Tuning Fano resonances of graphene-based gratings

We present a strategy to control Fano resonances in hybrid graphene-silicon-on-insulator gratings. The presence of a mono-or few-layer graphene film allows to electrically and/or chemically tuning the Fano resonances that result from the interaction of narrow-band, quasi-normal modes and broad-band, Fabry-Perot-like modes. Transmission, reflection and absorption spectra undergo significant modulations under the application of a static voltage to the graphene film. In particular, for low values of the graphene chemical potential, the structure exhibits a symmetric Lorentzian resonance; when the chemical potential increases beyond a specific threshold, the grating resonance becomes Fano-like, hence narrower and asymmetric. This transition occurs when the graphene optical response changes from that of a lossy dielectric medium into that of a low-loss metal. Further increasing the chemical potential allows to blue-shift the Fano resonance, leaving its shape and linewidth virtually unaltered. We provide a thorough description of the underlying physics by resorting to the quasi-normal mode description of the resonant grating and retrieve perturbative expressions for the characteristic wavelength and linewidth of the resonance. The roles of number of graphene layers, waveguide-film thickness and graphene quality on the tuning abilities of the grating will be discussed. Although developed for infrared telecom wavelengths and silicon-on-insulator technology, the proposed structure can be easily designed for other wavelengths, including visible, far-infrared and terahertz, and other photonic platforms.