Nonlinear Compton scattering in ultrashort laser pulses

A detailed analysis of the photon emission spectra of an electron scattered by a laser pulse containing only very few cycles of the carrying electromagnetic field is presented. The analysis is performed in the framework of strong-field quantum electrodynamics, with the laser field taken into account exactly in the calculations. We consider different emission regimes depending on the laser intensity, placing special emphasis on the regime of one-cycle beams and of high laser intensities, where the emission spectra depend nonperturbatively on the laser intensity. In this regime, we, in particular, present an accurate stationary phase analysis of the integrals that are shown to determine the computed emission spectra. The emission spectra show significant differences with respect to those in a long pulsed or monochromatic laser field: The emission lines obtained here are much broader, and more important, no dressing of the electron mass is observed.

Figure 1

Feynman diagrams of multiphoton Compton scattering drawn in a conventional QED picture (left) and in the Furry picture (right).

Figure 2

General setup of the considered process.

Figure 3

Shape functions according to Eq. (12): ${\psi }_{\mathcal{A}}$ (solid red line) and ${\psi }_{\mathcal{E}}$ (dashed blue line).

Figure 4

Shape functions according to Eq. (14): ${\psi }_{\mathcal{A}}$ (solid red line) and ${\psi }_{\mathcal{E}}$ (dashed blue line).

Figure 5

Electric fields in frequency space for ${\psi }_{\mathcal{A}}=\text{sech}(\varphi )$ (solid red line) and for ${\psi }_{\mathcal{A}}=\text{sech}(\varphi )\text{tanh}(\varphi )$ (dashed blue line).

Figure 6

Diagrams contributing to single-photon Compton scattering. Note that, as it is known, two diagrams contribute to the lowest order Compton scattering. By working in the Furry picture, both diagrams are automatically taken into account.

Figure 7

Energy emission spectra for $\xi =0.05$ and (a) $\gamma =10$ ($\varrho \approx 4\times {10}^{-5}$) and (b) $\gamma =2\times {10}^5$ ($\varrho \approx 0.8$). The blue crosses in both spectra have been obtained by a classical calculation.

Figure 8

Energy emission spectrum for $\xi =2$ and $\gamma =2500$ ($\varrho ={10}^{-2}$). The crosses have been obtained by a classical calculation.

Figure 9

Classical electron trajectory (solid line) inside a field given by Eq. (13) (dashed blue line).

Figure 10

Energy emission spectra for $\xi =5$ and (a) $\gamma =2500$ ($\varrho \approx 2.5\times {10}^{-2}$) and (b) $\gamma =2\times {10}^5$ ($\varrho \approx 0.8$). The crosses in (a) have been obtained by a classical calculation.

Figure 11

Envelopes of the energy emission spectra for $\gamma =\xi =100$ for the emission angles $\vartheta ={127}^{°}$ (solid red line), $\vartheta ={147}^{°}$ (dashed blue line), and $\vartheta ={167}^{°}$ (dotted green line).

Figure 12

Envelopes of the energy emission spectra for $\gamma =50$ and $\xi =100$ for the emission angles $\vartheta ={91}^{°}$ (solid red line), $\vartheta ={122}^{°}$ (dashed blue line), and $\vartheta ={154}^{°}$ (dotted green line).

Figure 13

Envelopes of the energy emission spectra for $\gamma ={10}^4$ and $\xi =100$ for the emission angles $\vartheta ={179.5}^{°}$ (solid red line), $\vartheta ={179.6}^{°}$ (dashed blue line), and $\vartheta ={179.8}^{°}$ (dotted green line).

Figure 14

(a) Envelopes of the energy emission spectra for $\gamma =\xi =100$ at the emission angles $\vartheta ={152}^{°}$ (solid red line), $\vartheta ={160}^{°}$ (dashed blue line), and $\vartheta ={167}^{°}$ (dotted green line). (b) Envelopes of the energy emission spectra for $\gamma =50$, $\xi =200$ at the emission angles $\vartheta ={90}^{°}$ (solid red line), $\vartheta ={110}^{°}$ (dashed blue line), and $\vartheta ={131}^{°}$ (dotted green line).

Figure 15

Envelope of the energy emission spectrum for $\gamma ={10}^4$ and $\xi =100$ for the emission angle $\vartheta ={179.8}^{°}$.