Figure 9

Electric field temporal structure in 3D Particle-In-Cell (PIC) simulation with \({a_0 = 100}\), \({\bar{n}_\mathrm{e}}\) = 100. (a) Temporal variation of the normalised vector potential of the incident and reflected laser pulses along the polarisation axis of the incident laser pulse. The reflected pulse demonstrates attosecond radiation spikes without the need for spectral filtering. (b) The spectral intensity of the reflected radiation obtained via a Fourier transform of the pulse in (a). The fit is calculated following the methodology of Edwards and Mikhailova⁴²: \(\omega _\mathrm{b}/\omega _\mathrm{L}\) defines the cut-off above which an ordinary least squares fit to \(\sim n^{-p}\) yields an exponent, \(p > 4/3\). Beyond the cut-off, the spectrum is predicted to scale as \(\sim n^{-10/3}\). The fit is a simple weighted polynomial fit to the logarithm of the data using the NumPy polyfit module.