Raman Amplification with a Flying Focus

We propose a new laser amplifier scheme utilizing stimulated Raman scattering in plasma in conjunction with a “flying focus”—a chromatic focusing system combined with a chirped pump beam that provides spatiotemporal control over the pump’s focal spot. Pump intensity isosurfaces are made to propagate at $v=-c$ so as to be in sync with the injected counterpropagating seed pulse. By setting the pump intensity in the interaction region to be just above the ionization threshold of the background gas, an ionization wave is produced that travels at a fixed distance ahead of the seed. Simulations show that this will make it possible to optimize the plasma temperature and mitigate many of the issues that are known to have impacted previous Raman amplification experiments, in particular, the growth of precursors.

Figure 1

A Negatively linearly chirped pump combined with a chromatic focusing system causes the high-intensity focus to propagate backward at $v\approx -c$ when the pump duration is $2L/c$, where $L$ is the distance between the foci of the pump’s bandwidth extrema.

Figure 2

Results of three-wave model simulations. (a) With the flying focus, the pump first reaches high intensity at the right edge, where ionization is initialized. Constant intensity moves at $v=-c$ as different colors converge to different locations, so the ionization wave propagates at a nearly fixed distance ahead of the injected seed pulse. Ideal plasma amplifier behavior is observed. (b) When the pump is collimated within the interaction region and above threshold for ionization, the seed encounters higher temperatures along nearly its entire path, which reduces growth via increased Landau damping. (c) With a collimated beam as in case 2, but holding $T_e$ fixed to be similar to case 1, spontaneous SRS grows during the long time in which the pump propagates across the ionized plasma. Premature pump depletion degrades the resulting seed amplification. FFRA case 1 with noise initialized at the same level did not produce such precursors.

Figure 3

(a) In case 1, the temperature encountered by the seed was nearly constant everywhere because of the ionization wave propagating ahead of the seed. In case 2, the seed encountered progressively higher temperatures because each slice of plasma was heated for a longer duration. Case 3 used the flying focus (like case 1), but delayed the seed injection by 3 ps, which shows that $T_e$ is tunable. Case 4 used a collimated pump (like case 2), but $T_e$ was artificially fixed to be similar to case 1; this case illustrates the negative effect of precursor growth. (b) The electron plasma wave damping is minimized around $T_e\approx 40\mathrm{eV}$, so the flying focus Raman amplification scheme can be tuned to operate close to this temperature.