  An electromagnetic pair-creation cascade seeded by an electron or a photon in
an intense plane wave interacts in a complicated way with the external field.
Many simulations neglect the vector nature of photons by including their
interaction using unpolarised cross-sections. After deriving rates for the
tree-level processes of nonlinear Compton scattering and pair creation with an
arbitrary linearly-polarised photon in a constant-crossed field, we present
results of numerical simulations that include the photon's vector nature. The
simulations of seed electrons in a rotating electric field of optical frequency
on the one hand support the approximation of using unpolarised cross-sections
for tree-level processes, which predicts the same number of created particles
when using polarised cross-section to within around 5 percent. On the other
hand, these simulations show that when the polarisation of the photon can be
influenced by its environment, the asymmetry in the polarisation distribution
could be used to significantly increase the rates of each process.
