  Laser-driven grating type DLA (Dielectric Laser Accelerator) structures have
been shown to produce accelerating gradients on the order of GeV/m. In simple
$\beta$-matched grating structures due to the nature of the laser induced
steady-state in-channel fields the per period forces on the particles are
mostly in longitudinal direction. Even though strong transverse magnetic and
electric fields are present, the net focusing effect over one period at maximum
energy gain is negligible in the case of relativistic electrons. Stable
acceleration of realistic electron beams in a DLA channel however requires the
presence of significant net transverse forces. In this work we simulate and
study the effect of using the transient temporal shape of short Gaussian drive
laser pulses in order to achieve suitable field configurations for potentially
stable acceleration of relativistic electrons in the horizontal plane. In order
to achieve this, both the laser pulse and the grating geometry are optimized.
Simulations conducted with the Particle-In-Cell code VSim 7.2 are shown for
both the transient and steady state/long pulse case. Finally we investigate how
the drive laser phase dependence of the focusing forces could affect a
potential DLA-based focusing lattice.
