1：Experimental Design and Method Selection:

The study used a picosecond laser with a wavelength of 355 nm and a pulse duration of 10 ps to induce filamentation in sapphire. The nonlinear propagation of ultrashort laser pulses in transparent media was analyzed.

2：Sample Selection and Data Sources:

Sapphire single crystals of size 10 mm × 5 mm × 10 mm were used as specimens.

3：List of Experimental Equipment and Materials:

A picosecond laser (PX-PS 449, Edgewave), transmitted polarizing microscopy (DM2700 M, Leica), an ICCD camera (iStar DH734, Andor), a confocal Raman microscopy (inVia?, Renishaw), and SEM (S-3400 N, Hitachi) were used.

4：Experimental Procedures and Operational Workflow:

Filamentary propagation was produced by one burst consisting of 1000 pulses at the repetition rate of 200 kHz, with pulse energies of 2.7 μJ, 30 μJ, and 40 μJ respectively. The characteristics of picosecond laser filamentation in sapphire were observed through morphology and instantaneous plasma images.

5：7 μJ, 30 μJ, and 40 μJ respectively. The characteristics of picosecond laser filamentation in sapphire were observed through morphology and instantaneous plasma images. Data Analysis Methods:

5. Data Analysis Methods: The morphology and microstructure of the filamentary traces were analyzed using optical transmission microscopy, cross-polarized microscopy, Raman spectroscopy, and SEM.