Abstract
Keywords
compound gratingsfigure of meritsensitivitysensor
1. Introduction
Optical biosensors are needed in many fields, such as biomolecular testing[
CWG structures are often designed to reduce the bandwidth of the resonant peaks for devices[
In this Letter, a DCSG-based structure is proposed in order to better improve the performance of the sensor. Then, the device structure is designed by the rigorous coupled-wave algorithm (RCWA)[
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2. Structure and Theory
Figure1 shows a schematic diagram of the proposed DCSG-based optical sensor structure, which contains four separate and identical grating strips (two at the top and two at the bottom) in each period. Additionally, the structure is completely symmetrical and entirely covered by a liquid with a refractive index of . The material used throughout the grating is NOA73 with a refractive index of 1.56. The DCSG is considered to be infinite in the -direction and periodic in the -direction. The parameters of the proposed sensor are as follows: the period of the compound gratings is , the grating filling factor is , the width and height of the four identical grating strips in each period are and , respectively, the interspacing between the two grating strips in each period is , and the homogeneous film thickness is . In our proposed model, the DCSG is viewed as a single-mode resonator. The eigenmode of the grating structure is determined by FEM simulation, and the reflection spectrum is then calculated using the theoretical model.
Figure 1.Schematic of the sensor based on the DCSG structure.
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In this method, a single period of the DCSG structure is defined as a unit cell, and NOA73 can be considered lossless. First, we use the FEM to calculate the eigenmode information of the resonant grating structure. During the simulation, we choose Floquet periodic boundary conditions as the lateral boundary conditions, while the upper and lower boundaries use scattering boundary conditions[
According to the effective medium theory, the effective refractive index can be defined as[
The sensitivity () and FOM are usually utilized to evaluate the performance of the sensor and can be expressed as[
3. Results and Discussion
First, we compared the spectral response of the DG and DCSG using the RCWA, as shown in Fig.2. We assumed the following structural parameters for the DCSG: , , , , , and (). for the DG structure. TE polarized light was used as the incident light source and was incident normally. Figure2 shows a sharp narrowing of the FWHM and a blue shift of the resonance peak when the compound structure is introduced. To illustrate the effect of the parameter on the performance of the sensor, we performed a detailed analysis when , 220, 240, and 260nm. The FEM was used to calculate the eigenvalues for different , which are listed in Table1.
Table 1. Eigenvalues of the TE Eigenmode with Different
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Figure 2.Reflection spectra of DG and DCSG at normal incidence of TE waves.
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According to Eq.(1) and Table1, the central resonant frequencies and quality factors of the DCSG structure can be obtained. It can be seen that the real part of the eigenvalues exhibits a small variation with increasing , while the imaginary part decreases sharply. This indicates a very significant improvement in the quality factor of the DCSG structure as increases. The physical meaning of the quality factor in a resonator is expressed as the ratio of stored energy to the consumed energy. As the spacing between the two grating strips increases, the amount of energy stored within the optical resonator is increasing. This further illustrates the increasing confinement capability of the grating structure for incident light waves.
To further understand the physical properties of this eigenmode, we simulated the electric field intensity distributions for different in each cell of the DCSG structure by using the FEM, the results of which are shown in Fig.3. It can be seen that as increases, more of the electric field is confined between the two grating strips.
Figure 3.Electric field intensity distributions of the eigenmode in different DCSGs with various spacings: (a)d = 200nm, (b)d = 220nm, (c)d = 240nm, (d)d = 260nm.
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Next, the reflectance spectrum of different at TE polarization is calculated by using Eq.(3), as shown in Fig.4. In Fig.4, we compared the calculated reflection spectrum with the simulated results of RCWA, showing that the calculated spectrum is in good agreement with the simulated results. Our calculations show that it is feasible to analyze and predict spectral line shape variations with the help of eigenmodes.
Figure 4.Reflection responses of the DCSG for the TE polarization with different d: (a)d = 200nm, (b)d = 220nm, (c)d = 240nm, (d)d = 260nm.
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Finally, the performance indicators of the designed DCSG structure sensor were analyzed. Its sensitivity and FOM are calculated by Eqs.(4) and (5), respectively. The sensing performance parameters of the DCSG structure with different are calculated in Table2. It can be seen that the FWHM decreases by a factor of approximately 54 as changes from 200nm to 260nm. However, the increase in sensitivity is not significant. This is explained by the fact that there is a trade-off between sensitivity and FOM in the GMR-based sensors[
FWHM (nm) | S (nm/RIU) | FOM | |
---|---|---|---|
200 | 0.811 | 461 | 568 |
220 | 0.414 | 469 | 1133 |
240 | 0.146 | 471 | 3226 |
260 | 0.015 | 472 | 31,467 |
Table 2. FWHM,
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By the analysis in Table2, the other structural parameters of the grating remain unchanged, with chosen. As the refractive index of the analyte is changed from 1.331 to 1.339, its eigenvalue is calculated by FEM, as listed in Table3.
Refractive Index | Eigenvalue |
---|---|
1.331 | |
1.333 | |
1.335 | |
1.337 | |
1.339 |
Table 3. Eigenvalues of TE Eigenmodes Corresponding to Different Refractive Indices
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It can be noticed that when changes from 1.331 to 1.339, a red shift of the resonance peak can be seen according to Eq.(1). To further verify the results of the eigenvalue analysis, the reflectance spectrum was calculated using RCWA as increased from 1.331 to 1.339, and the results are shown in Fig.5. It shows that the resonance peak has red shift with increasing analyte refractive index, and the FWHM remains almost unchanged. The central wavelength of the GMR grating structure is related to the resonant condition. A change in the refractive index of the analyte will change the conditions under which the GMR is generated[
Figure 5.DCSG reflection spectra for TE polarization with different nc.
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Further analysis of the fitted curve as the position of the resonance peak varies with analyte refractive index shows a linear relationship between the resonance wavelength and the refractive index, which can be seen in Fig.6. Based on the above results, we can obtain a high performance optical sensor with a sensitivity of 472nm/RIU and an FOM of 31,476.
Figure 6.DCSG resonance peak wavelength versus nc.
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4. Conclusion
In conclusion, a DCSG-based optical sensor is proposed, concentrating on the performance of the device at different compound spacings. By changing the spacing between the compound gratings, the eigenmode of the grating can be regulated, changing the magnitude of the eigenvalue to achieve the purpose of regulating the reflectance spectral linewidth and optimizing the performance of the sensor. The theoretical simulation results show that the sensitivity of the sensor is 472nm/RIU, the FWHM is only 0.015nm, and the FOM value is 31,467. The research work in this Letter provides a reference for the design of new grating sensors.
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