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Actively Controlled Frequency-Agile Fano-Resonant Metasurface for Broadband and Unity Modulation

The active control to the local resonant mode of metasurface is a promising route for improving the operation bandwidth limitation of metasurface. Here, we propose and experimentally demonstrated the active tunabilities in a frequency-agile Fano-resonant metasurface. The metasurface with a pair of asymmetric split ring resonators is integrated with double varactor diodes for active control of the sharp Fano resonance. It is found that the sharp Fano-type spectrum appears due to the near-field interferences between the collective electric and magnetic dipole modes. The physical insight is revealed through local field analysis, multipole decomposition and temporal coupled-mode theory. It is also found that the metasurface can be employed as a broadband and unity modulator. Hopefully, our results could inspire sophisticated electrically controlled photonic devices with novel functions.

Fano resonance appears when a discrete localized state interferences with a continuum band of states [23]. In general, Fano resonance is always accompanied by a high-Q factor and significant local field enhancement, showing a sharp transmission or reflection curves [24,25]. Recently, metasurfaces with so-called bright and dark modes are designed to resemble the original physical mechanism of Fano resonance [26][27][28], i.e., interference between a narrow discrete resonance with a broadband spectral line in a quantum system. The bright and dark modes have different scattering pathways for the incident waves. The bright mode can be directly excited by incident waves in free space, while the dark mode is weakly coupled to incident waves and can be excited through near field coupling with the bright mode by breaking the geometric symmetry [29][30][31]. Fano resonances with high quality factors can be generated through the interference between the new-emergent narrow dark mode and the original continuum mode [32][33][34]. The Fano metasurfaces are generally accompanied with extremely sharp reflection or transmission curves and are widely studied due to the attractive feature of high-Q response [35][36][37][38].
Fano metasurfaces have been proven and considered as a very promising platform for the high-Q response with enhanced lightmatter interactions, but the intrinsic narrow operation bandwidth may significantly hinder them towards practical applications due to their resonant natures. Although it can be optimized by incorporating changeable materials [39][40][41][42] or employing reconfigurable structures [43,44] to extend the bandwidth, this greatly complicates the manufacturing process and also makes it more expensive/difficult to embed into increasingly integrated photonic systems. Here in this paper, we experimentally demonstrated an electrically tunable frequency-agile Fano-resonant metasurface with a pair of asymmetric split ring resonators (ASRRs) configuration. The ASRRs metasurface is integrated with double varactor diodes for active control of the sharp Fano resonance. Remarkable blue shift on the Fano resonance frequency was demonstrated by increasing the bias voltage from 0 to 8 V to electrically tune the capacitances of the varactor diodes. The sharp Fano-type spectrum appears due to the near-field couplings between the collective electric and magnetic dipole modes, and its physical insight is revealed through local field analysis, multipole decomposition and temporal coupled-mode theory (TCMT). Moreover, we also found that the metasurface can be employed as a broadband and unity modulator. The proposed strategy provides an alternative way to overcome the limited bandwidth of conventional meta-devices, which may facilitate the development of low-cost and high-performance active photonic applications.

RESULTS AND DISCUSSION
The schematic of our designed metasurface is shown in Figure 1A. It consists of a pair of asymmetric split ring resonators (ASRRs) with different side lengths. To realize the electrically tunable frequency-agile Fano resonance, double varactor diodes (BBY52-02W, Infineon) are soldered at the middle gap of the ASRRs pair and are biased through four copper wires. The varactor diodes have a series resistance of 0.9 Ω and inductance of 0.6 nH, respectively. Four inductors are located between the bias wires and ASRRs to effectively avoid the cross talk. By applying external bias voltage on the varactor diodes, their capacitance can be significantly changed and the Fano resonance can be dynamically modulated accordingly. The photograph of a fabricated sample is shown in Figure 1B. The metallic pattern is 0.035 mm thick copper on a 1 mm thick Teflon base and is fabricated through standard printed circuit board (PCB) technology. The Teflon substrate was cut to a dimension of 72.14 × 34.04 mm 2 corresponding to the cross-section of a standard waveguide WR284, and simultaneously ensuring the metallic patterns at the center of the substrate. In our experiments, the scattering parameters of the metasurface are measured inside a standard waveguide of WR284, where the TE 10 mode with an electric field polarizing along the y direction is normally incident on the metasurface, and are recorded through a vector network analyzer (AV3629D).
To understand the design strategy of the Fano-resonant metasurface, we would like to firstly consider the spectral response of the coupled metasurface design (see Figure 2A). The calculations were carried out within a perfect electric conductor (PEC) around an air box to simulate a standard waveguide of WR284. In the simulations, PEC boundaries are set along x and y directions, and open boundaries are set along z direction. An excitation source is applied at the boundary of z direction. For a metasurface with only left split ring resonator (SRR), a typical symmetric Lorentz-type resonance dip appears at f 1 (2.99 GHz), while for a metasurface with only right SRR, another typical symmetric Lorentz-type resonance dip occurs at frequency f 2 (2.77 GHz). These resonators show electric dipolar resonances arising from the current induced by the incident electric field in the asymmetric metallic sides of SRR, which are further confirmed by the electric field and surface current distributions shown in Figures 2C,D. Since their resonant frequencies are close to each other, we may expect some interesting phenomena when we set the asymmetric SRRs in a close proximity, resulting from the near-field interference. The red curve in Figure 2A shows the calculated transmission spectrum of the ASRRs metasurface. The near field coupling between the ASRRs leads to an asymmetric Fano-shaped profile with a sharp change between the dip and peak. The destructive interference between the ASRRs also results in a sharp transparency window around frequency f 3 (2.89 GHz), which is similar to the analogy of the electromagnetically induced transparency [28]. Note that the transparency peak of the metasurface is quite sharp with a full width at half-maximum (FWHM) of 0.0558 GHz, reaching a high quality factor of 52. The calculated transmission group delay and phase are shown in Figure 2B, from which we can see that around the transparency peak, the transmission phase experiences an abrupt variation, leading to strong dispersion of the effective parameters and a large group delay of 5.4 ns. To explore the underlying mechanism of the Fano-type resonance and the sharp transmission window, we calculated the surface current and electric field distribution at the transmission peak f 3 (see Figure 2E). The induced surface currents on the ASRRs are oscillating in-phase, forming a collective magnetic mode M z . This new emergent mode M z , as a non-radiative dark state (sharp discrete mode), is weakly coupling with the incident electromagnetic field, and destructively interfering with the background electric dipole mode P y (broadband continuum mode), resulting in the sharp transparency window.
To further understand the near-field coupling mechanism of the metasurface, we calculated the contributions of various multipole moments induced in the metasurface. The electric and magnetic dipole moments of the metasurface can be quantitatively evaluated with the following formula [45].
where j is the current density, ω is the angular frequency, and c is the speed of light in vacuum. The multipole moments can be calculated by integrating spatially distributed current density extracted from the simulation. The calculated normalized magnitude and the corresponding phase of the electric dipole moment P y and the magnetic dipole moment M z are presented in Figures 3A,B, respectively. We can find that the electric dipole P y , as a bright mode resonance, shows strong scattering over the entire interesting frequency band, indicating that the ASRRs metasurface strongly couples to the y-polarized electric field component in the waveguide. The collective oscillations of the electric dipoles can be considered as a broadband continuum mode. Around the transparency peak frequency f 3 , the P y is significantly suppressed, while the M z is excited and enhanced to a similar magnitude as P y , and the phase difference between the P y and M z is about 180°, which further confirms the fact that these two modes interference destructively, and their scattering cancellation results in the non-radiating configuration and the sharp transparency window. We notice that the collective magnetic dipole mode cannot be directly excited by the incident wave, as the metasurface is placed in a standard rectangular waveguide where only the fundamental TE 10 mode can propagate in the frequency band of interest. However, the collective magnetic dipole mode can be excited through near-field coupling, leading to the collective oscillation of the ASRRs and the suppression of electric dipolar mode, and forming the dark mode resonance.
To quantitatively evaluate the interaction between the incident wave and the metasurface, we also employed TCMT to analyze the mode coupling between the collective electric and magnetic dipoles. The transmission spectrum of the metasurface excited by a monochromatic wave can be expressed as below [46,47].
It can be found that the ω 1 and ω 2 correspond to the dip of electric dipole moment P y (as bright mode) and the peak of magnetic dipole moment of M z (as dark mode), respectively, ( Figure 3A), indicating that our metasurface systems are dominated by these two modes. For the collective electric dipole mode, the radiative decay rate, Γ e1 , is about 56 times larger than the non-radiative decay rate, Γ i1 . Both the radiative and non-radiative decay rate of collective magnetic dipole mode, Γ e2 and Γ i2 are much less than Γ e1 and Γ i1 , so they are negligible. The frequency interval between the two transmission dips of our metasurface is only 0.15 GHz, since the coupling coefficient κ is much less than the resonant frequencies, ω 1 and ω 2 , and even the radiative decay rate, Γ e1 . The TCMT accurately predicts the transmission spectrum of the metasurface, as shown in Figure 4.  The tunabilities of the metasurface can be understood as a LC circuit with changeable capacitances. The electric resonance frequency is determined by ω (LC) −1/2 . So the resonance frequency of SRR and the Fano-type resonance frequency can be manipulated significantly by applying voltage to alter the capacitance of varactor diodes. Next, the transmission properties of the SRR alone under different bias voltages are investigated. The measured and calculated transmission spectra of the single SRR with different voltages (capacitances in simulations) are shown in Figure 5. As the bias voltage gradually increases from 0 to 8 V, the capacitance of the varactor diode decreases from 2.63 to 0.76 pF, and the corresponding transmission spectrum undergoes a remarkable blue shift; the experimental resonant frequency of the left SRR alone undergoes a blue shift of 0.22 GHz from 3.09 to 3.31 GHz (see Figure 5A), and similarly, the experimental resonant frequency of the right SRR alone undergoes a blue shift of 0.21 GHz from 2.93 to 3.14 GHz (see Figure 5B). The  To actively control the Fano-type resonance, double varactor diodes are then integrated into the ASRRs metasurface system. The dynamic modulation on Fano resonance of the frequencyagile metasurface is illustrated in Figure 6. When no voltage is applied, the measured Fano resonance peak occurs at 2.98 GHz (see Figure 6A). As the bias voltage gradually increases from 0 to 8 V, the Fano resonance peak gradually shifts from 2.98 to 3.2 GHz, exhibiting a blue shift of 0.22 GHz. Although there is a small amplitude variation, the significant sharp transmission feature is preserved. Meanwhile, the transmission dips of the Fano resonance also exhibit blue shifts of 0.2 and 0.22 GHz, respectively. The calculated results ( Figure 6B) show good agreement with our measured results. It is worth mentioning that the lower frequency dip completely exceeds the upper frequency dip when the applied voltage is changed from 0 to 8 V, thanks to the sharp dispersion characteristic of Fano resonance. It indicates that our metasurface can be employed not only for a frequency-agile device, but also for a broadband and unity amplitude modulator.
To show the amplitude modulation performance of our metasurface, we here plot the transmission with different bias voltages, as shown in Figure 7. Remarkable modulation on transmission can be realized through electric biasing at several frequency points. For example, the measured transmission curves at three selected frequencies of 2.89, 3.10 and 3.32 GHz with different voltages are plotted. As the voltage changes from 0 to 8 V, the transmittance at 2.89 GHz monotonously increases from −19.31 dB to −1.63 dB (red curve), while at 3.32 GHz monotonously decreases from −0.59 dB to −16.29 dB (blue curve), showing a remarkable modulation performance. In particular, the transmittance at 3.10 GHz (green curve), shows a growing trend from −14.31 dB to −1.16 dB with the voltage increased from 0 to 4 V, while a downward trend from −1.16 dB to −19.62 dB when further increasing the voltage to 8 V. Note that although our results were obtained in a waveguide system, the similar modulation performance can also be achieved with periodic structures in free space.

CONCLUSION
In conclusion, we have experimentally demonstrated the active tunabilities in a frequency-agile Fano-resonant metasurface. The sharp Fano resonance can be dynamically modulated by integrating a pair of varactor diodes in the metasurface. We found that the non-radiative collective magnetic dipole mode was excited in our metasurface and its physical insight is uncovered through local field analysis, multipole decomposition and TCMT. We also found significant manipulation on both frequency tuning and amplitude modulation by applying bias voltage on the varactor diodes. The demonstrated frequency-agile Fanoresonant metasurface is promising for realizing sophisticated electrically controlled microwave devices with novel functions, which may facilitate the development of high-performance active photonic applications in, e.g., smart sensing or signal processing.

METHODS
Numerical Simulation: Numerical simulations are carried out using the finite-element frequency-domain solver. The metallic pattern with a conductivity of 5.8 × 10 7 S/m is standing on a Teflon substrate with a relative permittivity of 2.65 and a tangent loss of 0.0004. In the simulations, PEC conditions are applied in both the x and y directions and open boundaries are set along z direction. An excitation source is applied at the boundary of z direction. The multipole moments P y and M z can be calculated by integrating spatially distributed current density extracted from the simulation utilizing the commonly used formulas (Eqs. 1, 2).
Experiments: The printed circuit board (PCB) technique was used to fabricate the metallic ASRRs pattern. The Teflon substrate was cut to a dimension of 72.14 × 34.04 mm 2 corresponding to the cross-section of a standard waveguide WR284, and simultaneously ensuring the metallic patterns at the center of the substrate. In the measurements, the sample was placed inside a WR284 rectrangular waveguide, and was measured through a vector network analyzer (AV3629D).

DATA AVAILABILITY STATEMENT
The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding authors.

AUTHOR CONTRIBUTIONS
QF, YF, and FZ conceived the idea and guided the research. RY designed the metasurface, characterized the samples, and wrote the article. JX, WZ and WC contributed to the final version of the article. All authors discussed the results and commented on the paper.