Fig. 3: Mode structure of the laser beam at higher and lower target densities.
From: Electron acceleration from transparent targets irradiated by ultra-intense helical laser beams
a Amplitude of the complex field \({B}_{z}^{{{{{{{{\rm{H}}}}}}}}}\) determined by the Hilbert transform from a snapshot of Bz at t = 88.3 fs in the 3D PIC simulation for a target with \({n}_{\max }=2.5{n}_{{{{{{{{\rm{c}}}}}}}}}\). b The amplitude of the dominant mode with l = −1 and p = 0 obtained by mode decomposition of \({B}_{z}^{{{{{{{{\rm{H}}}}}}}}}\) in (a). c The amplitude of a generated mode with l = −1 and p = 2 obtained by mode decomposition of \({B}_{z}^{{{{{{{{\rm{H}}}}}}}}}\) in (a). d Amplitude of the complex field \({B}_{z}^{{{{{{{{\rm{H}}}}}}}}}\) determined by the Hilbert transform from a snapshot of Bz at t = 88.3 fs in the 3D PIC simulation for a target with \({n}_{\max }=0.5{n}_{{{{{{{{\rm{c}}}}}}}}}\). e The amplitude of the dominant mode with l = −1 and p = 0 obtained by mode decomposition of \({B}_{z}^{{{{{{{{\rm{H}}}}}}}}}\) in (d). f The amplitude of a generated mode with l = −1 and p = 2 obtained by mode decomposition of \({B}_{z}^{{{{{{{{\rm{H}}}}}}}}}\) in (d).
