In this paper, we propose a borophene-based double-dielectric-grating structure (BDDGS) to realize the Fano resonance electro-optical modulator and sensor. The Fano resonance originated from the coupling of two resonance modes excited by the upper borophene grating (UBG) and the lower borophene grating (LBG). The coupling mode theory (CMT) is utilized to fit the Fano transmission spectrum. The calculated result fits well with the simulated spectrum. We found the Fano resonance wavelengths exhibit a blue shift with increasing the carrier density of the borophene layer. Further, we utilize this property to achieve a Four-state Fano resonance electro-optical modulator. The working wavelengths of the ON-ON (11), ON–OFF (10), OFF–ON (01), and OFF-OFF (00) states are 1.321 μm and 1.676 μm, respectively. The asymmetric Fano spectra exhibit high sensing sensitivity S=21THz/RIU and figure of merit FOM=3.9RIU−1. Moreover, our proposed structure possesses a slow-fast light effect with the maximum group index are 57.84 and −332.3, respectively. Although several Fano resonance and electro-optical modulators based on two- dimensional (2D) material, like graphene, black phosphorus, and transition metal dichalcogenides (TMDs) are previously reported, this paper designed a borophene-based metamaterial to achieve Fano resonance electro-optical modulator and sensor, because borophene possesses a series of excellent physical and chemical properties, for example, mechanical compliance, high carrier mobility, and optical transparency. Therefore, the proposed borophene-based metamaterial will be beneficial in the fields of high-performance plasmonic sensors, slow light, and electro-optical modulators in the near future.
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