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Perturbative Generalization Of Nonparaxial Ultrashort Tightly-Focused Elegant Laguerre-Gaussian Beams, Andrew M. Vikartofsky

Department of Physics and Astronomy: Dissertations, Theses, and Student Research

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 …