Abstract
Nonlinear Compton scattering is calculated for the collision of an electron with a plane wave pulse. A mid infra-red (IR) peak arises in the photon spectrum due to long-range interference associated with the pulse envelope. The case of a flat-top pulse is studied as a toy model for pulse envelope effects and reduced to two final-state momentum integrations; the case of a sine-squared pulse is studied numerically. A perturbative expansion in charge-field coupling reveals that already at intermediate intensities, many orders are required to correctly capture the structure of the mid-IR peak. By regularising the classical result, it is shown that the mid-IR peak is due to plane-wave ponderomotive effects on the pulse envelope. Finally, it is shown that the mid-IR peak can be isolated using energy, angle and polarisation filters.
Highlights
The amplitude for a probe particle to undergo a given process in a laser pulse is proportional to an integral over all spacetime
The effect of the background’s pulse envelope on the spectrum of single nonlinear Compton scattering has been investigated. This corresponds to taking into account exactly interference from emissions by the electron at different points in the pulse, up to the length scale of the entire pulse envelope
This was done, first in the toy model of a flattop pulse, for which we presented the total probability as a sum over harmonics of an integral over two outgoing photon momentum components
Summary
The amplitude for a probe particle to undergo a given process in a laser pulse is proportional to an integral over all spacetime. Various approximations have been devised to define a “probability rate,” which, when integrated over the entire pulse, gives the total probability for the process to occur. The regularization, which includes interference over arbitrarily large scales, leads to a broad mid-IR peak, which is nonperturbative in the charge-field coupling just like the wellknown harmonic structure While this mid-IR peak can be seen in the numerical results of several authors [22,23,29], to the best of our knowledge, it has yet to be analyzed or discussed in detail.
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