# Enhanced FANO Structure Based on Tip-Field-Enhancement Theory
## 1 Introduction  
Metasurfaces are 2D arrays that consist of a series of elements that can be used, for example as filters, modulators, sensors, and vortex-beam generators [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13]. Nevertheless, a very-high-Q factor usually cannot be achieved on a metasurface with planar structures. A high-Q factor is essential to many devices since it leads to better frequency selectivity, which can enable the detection of narrow-band signals from noise. A high-Q resonator can also be used as a frequency probe. The complex biological molecules of different structures usually have different resonant frequencies, and using sharp frequency probes, one can distinguish them from one another. Such a method is very useful, especially when the resonant frequencies of the two different molecules to be tested are close to each other. Unlike dipole structures and LC resonant structures that have low-Q factors, FANO is a group of metasurfaces that can reach high-Q resonances, usually based on asymmetric structures [14; 15; 16]. For example, if a metal ring is cut asymmetrically, it makes up a FANO structure [14; 17; 18]. Besides two individual broad-band dipole resonances, a narrow-band FANO resonance is introduced between the frequencies of the former ones. The upper and lower arcs act as two individual dipole resonators. The gap between the arcs induces coupling into the structure thus the resonances could interfere with each other [19; 20]. The two dipole resonances will affect each other remarkably provided that the coupling is strong enough. At FANO resonant frequency, the current flowing at the two arcs will shift from out-phase to in-phase. Moreover, the current will increase a lot at FANO resonant frequency compared with other ones with frequencies nearby. Out-phased current will counteract and make THz wave propagate unencumbered through the chip. However, in-phase current will strengthen themselves and neutralize the stimulation, thus caused transmission zero point. Furthermore, stronger coupling will cause the current phase shift in a narrower band, which means strong coupling forms high Q resonance. FANO resonance can also be introduced by using many other asymmetric structures can also introduce FANO resonance. Rectangular asymmetrically split rings can also perform this task [21]. Not only the coupling inside the ring but also the one between the asymmetric rings can make up FANO structures and lead to high-Q resonances [22]. The asymmetric structures lead to asymmetric charge distribution and excite unbalanced current mode, causing strong destructive interference with input THz wave, resulting in FANO resonances [19; 20]. The impact of conductivity on metal FANO structures is studied [23]. Materials other than metal that can be used in FANO structures are proposed, including a nanoscale subwavelength dielectric resonator array[24], an asymmetric ferroelectric wire pair [25] in order to achieve a high-Q factor that can expend the slope of application for all-dielectric meta resonators. Active FANO structures working in the terahertz and the infrared band were also investigated, allowing for a tunable and high-Q factor [26; 27]. FANO structures of different shapes have also attracted much attention [28; 29]. Besides high-Q resonance, other features, such as low loss, were also proposed by scholars using asymmetric split-ring resonators in the microwave band [22]. However, most of the methods used to increase the Q factor are complex or the structures are difficult to fabricate. Moreover, it is difficult for FANO structures to achieve high-Q factor and high resonance intensity at the same time, which may be useful for sensors. A high-Q FANO structure [17] was proposed reaching up to 50 Q factor, but its resonance intensity is less than 6 dB, which limits its application in microfluidic sensors, because the resonance-frequency drift caused by liquid flow beneath the structure does not lead to a huge transmission difference in a given frequency due to its low resonance intensity.