Abstract
With the rapid development of laser technology[
Plasma mirrors may be a feasible method by which to solve these problems. Using a double plasma mirror[
Ref. [
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In this letter, the effects of ion motion on the generation of short-cycle relativistic laser pulses are investigated by analytical modeling and particle-in-cell (PIC) simulations. The generation of a near single-cycle laser pulse has been obtained in the simulations, and the corresponding theoretical analysis has been discussed[
Figure
1D PIC simulations are used to study the effects of ion motion on the generation of a short-cycle relativistic laser pulse. A CP laser pulse with wavelength is incident on the target from the left boundary. The laser front arrives at the front surface of the target at , where is the laser cycle and is the speed of light. The laser pulse has a trapezoidal shape profile (linear growth–plateau–linear decrease) with a duration of (). Here, the short width of the flat top () is used to reduce the content of high frequencies. The frequency of the trapezoidal laser pulse used in this case is mainly at the base frequency . The laser amplitude gradient is ( and ). Here, is the normalized amplitude, where and are the electron mass and charge, respectively, is the laser electric field, is the laser frequency, and is the rising time of the laser pulse. The front surface of the target is located at . The foil density is and the foil thickness is . Here, is the critical density. Low-density plasma with a step density profile is used to simplify the model and reduce the simulation time. The longitudinal length of the 1D simulation box is . The mesh size is . Each cell contains 100 numerical macro particles in the plasma region.
Figure
The simulations above show that the ion motion is important for the generation of short-cycle laser pulses. The main reason is that the re-entering of the ions into the CEL at the back side of the foil can further reflect the rear part of the laser pulse. In the case of Figure
The dynamics of the electrons and ions are investigated to obtain insights into the generation of short-cycle lasers. The action of the electric field in the CEL (Figure
For electrons, a uniform velocity of the CEL can be obtained for a laser with a linearly increasing front in simulations[
For ions, the velocity for the ion initially at rest at () can be approximated by[
The velocity of the ions initially at rest in the middle of the foil () is obtained using Equation (
From the discussion above, two conditions are required for the generation of an intense short-cycle transmitted pulse. First, the peak of the incident pulse must arrive at the back surface when the CEL disperses, thereby generating a short-duration transmitted pulse with higher amplitude. This condition is simply an approximation because the exact amplitude of the transmitted pulse is not considered. Second, the ions must not catch up to the CEL during the hole-boring stage. Otherwise all of the laser pulses may be reflected.
For the first condition, the laser and foil parameters are as follows:
For the second condition, the laser and foil parameters are[
Different simulations of carbon ions are also performed to verify the theory. The velocity of the CEL is obtained for and according to Equation (
A clean laser pulse is used to simplify the model in this work. In fact, the effect of a laser prepulse is always critical for a thin foil and it may alter the conditions [see Equations (
To verify our theoretical model, we also carried out 2D PIC simulations. The same parameters as in the 1D PIC simulations [see Figures
Figure
In conclusion, the effects of ion motion on the generation of a short-cycle relativistic laser pulse are investigated by analytical modeling and PIC simulations. 1D PIC simulations show that the ion shutter can further modulate the transmitted short-cycle pulse compared with the case of the electron shutter only. Two conditions are theoretically proposed to generate short-cycle transmitted laser pulses, which are proven by the simulations. A near single-cycle (3.9 fs) laser pulse with an intensity of is generated by properly controlling the electron and ion shutters in 2D PIC simulations.
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