Perturbative Generalization of Nonparaxial Ultrashort Tightly-focused Elegant Laguerre-Gaussian Beams

An analytical method for calculating the electromagnetic fields of a nonparaxial elegant Laguerre-Gaussian (eLG) vortex beam is presented for arbitrary pulse duration, spot size, and LG mode. This perturbative approach provides a numerically tractable model for the calculation of arbitrarily high radial and azimuthal LG modes in the nonparaxial regime, without requiring integral representations of the fields. A key feature of this perturbative model is its use of a Poisson-like frequency spectrum, which allows for the proper description of pulses of arbitrarily short duration. The time-domain representation of this model is presented as a non-recursive closed-form expression to any order of perturbative correction. This presentation enables calculation of the complex EM fields for such general beams without requiring evaluation of any Fourier integrals, and is therefore straightforward to implement for both analytical and numerical applications. Other recent models are discussed and compared. In addition, numerical simulations are carried out in which high energy electron bunches are generated via vacuum acceleration by a tightly focused eLG beam. By examination of accelerated electron properties far from the beam waist, it is shown that eLG beams of higher radial index can increase the electronic energy gain. The utility of such an acceleration model applied to ensemble acceleration is explored, and compared to standard modern techniques