In this paper, the generation of relativistic electron mirrors (REMs) and the reflection of an ultra-short laser off this mirrors are discussed, applying two-dimensional particle-in-cell (2D-PIC) simulations. REMs with ultra-high acceleration and expanding velocity can be produced from a solid nanofoil illuminated normally by an ultra-intense femtosecond laser pulse with a sharp rising edge. Chirped attosecond pulse can be produced through the reflection of a counter-propagating probe laser off the accelerating REM. In the electron moving frame, the plasma frequency of the REM keeps decreasing due to its rapidly expanding. The laser frequency, on the contrary, keeps increasing due to the acceleration of REM and the relativistic Doppler shift from the lab frame to the electron moving frame. Within an ultra-short time interval, the two frequencies will be equal in the electron moving frame, which leads the resonance between laser and REM. The reflected radiation near this interval and the corresponding spectra will be amplified due to the resonance. Through adjusting the arriving time of the probe laser, certain part of the reflected field could be selectively amplified or depressed, leading to the selectively adjusting of the corresponding spectra.

In this paper, the generation of relativistic electron mirrors (REM) and the reflection of an ultra-short laser off the mirrors are discussed, applying two-dimension particle-in-cell simulations. REMs with ultra-high acceleration and expanding velocity can be produced from a solid nanofoil illuminated normally by an ultra-intense femtosecond laser pulse with a sharp rising edge. Chirped attosecond pulse can be produced through the reflection of a counter-propagating probe laser off the accelerating REM. In the electron moving frame, the plasma frequency of the REM keeps decreasing due to its rapid expansion. The laser frequency, on the contrary, keeps increasing due to the acceleration of REM and the relativistic Doppler shift from the lab frame to the electron moving frame. Within an ultra-short time interval, the two frequencies will be equal in the electron moving frame, which leads to the resonance between laser and REM. The reflected radiation near this interval and corresponding spectra will be amplified due to the resonance. Through adjusting the arriving time of the probe laser, a certain part of the reflected field could be selectively amplified or depressed, leading to the selective adjustment of the corresponding spectra.

To control the shape of the ultra-thin electron layer produced by directly interaction of ultrahigh contrast laser with ultra-thin foil target, we investigated the spacial distribution and temporal evolution of electron layers produced from single and double foil targets through two-dimensional particle-in-cell simulations. Results show that electron layers produced from double foil targets can fly with unperturbed velocity for a much longer time than in the single foil case, which can be explained by the integrated contribution of charge separation field from both the two foils. Further studies show that through adjusting the foil expansion, electron layers with different shapes can be obtained. Detailed studies on the forming process of layers show that electron momentum distribution evolves rapidly along with the pump laser and then the vanishing of electron transverse momentum induced by the reflected laser results in the forming of layer shape. So different foil expansion corresponds to different moments that reflected laser interact with electron layer, when the electron transverse momentum distribution is different. After the reflected laser interact with electron layer, the resultant longitude momentum distribution will finally lead to various electron layer shapes.