Exact solutions for the electromagnetic fields of a flying focus

TL;DR

This paper derives exact analytical solutions for the electromagnetic fields of a flying focus laser beam, enabling precise modeling of their propagation and potential applications.

Contribution

It introduces a generalized method combining complex source-point and Lorentz invariance to obtain exact solutions for flying focus electromagnetic fields.

Findings

Exact solutions for arbitrary polarization and orbital angular momentum.

Conditions for using paraxial approximations in modeling.

Method to determine laboratory field configurations.

Abstract

The intensity peak of a "flying focus" travels at a programmable velocity over many Rayleigh ranges while maintaining a near-constant profile. Assessing the extent to which these features can enhance laser-based applications requires an accurate description of the electromagnetic fields. Here we present exact analytical solutions to Maxwell's equations for the electromagnetic fields of a constant-velocity flying focus, generalized for arbitrary polarization and orbital angular momentum. The approach combines the complex source-point method, which transforms multipole solutions into beam-like solutions, with the Lorentz invariance of Maxwell's equations. Propagating the fields backward in space reveals the space-time profile that an optical assembly must produce to realize these fields in the laboratory. Comparisons with simpler paraxial solutions provide conditions for their reliable use when modeling a flying focus.