Energy stability of supercontinuum via femtosecond filamentation in sapphire

Supercontinuum (SC) generation in bulk materials offers a versatile, broadband coherent light source for ultrafast spectroscopy and nonlinear optics. The filamentation process underlying SC generation is primarily governed by three critical parameters: input pulse energy, focusing numerical aperture, and crystal thickness. Using femtosecond pulses and sapphire crystals, we systematically investigate how these parameters affect SC energy stability. Depending on the number of pulse-splitting events, filamentation can manifest in either single- or multi-filament regimes, with the latter leading to undesirable spectral modulation and thus requiring avoidance. Our study reveals that within the single-filament regime, two distinct dynamical states can arise: a critical state, in which pulse-splitting dynamics and SC spectra evolve rapidly with increasing input pulse energy, and a steady state, which ensures optimal stability. Experimental results show that steady-state SC generation yields the highest stability, exceeding that of the driving laser. These findings deepen the physical understanding of filamentation and provide clear guidelines for parameter selection to achieve stable SC in bulk media, offering practical insights for optimizing broadband coherent sources in ultrafast applications.