A Plasmonic Structure of Fano Resonance in the MIM Waveguide with r-Shaped Resonator for Refractive Index Sensor

A plasmonic structure of metal-insulator-metal (MIM) waveguide consisting of a single baffle waveguide and an r-shaped resonator is designed to produce Fano resonance. The finite element 16 method uses the finite element method to analyze the transmission characteristics and magnetic 17 field distributions of the plasmonic waveguide distributions. The simulation results exhibit two 18 Fano resonances that can be achieved by the interference between a continuum state in the baffle 19 waveguide and a discrete state in the r-shaped resonator. The Fano resonances can be simply tuned 20 by changing geometrical parameters of the plasmonic structure. The value variations of 21 geometrical parameters have different effects on sensitivity. Thus, the sensitivity of the plasmonic 22 structure can achieve 1333 nm/RIU, with a figure of merit of 5876. The results of the designed 23 plasmonic structure offer high sensitivity and nano-scale integration, which are beneficial to 24 refractive index sensors, photonic devices at the chip nano-sensors, and biosensors applications. This paper designs a plasmonic structure of a MIM waveguide consisting of a baffle waveguide 247 and an r-shaped resonator to produce Fano resonance and investigate its Fano transmission 248 characteristics using the Finite Element Method. Two Fano resonances can be produced and tuned 249 by changing the geometrical parameters of the plasmonic structure. The value variations of 250 coupling distance, baffle width, height of the rectangular resonator, and outer radius of the quarter- 251 ring resonator have different effects on the sensitivity. Thus, the maximum sensitivity can achieve 252 1333 nm/RIU, with a FOM of 5876. In addition, this plasmonic structure also has the ability of 253 sucrose concentration sensing. Based on these results, the designed plasmonic structure has prospective applications in refractive index nanosensors, nano-photonic devices, and biosensors.

Surface plasmon polaritons (SPPs), which originate from the interaction of incident photons and 56 free electrons on the metal surface, propagate along with the metal-dielectric interface and have 57 the potential to overcome the light diffraction limit, localization of light in subwavelength, and 58 high level of integration capability [1][2][3]. SPPs have applications in optical devices such as 59 switches [4,5], sensors [6][7][8][9], integrated photonic devices [10], demultiplexers [11], and filters 60 [12,13]. One of the greatly pledging waveguide structures is the metal-insulator-metal (MIM) 61 waveguide, which has excesses such as low bending loss, simple structure, long propagation 62 distance, deep sub-wavelength confinements, and easy integration [14][15][16][17][18]. Fano resonance is a 63 fundamental resonance phenomenon excited by the interference between a continuum state and a 64 discrete state and typically has sharp resonance peaks and asymmetrical line shapes [19,20]

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The plasmonic structure of the MIM waveguide consists of a single baffle waveguide and an r-86 shaped resonator is schematically designed in Fig. 1. The r-shaped resonator is formed of a 87 rectangular resonator and a quarter-ring resonator. The width W of the bus waveguide and r-shaped 88 resonator is set at 50 nm to assure that only the fundamental transverse magnetic mode (TM 0 ) 89 mode exists in the MIM waveguide [25]. The width of the baffle is S, the coupling distance 90 between the bus waveguide and the r-shaped resonator is g, the height of the rectangular resonator 91 is H, and the effective radius of the quarter-ring resonator is defined as R'=(R+R0)/2, where R and R0 92 are the outer and inner radii of the quarter-ring resonator. 176 nm, as shown in Fig. 6b. Transmission spectra of the plasmonic structure for different outer radius 177 R of the quarter-ring resonator are shown in Fig. 7a. As the increasing value of R, the transmission 178 of FR 1 and FR 2 gradually decreases, whereas the resonance wavelength of FR 1 and FR 2 produce 179 obvious redshifts from 700 nm to 755 nm and 1225 nm to 1340 nm shown in Fig. 7b. It is also 180 seen that the shift of FR 2 is also more significant than that of FR 1 .

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where Δλ is the resonance wavelength shift, Δn is the change of the refractive index, T is the 195 transmittance, and ΔT is the transmittance change induced by Δn at a fixed wavelength [32].

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The transmission spectra of the plasmonic structure with different refractive indices are shown 197 in Fig. 8a, wherein the refractive index is enhanced from 1.00 to 1.12 with an interval of 0.03, and 198 the other parameters are set as R=200 nm, R0=150 nm, H=300 nm, S=10 nm, and g=10 nm. From

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To prove that the designed plasmonic structure can be applied for biosensors, we study sensing

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He Tian has contributed to Supervision, Funding acquisition, review, and editing manuscript.  The schematic and geometrical parameters of the designed plasmonic structure Figure 2 Transmission spectra of the single ba e waveguide (black line), the single r-shaped resonator (red line), and the entire structure (blue line)

Figure 3
Magnetic eld intensity distributions of the plasmonic structure at a λ=720 nm (FR 1 peak), b λ=735 nm (FR 1 dip), c λ=1265 nm (FR 2 peak), and d λ=1305 nm (FR 2 dip) Figure 4 a Transmission spectra of the plasmonic structure with different coupling distances g, b Relationships between Fano resonance wavelengths and different values of g  Sensitivities of the plasmonic structure on FR 1 and FR 2 for the different parameters at a the coupling distances g, b the ba e widths S, c the height of rectangular resonator H, and d the outer radius of the quarter-ring resonator R Figure 10 FOM for different refractive indices Figure 11 a Transmission spectra of the plasmonic structure with the different refractive indices of sucrose solution concentrations, b Relationships between Fano resonance wavelengths and the refractive indices