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arXiv · 0808.3913

Ultrashort Focused Electromagnetic Pulses

Daniel an der Brügge·Alexander Pukhov
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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.

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Daniel an der Brügge, Alexander Pukhov. 2008-08-28. Ultrashort Focused Electromagnetic Pulses. https://doi.org/10.1103/physreve.79.016603

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