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Abstract
The Fano profile inspired by bound states in the continuum (BICs) has emerged as an effective approach to obtain high quality factor (QF) resonances. However, achieving polarization-independent high QF Fano resonances through the excitation of BICs is still challenging. Herein, we demonstrate that dual-band polarization-independent high QF Fano resonances can be realized by using a twisted tetrameric nanohole slab (TTNS). By twisting the nanoholes of the tetramerized slab, two quasi-BICs can be transformed into dual-band high QF Fano resonances due to the Brillouin zone folding as well as the symmetry breaking from ${C_{4v}}$ to ${C_{2v}}$ of the structure. The variation of the twist angle ($\theta$) significantly alters the location of the Fano resonance in the longer wavelength, but it has slight influence on the Fano resonance in the shorter wavelength. A larger QF corresponds to a larger average electric-field enhancement-factor (AEE) for both of the Fano resonances, but the QF of the Fano resonance at the longer wavelength is more robust to the variation of $\theta$ due to its larger scaling rule as ${\rm QF}\sim|\theta {|^{- 6}}$. According to multipole decompositions, Fano resonances at the longer and shorter wavelength correspond to toroidal dipole (TD) mode and hybrid TD-magnetic quadrupole (MQ) mode, respectively. In addition, both the two Fano resonances survive even if the structural parameters are significantly altered, and they exhibit polarization-independent features because the rotational symmetry of the structure can be maintained as $\theta$ is varied.
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