Two-Way Fano Resonance Switch in Plasmonic Metamaterials

A two-way Fano resonance switch in the plasmonic metamaterials has been proposed and experimentally demonstrated. The electrical Fano switch is composed of two concentric spoof localized surface plasmon (LSP) resonators. By adjusting the slit in the inner spoof LSP resonator, two different Fano resonance modes could be supported. By loading a Schottky barrier diode (SBD)across the slit in the inner LSP resonator, both Fano resonance modes can be simultaneously switched when the SBD is forward biased or reverse biased, and their switch status is opposite. Both simulated and measured results agree well at microwave frequencies and verify the two-way Fano resonance switch. The devices could be applied in many applications such as plasmonic circuits, multiway sensing or switching, and so on.

Active metamaterials are promising for the multifunctional systems with tunable, switchable, and non-linear functionalities [27]. For example, to conquer the bottleneck of Fano resonance sensing that the high Q factor Fano resonance is accompanied with an extremely small resonance intensity [28,29], gain-assisted active spoof plasmonic Fano resonance is proposed to enhance both the Q factor and resonance intensity simultaneously [30]. Active Fano resonance switches were also demonstrated. The on-off switching of the Fano resonance of a plasmonic cluster by its incorporation into a polarization rotating liquid crystal device was demonstrated in a voltage-dependent manner [31]. Electrically controlled damping of Fano resonance in a graphene-nanoantenna hybrid device was observed [32]. Active photoswitching of sharp Fano resonances in silicon-implanted terahertz asymmetric metallic split-ring resonator structure was demonstrated, where the strength of the Fano resonance is modulated by changing the optical pump powers [33]. By changing the pH value of the solution environment, the active plasmonic Fano resonance switching is enabled by varying the refractive index of a layer of polyaniline between the Au nanosphere and the Au nanoplate [34]. The Fano resonance generated in Si nanosphere dimers on a VO 2 layer can be actively tuned by utilizing the phase transition of VO 2 with temperature [35]. However, there are still great challenges that are difficult to overcome, such as slow switching speed, high operation voltage, low contrast of modulation, etc. Furthermore, it is impossible to achieve two-way or multiway Fano switches based on the discussed mechanisms.
Here, we investigated an electrically two-way Fano resonance switch in the plasmonic metamaterials, which is composed of two concentric spoof localized surface plasmon (LSP) resonators. It has been demonstrated that there would be two different Fano resonance modes when adjusting the slit in the inner spoof LSP resonator. By loading a Schottky barrier diode (SBD) across the slit in the inner LSP resonator, both Fano resonance modes can be simultaneously controlled (OFF/ON) when the SBD diode is forward biased or reverse biased. Hence, a two-way Fano resonance switch can be realized. Both simulated and measured results agree well at microwave frequencies.

PASSIVE SPOOF PLASMONIC FANO RESONANCE
To understand the physical mechanism of the two-way Fano resonance switch, we first investigate the Fano resonances of two spoof plasmonic Fano resonance Structures A and B. The three-dimensional (3D) schematic of Structure A is illustrated in Figure 1A, which contains two vertically stacked layers. The top layer is the spoof plasmonic Fano resonator, and the bottom layer is a microstrip feeding line. The top view and side view of Structure A are shown in Figure 1B, where the length l of the spoof plasmonic Fano resonator is 52 mm. The width w of the microstrip line is 1.3 mm, and the thickness h of the substrate and the thickness t m of the copper are 0.5 and 0.018 mm, respectively. As demonstrated in Figure 1C, the spoof plasmonic Fano resonator is composed of two concentric spoof LSP resonators. The outer and inner corrugated metallic rings are printed on the dielectric substrate (F4B), whose relative dielectric permittivity is 2.65, and loss tangent is 0.002. The radiuses r 1 and r 2 of the inner and outer corrugated rings are 1.5 and 10.5 mm, respectively. Both the lengths l 1 and l 2 are 2.5 mm, and the groove depths l 3 and l 4 are 5 and 7.5 mm, respectively.
The transmission coefficients (S 21 ) are plotted in Figure 2a, which are obtained by using the commercial software HFSS. The driven modal solver is used. The wave port and the radiation boundary condition are adopted. The minimum mesh size is 0.06 mm. The spoof LSP modes with Lorentzian lineshapes of outer and inner corrugated rings are marked as O 1 , O 2 , O 3 , and I 1 modes. The corresponding resonant frequencies are 1.0, 2.02, 2.78, and 2.52 GHz, respectively. Figure 2b illustrates the 2D E z -field distributions on the xoy plane 2 mm above the spoof LSP resonators, where it can be seen that the spoof LSP modes O 1 -O 3 are dipolar mode (n = 1), quadrupolar mode (n = 2), and hexapolar mode (n = 3) for the outer corrugate ring. The spoof LSP mode I 1 is the dipolar mode (n = 1). For structure A, the resonant peaks are denoted by A 1 , A 2 , A 3 , and A 4 . The corresponding resonant frequencies are 1.03, 1.98, 2.44, and 2.65 GHz, respectively. It can be seen that there exists an asymmetric Fano lineshape between A 2 and A 4 , which stems from the destructive interference of the narrow discrete spoof LSP mode I 1 with the broad continuum state between modes O 2 and O 3 of the outer corrugated ring. Figure 2c illustrates the 2D E z -field distributions on the xoy plane 2 mm above Structure A. It can be clearly observed that the modes A 1 , A 2, and A 4 are corresponding to the spoof LSPs modes O 1 , O 2, and O 3 , respectively, while the resonant peak A 3 corresponds to the spoof LSPs mode I 1 .
Next is structure B, whose 3D schematic is illustrated in Figure 3A. The top view of Structure B is shown in Figure 3B. From Figure 3C, it can be seen that Structure B is also composed of two concentric LSP resonators. The difference with Structure A is that there is a slit in the inner corrugated ring, where the slit is cut at the position of θ = 90 • .
The simulation transmission coefficients S 21 of Structure B, outer corrugated ring, and inner corrugated ring with a slit are given in Figure 4a. The LSP modes are different for the inner corrugated ring and the corrugated ring with a slit. Here, the spoof LSP modes of outer and inner corrugated rings are also marked as O 1 , O 2 , O 3 , and I 1 modes. Figure 4b illustrates the corresponding 2D E z -field distributions on the xoy plane 2 mm above the spoof LSP resonators. The resonant frequencies of the outer corrugated ring are the same, and the spoof LSP modes E zfield distributions are also unchanged, as shown in Figure 4b. It can be seen that the resonant frequency of the inner ring with a slit has changed from 2.52 to 1.76 GHz, as the mode I 1 of the inner ring with a slit is the half-integer LSP mode (n = 0.5). For structure B, the resonant peaks are marked as B 1 , B 2 , B 3 , and B 4 . The corresponding resonant frequencies are 1.12, 1.53, 2.22, and 3.05 GHz, respectively. We can see that there appears an asymmetric Fano lineshape between B 1 and B 3 , which results from the destructive interference of the narrow discrete mode I 1 with the broad continuum state between modes O 1 and O 2 of the outer corrugated ring, and there is no resonance mode between modes O 2 and O 3 of the outer corrugated ring. Figure 4c illustrates the 2D E z -field distributions on the xoy plane 2 mm above Structure B. It can be clearly observed that the modes B 1 , B 3 , and B 4 are corresponding to the spoof LSPs modes O 1 , O 2 , and O 3 , respectively, whereas the resonant peak B 2 corresponds to the mode I 1 .

ACTIVE TWO-WAY FANO RESONANCE SWITCH
Considering the responses of passive Structure A and Structure B, it can be concluded that when there exists a slit in the inner corrugated ring, the Fano resonance appears between the O 1 and O 2 modes, and when there is no slit in the inner corrugated ring, the Fano resonance appears between the O 2 and O 3 modes. Hence, if a switch diode is loaded across the slit, the two Fano resonance modes could be switched. As there is no charge carrier depletion region at the junction, the SBD diode has a shorter recovery time than the PIN diode. For a small signal, the switching time of the SBD diode is only 100 ps. Here, an SBD diode (MACOM MA4E 1317) is used to switch the Fano resonance mode, whose operating bias voltage is 0.6-0.8 V. The optimum bias voltage is 0.75 V. The DC voltage source  is GW Instek linear DC power supplies GPS-1850D. Figure 5a illustrates the schematic of the active two-way Fano resonance switch, where an SBD diode is mounted across the slit in the inner corrugated ring. The capacitance is used to isolate the DC signal, whereas the inductance is used to isolate the AC signal. The fabricated sample is shown in Figure 5b. In the simulation, the SBD is equivalent to an RLC series circuit, where R s is the series resistance, L s is the inductance arising from the metallic contacting strap, and C j is the diode junction capacitance, and the values are 4 , 0.45 nH, and 0.02 pF, respectively. The simulated transmission coefficients S 21 are plotted in Figure 5c. It can be seen that when the SBD diode is forward biased (ON), there is no  slit in the corrugated ring. The structure is equivalent to Structure A, where the second Fano resonance appears. When the SBD diode is reverse biased (OFF), there is a slit in the corrugated ring. The structure is equivalent to Structure B, where the first Fano resonance appears. Hence, a two-way Fano resonance switch could be realized. The sample is measured by using a vector network analyzer (Agilent N5227A). The experimental results shown in Figure 5d agree well with the simulation results. When the diode is ON, the Fano resonance appears between the quadrupolar mode and hexapolar mode. When the diode is OFF, the Fano resonance appears between the dipolar mode and the quadrupolar mode. The measured transmission coefficients are almost 10 dB lower than the simulation results, which may be caused by the higher series resistance R s and the welding quality in the measurements.

CONCLUSION
In summary, we have proposed and experimentally demonstrated an active two-way Fano resonance switch in the microwave frequency. When the SBD diode is forward biased, the second Fano resonance appears between the quadrupole mode and hexapole mode. When the SBD diode is reverse biased, the first Fano resonance appears between the dipolar mode and the quadrupole mode. The experimental results agree well with the simulated results. The Fano resonance switch has advantages such as two-way switches, fast switching speed, and low operation voltage, which could find applications in plasmonic circuits, sensors, devices, etc.

DATA AVAILABILITY STATEMENT
All datasets presented in this study are included in the article/supplementary material.