Based on the above results, it is evident that the coupling rate c1
varies periodically with the substrate thickness h, and the period h0
is about 3.5 lm. Interestingly, we find that the period h0 is
determined by the resonant wavelength of plasmonic mode
through h0 = ka/2n, with n = 1.5 being the refractive index of the
substrate and ka = 10.5 lm being the resonant wavelength, which
suggests that c1 is proportional to the light intensity in the vicinity
of graphene. Because the light intensity is the strongest when h
satisfy h = m ka/4n with m being an integer, hence c1 reaches the
maximum value at these substrate thicknesses (e.g., the h are 1.5
and 4.3 lm in the above simulations). In contrast, the light intensity
is nearly zero at h = m ka/2n, causing c1 also decreases to zero
at theses thicknesses (e.g., the h are 3.5 and 7 lm in the above
simulations).