The excitation of wake field plasma waves by a short laser pulse propagating through a parabolic plasma channel is studied. The laser pulse is assumed to be initially chirped. In this regard, the effects of initial and induced chirp on the plasma wake field as well as the laser pulse parameters are investigated. The group velocity dispersion and nonlinear relativistic effects were taken into account to evaluate the excited wake field in two dimension using source dependent expansion method. Positive, negative, and un-chirped laser pulses were employed in numerical code to evaluate the effectiveness of the initial chirp on 2-D wake field excitation. Numerical results showed that for laser irradiances exceeding 1018W=cm2, an intense laser pulse with initial positive chirp generates larger wake field compared to negatively and un-chirped pulses.
