  We show that the application of circularly polarized electromagnetic
radiation on the surface of a Weyl semi-metal can generate states at that
surface. These states can be characterized by their surface momentum. The
Floquet eigenvalues of these states come in complex conjugate pairs rather than
being equal to $\pm 1$. If the amplitude of the radiation is small, we find
some unusual bulk-boundary relations: the Floquet eigenvalues of the surface
states lie at the extrema of the Floquet eigenvalues of the bulk system, and
the peaks of the Fourier transforms of the surface state wave functions lie at
the momenta where the bulk Floquet eigenvalues have extrema. For the case of
zero surface momentum, we can analytically derive scaling relations between the
decay length of the surface states and the amplitude and penetration length of
the radiation. For topological insulators, we again find that circularly
polarized radiation can generate states on the surfaces; these states have much
larger decay lengths than the surface states which are present even in the
absence of radiation. Finally, we show that radiation can generate surface
states for trivial insulators also.
