Fields and propagation characteristics in vacuum of an ultrashort tightly focused radially polarized laser pulse

Abstract

Analytic expressions for the electric and magnetic fields of a radially polarized ultrashort and tightly focused laser pulse, propagating in vacuum, are derived from scalar and vector potentials satisfying simple initial conditions. It is shown that for a pulse of axial length comparable to a wavelength, only the zeroth (lowest-order) term in a power-series expansion of the vector potential is needed. A procedure is outlined which may be used to obtain the fields analytically, to any desired order. Most of the needed analytic work is done that would lead to the vector potential from which the fields may be derived and the main expressions are given.