Ultrashort Focused Electromagnetic Pulses

TL;DR

This paper provides a comprehensive analytical framework for modeling ultrashort, focused electromagnetic pulses of arbitrary duration and phase, enabling precise descriptions crucial for vacuum particle acceleration research.

Contribution

It introduces a novel method using a second potential to construct fully consistent 3D wave-packet solutions for ultrashort pulses based on scalar wave equations.

Findings

Closed-form solutions using complex error functions

Validated numerical accuracy of the pulse models

Applicable to vacuum particle acceleration simulations

Abstract

In this article we present a closed analytical description for few-cycle, focused electromagnetic pulses of arbitrary duration and carrier-envelope-phase (CEP). Because of the vectorial character of light, not all thinkable one-dimensional (1D) shapes for the transverse electric field or vector potential can be realized as finite energy three-dimensional (3D) structures. We cope with this problem by using a second potential, which is defined as a primitive to the vector potential. This allows to construct fully consistent 3D wave-packet solutions for the Maxwell equations, given a solution of the scalar wave equation. The wave equation is solved for ultrashort, Gaussian and related pulses in paraxial approximation. The solution is given in a closed and numerically convenient form, based on the complex error function. All results undergo thorough numerical testing, validating their correctness and accuracy. A reliable and accurate representation of few-cycle pulses is e.g. crucial for analytical and numerical theory of vacuum particle acceleration.