  Control of quantum systems via lasers has numerous applications that require
fast and accurate numerical solution of the Schr\"odinger equation. In this
paper we present three strategies for extending any sixth-order scheme for
Schr\"odinger equation with time-independent potential to a sixth-order method
for Schr\"odinger equation with laser potential. As demonstrated via numerical
examples, these schemes prove effective in the atomic regime as well as the
semiclassical regime, and are a particularly appealing alternative to
time-ordered exponential splittings when the laser potential is highly
oscillatory or known only at specific points in time (on an equispaced grid,
for instance).
  These schemes are derived by exploiting the linear in space form of the time
dependent potential under the dipole approximation (whereby commutators in the
Magnus expansion reduce to a simpler form), separating the time step of
numerical propagation from the issue of adequate time-resolution of the laser
field by keeping integrals intact in the Magnus expansion, and eliminating
terms with unfavourable structure via carefully designed splittings.
