Table 2.

Summary of Thermal Lensing Simulations Based on Linear-Absorption-Induced Heating ^{a, b, c, d, e}

Material	τc [μs]	α0 [m−1]	dn/dT × 10−6 [K−1]	ΔT(0, t=3 s) [K]	ΔΦTL [mrad]	ΔΦ10 MHz/10 W – ΔΦ0 [mrad]
N-BK7	690	0.12	1.2 [23]	0.82	18	334 ± 36
CaF2	100	0.08	−11.5 [24]	0.07	−16	172 ±29
MgF2	54	4.00	1.0 [24]	1.83	33	40 ± 25
BaF2	61	0.03	−16.2 [24]	0.03	−5	−7 ± 18

^aThermo-optic coefficients (dn/dT) for CaF₂, Baf₂, and MgF₂ were taken from Feldman et al. [24] at 293 K and λ = 1.15 μm.

^bdn/dT for borosilicate glass (N-BK7) was taken from Frey et al. [23] at 295 K and λ = 1 μm.

^cTemperatures at the beam center after 3 s exposure to 1 μJ, 300 fs laser pulses at 10 MHz repetition rate ΔT(0, t = 3 s) were determined from heat transfer simulations (Fig. 4).

^dΔΦ_TL the predicted thermal phase shift from our simulations, ΔΦ₀ is the measured average nonlinear phase shift from 10 kHz z-scans, and ΔΦ_{10 WHz/10 W} is the measured phase shift during 10 MHz/10 W z-scans.

^eThe last column shows the difference between ΔΦ_{10 MHz/10 W} and ΔΦ₀, which should be similar to ΔΦ_TL if linear-absorption-induced thermal lensing is the primary mechanism contributing to the increase in measured phase shift during high-repetition-rate/high-average-power z-scans.