Analytical solutions for the electromagnetic fields of tightly focused laser beams of arbitrary pulse length.

The analytical solution for a monochromatic focused laser beam was recently published [Opt. Lett.31, 1447 (2006)]. The effect of introducing bandwidth by including a finite-length temporal pulse envelope is included exactly. This is done formally first in the frequency domain for an arbitrary pulse shape, and the specific case of a cosine-squared envelope is then solved analytically for all pulse lengths, thereby decreasing the computation time by 2 orders of magnitude. The inclusion of longer wavelengths reduces the fraction of laser energy in the focus from 86.5% to 83.5% for a 5 fs Ti:sapphire laser and 72.7% in a single-cycle pulse.