Super High Sensitivity Plasmonic Temperature Sensor Based on Square Ring Shape Resonator with Nanorods Defects

: A super high sensitivity plasmonic temperature sensor via a metal-insulator-metal (MIM) waveguide system is presented in this paper, the waveguide structure is composed of a square ring shape resonator with nanorods defects and a nanodisk resonator. Finite difference-time domain method (FDTD) is used to study the structure’s transmission characteristics and electromagnetic field distributions. Results show that sensitivity will be increased due to the gap plasmonic in the nanorod defect, the nanodisk resonator provides more plasmonic resonant modes for sensing. The positions and intensities of plasmonic resonant modes can be tuned by the radius of nanorod defects and coupling distance. The calculated maximum refractive index and FOM are RIU nm / 4265 and 3500, respectively. sensing, high sensitivity of about C nm o / 1.2 . structure basis for designing sensitivity nano-biosensing, refractive sensing. square convex ring resonator with metallic baffle. Results

In the past decade, plasmonic sensors with different configurations have been designed and investigated. For example, in 2020, Chen et al. reported and investigated plasmonic Fano resonance in MIM waveguide coupled to an isosceles triangle resonator [16]. Cui et al. proposed and studied sharp fano resonance based on the coupling between plasmonic stub and circular cavity resonators [17]. Cselyuszka et al.
investigated multiple Fano-like MIM plasmonic structure base on triangular resonator for refractive index sensing [18]. Yang et al. proposed concentric rings resonator, with a sensitivity of 1060 nm/RIU and FOM of 203.8 are achieved [19]. To achieve high sensitivity, much attention has been focused on the structural configuration, system material, and geometrical dimensions, on one hand, the resonance modes are highly sensitive to the environment refractive index and resonator dimensions, but the fabrication complexity is inevitable. On the other hand, the defects often exist in the manufacturing process. How the defects affect the transmission spectrum and the sensing performance, how the defects affect the coupling efficiency between the resonator and the bus waveguide, further research is still needed.
Motivated by the work [20][21], in this paper, multimodes resonance is numerically realized in a compact plasmonic MIM waveguide system. The proposed structure is composed of two bus waveguides, a square ring shape resonator with sixteen nanorods defects, and a middle nanodisk resonator. The introduction of nanorod defects inside the square ring shape resonator can improve the sensitivity by 33% due to the enhanced gap plasmonic resonance. Results show that the designed plasmonic structure can work as an excellent sensor, a refractive index sensitivity of about 4265 nm/RIU, and a temperature sensitivity of about C nm o / 1.2 are obtained in near-infrared band. The results of this paper may have potential application in on-chip multi-wavelength plasmonic nanosensor and multi-band slow light [22][23][24][25][26].

Geometry and Simulation method
The proposed plasmonic sensor is schematically depicted in Fig. 1, which consists of two MIM waveguides, and a square ring shape resonator with sixteen nanorods defects uniformly distributed, a nanodisk resonator is located in the center of the square ring shape resonator.The center of nanodisk and square ring resonator is located in the orgin point. The geometrical parameters are as follows: the outer and inner lengths of the square ring resonator are 1 L and 2 L , the coupling distance between the square ring resonator and the bus waveguide is s . The radius of the nanodisk resonator and the nanorod defect are R and r . The width of the bus waveguide is nm w 50  . The grey and white parts in Fig.1 represent Ag and air, respectively. In the following FDTD simulations, the metal is silver whose frequency-dependent complex relative permittivity is characterized by the Drude model [27][28]: are applied in the X direction and metal boundary condition was selected in the Y direction.
Based on the standing wave theory, for the square ring resonator, the resonance wavelength is determined by the equation [30]: Where  is the phase shift induced by the reflection, ) ( eff n Re is the real part of the effective refractive index, and k is the order of the resonance mode. eff n can be described as: According to the coupled-mode theory [31], the transmittance can be calculated by : is the normalized frequency,  is the frequency of the incident spp mode, . When there are no nanorod defects, it can be seen five resonances modes (labeled by mode 1, mode 2, mode 3, mode 4, mode 5) of plasmon resonances in the square ring resonator, according to equation 2, the resonant wavelength 0  is proportion to the effective refractive index, the introduction of silver nanorod defects will lead to a larger eff n and make the resonant wavelength redshift. To investigate the physical mechanism of the resonant resonance, Fig. 3 shows the electric field patterns E of the corresponding wavelengths from mode 1 to mode 6, for mode 5, we can see that most of the energy is concentrated in the nanodisk resonator, it can be deduced that mode 5 is the nanodisk resonant mode, for the mode 1, 2, 3, 4, 6, the input SPPs are confined in the silver nanorod defects. The gap plasmonic resonance in nanorods and cavity plasmonic resonance offers more flexible control than a popular square ring resonator. The influence of dimensions of the nanorod defects r on the transmittance of the proposed structure is then investigated. As shown in Fig. 5, when the radius of nanorod defects increases from 12 r nm  to 21 nm with a step of 3 nm, it can be seen that the resonant wavelengths are red-shifted, the increasing r will change the resonant condition and the optical path in the square ring resonator. The transmittance peaks are also changed with the increase of r , this is because the impedance matching condition is changed when varing r . According to equation 3, the Fullwave at half maximum (FWHM) is becoming larger with the increase of r , since the separation region between neighboring nanorods is becoming smaller, which is benefit to the gap plasmonic resonance.
Therefore, the resonant modes can be tuned by the radius of the nanorod defects.
The effect of coupling distance s on the transmittance of the proposed structure is studied in details. As shown in Fig. 6, when the coupling distance s increases from 5 s nm  to 20 nm with a step of 5 nm, it can be seen that the resonant wavelengths are slightly blue-shifted, and the transmittance peaks and FWHM are becoming smaller, the results are in line with the paper [20][21]. Fig. 7 shows the transmission spectra of the plasmonic Fano system with nanodisk radius R , when R decreases from 195 R  to 180 with a step of 5 , it can be seen that the resonant wavelengths are blue-shifted, the transmittance peaks of mode 1, 2, 3, 4 are becoming larger, but the transmittance peak of mode 5 is becoming smaller. The different behaviors are attributed to the different formation mechanisms of mode 5, when R decreases to less than 175 nm, the mode 5 will disappear since the coupling distance between the nanodisk resonator and the inner square ring resonator is larger than 25 nm.
Finally, we investigated the refractive index sensing characteristics of the proposed structure, changing the medium filled in the white part of the structure in Fig 1. When the refractive index is increased from 1 to 1.08 with a step of 0.02, the corresponding transmission spectra are shown in Fig 8 (a), it can be seen that the resonant wavelengths have a considerable red-shifts. The refractive index sensitivity S is an important parameter to evaluate the sensor's attributes, it can be defined as , where  d is the change of the resonance wavelength and dn is the change of refractive index. Fig. 8  , it can be seen that the resonant wavelengths have a red-shifts. Fig. 9 (b) shows the linear relationships between the ambient temperature and the resonant wavelength of modes 1-6. The temperature sensitivity can be defined as where  d is the change of the resonance wavelength and dT is the change of ambient temperature. From Fig. 9 (b , where dT is the change of the transmittance and dn is the change of refractive index. The FOM distribution of the wavelength is shown in Fig.   9 (c), the calculated maximum FOM is 3500. Therefore, a remarkably sensitivity and FOM can be achieved for mode 1 with the proposed nanorod defect structure.The sensing performance of other related structures is compared and the results are shown in Table 2. The sensitivity of the present nanorod defect coupled square ring resonator structure is relatively good compared to previous work [].

Conclusion
In conclusion, we have investigated by FDTD simulation a refractive index and temperature sensor based on a square ring resonator with nanorods defects and a nanodisk resonator. Results show that resonances modes, transmittance peaks, and Sensitivity is increased by 33% for mode 1 when comparing with the structure without nanorod defect. The designed structure can be applied to the areas of on-chip plasmonic nanosensor and the design of multichannel sensor.

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