Optimization of the Performance of Biosensor Based on Photonic Crystal Resonant

In recent decades, extensive studies have been conducted on biosensors. Of these, biosensors are of great importance, and various photonic structures have been used to design these types of sensors. In this work, optimization of the performance of photonic crystal-based biosensor has been addressed. The nano-resonant sensor is within the structure and is surrounded by two waveguides. The resonator is formed by the smaller air cavities. In order to increase the optical constraint and better coupling of light between the waveguides and the resonator, two finis waveguides have been used. By connecting the biological molecule to the measuring cavity wall, its refractive index will change and the wavelength of the resonant structure will be shifted. Several parameters such as number, thickness of layers and slope affect this sensitivity. By optimizing these parameters, changes in the refractive index can be detected.


Introduction
Nowadays, various biosensors are presented for the rapid and reliable analysis of various parameters in the fields of nanotechnology, food preservation, biomedical research, production and testing of medicines, etc. [1,2,3]. A biosensor is a device that consists of two components of the bio-receiver and converter [2]. A bio-receptor is a bio-identification molecule that identifies the target biomolecule. The converter is also used to convert the bio-molecule recognition event into a measurable signal. The point that is unique in bio-sensors is the integration of the two components into one device. This compound enables the measurement of the target biochemical molecule without the use of a reactor [4,5]. Applications of biosensors are high and most notably include the detection of harmful bacteria or pesticides in air, water or food, used as an biofire device, used in chemical and biological wars to detect and prevent exposure to chemical gases, and infections are present, used on small and portable devices by the human body to monitor vital signs, correct disturbances, or even detect specific signals for emergency assistance [6,7,8,9,10]. Until now, a variety of biosensors have been introduced. These sensors include surface plasmon based biosensors, interference-based biosensors, optical waveguides biosensors, optical fiber-based biosensors, resonant-circuit-based biosensors and photonic crystal-based biosensors [11]. Photonic crystals are alternate structures made of dielectric materials. A photonic crystal is created by alternating changes in the dielectric deflection coefficient or by filling the dielectric material with regular rows of holes [12,13,14,15]. When the light propagates in the alternating structure, it is reflected in any contrast to the dielectric material. As a result, the overall reflection interference occurs at a certain wavelength. Certain wavelength light cannot pass through and out of the material. This is the wavelength or banned frequency of the photonic band gap, which is the basis of photonic crystal performance [16,17,18]. In recent decades, extensive researches have been performed on biosensors. Of these, biosensors are very important, and various photonic structures have been utilized to design these types of sensors [19,20]. Photonic crystals have special decomposition properties that can be used to create leftover materials, charts, filters, sensors and lasers with lower thresholds for stimulating the current and therefore photonic crystals as the main choice for the realization of optical communication devices for future generations are posed [21].
Design optimization of semiconductor photonic crystal laser (PCSEL) structure is discussed mode confinement is compared for all-semiconductor and void PCSELs. A regrown PCSEL, lasing at room-temperature based on GaAs/InGaP regrowth is realized, and device characteristics are described [22]. Kemiche et al (2018) show slow light states in photonic crystals to prepare a compact cavity that prepare an attractive path to the summary of near-infrared integrated accelerated pulsed lasers. The application of slow light stats in planar photonic crystal run according to cavities so relaxes the usual constraints which intensively joint into the tool size and the quality of the pulsed laser signal [23]. Ota et al (2018) proposed an injection photonic-crystal lasers characterized ultralow power consumption that were obtained by applying photonic-crystal nanocavities and tiny buried active areas constructed by a crystal regrowth procedures. They must create light sources appropriate for future lower-power-consumption data and information communications technology (ICT) tools [24]. Asano and Noda (2018) examine the literature on two-dimensional photonic crystals with a highlight on point-defect cavities which may similarity determine with ultra-small modal volumes and ultrahigh quality features. A main design concept to propose radiation loss is prepared: the development of the cavity state field must have no absolute shift and may ideally peruse a Gaussian equation. They also explain light/photon manipulation methods that are powered by the appearance of photonic crystal nano-cavities, consisting ultra-compact channel add/drop filters, strong coupling between distant nano-cavities, as well as ultralow-threshold silicon nano-cavity Raman lasers by the adiabatic assignment of photons [25].
Xiaoyu et al (2016) examine the vital technique using long single-crystal silicon fibers that are new base for silicon photonics can be obtained by this step. Applying limit features modeling, we made a laser processing plan which shows a parameter space in that a crystals can be developed. Applying this plan, we show the production of single-crystal silicon core fibers using laser crystallizing amorphous silicon entrusted in silica capillary fibers by high-pressure chemical vapor deposition. It reveals a photosensitivity which is comparable to bulk silicon. Make such laser processing plans can prepare a total base for growing single-crystal fibers in another materials of technological importance [26]. Lin et al (2018) proposed our opinion on the burgeoning area of mid-IR integrated photonics on silicon. A total study on the state-of-the-art of key photonic tools for example waveguides, light sources, modulators, and a detector is proposed. Moreover, on-chip spectroscopic chemical sensing is quantitatively examined as samples of mid-IR photonic system integration according to these main building blocks, and the constituent parameters selection are elaborated and formed in the text of system performance and integration technologies [27]. Ota et al (2018) elaborate our new development in photonic crystal nanocavity quantum dot lasers. We revealed how increased light-matter interactions in the nanocavity cause to different and absorbing event which are in total unreachable by traditional bulky semiconductor lasers. In this study, we show peak less lasing, that every obvious kink in the output laser curve does not observe. The result of near unity coupling of spontaneous emission into the lasing cavity mode, obtained by the powerful impact determined in the nanocavity. So, we elaborate self-frequency conversion nano-lasers, so both near infrared lasing oscillation and nonlinear optical frequency adaptation to obvious light are similarly provided in the individual nanocavity. Owing to the tight optical confinement both in time and space, high normalized transition efficiency during a few hundred %W is shown. These new event will be proper for increasing different nano-optoelectronic tool with advanced functionalities [28]. Goyal et al (2016) examined a 2D photonic crystal jointed resonating optical waveguide according to integrated-optic sensor base is prepared. The desired feature show a quality agent (Q) of about 104 and 0.40 nm mean change in resonance wavelength by shifting refractive indicator in the rank of 10−4. Sensing method is according to the detection of change in resonance wavelength of cavity according to the shift in refractive indicator of analyte [29]. Rifat (2015) show a surface plasmon resonance (SPR) sensor according to the photonic crystal fiber (PCF) with selectively filled analyte channels. Silver is applied as the plasmonic feature to obviously determine the analytes and is filled with a tiny graphene layer to keep oxidation. Numerical study of the fiber's features and sensing function are carried by the finite element method (FEM). The desired sensor is appropriate for determining different high RI chemicals, biochemical and organic chemical analytes. Moreover, the impact of fiber structural parameters on the features of plasmonic excitation are studied and developed for sensing function as well as decreasing the sensor's footprint [30]. Chen (2018) showed a new D-shaped photonic crystal fiber refractive indicator sensor according to surface plasmon resonance (SPR). The coupling features and sensing function of this structure are studied by finite element method. Simulation findings show that the sensor has a sensing rank from 1.20 to 1.29. For the goal of developing sensing function, the impact of the structure features on the resonant spectra is also examined. The proper sensing function forms the determined SPR sensor as a competitive candidate in low refractive index detector [31].
Xudong et al (2018) show a gold-plated photonic crystal fiber (PCF) refractive index sensor according to surface plasmon resonance (SPR), that gold is filled on the external surface of PCF for proper production and applied determination. By developing the sensor structure, the peak wavelength sensitivity can obtain 11000 nm/RIU and the peak amplitude sensitivity can obtain 641 RIU. According to the high sensitivity, the sensor can be applied biological and chemical sensing [32].
In this paper, we intend to optimize the performance of crystal-based biosensor in two-dimensional mode with the help of the FDTD method. In this way, we design two-dimensional photonic crystal biosensor using different important semiconductors at room temperature, which, by analyzing various diagrams related to the frequency structure and comparing them with each other, give the best semiconductor in its polarization for the square structure.

Structure of Photonic Crystal Waveguide Sensor
It is assumed that the structure of the photonic crystal waveguide is formed in a borehole waveguide with a 3-μm span with longitudinal rotation. The refractive index of the waveguide is 2.4 and its surrounding environment.
A one-dimensional photonic crystal composed of 8 rotations on the right and 8 rotations on the left, with a defect in the middle of it. Each frequency is composed of two layers with failure coefficients of 1.32 and 1.60, and 80 and 55 nm in length. The length of the environment is 860 nm and the silica glass is impregnated with nanoparticles of gold at 25 nm. The length and refractive index of the photonic crystal components are chosen in such a way that the forbidden photonic region and the defective mode are located at the surface of the plasmon aggravation. The schematic of the structure defined in Fig. 1.

Designing a Photonic Crystal Biosensor
The structure of the present crystal is formed by creating air cavities in a dielectric body made of silicon. The refractive index of air is equal to 1 and the dielectric body refractive index is 2.825. The radius of the air cavities in the structure is 90 nm and the distance between the centers of the two adjacent cavities is 360 nm. As can be seen in the figure, the defect is composed of two waveguides with closed ends and a bend and a resonator between the two waveguides. The waveguides are formed by filling the generated cavities and resonator with the decrease in the size of the cavity radius in the photonic crystal structure. At the beginning of the lower waveguide selected as input waveguide, an optical pulse source is used to stimulate the structure's resonate mode.
The light entering the structure is reached through the waveguide of the input to the resonator, and after the resonator is stimulated, it is exerted and transmitted to the upper waveguide, which is considered as the waveguide of the output. The light transmitted by the output waveguide at the end which detected by a monitor and the output transmission spectrum.
The waveguide design in the form of a waveguide whose end is closed and also bends over its own is due to the fact that both actions on the waveguide contribute to a higher coupling of light between the waveguide and the resonator. On the other hand, a high optical limit in the structure of biological sensors is considered. This design helps the waveguides to do this. In this structure, in order to increase the optical limitation, the resonator is formed by decreasing the holes.
The distance between the waveguides and the resonator, which is called the coupling distance, is effective in the light constraint and the proper coupling between the waveguides and the resonator. By increasing the coupling distance between the waveguides and the resonator, the interaction of the biological molecule and light in the cavity is reduced. In this case, the sensor quality increased. In addition to reducing the output range and making the detection more difficult, it reduces the sensitivity of the sensor. On the other hand, by reducing the coupling distance, the interaction of light and material increases, and improves the sensitivity of the sensor and improves the intensity of the output spectrum. But the quality factor of the structure decreased.
In this structure, in order to have an optimal mode for all the effective parameters in the investigation of photonic crystal biosensors, the coupling distance is equal to two rows of air cavities between the waveguides and the resonator.
The sensing mechanism in this biodegradable sensor is based on changing the wavelength of resonance for bio-molecular bonds to the sensor cavity wall. In this structure, the middle cavity of the resonator with the highest optical interaction is considered as a measuring cavity. By connecting the biochemical molecule to the measurement cavity wall, the refractive index varies in the range of this cavity. This change in the resonator's structure causes the resonant wavelengths to shift in the output transmission range. Usually, the wavelength of the resonator is shifted to longer wavelengths.
For biosensor analysis, two methods of finite difference in the time domain and wavelet expansion have been used. The finite difference method is used to study and simulate the propagation of electromagnetic waves and the plane-wave expansion method to obtain a photonic band gap. For this purpose, PML equal to 500 nm is considered. Figure 2 shows the structure bond gap. The band gap for TE mode does not have a range, and TM mode is in the range of 0.248 to 0.280. This range is within the wavelength range of 1285 to 1495 nm.
FDTD uses the YEE algorithm in a discrete time-dependent Maxwell equation for both E and H polarizations. Taking into account the Maxwell equations, the harmonic functions H (r, t) and E (r, t) can be written as the inverse Fourier transform in time and space, and in accordance with the Bloch theorem in solid state physics and the Brillouin Zone (BZ) [18], the main cells in the interconnected grid are obtained for polarization E and H respectively, as follows: Here G is the cross-grid vector and ω is the frequency. Now, with respect to the Poynting's theorem, we use electromagnetic waves for both TE and TM modes in a two-dimensional system.
It is confirmed that a Yee lattice includes various square sections. Every section of a Yee lattice is taken a mean dielectric constant amount considering to the form of the geometric structure of an object. To figure out very well, let's insert a triangular object into the Yee lattice in following Fig. 3. The triangular structure is on six Yee lattice sections. Three of them include air and dielectric material. Considering the rule, their dielectric constant amounts are given 5. Therefore our triangular object observed in Fig. 3. With this rule, any kind of structure that we examine can be inserted in a simulation space (see Fig. 4).

Figure 4. FDTD simulation space with PML that absorbs EM waves at simulation limits without any reflections
To obtain more actual findings, the Yee lattice must be inserted more than 18 sections. Moreover, it cannot be a various number due to computer technology limits. Before beginning a computation for a different type of structure, we must find an ideal number.
In Fig. 4 EM waves absorb at simulation limits without any reflections. It prepares us examining tiny simulation space without any reflection impacts from simulation limits. Then we obtain times during a computation.
According to Poynting's theorem there are two possibility for that EM waves propagate in yz plane. One of them is This is TE mode, due to that E is perpendicular to propagation aspect of EM wave. The other one is This is TM state, so H is perpendicular to propagation aspect of EM wave. The eigenvalue equation is blocking diagonal. Therefore it can be written two independent eigenvalue equations. With where = 0. Finally equation 7 is 2N ×2N generalized eigenvalue problem for TM states considering to Equation 4.
According to the findings we state that our frequency splitting device can separate different frequencies for TE modes. Moreover, the device behaves like a reflector for TM modes. We have applied the dimensionless frequency range 0.415 < w < 0.389. In addition our calculations are for visible light range of EM spectrum so we have given for visible spectrum.

Simulation
Now, by programming with Matlab code, we calculate and plot the frequency band of the important semiconductors in the electronics industry, especially the industry of producing photonic crystal biosensors in E and H polarizations in square Brillouin Zone at room temperature equivalent to 400 0K . Where N is the number of flat plate waves for expansion in any direction. Considering this, we can obtain the total number of waves from equation (8) = (2 + 1) × (2 + 1) It should be noted that in this regard we consider the value of N to be 7. So the total number of waves is 0.451. Also, for these calculations, the number of longitudinal divisions along the circumference of the irreducible zone is 10. The genus of the cavities contained in the photonic crystal biosensors used in all semiconductor materials here is composed of air and is considered to be equal to 1. To calculate these semiconductor materials in equal and identical conditions, and to obtain the appropriate results for comparing the semiconductors with each other to make the biosensors more efficient, we consider the ratio of the radius to the constant of the network to be equal to 0.435. In this way, we examine the most important semiconductors under the same conditions. These semiconductors include ZnS, Ge, CdTe, AIN, SiC, GaSb, GaAs, Si, GaN, InN, InAs, InP, InSb, AlSb, CdS, GaP, PbS, and PbTe.
In the following, we describe the results of several of the best semiconductors.
In Fig. 5, numerical results are used to calculate the band structure of ZnS photonic crystal biosensors that is arranged in a two-dimensional array of square cylinders with an electrical charge of 2.5 which are located in the air host environment. The red magnetic polarization lines and the polarized blue lines show the electric polarization. For the polarization of electric, two first and second gaps are 208 Optimization of the Performance of Biosensor Based on Photonic Crystal Resonant shown. According to this form, the bandwidth in the square structure of the polarization E in the range of 0.354 to 0.3598 is equals to 0.1245 and in the polarization H in the range of 0.284-0.365 is equal to 0.0223.     Table 1. Here, the photonic crystal biosensors bandwidth structure of GaAs with an electrical permeability ratio of 1.13 in the air is presented. The photonic crystal biosensors bandwidth structure for calculating the GaAs bandwidth for the polarization E and H in the square structure is presented in Fig. 11, which range 0.1547 and 0.1899 and 0.2569 to 0.2348 is equal 0.0247 and 0.1246 respectively.

Conclusions
In this paper, the performance of a two-dimensional photonic crystal biosensor improved with the optimization of different parameters and the FDTD method. The photonic crystal used in the biosensor structure consists of periodic layers of ZnS, Ge, CdTe, AIN, SiC, GaSb, GaAs, Si, GaN, InN, InAs, InP, InSb, AlSb, CdS, GaP, PbS, and PbTe. In the center of this structure, a defect layer is embedded with a radial refraction distribution function. Around the central defect layer, there are two channels that allow the fluid to flow through the biological material. As a result of the presence of the central defect layer, the intensity of the light output of the circular distribution is determined by the radius of this ring depending on the refractive index of the fluid flow in the channels. Using this sensor lead to changes in the current flow failure rate in channels is detectable. The surface layer near to the channels with ligands provides the ability to analyte on the surfaces. Hence, the concentration of the analytic in the channels will be increased and the major changes in the refractive index in the channels will be due to the presence of these materials, which will lead to the selection of the sensor function. By optimizing different parameters such as channel thickness, the number of alternating layers of photonic crystal structure, as well as constant in the distribution function of the defect coefficient of the central defect, the sensor function is enhanced and the coefficients of refraction can be detected.
According to the results, the best semiconductors are examined based on the bandwidth obtained in polarization E, the ZnS semiconductor square structure with the highest bandwidth of 0.1135 is the best semiconductor to fabricate photonic crystal biosensors, and then the semiconductors CdS and AIN are the best semiconductors. In polarization H, the square structure of the CdTe semiconductor band with a bandwidth of 0.1125 and later GaP and PbTe equivalent bandwidth are the best semiconductors for making photonic crystal biosensors.