Abstract
The self-steepening of laser pulses with intensities in excess of 1018 W cm-2 and with typical durations shorter than 30 fs propagating in underdense plasmas is examined by resorting to the framework of photon kinetics. Thresholds for self-steepening at the back/front of short laser pulses are determined, along with the self-steepening rates, and the connection between self-steepening, self-compression and frequency chirps is established. Our results are illustrated with particle-in-cell simulations, revealing the key physical mechanisms associated with the longitudinal laser dynamics, critical for the propagation of intense laser pulses in underdense plasmas.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. In the presence of an intense and short laser pulse, the electrons in an underdense plasma quiver with relativistic velocities and are violently pushed away from the laser, strongly modifying the plasma refractive index. The modified plasma refractive index can, in turn, transform the laser pulse intensity profile significantly. The plasma can act as an optical fiber, which may be used to focus, or to guide, the laser pulse beyond the Rayleigh length in the transverse direction, while compressing it in the longitudinal direction. Ultimately, the longitudinal compression may lead to the formation of ultra-intense single cycle pulses.
Main results. An important mechanism closely connected with single-cycle laser pulse generation is self-steepening, i.e. the asymmetric evolution of the laser intensity profile. In this work we investigate self-steepening analytically using photon kinetic theory, where the laser pulse is described by its Wigner transform. We have identified the conditions for the onset of self-steepening in conditions which are directly relevant for state-of-the-art experiments. Moreover, we have interpreted self-steepening as an asymmetric longitudinal self-focusing, establishing a link between self-steepening and optical shock formation.
Wider implications. Our analytical formalism can be readily generalized to include transverse laser dynamics, thereby contributing to a consistent picture of the evolution of laser pulses, and opening the way for the design of experiments that optimize self-steepenening for laser wakefield acceleration, and for the formation of single cycle few-fs laser pulses.
Figure. In the photon kinetic theory, light waves are represented by a classical photon distribution function which corresponds to the Wigner transform of their electromagnetic fields. This figure shows the Wigner transform of the laser pulse intensity profile after interacting with the plasma wave it creates. The vertical axis measures the shift of the laser wavenumber to its initial central wavenumber (represented by the dashed line). The horizontal axis is the axial/propagation coordinate. The laser pulse frequency is globally downshifted due to photon deceleration. However, the frequency downshift at the laser front (higher ζ) is much stronger than the frequency downshift at the laser back (lower ζ). Thus, the front of the laser compresses more quickly than the back of the laser, and self-steepening occurs at the front of the pulse.