The need for low cost, compact, high- power laser systems with their applications in medicine and high energy physics is growing rapidly. Counter propagating laser pulses amplification promise a breakthrough by the use of much smaller amplifying media, that is, millimeter plasma scale. The full-wave solution for the two laser pulses interact in almost homogenous or plasma channel is conducted along with particle-in-cell simulation for the same pulses parameters. Motivated by the promise of reduced cost and complexity of the intense lasers, the amplitudes of laser pulses are taken to be small (a0 < 1). The growth rate of the seed pulse and the dephasing limitations are calculated. The results show that the energy is transferred from the pump pulse to the seed pulse effectively depending on the length of amplification and the isolation of the limiting conditions. A wide variety of system parameters such as frequency of laser pulses, plasma density matched to three waves interaction, and intensity of the pump wave and seed wave are studied. The influence of plasma and pulses parameters on simulation results are thoroughly investigated using a moving window technique and are compared with theoretical and numerical predictions. The comparison shows that the numerical full wave solution is very sensitive to any plasma density changes near the entrance of the pump pulse into the plasma.
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