with different designs [10][11][12][13][14][15][16].
In this paper, an optical sensor based on a one-dimensional photonic crystal for detecting five categories of cancer cells (Jurkat, Hela, PC12 MDA-MB-231, and MCF-7) is presented. The optical properties of the designed structure are analyzed using the transfer matrix method (TMM). In our design, a vertical slot (VS) is used as the sensing medium. To increase the sensitivity of the structure, the presented sensor needs to be optimized. The final optimization device provides very high sensitivity; it reaches 3021 nm/RIU. The results obtained are very satisfactory compared with other similar structures. The design scheme, optimization process, sensing principle, and TMM results are discussed in the following sections.

SENSOR DESIGN AND MODELING APPROACH
Our goal of the research is to design an optical sensor based on a one-dimensional photonic crystal capable of detecting different types of cancer cells. The geometric model under study is illustrated in Fig. 1. It is formed of periodic arrays of SiO 2 (A) and TiO 2 (B) with refractive indices n 1 and n 2 , respectively. The period of the perfect structure is d = d 1 + d 2 , where d 1 and d 2 are the thicknesses of layers A and B, respectively. To study this device for detecting cancer cells, we would introduce a vertical slot (VS) denoted as C in the symmetry center of the structure, which is considered as the sensing medium. All layers are a quarter wavelength (n 1 d 1 = n 2 d 2 = λ 0 /4), in which λ 0 is equal to 1.55 µm. The refractive indices and thicknesses of the PhC utilized in our study are n 1 = 1.44, n 2 = 2.6, d 1 = 269.097 nm, and d 2 = 149.038 nm, respectively. As depicted in Fig. 1, the designed system is presented symmetrically as Air/(SiO 2 /TiO 2 ) V /C/(TiO 2 /SiO 2 ) V /Air, where V is an integer and represents the number of periods (V = 13). To analyze the propagation of an optical signal through each layer of the structure, the transfer matrix method is employed. Based on TMM of the second order, the expression for a single layer takes the form [24][25][26] where d i is the layer thickness. The full transfer matrix of the 1D PhC is presented by the product of all single layering transfer matrices, shown as: where V is the number of binary layers in the Bragg mirrors, and Q C is the transfer matrix of the vertical slot. The transmission coefficient for the defective 1D photonic crystal is expressed as follows:

NON-OPTIMIZED SENSOR DESIGN
In this section, we discuss the optical properties of the proposed sensor. The transfer matrix method is utilized to calculate the transmittance and resonant defect shift of the device at normal incidence. The numerical results show that the presented structure without any defects possesses one PBG in the range of 1302.9 nm-1894.6 nm. As shown in Fig. 2, the PBG is relatively wide enough to meet the sensing demand where the transmission peak generates a large frequency shift. Initially, a normal cell with a refractive index n = 1.35 has been infiltrated into the vertical slot. As shown in Fig. 3, one narrow resonant peak is generated inside the PBG. This derived peak is a result of the localization of light inside the defect. Its position is located at 1534.525 nm, with an intensity of 99.5%. Thus, strong confinement of the optical field within the vertical slot is obtained. The thickness of the VS is assumed to be equal to 1700 nm. It can also be noted that the signal response outside the gap Bragg is affected by some fluctuation. This is due to the existence of the defect inside the structure. When different categories of cancer cells with known refractive indices (Table 1)     The most significant parameter utilized to evaluate the performance of the sensor is called the sensitivity (S), and it is expressed as: where ∆λ represents the wavelength shifting caused by the shift of the refractive index and is calculated in terms of nm/RIU. According to our simulation results, the designed structure sensitivity is equal to 812.025 nm/RIU. The variation tendency of the sensitivity and the resonant wavelength shift with the change of the refractive index is plotted in Fig. 5. As seen in this figure, the sensitivity decreases linearly towards 809.96 nm/RIU when RI varies from 1.35 to 1.401. In contrast, the displacement of the mode becomes larger when RI augments. It can also be noted that the transmission efficiency is unaffected and equal to unity.

OPTIMIZED SENSOR DESIGN
In this part, we focus our objective on the optimization of the previous sensor to improve the detection sensitivity of the structure. For the optimization process, we use two steps: Firstly, we surround the sensing region with a composite material. Secondly, we place a prism on the front of the structure and vary the incident angle (θ).

Effect of the Filling Factor f on the Sensitivity
In this section, the previous sensor is optimized by modifying the design of the structure in such a way that the sensitivity is improved. The optimization is done by removing two layers situated on each side of the VS and replacing them with composite material formed by Ag nanoparticles (Ag NP) dispersed in the TiO 2 matrix. A schematic of the modified structure is illustrated in Fig. 6. To describe the dielectric permittivityε(ω) of the obtained composite material (Ag + TiO 2 ), we use the Maxwell-Garnett formula, which is widely utilized in the analysis of composite media that contain various kinds of small particles inclusions [28] where ε m is the dielectric permittivity of TiO 2 matrix; f is the volume fraction occupied by Ag nanoparticles; ω is the radiation frequency; ε n is the dielectric permittivity of the silver nanoparticles and is obtained from a modified Drude model which has the following form [29,30]: where ε a = 5.45, ω p is the plasma frequency (ω p = 1.72 × 10 16 rad/s) [29], and γ is the plasma damping constant, which represents a size-dependent function for metallic nanoparticles of spherical shape and can be written as [29]: where v F = 138 × 10 6 m/s (Fermi velocity), l = 52 nm (electron mean free path at room temperature), and 2r = d with d being the silver Ag NP diameter. From Eqs. (6) and (7), we can deduce the real and imaginary parts of the composite material: We have plotted the real part of the dielectric permittivity in Fig. 7(a) and the imaginary part in Fig. 7(b) as a function of f, for r = 1, 2 and 5 nm, where r is the radius of the Ag aggregates. It can be seen from Fig. 7(a) that ε ′ m augments as the filling factor increases, but remains nearly invariant with the increase in r. The significant increase of ε ′ m is due to the presence of Ag NP in the matrix. Similarly, the imaginary part ofε(ω) is affected by the volume fraction f and the radius r of the metal. As shown in Fig. 7(b), ε ′′ m increases when f varies from 1% to 15% and decreases when r increases. The increase of ε ′′ m implies that the composite material will absorb the optic wave passing through its region. For this raison, we have chosen r = 5 nm as the size of rod radius in all the following studies. To further investigate the effect of the filling factor on the sensor performance, we have plotted the sensitivity versus f at normal incidence. Figure 8 represents the relationship between S and the filling factor for five kinds of cancer cells. It shows that the sensor sensitivity increases when f augments. The results reveal that the maximum values of S obtained at f = 4% for MCF-7, MDA-MB-231, PC12, Hela, and Jurkat are 840.49 nm/RIU, 840.816 nm/RIU, 841.444 nm/RIU, 841.9047 nm/RIU, and 842.25 nm/RIU, respectively, which seems a good result compared to the non-optimized structure. This significant increase is due to the strong shift of the resonant wavelength peak. Fig. 9 demonstrates that the transmission peak moves from 1547.625 nm to 1590.49 nm when n c of the VS varies from 1.35 (normal cell) to 1.401 (MCF-7). In addition, it can be noticed that the intensity of the resonant peak is reduced and attains 78% when f = 4%. This lower transmission efficiency is due to the lossless feature of the composite material.

Effect of the Prism and Angle of Incidence on the Sensitivity
Our optimization is not limited to doping the two neighboring layers of the VS, but it will be extended by adding a prism to the structure and varying the angle of incidence. To do so, we kept the same device presented in Section 4.1 and attached a prism in front of the structure. The filling factor and refractive index of the prism used in this section are 4% and n p = 1.6, respectively. The schematic presentation of the new optimized device is shown in Fig. 10. To analyze the effect of the incident angle (θ) on the resonant peak, we vary θ from 0 • to 50 • . The simulation results show clearly that the resonant mode is influenced by the change of θ. We also recorded that by increasing θ the peak of each type of cancer cells shifted towards lower wavelengths. In addition, we plotted S as a function of θ for two cases: with and without attaching prism, which gave us information about the sensibility of the sensor. It is clear from Fig. 11 that for θ more than 25 • , the sensitivity of the Jurkat cancer cell of the first case (with attached prism) improves significantly and gains the maximum value of 3201 nm/RIU when θ = 50 • . To further investigate the effect of the prism on the sensitivity, we have plotted the normalized transmission spectra of the optimized structure at incidence angle 50 • for different cancer cells. The results are presented in Fig. 12, and the inset shows the amplified image of all the transmission peaks. The detail of the calculated λ, ∆λ, and S are given in Table 2. In summary, one can say that the optimized structure is most sensitive for Hela cancer cells and is enhanced by about more than three orders magnitude better than the previous one reported in Section 4.1, which can be considered as an important improvement. In addition, the numerical simulations illustrate that our presented structure gives better performance than other proposed sensors with other designs. The comparison of our results with some recent works is summarized in Table 3. In summary, we believe that the obtained results render our device suitable for detecting different cancer cells.  1D-PhC vertical slot structure 3201 This work

CONCLUSION
In this work, a highly sensitive cancer cells sensor based on a 1D-PhC platform is investigated. The sensing region consists of a vertical slot (VS) introduced inside the periodic Bragg mirror. The structure operating principle is based on the change of the refractive index (RI) of the analyte incorporated in the VS, which leads to the shift in the resonant wavelength peak. The sensing properties have been numerically simulated and analyzed using the transfer matrix method (TMM). The study shows that the optimization process of the structure tends to enhance sensitivity. From the numerical simulation result, it is found that the final optimized sensor exhibits the higher sensitivity of 3201 nm/RIU than other similarly designed devices. We believe that the obtained results will be valuable for designing highly sensitive PhC cancer cells sensors.