We first compare the numerical result with the analytical one
given by Eq. (1) to demonstrate the validity of the temporal coupled
mode theory. The parameters of the device are set as follows,
the period, height and filling factor of the grating are 150 nm,
100 nm and 0.5, respectively. The thickness and refractive index
of the dielectric spacer are 20 nm and 1.5. The Fermi energy and
the electron relaxation time of the graphene are 0.4 eV and
0.3 ps. The thickness and refractive index of the substrate are
500 nm and 1.5. The metals of the grating and the back reflector
are taken as perfect metals. The numerical absorption spectrum
calculated by finite element method using COMSOL is shown in
Fig. 1(c). An absorption peak is observed at the free space wavelength
of about 10.5 lm, which corresponds to the excitation of
the first order graphene surface plasmonic mode, and the mode
pattern is shown in the inset. We also calculated the absorption
spectrum using Eq. (1) by setting c0 = 1.67 THz, c1 = 0.28 THz, and
plot the result in Fig. 1(c). It is clear that the analytical spectrum
is in good agreement with the numerical one, signifying the behavior
of the device can be well described by temporal coupled mode
theory.