Analytical solutions for the electromagnetic fields of flattened and annular Gaussian laser modes III Arbitrary length pulses and spot sizes

Abstract

In the first two parts of this study, the electromagnetic field components were derived for infinitely long, flattened Gaussian laser beams [J. Opt. Soc. Am. B23, 2157 and J. Opt. Soc. Am. B23, 2166 (2006)]. These results are now extended without approximation to allow for finite laser pulses having an arbitrary duration beginning with the standard Gaussian beam profile and then generalizing these results to a flattened Gaussian. The resulting models thus allow for all pulse durations and spot sizes from infinite, paraxial beams to single-cycle, wavelength-size spots, with a savings of more than 2 orders of magnitude in computation time. Pulses having fewer than ten cycles exhibit significant modification from the monochromatic fields as a result of the finite bandwidth. Specifically, the energy in the focus is shown to decrease from the theoretical value of 86.5% to as low as 72.2% for a single-cycle pulse.