Frequency shifts induced in laser pulses by plasma waves

An analytical theory is developed that describes how a radiation pulse is modified as it propagates through a plasma with arbitrary temporal and spatial density variations. Expressions are derived for the shifts induced in both the frequency and the wave number of the radiation pulse. The possibility of upshifting the frequency of the laser pulse using plasma waves is analyzed. It is found that maximum shifts occur when the phase velocity of the plasma wave is equal to the group velocity of the laser pulse. Nonlinear analysis of laser propagation in underdense plasmas (${\mathrm{\omega }}_{\mathit{p}}^2$/${\mathrm{\omega }}^2$≪1, where ${\mathrm{\omega }}_{\mathit{p}}$ is the plasma frequency and ω is the laser frequency) shows that the frequency shift scales asymptotically as the square root of the propagation distance. Furthermore, it is shown that the laser power remains constant as the pulse propagates through the plasma.