# Multiparameter Sensing Based on Tunable Fano Resonances in MIM Waveguide Structure with Square-Ring and Triangular Cavities

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{1}is the distance between the ITC and the bus waveguide, while G

_{2}is the distance between the SRCSB and the bus waveguide. The basic fabrication of the structure began with the preparation of an adequately thick Ag layer on a silicon substrate using chemical vapor deposition (CVD). Then, the bus waveguide, ITC, and SRCSB were etched onto the Ag layer using the electron beam etching technique.

_{eff}is the effective length of the resonant cavity, φ is the phase shift caused by the reflection, Re(n

_{eff}) is the real part of the effective refractive index, and m is the resonant mode order.

## 3. Results

_{1}= G

_{2}= 10 nm. w was set at 50 nm in order to make only the basic transverse magnetic mode exist in the structure. Figure 2 shows the transmission spectra of the structure without the silver baffle in the bus waveguide, the bus waveguide with the silver baffle, and the whole structure. The bus waveguide with the silver baffle provided a broadband continuous state for the structure, as shown by the blue line. In the absence of the silver baffle in the bus waveguide, the SRCSB and ITC coupled with the bus waveguide produced three transmission dips at 1041 nm, 1662 nm, and 2237 nm, which can be seen as narrowband discrete states indicated by the red line. Because of the interference between the continuous state and the discrete states, the whole structure formed three asymmetric Fano resonances at 1033 nm (FR1), 1617 nm (FR2), and 2208 nm (FR3).

_{1}of the ITC, only FR1 had an obvious shift, as shown in Figure 6a. On the contrary, when the refractive index n

_{2}of the SRCSB increased, FR2 and FR3 showed significant redshifts in Figure 6b. Therefore, the independent tuning of the triple Fano resonances was achieved by adjusting the refractive index of the structure. When n

_{1}was increased from 1.06 to 1.12 and n

_{2}was decreased from 1.06 to 1.00, the transmission spectra of the structure were obtained, as shown in Figure 7. In this case, FR1 showed a redshift, while FR2 and FR3 showed blueshifts. Meanwhile, FR1, FR2, and FR3 all had good linearity, and their linear correlation coefficients were as high as 0.99996, 0.99987, and 0.99994 respectively. The sensitivities of FR1 and FR2 were 1082.54 nm/RIU and 1595.48 nm/RIU, as shown in Figure 7b. According to Equations (2) and (3), it can be seen that the sensitivity is approximately proportional to L

_{eff}/m, so the sensitivity of FR3 is larger than those of FR1 and FR2 and is 2259.56 nm/RIU. In this way, the detection of refractive indexes at different positions in the structure, such as the ITC and the SRCSB, was achieved. Comparing the refractive index sensing sensitivity with that of other structures [12,13,19,24,30,33,42,43], as shown in Table 1, the sensitivity of the structure is relatively high.

_{p}is the plasma concentration, and C

_{g}is the concentration of glucose solution. In Figure 8, C

_{p}in the ITC is decreased from 400 g/L to 0 g/L with a step of 100 g/L, and C

_{g}in the SRCSB is increased from 0 g/L to 400 g/L with the same step. It is obvious that FR1 and the other two Fano resonances shifted in the opposite direction. The linear fitting relationships between the concentration and the resonant wavelengths of the triple Fano resonances are shown in Figure 8b. The linear correlation coefficients of FR1, FR2, and FR3 were 0.99993, 0.99989, and 0.99968 respectively, which are almost equal to those of refractive index sensing obtained in Figure 7b. The sensitivity of concentration sensing here was S = ∆λ/∆C, where ∆C is the variation of concentration. Then the sensitivity of FR1 for plasma concentration sensing was 0.198 nm·L/g, and the sensitivities of FR2 and FR3 were 0.195 nm·L/g and 0.260 nm·L/g for glucose concentration sensing. The results above show that time-sharing or simultaneous measurement of multiple parameters was achieved in the structure.

## 4. Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Scheme of the MIM waveguide structure composed of a square ring cavity with a silver baffle, an isosceles triangle cavity, and a bus waveguide with a silver baffle.

**Figure 2.**Transmission spectra of the structure without the silver baffle in the bus waveguide (red line), the bus waveguide with the silver baffle (blue line), and the whole structure (black line).

**Figure 3.**(

**a**–

**c**) Magnetic field patterns of FR1, FR2, and FR3. (

**d**–

**f**) Height expressions of the magnetic field patterns of FR1, FR2, and FR3.

**Figure 4.**(

**a**) Transmission spectra of the structure with different heights (H) of the ITC. (

**b**) Linear relationships between H and the resonant wavelengths of FR1 (blue), FR2 (green), and FR3 (red). (The parameters are t = 10 nm, b = 300 nm, d = 10 nm, a = 10 nm, R = 180 nm, L = 2(a + R), and G

_{1}= G

_{2}= 10 nm.)

**Figure 5.**(

**a**) Transmission spectra of the structure with different radii (R) of the internal circle of the SRCSB. (

**b**) Linear relationships between R and the resonant wavelengths of FR1 (blue), FR2 (green), and FR3 (red). (The parameters are t = 10 nm, b = 300 nm, H = 450 nm, d = 10 nm, a = 10 nm, L = 2(a + R), and G

_{1}= G

_{2}= 10 nm.)

**Figure 6.**(

**a**) Transmission spectra of the structure with different refractive indexes of the ITC (n

_{2}= 1.00). (

**b**) Transmission spectra of the structure with different refractive indexes of the SRCSB (n

_{1}= 1.00). (The parameters are t = 10 nm, b = 300 nm, H = 450 nm, d = 10 nm, a = 10 nm, R = 180 nm, L = 2(a + R), and G

_{1}= G

_{2}= 10 nm.)

**Figure 7.**(

**a**) Transmission spectra of the structure with different refractive indexes of the ITC and the SRCSB. (

**b**) Linear relationships between the refractive index and the resonant wavelengths of FR1 (blue), FR2 (green), and FR3 (red). (The parameters are t = 10 nm, b = 300 nm, H = 450 nm, d = 10 nm, a = 10 nm, R = 180 nm, L = 2(a + R), and G

_{1}= G

_{2}= 10 nm.)

**Figure 8.**(

**a**) Transmission spectra of the structure with different glucose solution and plasma concentrations. (

**b**) Linear relationships between the concentration and the resonant wavelengths of FR1 (blue), FR2 (green), and FR3 (red). (The parameters are: t = 10 nm, b = 300 nm, H = 450 nm, d = 10 nm, a = 10 nm, R = 180 nm, L = 2(a + R), and G

_{1}= G

_{2}= 10 nm.)

Reference | Waveguide Structure | Sensitivity |
---|---|---|

[12] | MIM waveguide with two silver baffles and a coupled ring cavity | 718 nm/RIU |

[13] | MIM waveguide with tooth cavity-coupled ring splitting cavity | 1200 nm/RIU |

[19] | MIM waveguide with a baffle and a circular split-ring resonator cavity | 1114 nm/RIU |

[24] | Two side-coupled semi-ring cavities and a vertical cavity | 1405 nm/RIU |

[30] | Square Convex Ring Resonator (SCRR) with single metallic baffle | 1120 nm/RIU |

[33] | Side-coupled rectangular cavity and rightward-opening semi-ring cavity | 1550 nm/RIU |

[42] | Circular split-ring resonance cavity and double symmetric rectangular cavity | 1180 nm/RIU |

[43] | MIM waveguides coupled with double rectangular cavities | 596 nm/RIU |

This paper | MIM waveguide structure with square ring and triangular cavities | 2260 nm/RIU |

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**MDPI and ACS Style**

Wang, M.; Tian, H.; Liu, X.; Li, J.; Liu, Y.
Multiparameter Sensing Based on Tunable Fano Resonances in MIM Waveguide Structure with Square-Ring and Triangular Cavities. *Photonics* **2022**, *9*, 291.
https://doi.org/10.3390/photonics9050291

**AMA Style**

Wang M, Tian H, Liu X, Li J, Liu Y.
Multiparameter Sensing Based on Tunable Fano Resonances in MIM Waveguide Structure with Square-Ring and Triangular Cavities. *Photonics*. 2022; 9(5):291.
https://doi.org/10.3390/photonics9050291

**Chicago/Turabian Style**

Wang, Mingyu, He Tian, Xing Liu, Jina Li, and Yajie Liu.
2022. "Multiparameter Sensing Based on Tunable Fano Resonances in MIM Waveguide Structure with Square-Ring and Triangular Cavities" *Photonics* 9, no. 5: 291.
https://doi.org/10.3390/photonics9050291