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Theoretical Investigation of a Highly Sensitive Refractive-Index Sensor Based on TM_{0} Waveguide Mode Resonance Excited in an Asymmetric Metal-Cladding Dielectric Waveguide Structure

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## Abstract

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_{0}waveguide mode resonance excited in an asymmetric metal-cladding dielectric waveguide structure, where the analyte serves as the guiding layer. By scanning the wavelength at fixed angles of incidence, the reflection spectra of the sensor were obtained. The results showed that the resonance wavelength redshifted dramatically with increases in the analyte RI, which indicates that this approach can be used to sense both the resonance wavelength and the analyte RI. Based on this approach, we investigated the sensing properties, including the sensitivity and figure of merit, at fixed incident angles of 60° and 45°, at which the sensitivity of the sensor reached 7724.9 nm/RIU (refractive index units) and 1339 nm/RIU, respectively. Compared with surface plasmon resonance sensors, which are based on a similar structure, the proposed sensor can accept a more flexible range of incident angles and a wider sensing range of analyte RI. This approach thus has tremendous potential for use in numerous sensing domains, such as biochemical and medical analyses.

## 1. Introduction

^{−4}RI units at a resolution of 1 nm, which was equivalent to 5948 nm/RIU [36]. Nevertheless, when using sensors that rely on a prism-coupled SPR method, the analyte’s RI must be less than that of the prism, which limits its applicability in some cases [37].

## 2. Sensor Design and Analysis

_{0}waveguide mode is resonant.

## 3. Sensor Performance

_{0}mode was excited by prism coupling, and the reflectivity was defined as I

_{out}/I

_{in}, where I

_{in}denotes the total intensity of light radiated from one side of the prism and I

_{out}denotes the total intensity of light emitted from the other side of the prism after being reflected by the AMDW. The reflection spectrum of our RI sensor was obtained by parametric wavelength scanning with a step of 1 nm. Furthermore, based on the above analyses and the simulated reflection spectra, we calculated the relationship between the resonance wavelength and the RI of the analyte. Moreover, the sensitivity and figure of merit (FOM) were calculated to depict the sensing performance.

_{0}resonance redshifted gradually and the dips rose with the increasing analyte RI. To further characterize the sensing capability of this scheme, we calculated the properties of this reflection dip.

_{0}resonance dip as a function of analyte RI, showing that the two are linearly related. Based on Equation (4), the slope of 7724.9 nm/RIU for the line in Figure 3a was the sensitivity obtained from wavelength scanning at a fixed 60° angle of incidence when using the equilateral prism for coupling. This sensitivity was much greater than previous reports [30,35,36], which attests to the remarkable performance of the proposed setup. In addition, the FOM was calculated using Equation (5) and plotted as a function of the analyte RI in Figure 3b. These two figures clearly show that the resonance wavelength and FOM increased with the increasing analyte RI. The FOM remained above 70 RIU

^{−1}and reached a highest point of 92.3 RIU

^{−1}. Thus, the proposed method to determine the RI based on the resonance of the TM

_{0}waveguide mode is clearly superior to previous techniques.

_{0}resonance dip. In other words, the TM

_{0}waveguide mode resonance was excited when the parameters satisfied the equations of the AMDW structure. Figure 4 shows three simulated optical distributions for the resonance dips. These plots illustrate that the energy from the TM-polarized plane-wave light was transferred due to the interactions between the Au film and the analyte layer [45].

## 4. Conclusions

_{0}waveguide mode excited in an asymmetric metal-cladding dielectric waveguide structure. For various incident wavelengths and at the angles of incidence of 60° and 45°, the sensitivity of the setup was found to be as high as 7724.9 nm/RIU and had a reasonable FOM with a 60° angle of incidence for analyte RIs between 1.30 and 1.40. This was much greater than the results that were found for the 45° angle of incidence. These results also demonstrated that the capabilities of the sensor depended on the wavelength range of the TM

_{0}waveguide mode resonances and the angle of incidence. This means that the light source and angle of incidence can be flexibly selected according to the requirements of the specific application. Compared with a similarly structured SPR sensor, the sensitivity of the proposed sensor was more stable and offered a better FOM, making it more effective for practical sensing measurements. The proposed method additionally enables the determination of the analyte RI over a wider range, which makes it more valuable for broader RI detection.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 2.**Reflection spectra of the AMDW structure for various refractive indices and for a fixed angle of incidence of 60°.

**Figure 3.**Two RI sensor properties for coupling via an equilateral triangular prism. (

**a**) The resonance wavelength as a function of analyte RI with a linear fit produced a slope of 7724.9 nm/RIU; and (

**b**) the FOM as a function of analyte RI.

**Figure 4.**Simulated optical field distributions for three TM

_{0}resonance conditions: analyte RI of (

**a**) 1.30, (

**b**) 1.35, and (

**c**) 1.40.

**Figure 5.**TM reflection spectra for AMDW structure and for several analyte RIs, all with a 45° angle of incidence.

**Figure 6.**Sensing properties for the isosceles right-angle prism. (

**a**) Resonance wavelength as a function of the analyte RI with a linear fit producing a slope of 1339 nm/RIU, and the (

**b**) FOM as a function of the analyte RI.

**Figure 8.**Resonance wavelength (

**a**) and FOM (

**b**) as a function of analyte RI for the SPR sensing structure.

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**MDPI and ACS Style**

Wang, X.; Wu, X.; Zhu, J.; Pang, Z.; Yang, H.; Qi, Y.
Theoretical Investigation of a Highly Sensitive Refractive-Index Sensor Based on TM_{0} Waveguide Mode Resonance Excited in an Asymmetric Metal-Cladding Dielectric Waveguide Structure. *Sensors* **2019**, *19*, 1187.
https://doi.org/10.3390/s19051187

**AMA Style**

Wang X, Wu X, Zhu J, Pang Z, Yang H, Qi Y.
Theoretical Investigation of a Highly Sensitive Refractive-Index Sensor Based on TM_{0} Waveguide Mode Resonance Excited in an Asymmetric Metal-Cladding Dielectric Waveguide Structure. *Sensors*. 2019; 19(5):1187.
https://doi.org/10.3390/s19051187

**Chicago/Turabian Style**

Wang, Xiangxian, Xiaoxiong Wu, Jiankai Zhu, Zhiyuan Pang, Hua Yang, and Yunping Qi.
2019. "Theoretical Investigation of a Highly Sensitive Refractive-Index Sensor Based on TM_{0} Waveguide Mode Resonance Excited in an Asymmetric Metal-Cladding Dielectric Waveguide Structure" *Sensors* 19, no. 5: 1187.
https://doi.org/10.3390/s19051187