Energy limit for linear-to-nonlinear femtosecond laser pulse focusing in air

•Spectral-angular and spatial laser pulse transformations when entering the filamentation regime.•Laser pulse after the filamentation propagates at highest angles to the optical axis.•Existence of numerical apertures with broadening of pulse frequency-angular spectra does not occur.•Numerical apertures and pulse energies providing maximal laser intensities with good beam quality. 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 = 2·10-3 to 5 10-3(for the 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 energes adequate for getting a maximum laser intensity with a good beam quality around the focal point suitable for various laser micropatterning and micromachining technologies.