  Transport of massless Dirac fermions in graphene monolayers is analyzed in
the presence of a combination of singular magnetic barriers and applied
electrostatic potential. Extending a recently proposed (J Phys. Cond. Matt. Vol
21, 292204 (2009)) analogy between the transmission of light through a medium
with modulated refractive index and electron transmission in graphene through
singular magnetic barriers to the present case, we find the addition of a
scalar potential profoundly changes the transmission. We calculate the quantum
version of the Goos-H\"anchen shift that the electron wave suffers upon being
totally reflected by such barriers. The combined electric and magnetic barriers
substantially modify the band structure near the Dirac point. This affects
transport near the Dirac point significantly and has important consequences for
graphene-based electronics.
