Propagation of axiparabola-focused laser pulses in uniform plasmas

An axiparabola-based flying focus laser possesses a long focal depth, a small focal spot, and a controllable group velocity. It has been proposed for wide applications, such as phase-locked laser wakefield acceleration and photon acceleration. We numerically study the propagation of axiparabola-focused laser pulses in plasmas and find that such lasers can propagate stably over long distances in plasmas at low intensity. When the laser intensity increases to the relativistic intensity, they no longer propagate stably. Pulse front deformation and fracture appear due to the formation of plasma density modulations. We propose three schemes to mitigate the unstable propagation of axiparabola-focused lasers: (i) adding a radially dependent pulse front delay, (ii) placing the plasma away from the beginning of the focal line, and (iii) using an axiparabola mirror with a negative focal line. All these methods are relatively easy to implement. Our studies can provide guidance for applications of axiparabola-focused lasers.