Interference effect in nonlinear Compton scattering

In this paper we make a theoretical investigation of a new type of high-energy nonlinear Compton scattering phenomenon. In particular we show how, under certain conditions, interference effects arise when two laser pulses of different photon energy are shone upon a high-energy electron beam. The semiclassical operator method of Baier et al. is revisited as the method of investigation of this phenomenon. We show how their result can be cast into a form very similar to the classical result of radiation emission. Experimental verification of the described interference phenomenon is possible with current technology.

Figure 1

A comparison of the radiation power spectra of an electron moving in a plane wave characterized by $\omega =2.35\mathrm{eV}$, $\eta =0.5$ and $\chi =0.25$ obtained by using the semiclassical operator method, Compton scattering as prescribed by second-order perturbative QED (Klein-Nishina), nonlinear Compton scattering by using transitions between Volkov states and finally the classical result.

Figure 2

A figure similar to Fig. 1, but in a stronger field, characterized by the parameters $\omega =2.35\mathrm{eV}$, $\eta =1.0$, $\chi =1.0$.

Figure 3

A figure of the power spectra using the semiclassical operator method for the electron in each wave separately, wave 1 and wave 2, and in the superposition of the two waves “superimposed waves.” The latter is noticeably different than the “incoherent sum,” which is the sum of the spectra of wave 1 and wave 2. The fields are characterized by ${\omega }_1=2.35\mathrm{eV}$, ${\eta }_1=\frac{1}{2}$, ${\chi }_1=\frac{1}{4}$ and ${\omega }_2=2{\omega }_1$, ${\eta }_2=\frac{1}{2\sqrt{2}}$, ${\chi }_2=\frac{1}{2\sqrt{2}}$.

Figure 4

A figure of the radiation power spectra in a weak field, $\eta \ll 1$. The spectrum “superimposed waves” is seen to overlap with the “incoherent sum” as expected. In “2nd order QED wave 1” we compare the result of “wave 1” to that of Compton scattering as obtained from the second order of perturbation in QED (Klein-Nishina).