  Propagation of a tightly focused high-power ultrashort laser pulse in an
optical medium is usually substantially influenced by the medium optical
nonlinearity that can noticeably affect the laser pulse parameters around the
nonlinear focus and lead to unavoidable and often undesirable spatial
distortions of the focal waist. We present the results of our experimental
study and numerical simulations on a femtosecond Ti-Sapphire laser pulse
propagation in air under different spatial focusing. We concentrated our study
on spectral-angular and spatial pulse transformations under different focusing
regimes, from linear to nonlinear one, when pulse filamentation occurs. For the
first time to the best of our knowledge, we found the laser pulse numerical
apertures range,namely, from NA=0.002 to 0.005 (for laser pulse energy of 1
mJ), where the laser pulse distortions both in frequency-angular spectrum and
pulse spatial shape are minimal. By means of the numerical simulations, we
found the threshold pulse energy and peak power in a wide range of focusing
conditions, within which a transition between the linear and strongly nonlinear
laser pulse focusing in air takes place. This energy limit is shown to decrease
with pulse numerical aperture enhancement. Our findings identify the laser
pulse numerical apertures and energy adequate for getting a maximum laser
intensity with a good beam quality around the focal point suitable for various
laser micropatterning and micromachining technologies.
