Introduction

Recently, optical structures have been the main field of research interest for various scientists. This happens due to their compact sizes, very low costs (compared with conventional technologies), extremely higher capacities and speeds (compared with electronic based devices). This is mainly due to the fact that in optical based devices, electrons (which are responsible for electronic device’s operations) are replaced by photons (which are responsible for optical device’s operations) [1,2,3]. Very high speed of light with other advantages attracted the attentions of many researchers (to the optical based devices). As a result, all of the elements considered in electronic circuits should be converted to optical ones (elements like, logic gates, filters, sensors or biosensors, receivers, transmitters and etc.) [4,5,6,7]. Photonic crystals (PhCs) are optical based devices which are periodic in one, two or three dimensions. They are basically made of at least two individual media (i.e. air and a dielectric) in a periodic (circular, hexagonal, cubic, etc.) pattern. PhCs in most configurations are defined by periodic cells (rods) in the background made of air. All of the materials utilized in PhC based devices and generally in optical structures are defined by their refractive indices (RIs). In fact, refractive index is the main identification factor for materials used in the designation of optical integrated circuits (OICs). The periodicity of the PhC based structures can be defined by the lattice constant parameter, which indicates the distance between adjacent rods [8]. An important parameter defining the functionality of the PhC based structure is the photonic bandgap (PBG). In fact, PBG diagram is a spectrum which shows regions of frequency (wavelength), where light can be transmitted or not. As a matter of fact, these regions are denoted as the forbidden (non-guided) or permitted (guided) regions. For different PhC based structures, by considering plane wave expansion (PWE) method, PBG can be obtained. In different applications, wavelengths (frequencies) situated in the forbidden or permitted regions can be considered. Mostly, signals with permitted wavelengths would be propagated in the PhC structure and would be eventually dispersed. Finally, they would lose their energies. On the other hand, signals with forbidden wavelengths wouldn’t be propagated in the PhC structure. They would be reflected in the structure after hitting other opposite side rods (this happens along the waveguide). Therefore, in the latter case total internal reflection (TIR) effect can help the light wave propagate along the waveguide with very low losses [9,10,11,12,13]. PhC based structures can be designed for various OICs. Elements like logic gates, filters, splitters, receivers, biosensors, transmitters and etc. can be designed by PhCs. PhC-based structures can be specially considered in designation of various sensors. Gas and liquid sensors are among the most important categories of PhC- based sensors [14]. Optical biosensors have attracted attentions of many researchers due to their compact size, integrability, ease of fabrication and high speed and can be designed based on various configurations [15].

Bio-optoelectronic structures can also take advantage of the benefits of optical structures [16, 17]. PhC based devices can be configured as biosensors for detection of various biological elements in blood samples [18, 19]. For diagnosing diabetes, Glucose concentration in blood samples should be considered (high levels of Glucose increase the risk of diabetes). In order to diagnose kidney failure, creatinine concentration should be measured (high levels of Creatinine may cause kidney failure) [20,21,22]. As stated, many researchers have reported their works on optical biosensors. In a research [23], a PhC- based biosensor with the sensitivity and limit of detection of 260 nm/RIU and 0.001 RIU, respectively, was proposed. In [24], ring resonators based on PhC structures were reported for detection of cancer cells. In another research [25], by considering layers of metal/defect/metal in the photonic crystal configuration, a biosensor for diagnosis of malaria was proposed. In [26], by considering irregular defects in the PhC structure, a biosensor for detection of blood plasma was suggested. Recently [27], a PhC based biosensor was considered and analyzed for diagnosing bio-molecules in urine and blood. In another work [28], 2-D PhC based biosensor was considered for diagnosis of DNA. In [29], by using Ti3C2Tx MXene material in a D-shaped PhC fiber, a sensitive biosensor was designed. In [30], by detecting plasma, platelets, red blood cell and uric acid in blood samples, chikunguniya virus was detected. The proposed biosensor was based on 2-D PhC structures [30]. In another research [31], a biosensor based on photonic crystal fiber in the shape of rectangular core was proposed which could diagnose red blood cell (RBC), white blood cell (WBC), plasma, water and Hemoglobin. This research proposes a simple, easy fabricated, integrable and functional biosensor by considering 2D PhCs. The proposed structure is utilized for detection of Glucose and Creatinine concentrations in blood samples (diagnosing diabetes and kidney failure). The PBG diagram and field distribution at the two individual output ports are considered. Eventually, the structure is considered as biosensors for detection of Glucose and Creatinine at outputs 1 and 2, respectively. In the following parts, first the methodology and design section (the proposed biosensor and its functionality), then the simulations and results (considering filed distribution and transmission-wavelength spectrum for various Glucose and Creatinine concentrations at outputs 1 and 2) and finally the conclusion section are presented.

Methodology and Design

In this work, a 30*20 biosensor based on PhCs is being designed and investigated. For investigating the functionalities of the proposed structure, PBG diagram and field distributions should be studied which can be conducted by considering Maxwell’s equations.

$$\frac{\partial B}{\partial t}=-\nabla *E-J$$
(1)
$$\frac{\partial B}{\partial t}=\nabla *H-J$$
(2)

where E, H, D, B and J indicate the electric field, magnetic field, electric displacement, magnetic induction fields and electric-charge current density, respectively.

Plane wave expansion (PWE) and finite difference time domain (FDTD) methods can be considered for extracting the PBG and field distribution diagrams, respectively [32, 33]. There are some important parameters which should be calculated and analyzed for defining the functionality of a biosensor. Quality factor (Q) is one of these parameters which is presented in the following equation [7, 34].

$$Q=\frac{\lambda_0}{\Delta\lambda_{FWHM}}$$
(3)

in which λ0 and ΔλFWHM, stand for the resonant wavelength and spectral with of half maximum for the central transmission spectrum, respectively. Sensitivity (S) is another important parameter defining the least possible detectable changes in the refractive index of the sensing medium.

$$S=\frac{\Delta\lambda}{\Delta n}(nm/RIU)$$
(4)

where Δλ and Δn define the transmission spectrum displacement and changes of the RI, respectively. Its unit is mostly stated as “nm/RIU”. Detection limit (DL) is another important parameter which is defined as below:

$$DL=\frac{\lambda}{10SQ}(RIU)$$
(5)

In which λ, S and Q stand for the resonant wavelength, sensitivity and quality factor, respectively.

Figure of merit (FOM) is also another important parameter presented in Eq. (6).

$$FOM=\frac{SQ}{\lambda}(RIU^{-1})$$
(6)

where S, Q and λ stand for sensitivity, quality factor and resonant wavelength, respectively [7, 34].

The proposed 2-D PhC based biosensor can be seen in Fig. 1.

Fig. 1
figure 1

The proposed biosensor based on 2-D PhCs

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As can be seen in Fig. 1, the proposed structure is consisted of 30*20 Si rods in the background of air. In order to make the structure functional and simple (designation and fabrication), only linear rods were considered. Line defects (omitting rods to form the Input, Output1 and Output2 pathways) and point defects (dark blue and dark green rods) were considered in the structure for ease of functionality. Dark blue rods act as the confining sensing media (reflecting rods) and are in contact with the tested materials (the hexagon shaped ring help filter the operating resonance frequency). Dark green rods function as the coupling rods filter the appropriate wavelengths for the Output2 port. The structural parameters of Fig. 1 are tabulated in Table. 1.

Table 1 Structural parameters of Fig. 1
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In the first step of a 2-D PhC based biosensor designation, the PBG diagram should be presented. PBG spectrum of the proposed biosensor can be seen in Fig. 2.

Fig. 2
figure 2

View of the PBG of the proposed biosensor

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As seen in Fig. 2, TE and TM modes were extracted for the proposed biosensor. TE modes are obtained in the wavelength ranges of 1.14 μm < λ < 1.895 μm and 0.813 μm < λ < 0.93 μm. TM modes are also achieved in the wavelength range of 0.75 μm < λ < 0.935 μm.

TE mode is considered for further simulations due to its wider and more dominant wavelength range. In the TE mode range, the light wave can be propagated through the structure (without being dispersed) by considering the total internal reflection effect (TIR). As a result, for the following simulations, the wavelengths situated in the PBG range would be considered as the input wavelength (for having the TIR effect). In order to have biosensors with the ability of detecting Creatinine and Glucose at individual output ports, various simulations with different input central wavelengths should be conducted.

In the following parts, first, field distributions at λ = 1550 nm and λ = 1290 nm for Outputs 1 and 2 are obtained. Then, by considering different concentrations of Creatinine and Glucose, their effects on the resonant wavelength are considered (transmission-wavelength for different RIs were depicted). Finally, Q, S, DL and FOM parameters are calculated.

Simulations and Results

In this part by considering the incident field at different wavelengths (in the TE range), field distributions and transmission-wavelength spectra are obtained.

Output 1 (λ = 1550 nm)

In this section, by considering λ = 1550 nm, the light wave would be transmitted to Output1 as shown in Fig. 3.

Fig. 3
figure 3

Field distribution at λ = 1550 nm

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As seen, most of the incident light wave would be transmitted to Output1 at λ = 1550 nm. In this section, by considering different concentrations of Glucose in blood samples (by their RIs), transmission spectrum versus wavelength would be obtained. Diabetes can be diagnosed by considering the obtained results (for people with different genders, ages and etc., specific values of Glucose concentrations can lead to diabetes). The following figure indicates the evolutions of the resonant wavelength by considering various concentrations of Glucose (defined by RIs) in blood samples.

Considering Fig. 4, the utilized RIs of 1.365, 1.375, 1.382, 1.394 and 1.405 are related to various Glucose concentrations in blood samples (n = 1.365 for 75 mg/dl, n = 1.375 for 100 mg/dl, n = 1.382 for 125 mg/dl, n = 1.394 for 150md/dl and n = 1.405 for 175 mg/dl [35]). As seen in Fig. 4, increasing RI would lead the transmission’s peak wavelength to higher values (red-shift) [18, 36].

Fig. 4
figure 4

Transmission spectrum vs. wavelength for various Glucose concentrations

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By considering Fig. 4 and Eqs. (3–6), the following parameters for the biosensor at Output1 can be obtained. Quality factor (Q): (163.6—169.8), Sensitivity (S): 1400 nm/RIU, detection limit (DL): (6.6e-4—6.8e-4) RIU, Figure of merit (FOM): (150.4–152.6) RIU−1.

Finally, by considering wavelengths in the range of 1522 nm < λ < 1578 nm, the mentioned concentrations of Glucose in blood samples can be detected. This can help in diagnosis of diabetes. In the following part, by considering incident field with λ = 1290 nm, various concentrations of Creatinine in blood samples at Output2 would be diagnosed.

Output 2 (λ = 1290 nm)

In this section, by considering λ = 1290 nm, the light wave would be transmitted to Output2 as shown in Fig. 5.

Fig. 5
figure 5

Field distribution at λ = 1290 nm

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As shown in Fig. 5, most of the incident light wave was transferred to Output2 at λ = 1290 nm. In this part, by considering various concentrations of Creatinine in blood samples (by their RIs), transmission spectrum versus wavelength could be obtained. Kidney failure diseases can be diagnosed by considering the obtained results (for people with different genders, ages and etc., specific values of Creatinine concentrations can lead to kidney failure). The following diagram indicates the evolutions of the resonant wavelength by considering various concentrations of Creatinine (defined by RIs) in blood samples.

The utilized RIs of Fig. 6, are related to various Creatinine concentrations in blood samples (n = 2.565 for 85.28 μmol/L, n = 2.589 for 84.07 μmol/L, n = 2.610 for 83.3 μmol/L and n = 2.639 for 82.3 μmol/L [21]). It is obvious from Fig. 6, that increasing RI would move the transmission’s peak wavelength to higher amounts [18, 36]. By considering Fig. 6 and Eqs. (3–6), the following parameters for the biosensor at Output2 can be obtained. Quality factor (Q): (53.5—58), Sensitivity (S): 795 nm/RIU, detection limit (DL): (0.0029—0.0030) RIU, Figure of merit (FOM): (33.07—34.56) RIU−1. Therefore, by considering wavelengths in the range of 1286 nm < λ < 1344 nm, the mentioned concentrations of Creatinine in blood samples can be detected. This can help in diagnosis of kidney failure diseases. Results of the propped sensor were compared with previous published works and are tabulated in Table 2.

Fig. 6
figure 6

Transmission spectrum vs. wavelength for various Creatinine concentrations

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Table 2 Comparison of our suggested biosensor with published works
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Conclusion

An efficient and compact biosensor based on 2-D PhCs was presented. The structure was designed based on 30*20 Si rods in the air background. For ease of fabrication and designation, only linear materials were considered. Various defect rods (dark blue and dark green rods) were responsible for the interference and scattering phenomena. They also confined light wave in the sensing medium. Application of the proposed structure was studied through PWE (extracting the PBG spectrum) and FDTD (extracting filed distribution diagram) methods. Output1 (operating at λ = 1550 nm) was considered for detection of Glucose concentrations in blood samples. The remarkable S, Q, FOM and DL of 1400 nm/RIU, (163.6–169.8), (150.4–152.6) RIU−1 and (6.6e-4–6.8e-4) RIU were achieved for Glucose concentration biosensor, respectively. In Output2 (operating at λ = 1290 nm), Creatinine concentrations were detected with S, Q, FOM and DL of 795 nm/RIU, (53.5–58), (33.07–34.56) RIU−1 and (0.0029–0.0030) RIU, respectively. Finally, by obtaining Glucose and Creatinine concentrations in blood samples, diabetes and kidney failure diseases can be diagnosed. The proposed biosensor can be a remarkable candidate for utilization in bio-optical integrated circuits.