Utilizing graph theoretical analysis to quantify the micro- and nano-structures formed on femtosecond laser processed copper

Femtosecond laser surface processing (FLSP) is a cutting-edge technique that enhances surface functionalities by creating intricate self-organized micro- and nano-scale structures. However, a significant challenge lies in accurately and quantitatively assessing these complex structures across different materials and processing parameters. To address this challenge, a graph theoretical (GT) approach was used to provide a systematic framework for the precise quantification and differentiation of FLSP-generated surface structures based on essential topological parameters and laser processing parameters. These parameters encompass characteristics such as the number of nodes, edges, graph density, graph diameter, and clustering coefficient. In addition to the GT parameters, we also utilized peak-to-peak distances, area of the mounds and mound density to elucidate the variations observed. In this study, we irradiated series of copper substrates with varying number of pulses at a fixed peak fluence. The outcome of this study showed two things: firstly, the ability to differentiate between FLSP Cu surface structures and secondly, that a mere survey of the surface features via GT parameters could predict the characteristics of the subsurface microstructure. The insights into both surface and subsurface changes to the material gained from the GT analysis provides understanding of the complex formation mechanisms.