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Abstract
A multi-parameter optical refractometric sensor based on lab-in-a-fiber is proposed and its sensing properties have been investigated. Based on the particular three suspended-core fiber, the sensor has three channels for liquid circulation and three suspended cores for detection. The multiple disease markers can be detected by coating the specific bio-recognition layer on the surface of three channels. The bio-recognition layer thickness, representing the concentration of the disease markers, can then be measured by the wavelength of fiber Bragg grating inscribed in each suspended core. Owing to the triple symmetry of the fiber, the sensitivity of each core is similar. The simulation results show that the grating wavelength linearly changes with the bio-recognition layer thickness variation. Through the sensitivity matrix, the sensitivity of the sensor is 0.362 nm/nm and the sensing accuracy is ± 1 nm.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The detection of biochemical or disease markers is of great significance to human health. To address this issue, numerous sensors have been proposed [1–5]. Among these methods, optical sensors, especially lab-on-a-fiber [2,6] or lab-on-a-chip [7–10], have attracted much attention due to its advantages of corrosion resistance, anti-electromagnetic interference and small sensor size. Comparing the lab-on-a-fiber and lab-on-a-chip, the two types of sensor all have good sensing characteristics, while lab-on-a-fiber can be perfectly connected to the optical fiber system [11].
Depending on the location of functional materials integrated, the lab-on-a-fiber can be subdivided in three classes, lab-around-a-fiber (LAF), lab-on-tip (LOT), and lab-in-a-fiber (LIF) [12]. In order to make the light fully interact with analyte, LAF typical has a taper waist region for coupling the core waveguide light to the fiber cladding surface. This may result in a brittle fiber structure [13]. In addition, tilted fiber grating can also be used to couple the light to fiber surface to excite surface plasma resonance (SPR) [14]. SPR-based fiber grating sensor has an enhanced sensitivity in biosensing and achieved remarkable measurement results in the experiments [15–17]. LOT has attracted wide attention of researchers, for the fiber tip can be modified freely [18,19]. But in pursuit of better performance, precise geometrical features are usually needed to be achieved, which requires complex technique or expensive equipment. In contrast, LIF relies on the photonic crystal fiber (PCF) [20], which evolved from the two-dimensional photonic crystal [21,22], having a flexible and adjustable structure. In virtue of the holey structure of PCF, the sensor features of LIF can be easy controlled. For instance, suspended core fiber (SCF) can be deposited with gold nanoparticles [23] or dielectric-gold layer [24] to stimulate the SPR phenomenon, used to detect refractive index or identify substance. Another sensing method is to deposit a bio-recognition layer on the internal surface of a SCF [25]. The detection can be realized by measuring the mode area or attenuation while the bio-recognition layer thickness changes. However, these methods can not be extended to multi-parameter detection. In order to realize multi-parameter sensing, researches have deposited the dielectric-gold layer on the inner hole surface of the SCF, and then exciting the higher order surface plasmon polaritons (SPP) modes [26]. Multi-parameter detection is realized by measuring the wavelength of each SPP mode spectrum. However, the spectra of higher-order SPP modes are partially overlapped, which will have a detrimental effect on the detection.
In this study, a multi-parameter optical refractometric sensor based on LIF has been designed and characterized. The sensor is mainly designed to detect three plasma components, albumin, fibrinogen, and $\gamma$-immunoglobulin [8,27]. As their combination of different concentrations will lead to the same bulk index change, but corresponding to different diseases. As a conceptual sensor, the sensing characteristics of the designed LIF are verified by finite element method. The sensor is based on a particular three suspended-cores fiber (TSF) [28], which has three pie-shaped holes surrounded the three suspended-core, separated by a small central air hole. In order to achieve multi-parameter detection, three pie-shaped holes are coated with specific bio-recognition layers. With the help of the fiber Bragg grating (FBG), inscribed in each suspended core with different periods, the thickness of each bio-recognition layer can be obtained based on the FBG wavelength. For simplicity, the bio-recognition layer thickness represents the concentration of analyte. Because of the triple symmetry of the fiber, the sensing characteristics of the three cores are the same. The simulation results show that the FBG wavelength linearly shift with the bio-recognition layer thickness variation. The sensitivity of the designed LIF is $0.362$ nm/nm and the sensing accuracy is $\pm$ $1$ nm.
2. Sensor design and modes analysis
The cross-section of the proposed LIF is shown in Fig. 1(a) with the enlarged core area shown in Fig. 1(b) for detailed illustration. The material of the TSF is fused silica (blue), and the three pie-shaped holes are injected liquid (purple) to be measured. Due to the pie-shaped holes are flow channels for fluid, they would then be called “channels.” The “channels” are separated by “spokes.” Each inner surface of the hole is coated with a specific bio-recognition layer (green). The small central hole is full of air (gray). The parameters of the fiber are listed as follows. The minimum distance between the central air-hole and adjacent “channels” ($a$) is 0.21 $\mathrm {\mu }$m, the diameter of central air-hole ($D_{\textrm{T}}$) is 3.34 $\mathrm {\mu }$m, the thickness ($d$) of “spokes” is 0.87 $\mathrm {\mu }$m, and the external circle diameter of the air-hole ($s$) is 36.2 $\mathrm {\mu }$m. Diameter ($d_{\textrm{c}}$) of TSF is 125 $\mathrm {\mu }$m. The white dashed circle depicted in the Fig. 1(b) represents the core of single mode fiber (SMF). The part that the SMF overlaps with the TSF can be regarded the core of TSF. The diameter of the SMF ($D_{\textrm{S}}$) is $8.3$ $\mathrm {\mu }$m [29]. The position of FBGs inscribed in the suspended cores are the orange part inside the white dashed circle.
Fig. 1. (a) Cross-sectional illustration of LIF in the position where the FBGs inscribed; (b) enlarged core area as indicated by red rectangle.
The simulations are performed with the finite element method (FEM) based on a commercial software COMSOL [30]. Perfectly matched layer (PML) is used in all simulations, which is the outermost ring area indicated as yellow as shown in Fig. 1(a). For simplicity, the bio-recognition layer thickness represents the concentration of the analyte in the liquid. The refractive index of the filled liquid is $1.35$, and the refractive index of bio-recognition layer is $1.45$, for detecting the three plasma components, albumin, fibrinogen, and $\gamma$-immunoglobulin [8,31]. The bio-recognition layer coated in the surface of each “channel” can only absorb one component.
The bio-recognition layer thickness variation would lead to the change of the effective refractive index ($n_{\textrm{eff}}$). Therefore, the thickness can be detected through the $n_{\textrm{eff}}$. The $n_{\textrm{eff}}$ used here comes from the fiber mode propagation constant $\beta$, and can be described as [32]:
where $\lambda$ is the wavelength of the fiber guided light.Generally, the $n_{\textrm{eff}}$ of the fiber core is difficult to measure directly, but it can still be obtained based on the first-order Bragg wavelength of FBG inscribed in each suspended core. Since the grating wavelength-based demodulation scheme is not affected by the light intensity, the coupling efficiency between SMF and TSF would influence the demodulation of the analyte concentration only through the intensity of the grating and the signal-to-noise ratio, which could be addressed by enhancing the input light. Therefore, we are not concerned with the coupling efficiency between the fibers.
The relationship between the wavelength of FBG $\lambda _{\textrm{FBG}}$ and $n_{\textrm{eff}}$ of fiber core can be expressed as:
where $\Lambda$ is the FBG period. Inscribing FBG in suspended core could be carried out by a femtosecond laser, which has been used to inscribe various types of FBG [33,34]. Since the inscribed grating is an ordinary Bragg grating, the FBGs would mainly influence the intensity of the transmitted light at the resonant wavelength, resulting in a Gaussian-like shaped reflection spectrum.The SMF core diameter is typically $8.3$ $\mathrm {\mu }$m at the wavelength of 1.55 $\mathrm {\mu }$m, which can cover the cross-section of the whole three suspended cores. Therefore, no additional fan-in and fan-out devices are required. The light can be transmitted to three core at the same time by using the commercial SMF. In order to distinguish the FBG signals of the three cores, the wavelength division multiplexing (WDM) is adopted by inscribing FBG with different $\Lambda$. The determination of the $\Lambda$ would require prior knowledge of the fiber core $n_{\textrm{eff}}$. With the help of COMSOL, the electric field distribution and mode $n_{\textrm{eff}}$ of the optical fiber can be obtained. The electric field distributions of the ${\textrm{LP}_{01}}$ mode, which is the degenerate mode of the two ${\textrm{HE}}_{11}$ modes of TSF at wavelength of 1.55 $\mathrm {\mu }$m, are shown in Fig. 2, with the three “channels” filled in liquid ($n_{\textrm{eff}}$=$1.35$). The electric field distributions and the electric field arrows can help for confirming the modes [35,36]. The bio-recognition layer thickness of upper “channels,” left “channels,” and right “channels” are the $0$ nm, which can be marked as $0-0-0$ nm, indicating no analyte in the liquid. The small central hole is still full of air.
Fig. 2. Electric field distributions of the fundamental ${\textrm{LP}_{01}}$ mode in TSF at the wavelength of $1.55$ $\mathrm {\mu }$m with the bio-recognition layer thickness $0-0-0$ nm.
Owing to the asymmetry of the core structure, the refractive index of two orthogonal directions of ${\textrm{LP}}_{01}$ mode has a large difference, which is usually expressed by birefringence coefficient. Even though the “channels” are filled with liquid, the birefringence coefficient of three cores reaches $1.3 \times 10^{-3}$ at 1.55 $\mathrm {\mu }$m. The orientation of electric field in Fig. 2 can be divided by parallel to the “spoke” and perpendicular to the “spoke,” marked as X and Y, respectively. The polarization orientation of ${\textrm{LP}_{01}}$ mode can then be expressed with two orthogonalized X-polarization and Y-polarization respectively. Because of the three “channels” filled with liquid, the refractive index difference between the core and cladding is too small to support independent transmission of the fundamental ${\textrm{LP}_{01}}$ mode. The mode coupling occurs between the suspended cores. As is shown in Fig. 2(a), the ${\textrm{LP}_{01}}$ mode of X-polarization in the bottom core has coupled to the left core and right core. The electric field has been extended to both the left core and right core. The mode coupling between the bottom core in X-polarization and left core in X-polarization can be denoted by Bx-Lx, where the B, L represent the bottom core and left core, x represents the X-polarization. The coupling of other modes between the cores can also be expressed in the same way. R represents the right core and y represent the Y-polarization. The electric field distribution as shown in Fig. 2 stimulated based on a $2$-dimensional profile can be considered as a cross-section of TSF in a $3$-dimensional. Therefore, the electric field distribution in the simulation is presented at a specific pattern. Due to the difference of $n_{\textrm{eff}}$ between each core, the fiber mode propagation constant $\beta$ of the three cores is not equivalence, which account for the different mode coupling. The electric field distributions of left core or right core can not be rotated from that of bottom core, even the TSF is triple-symmetry.
In order to minimize the cost of the sensing system and distinguish the FBGs in the three core of TSF, the commercial amplified spontaneous emission (ASE) or super-luminescent emitting diode (SLED) is selected as system light source. The light of ASE or SLED contains C and L wavelength band. Therefore, to make the FBG wavelength interval as large as possible, the initial FBG wavelengths of the bottom core, left core and right core are set as $1530$ nm, $1560$ nm and $1590$ nm, respectively. After the FBG wavelength determined, the FBG periods can be obtained through Eq. (2). The $n_{\textrm{eff}}$ of the bottom core, left core and right core versus wavelength with the thickness of bio-recognition layers at 0-0-0 nm are shown in Figs. 3(a), (b), and (c).
Fig. 3. The $n_{\textrm{eff}}$ of ${\textrm{LP}_{01}}$ modes in (a), (d) bottom core; (b), (e) left core; (c), (f) right core versus wavelength, with the thickness of bio-recognition layers $0-0-0$ nm and $5-0-0$ nm respectively.
As shown in Fig. 2, there are multiple modes in each core in virtue of the mode coupling between the cores. Due to the birefringence of the TSF and structure symmetry, the $n_{\textrm{eff}}$ curves are thus divided into two parts. The inset in Fig. 3(a) is an enlarged view of the pink dotted area in the figure. Each mode $n_{\textrm{eff}}$ line in Fig. 3(a) corresponds to a mode in Fig. 2. The modes have been described above. As shown in Fig. 3(a), the X-polarization and Y-polarization represent the modes originally existed in the bottom core. The Ly-By, Lx-Bx, Ry-By and Rx-Bx represent the modes coupling from the other cores. It is the same as that in Figs. 3(b) and (c). As shown in Fig. 3, the $n_{\textrm{eff}}$ of mode in Y-polarization is smaller than the $n_{\textrm{eff}}$ of mode in X-polarization. Based on Eq. (2), the $\lambda _{\textrm{FBG}}$ of Y-polarization mode is larger than $\lambda _{\textrm{FBG}}$ of X-polarization mode. To avoid wavelength confusing, the maximum wavelength of the FBG in the bottom core should not exceed the minimum wavelength of the FBG in the left core. Therefor, the FBG periods are calculated based on the $n_{\textrm{eff}}$ of the modes in Y-polarization. The periods of FBG inscribed in bottom core, left core and right core are $548.12$ nm, $559.43$ nm, and $570.75$ nm, respectively. To obtain the wavelength of the other modes reflected on the FBG, graphical method has been used. The relationship between $\lambda _{\textrm{FBG}}$ and $n_{\textrm{eff}}$ is shown as the black line in Fig. 3 based on Eq. (2). The intersection of the mode $n_{\textrm{eff}}$ line and FBG line is the wavelength that the mode can be reflected on FBG.
When the light containing these modes reflected on the FBG, modes will form their own FBG reflection spectrum. Due to the fiber birefringence, each mode forms two FBG reflection spectra. Since the $n_{\textrm{eff}}$ of each coupling mode is close to the $n_{\textrm{eff}}$ of the core itself, the FBG formed by each mode in the X-polarization or Y-polarization would superimpose as a FBG. The FBG in Y-polarization is denoted as Peak-A, and in X-polarization is denoted as Peak-B. The results are shown in Figs. 4(a), (b), and (c) with the thickness of bio-recognition layers $0-0-0$ nm. The intensity of each mode reflected FBG spectrum is obtained by squaring the electric field intensity. In Fig. 4(a), the superimposed FBG is marked as “The total.” The abbreviations of the FBGs formed by each mode are the same as in Fig. 3(a). The rest of the figures are similar to this.
Fig. 4. The reflected FBG spectra of the (a), (d) bottom core; (b), (e) left core; (c), (f) right core with the thickness of bio-recognition layers $0-0-0$ nm and $5-0-0$ nm respectively.
To further investigate the characteristics of each FBG in the core when the bio-recognition layer thickness varies, the thickness of the upper, left and right bio-recognition layer are set as $5$ nm, $0$ nm and $0$ nm in the model, marked as $5-0-0$ nm. Since the bottom core is far from the upper bio-recognition layer, the $n_{\textrm{eff}}$ would be weakly affected by the upper bio-recognition layer thickness variation. According to the simulation results, the $n_{\textrm{eff}}$ of the three cores and FBG versus wavelength are shown in Fig.s 3(d), (e), and (f), respectively. Different from Figs. 3(a), (b), and (c), several $n_{\textrm{eff}}$ lines are not shown in Figs. 3(d), (e), and (f) because of the very weak intensity. The inset in Fig. 3 is an enlarged view of the pink dotted area in the figure. Comparing Fig. 3(a) and Fig. 3(d), the mode $n_{\textrm{eff}}$ of X-polarization and Y-polarization in the bottom core has no significant change. There are weakly mode coupling between the bottom core and the other two cores. The FBG spectra of the bottom core are shown in Fig. 4(d). Comparing with Fig. 4(a), it has been clearly shown that the FBG wavelength has not shifted.
As the bio-recognition layer thickness are set as $5-0-0$ nm, the $n_{\textrm{eff}}$ of left or right core increases compared with the $n_{\textrm{eff}}$ when the bio-recognition layer thickness set as $0-0-0$ nm, which causes the FBG wavelength red-shifted, as shown in Figs. 4(e) and (f). The mode coupling has occurred between the two cores, for the modes $n_{\textrm{eff}}$ are close between the two cores.
Considering the refractive index of the bio-recognition layer maybe change during the growth, the refractive index of bio-recognition layer is varied from $1.44$ to $1.46$ with $0.01$ interval. To show the influence of the refractive index variation of bio-recognition layer on the sensing performance, the thickness of bio-recognition layer is set $0-0-0$ nm and $5-0-0$ nm respectively, simply used as a comparison. Considering that the left and right cores have the same sensitivity when the thickness of bio-recognition layer is $0-0-0$ nm and $5-0-0$ nm, we have studied the variation of the FBG reflection spectra in the bottom core and left core of TSF. The results are shown in Fig. 5.
Fig. 5. The FBG spectra of (a) bottom core and (b) left core with the upper layer thickness at $0-0-0$ nm or $5-0-0$ nm when the $n_{\textrm{eff}}$ of bio-recognition layer varied from 1.44 to 1.46.
Since the bottom core is opposite to the upper bio-recognition layer, the FBG reflection spectrum of bottom core would not shift when the upper layer thickness changed, as shown in Fig. 5(a). However, the left core is influenced by the upper layer thickness variation thus causing the reflection spectrum to shift, as shown in Fig. 5(b). As the refractive index of bio-recognition layer changed, the movement of FBG reflection spectrum of left core has slightly different. The central wavelength of FBG are $1562.955$ nm, $1562.937$ nm and $1562.920$ nm when the refractive index of bio-recognition layer is $1.46$, $1.45$ and $1.44$, respectively. Therefore, the refractive index variation of the bio-recognition layer has slight effect on the sensing performance.
3. Sensing property analysis
In the optical fiber, the core refractive index would vary with the cladding refractive index variation. In order to explore the relationship between the bio-recognition layer thickness and core refractive index, the case of single bio-recognition layer thickness variation is considered first. When the upper bio-recognition layer thickness varies from $0$ nm to $30$ nm with $5$ nm interval, and the other two layers maintain $0$ nm, the reflected FBG spectra are shown Figs. 6(a), (b), and (c). The corresponding FBG wavelength shifts are shown in Figs. 7(a), (b), and (c). As displayed in Fig. 6(a) and Fig. 7(a), the FBG spectra of bottom core have no obvious change with the upper bio-recognition layer thickness variation, consistent with the previous description.
Fig. 6. The FBG spectra of (a) bottom core, (b) left core, (c) right core with upper layer thickness varying from $0$ to $30$ nm; and (d) bottom core, (e) left core, (f) right core with thickness of upper, left layers varying from $0$ to $30$ nm simultaneously. The other layer thickness remains $0$ nm.
Fig. 7. The FBG wavelength shift of (a) bottom core, (b) left core, (c) right core with upper layer thickness varying from $0$ to $30$ nm; and (d) bottom core, (e) left core, (f) right core with thickness of upper, left layers varying from $0$ to $30$ nm simultaneously. The other layer thickness remains $0$ nm.
On the contrary, the FBG wavelength of left core and right core have a unambiguous linear relationship with the upper bio-recognition layer thickness, shown in Figs. 7(b) and (c). The R-squares of the fitted lines are all exceeded $0.99$. The linear sensitivities of the left core and right core are $0.32$ nm/nm, $0.32$ nm/nm for Peak-A, and $0.38$ nm/nm, $0.38$ nm/nm for Peak-B, respectively. Owing to the symmetrical fiber structure, the sensitivity coefficients of left core and right core are similar with each other. According to the electric field distributions of the ${\textrm{LP}_{01}}$ in X-polarization and Y-polarization shown in Fig. 2(a), the two orthogonal modes have different distributions, which will lead to diverse sensing characteristics. As shown in Figs. 7(b) and (c), the sensitivity of Peak-B corresponding to X-polarization is higher than that of Peak-B corresponding to Y-polarization. This avoids the overlap of the FBG spectra in large range detection.
To further prove that the thickness of the bio-recognition layer has little influence on the $n_{\textrm{eff}}$ of the opposite orientation core, the $n_{\textrm{eff}}$ of the bottom core has been calculated while the thickness of the recognition layer varies from $5-0-0$ nm to $30-0-0$ nm. The results are shown in Fig. 8.
Fig. 8. The refractive index of bottom core with the thickness of bio-recognition layers varied from $5-0-0$ nm to $30-0-0$ nm.
As shown in Fig. 8, the group of refractive indices are split into two parts due to the birefringence. However, even though the thickness of the upper bio-recognition layer changed, the effective refractive indices are very close to each other within any of sections of the spectra, indicating that thickness of the bio-recognition layer will not affect the $n_{\textrm{eff}}$ of the opposite orientation core. From the relationship between the wavelength of FBG $\lambda _{\textrm{FBG}}$ and $n_{\textrm{eff}}$ of the fiber core shown in Eq. (2), $\lambda _{\textrm{FBG}}$ is proportional to the $n_{\textrm{eff}}$. The variation of the $n_{\textrm{eff}}$ of fiber core can be reflected in the change of wavelength $\lambda _{\textrm{FBG}}$ of FBG. As shown in Fig. 6(a), the spectra of the FBG inscribed in the bottom core does not move when the thickness of bio-recognition layer varied from $0-0-0$ nm to $30-0-0$ nm, which is consistent with the unchanged refractive index in Fig. 8.
Because of the triple symmetry of TSF, the three cores have the same characteristics. Based on the linear variation of the FBG wavelength with the single bio-recognition layer thickness, it can be assumed that the wavelength of FBG in each core changes linearly with each bio-recognition layer thickness. The relationship between FBG wavelength and the thickness can then be expressed as:
Due to the existence of the central air hole, the bio-recognition layer thickness has little influence on the $n_{\textrm{eff}}$ of the opposite orientation core. Therefore, $k_1$, $q_2$, $t_3$ can be regarded as $0$ according to the position of bio-recognition layer and the fiber core shown in Fig. 1. Meanwhile, the influence of bio-recognition layer thickness on $n_{\textrm{eff}}$ of the two adjacent cores is the same. The Eq. (3) can then be simplified as:
In order to further verify the assumption, thickness of upper and left bio-recognition layer are altered from $0$ nm to $30$ nm with $5$ nm interval. The thickness of right bio-recognition layer is $0$ nm and maintained during the simulation. The results are shown in Figs. 6(d), (e), and (f). The corresponding FBG wavelength shifts are shown in Figs. 7(d), (e), and (f). As shown in Fig. 6(d), the FBG spectrum of the bottom core is only affected by the left bio-recognition layer thickness when the upper and left and left bio-recognition layer thickness various. The results are similar to the FBG spectra shift of the left or right core when the upper bio-recognition layer thickness varies alone. As the upper and left bio-recognition layer thickness are varied simultaneously, the $n_{\textrm{eff}}$ of the left core will be affected by both of left and right bio-recognition layer thickness at the same time. As shown in Fig. 7(e), the FBG spectra shift is significantly larger than that in Fig. 6(b). The movement of the FBG spectra in the right core is very similar to that of the bottom core with upper and left bio-recognition layer thickness various, for it is only affected by a single bio-recognition layer.
When upper and left bio-recognition layer thickness reaches $30$ nm as shown in Fig. 6(e), the FBG spectra shift does not exceed $30$ nm, which ensures the FBG spectra does not overlap with another FBG spectra in other core. But the maximum FBG wavelength shift is $21.2$ nm, closing to $30$ nm spectral spacing, which indicates the upper concentration limit that can be detected by the sensor. The upper detection limit can be promoted simply by using supercontinuum light source with redesigned FBG period.
As shown in Fig. 7, the R-squares of all the fitted lines are all exceeded $0.99$. Comparing Figs. 7(b) and (e), the linear sensitivity of FBG in left core are $0.32$ nm/nm for Peak-A and $0.38$ nm/nm for Peak-B as the upper bio-recognition layer thickness various. The linear sensitivity are $0.60$ nm/nm for Peak-A and $0.70$ nm/nm for Peak-B as the upper and left bio-recognition layer thickness various simultaneously. According to the above assumption, the influence of the bio-recognition thickness on the FBG wavelength is linear superposition. Therefore, when the thickness of adjacent two layers changed, the slope of the FBG wavelength versus the thickness should be twice the slope when thickness of the adjacent single layer varies. However, the sensitivity shown in Fig. 7(e) is about $1.88$ times larger than the sensitivity shown in Fig. 7(b) for Peak-A and is about $1.84$ times for Peak-B. The multiple values are not exactly $2$, indicating that the influence of bio-recognition layers to the refractive index of a suspended-core is not simple adding together as assumed above. But $1.88$ and $1.84$ is close to $2$, implying that the hypothesis model can be used to approximate the thickness of each detection layer.
In order to increase the accuracy of the simulation results, the scenario that the three bio-recognition layer thickness varies from $0$ nm to $30$ nm with $5$ nm interval has been simulated. Because the sensing characteristics is similar with the single bio-recognition layer various or double bio-recognition layer various, the specific simulation will not be described in detail. The slopes of each line with single, double and triple bio-recognition layer thickness variation are gathered in Table 1.
Table 1. The line slopes of the FBG wavelength versus bio-recognition layers thickness variation. (Unit: nm/nm)
As shown in Table 1, the linear sensitivity of the FBG in each is not exactly the same. The disturbance of the slopes come from the possibility that the refractive index does not change completely linearly with the thickness, because of the fact that the R-squares of fitting lines are not exactly $1$. In order to minimize the error, the sensitivity coefficient $k_A$ is the average value of each slope when adjacent single bio-recognition layer thickness various, which is $0.306$ nm/nm for peak-A and $0.362$ nm/nm for peak-B, respectively. The thickness of upper, left and right bio-recognition layer can then be calculated by:
In order to verify the performance of the proposed LIF, thickness of the three bio-recognition layers are set randomly. The thickness is then demodulated by measuring the FBG wavelength of the three cores based on Eq. (4). Three simulation modes has been verified with the thickness of the upper, left and right bio-recognition layer $0-0-8$ nm, $0-3-17$ nm and $13-1-27$ nm, respectively. The FBG spectra of each core are shown in Fig. 9.
Fig. 9. The FBG spectra of (a) bottom core, (b) left core, (c) right core with thickness $0-0-8$ nm, surrounded by cyan solid lines; (d) bottom core, (e) left core, (f) right core with thickness $0-3-17$ nm, surrounded by fuchsia solid lines; and (g) bottom core, (h) left core, (i) right core with thickness $13-1-27$ nm, surrounded by orange solid lines.
Figures 9(a), (b), and (c) have shown the FBG spectra of the bottom core, left core and right core respectively, surrounded by cyan solid lines. The thickness of the three bio-recognition layers are $0-0-8$ nm. Figures 9(d), (e), and (f) have shown the FBG spectra of the bottom core respectively, left core and right core, surrounded by fuchsia solid lines. The thickness of the three bio-recognition layers are $0-3-17$ nm. Figures 9(g), (h), and (i) have shown the FBG spectra of the bottom core respectively, left core and right core, surrounded by orange solid lines. The thickness of the three bio-recognition layers are $13-1-27$ nm. Based on Eq. (5), thickness of the three bio-recognition layers can be calculated by the FBG wavelength of the three cores. The demodulation results are displayed in Table 2.
Table 2. The thicknesses of demodulated and setting values. (Unit: nm)
As it is shown in Table 2, the demodulated results by using the linear sensitivity of Peak-A is the same by using the linear sensitivity of Peak-B. As described above, the FBG wavelength does not shift strict linearly with the thickness variation of the bio-recognition layers. Meanwhile, the influence of the bio-recognition layer is also not linearly added. Therefore, the demodulated values have a deviation from the setting values, but the demodulated values are close to the setting values. The deviation is within $\pm$ $1$ nm.
4. Conclusion
In summary, a multi-parameter optical refractometric sensor based on LIF is proposed and its sensing properties have been investigated by the finite element method. Based on the particular three suspended-core fiber (TSF), the LTF has three “channels” for liquid circulation and three suspended cores for detection. After coated with a specific bio-recognition layer on the inner surface of each “channel,” the proposed LIF can be used for multi-parameter detection, such as the three plasma components albumin, fibrinogen, and $\gamma$-immunoglobulin. Due to the small core spacing in TSF, the light can be delivered to the three cores simultaneously by using commercial single mode fiber (SMF). The fiber Bragg grating (FBG) with different periods are written in the three suspended cores within C and L wavelength band. The thickness variation can be detected by measuring FBG wavelength shift. Due to the triple symmetry of the TSF, the sensing characteristics of the three cores are similar. According to the sensitivity matrix, the thicknesses of three bio-recognition layers can be demodulated based on the FBGs wavelength. The sensitivity of the designed LIF is $0.362$ nm/nm and the sensing accuracy is $\pm$ $1$ nm.
Funding
National Natural Science Foundation of China (61735013, 62075173); Youth Program of National Natural Science Foundation of China (61905184).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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