couairon_2005#

A. Couairon, L. Sudrie, M. Franco, B. Prade and A. Mysyrowicz, “Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses”, Phys. Rev. B 71, 125435 (2005)

Source record · Catalogue · Review register

DOI: 10.1103/physrevb.71.125435

Source kind: measurement

Recorded technique: 800-nm Ti:sapphire pulses (160 fs, 200 kHz regenerative amplifier; 50 fs, 1 kHz CPA chain) focused into bulk fused silica by microscope objectives (Table I; mostly 20x, NA 0.5, waist 1.1 um measured in air). Measured: the position of the damage track against pulse energy (the shift of the nonlinear focus, giving P_cr and n2, Sec. IV A), the transmitted energy against input energy (Sec. IV B), damage-track morphology by optical and electron microscopy (Sec. V), and pump-probe absorption (Sec. VI). Simulated with a nonlinear envelope equation (Sellmeier dispersion, Kerr with delayed Raman, self-steepening, Drude plasma, Keldysh photoionization, avalanche and recombination), Eqs. (2)-(8).

Materials in structured entries: SiO2

Dataset quantities: atom_density, band_gap, critical_power, damage_threshold_energy, effective_mass, electron_collision_time, electron_trapping_time, group_delay_dispersion, ionization_rate, multiphoton_ionization_cross_section, nonlinear_index, raman_fraction, raman_response_time, refractive_index

Contents: 23 datasets; 4 formulas.

Curation notes#

Journal pages 125435-1 to -11 = PDF pages 1-11. Identity validated.

MEASURED (datasets primary): P_cr = 1.98 MW and n2 = 3.54e-16 cm2/W from the shift of the nonlinear focus with power (160-fs pulses, 20x NA 0.5), p. 125435-5: ‘This function vanishes when sqrt(P_in) = 1.4 MW^(1/2), which corresponds to sqrt(P_cr*). Thus, the critical power for self-focusing is P_cr = 1.98 MW, corresponding to the nonlinear refraction index n2 = lambda0^2/2 pi n0 P_cr = 3.54 x 10^-16 cm2/W.’ Checked: lambda0^2/(2 pi 1.45 x 1.98 MW) = 3.548e-16 cm2/W; 1.4^2 x 1.002 = 1.964 MW, so 1.98 rests on an unrounded intercept (2026-09-26). The collision time tau_c = 1e-14 s from the transmission (p. 125435-5: ‘we obtained the best agreement for the value tau_c = 10^-14 s’; the calculated transmission of a 1-uJ pulse goes from ~30 % at 1e-15 s to >70 % at 1e-14 s). The electron-hole plasma lifetime ‘around 150 fs’ (pump-probe, p. 125435-10), which the simulations also use (from Audebert et al., ref. 37).

The pulse powers: ‘various energies from 0.25 uJ (1.56 MW) to 1.25 uJ (7.8 MW)’ (p. 125435-4) are E/tau_FWHM (0.25 uJ / 160 fs = 1.56 MW), not the model’s P_in = E_in/(t_p sqrt(pi/2)) (1.47 MW for t_p = 136 fs) of p. 125435-2 (checked 2026-09-26): the P_cr of Fig. 4 is on the E/tau_FWHM scale if the axis uses those powers; the paper does not say which the fit used (doubt).

MODEL INPUTS (assumed, datasets check; p. 125435-2 to -3): n0 = 1.45; the Sellmeier formula Eq. (3) (Malitson’s coefficients rounded to four decimals, uncited, see the formula); k’’ = 361 fs2/cm computed from it (checked: 361.38 fs2/cm at 800 nm); f_R = 0.18, tau_d = 32 fs, tau_s = 12 fs for R(t) ‘From Refs. 23 and 25 ... (see Ref. 23)’ (Junnarkar 2001; Stolen et al. 1989 = stolen_1989); U_i = 9 eV (‘A gap of 9 eV is found in Refs. 23, 31, 35, 36, 40, and 43. A lower gap of 7.8 eV is found in Refs. 44-46. Recently, a gap of 7.1 eV has been also determined (47) ... the results computed with a gap of 7.6 eV could not be satisfactorily compared with experiments’, p. 125435-4: note 7.8 in one sentence, 7.6 in the next); m = 0.64 m_e the reduced mass (ref. 40, Fischetti et al. 1985); rho_at = 2.1e22 cm^-3 ‘the background atom density’; tau_r = 150 fs (ref. 37). The multiphoton coefficient sigma_6 = 9.6e-70 s^-1 cm12/W6 is the weak-field limit of their Keldysh rate, not an input. Checks (2026-09-26): gamma = 1 at 3.5e13 W/cm2 with m = 0.64 m_e, U_i = 9 eV and I = n0 c eps0 |E|^2/2 (0.999); W_MPI = sigma_6 I^6 rho_at = 3.706e34 cm^-3 s^-1 (printed 3.7e34); rho_c = omega0^2 eps0 m_e/e^2 = 1.742e21 cm^-3 (printed 1.74e21, with the free-electron mass although the symbol is m*); omega0^-1 = 0.425 fs (printed 4.2e-16 s); t_p = 135.9 fs for 160 fs FWHM (printed 136) and 42.5 fs for 50 fs (printed 42).

LITERATURE (datasets reproduced): n2 = 3.75e-16 cm2/W and P_cr = 1.72 MW ‘from Ref. 29’ (Boyd, Nonlinear Optics, 1992; wavelength not stated). Checked: with n0 = 1.45 and lambda0 = 800 nm, lambda^2/(2 pi n0 n2) gives 1.87 MW and 3.77 lambda^2/(8 pi n0 n2) 1.77 MW; neither is 1.72 (2026-09-26). sigma_6 = 1.5e-71 s^-1 cm12/W6 (ref. 36, Li et al. 1999) and 3 x 10^(-67 +- 0.9) s^-1 cm12/W6 (ref. 43, Lenzner et al. 1998), both ‘per atom’ in this paper’s convention W_MPI = sigma_6 I^6 rho_at. FINDING: schaffer_2001 and jing_2012 quote Lenzner’s rate per volume as 6.0e-52 cm^-3 s^-1 (cm2/W)^6, i.e. 2.9e-74 per atom with rho_at = 2.1e22 cm^-3, and jing_2012 quotes Li’s as 3.0e-56 per volume (1.4e-78 per atom): Couairon’s per-atom values are ~1e7 larger than both, for both references. Lenzner et al. is now curated (lenzner_1998), which confirms the per-volume reading (6 x 10^(8 +- 0.9) cm^-3 ps^-1 (cm2/TW)^6); Li et al. is not in the library.

DAMAGE (reproduced): Fig. 5’s ‘two vertical lines correspond to the onset of damage in bulk silica measured by Sudrie et al. (51)’: type I (a permanent index change, annealed at 900 C for about 1 hour) and ‘The second damage threshold at 0.31 uJ (type II) is accompanied by an induced birefringence ... cannot be cured by heating’ (p. 125435-5); the type I value is given as 0.1 uJ in the abstract, on p. 125435-5 and p. 125435-9 (‘the type I damage threshold is about 0.1 uJ’), type II as 0.3 uJ in the abstract. Focusing 20x, NA 0.5; the pulse duration of these thresholds is not stated (Fig. 5’s transmission is 50 fs, 1 kHz; the damage tracks 160 fs). The simulation infers that type II damage forms above an electron density of ~2e20 cm^-3 (p. 125435-6); the maximum density is clamped at 2-4e20 cm^-3, and the maximum intensity is 5 +- 0.5 x 10^13 W/cm2 up to 2 uJ (model results, no quantity).

TABLE I (p. 125435-2, tbl_39c4ea3b4fb9, image checked): objective magnification, NA and the 1/e2 waist in air: 2.5x 0.07 4.8 um; 4x 0.12 3.5 um; 10x 0.25 1.8 um; 20x 0.5 1.1 um; 40x 0.65 0.7 um (the library renders ‘um’ as ‘smmd’ and ‘x’ as ‘3’). Focusing characteristics, not material data: not extracted.

FIGURES ONLY: Fig. 2 (the Keldysh, multiphoton and tunnel rates for silica against intensity), Fig. 4 (the focus shift against power and its linearization), Fig. 5 (transmission against energy, measured and simulated), Figs. 6-13 (simulated fluence, intensity, electron density, losses), Fig. 15 (pump-probe absorption against delay).

Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.