Ultrashort Focused Electromagnetic Pulses
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.
Cite
@article{arxiv.0808.3913,
title = {Ultrashort Focused Electromagnetic Pulses},
author = {Daniel an der Brügge and Alexander Pukhov},
journal= {arXiv preprint arXiv:0808.3913},
year = {2011}
}
Comments
8 pages, 5 figures