  We show that, on general theoretical grounds, transmission of light in
graphene always presents a non-vanishing minimum value independently of any
material and physical condition, the transmission coefficient being higher in
the presence of a substrate, and getting increasing when QED corrections higher
than alpha come into play. Explicit numerical calculations for typical cases
are carried out when an external magnetic field is applied to the sample,
showing that, in epitaxial graphene, a threshold effect exists leading to a non
trivial minimum transmission, for a non vanishing light frequency, only for
field values larger than a critical one, both in the large and in the
intermediate chemical potential regime. Such a threshold effect manifests even
in the maximum Faraday rotation polarization of light, which is substantially
controlled by the applied magnetic field. Instead, more transmission minima in
suspended graphene enters in the considered light frequency region for
increasing magnetic field, displaying an effective shift of frequency bands
where the sample gets more or less absorptive with a suitable tuning of the
external field. Two transition regions in different magnetic field ranges are
found, where the shift effect towards higher frequency values occurs both in
the transmission coefficient and in the Faraday rotation angle. Potential
technological application of the results presented are envisaged.

Mesoscale and Nanoscale Physics;Materials Science;Optics