Heat transfer in Z-scan experiments

Abstract

In this study, we present the results of theoretical calculations concerning heat exchange in materials subjected to laser irradiation, with particular emphasis on Z-scan experiments. Using explicit difference methods, we model the temperature distribution in three-dimensional samples of various sizes, such as [4 ×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes$$\\end{document} 4 ×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes$$\\end{document} 2] mm, [5 ×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes$$\\end{document} 5 ×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes$$\\end{document} 2] mm, and [6 ×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes$$\\end{document} 6 ×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes$$\\end{document} 2] mm. The simulations encompass two different types of pulsed lasers with durations of 10 (ns) and 100 (ps), adjusting laser parameters to achieve a peak irradiance intensity of 5 GW/cm2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${^2}$$\\end{document}. The temperature distribution in samples, denoted as T(x, y, z, t), is computed using a novel laser heat source model specifically designed for this problem. The computational program Z-lambda enables not only the simulation of thermal processes during the Z-scan experiment but also post-experiment analysis. The development of this software was one of the main objectives of this study. The results indicate that the thermal analysis of Z-scan experiments requires consideration of factors such as laser pulse duration, laser repetition time, sample geometry, and heat exchange between the studied material and the surroundings. Especially in the Z-scan technique, controlling thermal parameters before the experiment is crucial for obtaining precise and reproducible results. It is noteworthy that sample heating during the experiment can significantly influence charge carrier density, subsequently affecting the parameters of nonlinear optics (NLO). Tools like the Z-lambda program allow for the optimization of laser parameters, minimizing sample heating, and reducing the thermal impact on NLO parameters.