Spoiling of tunability of on-substrate graphene strip grating due to lattice-mode-induced transparency.

We report a prediction of the optical effect apparently not discussed earlier. As known both from theory and experiment, the gratings of flat graphene strips lying on dielectric substrates display moderate-Q resonances on the strip plasmon modes in the H-polarization case. In the plasmon resonances, high reflectance and absorbance are observed. These characteristics are tunable with the aid of the graphene chemical potential, which controls the plasmon-mode frequency. However, if this frequency coincides with the high-Q lattice-mode frequency, a narrow-band regime of electromagnetically induced transparency (EIT) appears. A new point in our finding is that, in the EIT regime, the tunability of the reflectance and absorbance of a grating of narrow graphene strips get spoiled profoundly. This is established using a full-wave meshless code based on the method of analytical regularization, which leads to a Fredholm second-kind matrix equation that guarantees the code convergence. Numerical results are presented for the strip width and period, having the microsize dimensions so that all resonances lie in the THz range. However, the same effect takes place in the infrared range for narrower strips and smaller periods. The lattice modes are caused by the periodicity and can have ultra-high Q-factors; however, they do not exist if the substrate is absent. The loss of tunability at EIT is explained by the lattice-mode field pattern, which has deep E-field minima at the strips.