Photon frequency up-shifting by an amplified plasma density wake due to two co-propagating laser pulses

An analytical study of significant photon acceleration (frequency up-shift) in a plasma density wake produced by two laser pulses in the mildly relativistic and linearized regime is presented. The wake amplitude is amplified and its phase controlled using two coaxially, co-propagating laser pulses, which are considered to be identical but separated by a fixed time. A third probe pulse, with a variable delay, is considered as ``test particle'' or quasi-photon propagating through the amplified density wake, which experiences significant photon acceleration because of the local temporal and spatial variation of the permittivity. The evolution of the ``photon'' is studied using Hamiltonian theory. The significant frequency up-shift is much larger than that produced by the wake of a single relativistic laser pulse in the highly relativistic nonlinear wake regime. Our study demonstrates that the inter-pulse separation between the ``controlling'' pulse and the ``driver'' pulse, producing the amplified density wake, can provide an additional degree of freedom for tuning the maximum up-shift of the probe photon frequency.