  The generalized tight-binding model with exact diagonalization method is
developed to calculate the optical properties of monolayer graphene in the
presence of composite magnetic fields. The ratio of the uniform magnetic field
and the modulated one accounts for a strong influence on the structure, number,
intensity and frequency of absorption peaks, and thus the extra selection rules
that are subsequently induced can be explained. When the modulated field
increases, each symmetric peak, under a uniform magnetic field, splits into a
pair of asymmetric peaks with lower intensities. The threshold absorption
frequency exhibits an obvious evolution in terms of a redshift. These
absorption peaks obey the same selection rule that is followed by Landau level
transitions. Moreover, at a sufficiently strong modulation strength, the extra
peaks in the absorption spectrum might arise from different selection rules.
