Description
Flying focus beams are exact solutions of the Maxwell equations with spatial focusing, a feature which is absent in plane waves. In the first instance, these flying focus solutions are complex-valued; unfortunately, taking the real part of this field results in background-coupled wave equations for particles interacting with the real background field that are complicated PDEs that must be dealt with numerically or via approximations. We'll discuss how, on the other hand, keeping the original, complex flying focus field enables remarkable analytic calculations. In particular, the complex-valued flying focus beam is a self-dual Maxwell field, and the hidden integrability associated with this fact makes it possible to solve background-coupled wave equations exactly in the ultrarelativistic (massless) regime. This allows for analytic computation of non-linear Compton scattering, as well as multi-emission amplitudes in 'maximal helicity violating' configurations. Furthermore, these scattering amplitudes in the self-dual have a physical interpretation, encoding total depletion effects. This is joint work with Anton Ilderton.
