Dynamics of laser-induced tunable focusing in silicon

We report here on focusing of a probe IR (λ = 1.55 μm) laser beam in silicon. The focusing is done by a second pump laser beam, at λ = 0.775 μm and 30 ps pulse width, with a donut shape that is launched collinearly and simultaneously (with some delay time) with the IR beam pulse. The pump beam pulse is absorbed in the silicon and creates, temporally, a free charge carriers (FCCs) donut pattern in the silicon. Following the plasma dispersion effect, the donut FCCs shapes a complex index of refraction pattern in the silicon that serves as a sort of dynamic GRIN lens for the probe beam due to the diffusion of the FCCs towards the donut center. This lens can be tuned to its focal point by the pump-probe delay time to reduce the point spread function (PSF) of the IR probe beam. We start seeing the focusing of the probe beam at pump-probe delay time of Δt≈100ps\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{\Delta t }\approx 100\mathrm{ ps}$$\end{document}. The best focusing (results in PSF <2μm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$< 2\mathrm{ \mu m}$$\end{document}) was observed at Δt≈350ps\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{\Delta t}\approx 350\mathrm{ ps}$$\end{document} and it slowly degrades before the FCCs full recombination at Δt∼12ns\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{\Delta t }\sim 12\mathrm{ ns}$$\end{document}. We propose this beam shaping method to overcome the diffraction resolution limit in silicon microscopy on and deep under the silicon surface dependent on the pump wavelength and the pulse width. We also proposed this technique for direct measurement of the FCCs dynamics.