Experimental and Theoretical Determination of the Effective Penetration Depth of Ultrafast Laser Radiation in Stainless Steel

Abstract

This study intends to present a simple two-temperature model (TTM) for the fast calculation of the ablation depth as well as the corresponding effective penetration depth for stainless steel by considering temperature-dependent material parameters. The model is validated by a comparison of the calculated to the experimentally determined ablation depth and the corresponding effective penetration depth in dependence on the pulse duration (200 fs up to 10 ps) and the fluence. The TTM enables to consider the interaction of pulsed laser radiation with the electron system and the subsequent interaction of the electrons with the phonon system. The theoretical results fit very well to the experimental results and enable the understanding of the dependence of the ablation depth and of the effective penetration depth on the pulse duration. Laser radiation with a pulse duration in the femtosecond regime results in larger ablation depths compared to longer-pulsed laser radiation in the picosecond regime. Analogously to the ablation depth, larger effective penetration depths are observed due to considerably higher electron temperatures for laser radiation with pulse durations in the femtosecond regime.

Fluence-Dependent Transient Reflectance of Stainless Steel Investigated by Ultrafast Imaging Pump–Probe Reflectometry

“…The decrease of the ablation efficiency with increasing fluences above 1 J/cm 2 might therefore be also explained by the reduction of the mechanical contribution to the material removal due to the pronounced thermal contribution of the phase explosion with vapor and vapor–liquid formation during the ablation. This supports and complements the previous investigations and interpretations of single and multipulse laser material processing. − …”

“…Based on the calculated T e ( t , H 0 ), the temporal evolution Δ R / R ( t , H 0 ) is derived using the transient optical parameters from the literature . Because the transient optical properties of stainless steel in the literature are only calculated for T e < 25 kK, the optical properties are extrapolated for larger electron temperatures, following the approach of a recent study . A detailed explanation of the numerical calculation and the derivation of the thermophysical and optical parameters according to recent literature ,, is given in the Supporting Information (S.V and S.VI).…”

“…Left: electron temperature T e and phonon temperature T ph on the surface of stainless steel (EN 1.4301) as a function of time during and after the irradiation with the pump radiation (black dashed line) at the wavelength λ pump = 800 nm and the pulse duration τ H,pump = 40 fs at the peak fluence Ĥ 0 = 2 J/cm 2 and the threshold temperature (red dashed line) for phase explosion being 90% of the thermodynamic critical temperature T c ; ,− , right: resulting maximum electron temperature T e and phonon temperature T ph as a function of the applied fluence H 0 of the pump radiation.…”

“…Irradiating the material at fluences H 0 > 1.0 J/cm 2 results in an increased occupation at E – E F > 5 eV and a further decreased occupation at E – E F < 0 eV (Figure c red graph). Now, the photon energy of the probe radiation is sufficient to induce direct transitions within the d-block and the conduction band close to the L point in the first Brillouin zone (Figure c and d green arrows), resulting in an increased absorption coefficient and reflectance. , This increased reflectance is not considered in the approximation of the optical parameters from ref , as only electron temperatures up to 25 kK were considered there, and the data was extrapolated according to the correlations up to 25 kK . Therefore, the trend of the simulated Δ R / R differs from the measured Δ R / R at higher electron temperatures and fluences H 0 > 1.0 J/cm 2 , respectively.…”

“…Thus, in addition to hydrodynamic mechanisms and plasma dynamics, the transient reflectance directly affects the ablation efficiency during laser processing. In recent experimental studies, the optimum ablation efficiency on stainless steel in terms of volume removed per pulse energy has been reported at about H 0 ≈ 1 J/cm 2 for laser irradiation with both single and multipulses. , However, at higher fluences H 0 > 1 J/cm 2 , a steady decrease of the ablation efficiency was determined. − One physical explanation for this decreasing ablation efficiency, besides other contributions such as the increased amount of material phase changes, might be originated by an increased transient Δ R / R for large fluences. Therefore, this article discusses the relative change of the reflectance Δ R / R of stainless steel (EN 1.4301) after excitation by ultrashort pulsed laser radiation at fluence up to 2 J/cm 2 , measured by spatially resolved pump–probe reflectometry ,,,, with a temporal resolution of 50 fs.…”