  We study the inelastic scattering of two-dimensional massless Dirac fermions
by an inhomogeneous time-dependent driving field. As a physical realization we
consider a monolayer graphene normally illuminated with a circularly polarized
laser of frequency $\Omega$ in a given region. The interaction Hamiltonian
introduced by the laser, being periodic in time, can be treated with the
Floquet method which naturally leads to a multi-channel scattering problem. We
analyze planar and circular geometries of the interface separating the
irradiated and non-irradiated regions and find that there is an anomalous
Goos-H\"anchen shift in the inelastic channel. The latter is independent of the
amplitude of the driving while its sign is determined by the polarization of
the laser field. We related this shift with the appearance of topological edge
states between two illuminated regions of opposite chiralities.
