Dual-Fano resonances and sensing properties in the crossed ring-shaped metasurface

We study dual-Fano resonances and its sensing properties in a crossed ring-shaped metasurface by use of the finite-different time-domain (FDTD) simulation. The results show that the dual-Fano resonances in the proposed crossed ring-shaped metasurface are caused by the interaction among three local surface plasmon resonances (LSPRs), and the spectra of dual-Fano resonances can be tuned by the radius of the circular ring (CR) nanostructure, the distance between the center of the two CRs in x direction, and the polarization of the incident light. Interestingly, single Fano resonance splits into dual-Fano resonances in the case of asymmetric ring structure arrangement or non-y-axis polarized incident or the distance d<120 nm. Moreover, we can also find that the refractive sensitivity in the proposed crossed ring-shaped metasurface can reach up to 1010 nm/RIU and 1300 nm/RIU at Fano resonance peak 1 and Fano resonance peak 2, respectively. These results may play an important role for designing high sensitive plasmonic sensors.

Fano resonance has the asymmetrical spectra caused by the interaction between the continuous mode and discrete mode [36,37], the sharp spectra of Fano resonance makes the strong dispersion appearing at the wavelength of Fano resonance. Thus, Fano resonance is widely used in enhancing sensing, light filed enhancement, optical storage, and so on [38][39][40]. And Fano resonance is studied in a variety of structure, such as metallic waveguides [41,42], dielectric waveguides [43,44], optical gratings [45,46], graphene systems [47][48], and so on. There are also many kinds of metasurface, which can also achieve Fano resonance, such as single nanodisk, dimer and multiparticle oligomers. For the single nanodisk nanostructure, Fano resonance is often caused by introducing arranged defects, such as narrow split gap, cut-out wedge, and so on [49,50].
For dimer and multiparticle oligomers structures, Fano resonance is always caused by the interaction among the closely adjacent metallic nanoparticles in different size or shape [51,52] [57]. However, there are few works about Fano resonance and its sensing properties in the crossed nanostructure metasurface. Different from single nanodisk, separated dimer and multiparticle, the crossed metasurface can form more possible plasmonic resonance modes, so multiple Fano resonances can be achieve in the simple crossed nanostructure metasurface.
In this paper, we proposed a crossed ring-shaped metasurface, and dual-Fano resonances and high sensitivity sensing are also discussed in the proposed metasurface through FDTD simulation method. We find that the dual-Fano resonances can be effectively tuned by the radius of the CR nanostructure, the distance between the center of the two CRs in x and y directions, and the polarization of the incident light. Especially, single Fano resonance splits into dual-Fano resonances through adjusting structural parameters and polarization directions. What is more, the maximum of sensitivity Max[s] = 1010 nm/RIU and Max[s] = 1300 nm/RIU for Fano resonance peak 1 and Fano resonance peak 2 are observed in the proposed crossed ring-shaped metasurface. These research results may play important roles for designing ultra-high sensitive sensors.

Structure Model And Simulation Method
We propose a crossed ring-shaped metasurface as shown in Fig. 1. The metal is chosen to be Au, and the substrate is SiO 2 , the permittivity of Au and SiO 2 reference to the reported articles [58][59][60]. Figure 1(a) shows the schematic diagram of the proposed crossed ringshaped metasurface, and Fig. 1(b) shows the x-y plane view of the proposed metasurface. Px = Py = 400 nm are the length of each cell in x and y directions, respectively. r 1in = 75 nm and r 1out = 100 nm are the inside radius and outside radius for the left RC structure, respectively. r 2in and r 2out are the inside radius and outside radius for the right RC structure, respectively. d is the distance between the center of the proposed two RCs in x direction. The transmission spectra of the proposed crossed ring-shaped metasurface is simulated by use of FDTD simulation method. In our simulation process, the effective area is divided into uniform Yee cells with △x=△y=△z = 1 nm and the △t =△ x/2c, where c is the velocity of light in vacuum [61,62], and the perfectly matched layer (PML) is chosen in this numerical simulation process [63][64][65]. The Gaussian beam incidents from the positive direction of z axis in our simulation.

Results And Discussions
Firstly, we investigate the transmission responses of the proposed crossed ring-shaped metasurface when the polarization of the incident light is x direction as depicted in Fig. 2 (a). We can see that a transmission dip appears at the wavelength of 994.2 nm (red line) when there is only left CR nanostructure arranged on the substrate. The transmission dip is caused by LSPR on the surface of left CR. The other transmission dip appears at the wavelength of 1023 nm (black line), which is caused by LSPR on the right CR.

Interestingly, double Fano resonances can be observed (blue line) when the left and right
CRs are arranged on the substrate as shown in Fig. 2(a). Different from the separated dimer and multiparticle metasurface, the crossed metasurface can form more possible plasmonic resonance modes, so multiple Fano resonances can be achieve in this simple crossed metasurface. Then we study the electric field distribution Ez as shown in  Then we study the dual-Fano resonances as a function of the radius r 2out for the right CR with △r 2 = r 2out -r 2in = 25 nm when the polarization of the incident light is the x direction as depicted in Fig. 3 (a). We can see that Fano resonance shows red shift as the radius r 2out increases from 80 nm to 120 nm. But there is a special case when r 2out = 100 nm, it is because that the symmetric ring-shaped structure when r 2out = 100 nm, so the dual-Fano resonances turn into single Fano resonance. Then we discuss the electric field distribution Ez at 827.4 nm for r 2out = 80 nm, 955 nm for r 2out = 90 nm, 1023 nm for r 2out = 110 nm, and 1045 nm for r 2out = 120 nm as shown in Fig. 3(b)-2(e). Figure 2(b) shows that the electric field are confined at the right side of the crossed nanostructure, and the same symbols of electric charges are distributed on the same CR, it is because that the r 2out for the right CR is so small. As the r 2out = 90 nm for the right CR, the electric field are confined at the left side of the crossed nanostructure. Especially, the inverse symbols of electric charges are distributed on the same CR when r 2out = 110 nm and 120 nm. Thus, we can see that the electric field distribution is completely opposite when the right CR is smaller or bigger than left one. But the dual-Fano resonances can always be observed in the asymmetric case for the proposed crossed metasurface. Thus, we investigate the transmission spectra as a function of the distance d when r 1in = 75 nm, r 1out = 100 nm, r 2in = 65 nm, r 2out = 90 nm and the polarization of the incident light is the x direction. We can see that the transmission dip 1 and dip 2 show blue shift as d increases from 60 nm to 120 nm as shown Fig. 4(a). However, the transmission dip 3 shows red shift as d increases. The most interesting thing is that the transmission dip 2 gradually disappeared and the transmittance for the dip 1 increases with the increasing of the distance d. This is because the additional LSPR mode disappears as the distance d increases. Then we discuss the transmission spectra as a function of θ between the direction of polarization and the x-axis in the x-y plane when r 1in = 75 nm, r 1out = 100 nm, r 2in = 65 nm, r 2out = 90 nm, and d = 60 nm. We can see that the dual-Fano resonances turn into single Fano resonance when the θ increases from 30 to 90 , and the transmission spectra show blue shift with the increasing of θ as shown in Fig. 4(b). These results will provide guidance for the regulation of Fano resonance. Transmission spectra of the proposed crossed metasurface as a function of θ with r 1in = 75 nm, r 1out = 100 nm, r 2in = 65 nm, r 2out = 90 nm, d = 60 nm.
As is well-known, the sharp spectral lines for Fano resonance can effectively enhance the sensitivity of refractive sensing. Thus, we study sensing properties versus refractive index (RI) of external environment in the proposed crossed ring-shaped metasurface when θ = 0 , r 1in = 75 nm, r 1out = 100 nm, r 2in = 65 nm, r 2out = 90 nm and d = 60 nm. We can see that the dual-Fano resonances show red shift when RI increases from 1.00 to 1.04 as shown in Fig. 5(a). We can see that the resonant wavelength (FW) for Fano resonance peak 1 shows a linear increase with the increasing of RI as shown in Fig. 5(b). In order to investigate the sensing performance of the proposed crossed metasurface, we introduce the definition of the sensitivity as s=△λ/△RI, where λ is the FW for Fano resonance peak.  The FW of Fano resonance peak 1 versus RI (c) The FWof Fano resonance peak 2 versus RI.

Conclusions
In summary, we have studied dual-Fano resonances and high-sensitivity sensing performance in the proposed crossed ring-shaped metasurface by use of FDTD simulation method. We can find that the dual-Fano resonances in the proposed crossed ring-shaped metasurface is caused by the destructive interference among three LSPRs (LSPR at the surface of left CR, right CR, and the crossed part at the middle of the left and right CRs).
In addition, we can also see that the spectra of dual-Fano resonances can be effectively tuned by the radius of the CR, the distance between the center of the two CRs in x direction, and the polarization of the incident light. Especially, We can see that the dual-        Transmission spectra of the proposed crossed metasurface as a function of θ with r1in=75 nm, r1out=100 nm, r2in =65 nm, r2out=90 nm, d=60 nm. Figure 5 (a) Transmission spectrum of the proposed crossed metasurface as a function of RI with r1in=75 nm, r1out=100 nm, r2in =65 nm, r2out=90 nm, d=60 nm, θ=0 .
(b) The FW of Fano resonance peak 1 versus RI (c) The FWof Fano resonance peak