Energy shift between two relativistic laser pulses copropagating in plasmas

The interactive dynamics of two relativistic laser beams copropagating in underdense plasmas is studied using a coupled model equation for the relativistic laser propagation. It is shown that the relative phase difference between the two laser pulses plays a significant role in their interaction processes. When the relative phase varies, the two laser beams display different features, such as attraction, repulsion, and energy shift. In particular, energy flow from the phase-advanced beam to the spot domain of the phase-delayed beam is observed when the relative phase difference is between zero and $\ensuremath{\pi}$. When the relative phase is larger than $\ensuremath{\pi}/2$, repulsion is dominant and the interaction gradually becomes weak. When the relative phase difference is smaller than $\ensuremath{\pi}/2$, attraction becomes dominant and, as the phase difference decreases, the phase-advanced beam shifts most of its energy into the spot domain of the phase-delayed beam. These conclusions are verified by our three-dimensional particle-in-cell simulations. This provides an efficient way to manipulate the energy distribution of relativistically intense laser pulses in plasmas by adjusting their relative phase.