Determination of the carrier envelope phase for short, circularly polarized laser pulses

We analyze the impact of the carrier envelope phase on the differential cross sections of the Breit-Wheeler and the generalized Compton scattering in the interaction of a charged electron (positron) with an intensive ultrashort electromagnetic (laser) pulse. The differential cross sections as a function of the azimuthal angle of the outgoing electron have a clear bump structure, where the bump position coincides with the value of the carrier phase. This effect can be used for the carrier envelope phase determination.

Figure 1

Left column: The differential cross section as a function of the azimuthal angle of the direction of flight of the outgoing electron ${\varphi }_e$, for different values of the carrier phase $\tilde{\varphi }$ and for different pulse duration $\mathrm{\Delta }=N\pi$ with $N=0.5$, 1, 1.5 and 2 (from the bottom panels). The solid, dash-dash-dotted, dashed and dash-dotted curves are for the CEP equal to 0, 90, 180 and 270 degrees, respectively. Right column: The anisotropy (14) for different values of $\tilde{\varphi }$ and $N$, as in the left column. ${\xi }^2=0.5$ and $\zeta =4$.

Figure 2

Left panel: The cross section of the $e^{+}{e}^{-}$ production as a function of scale variable $\mathrm{\Phi }={\varphi }_e-\tilde{\varphi }$ for different values of e.m. field intensities $\xi$. The solid, dashed and dash-dotted curves are for ${\xi }^2=0.1$, 1, and 10, respectively. Right panel: The cross section of $e^{+}{e}^{-}$ pair production integrated over ${\varphi }_e$ as a function of ${\xi }^2$ for $\tilde{\varphi }=0$ (solid curve) and $\pi$ (crosses). $N=0.5$ and $\zeta =4$.

Figure 3

Left column: The differential cross section (19) as a function of the azimuthal angle of the outgoing electron momentum ${\varphi }_{e^{\prime }}$ for different values of the carrier phase $\tilde{\varphi }$ and different numbers of cycles in a pulse, $N$, as depicted in the plots. The solid, dash-dash-dotted, dashed and dash-dotted curves correspond to the carrier phases equal to 0, 90, 180 and 270 degrees, respectively. Right column: The anisotropy as a function of ${\varphi }_{e^{\prime }}$ for different $\tilde{\varphi }$, for the hyperbolic secant shape with $N=0.5$. ${\xi }^2=0.5$ and $\kappa ={\omega }^{\prime }/{\omega }_1^{\prime }=3$.

Figure 4

The same as in Fig. 3 but for $\kappa =2$ and for two values of $N=0.5$ (top row) and 2 (bottom row).