  We present theoretical studies of above threshold ionization (ATI) using
sculpted laser pulses for noble gas atoms. The time-dependent Schroedinger
equation is solved to calculate the ATI energy and momentum spectra, and a
qualitative understanding of the electron motion after ionization is explored
using a classical model that solves Newton's equation of motion. Results are
presented for Gaussian and Airy laser pulses with identical power spectra, but
differing spectral phases. The simulations show that the third order spectral
phase of the Airy pulse, which can alter the temporal envelope of the electric
field, causes changes to the timing of ionization and the dynamics of the
rescattering process. Specifically, the use of Airy pulses in the ATI process
results in a shift of the Keldysh plateau cutoff to lower energy due to a
decreased pondermotive energy of the electron in the laser field. Additionally,
the side lobes of the Airy laser pulse change the number and timing of
rescattering events, which results in changes to the high-order ATI plateau.
Our results also show that laser pulses with identical carrier envelope phases
and nearly identical envelopes yield different photoelectron momentum
densities, which are a direct result of the pulse's spectral phase.
