lenzner_1998#

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond optical breakdown in dielectrics”, Phys. Rev. Lett. 80, 4076-4079 (1998)

Source record · Catalogue · Review register

DOI: 10.1103/physrevlett.80.4076

Source kind: measurement

Recorded technique: Front-surface optical breakdown (ablation) of fused silica (FS, Corning 7940) and barium aluminum borosilicate glass (BBS, Corning 7059), both with drawn surfaces (roughness < 10 and < 13 nm), by linearly polarized 780-nm pulses of 5 fs to 5 ps: a Ti:sapphire amplifier (20 fs, 1 mJ, 1 kHz) and a hollow-fibre chirped-mirror compressor (5-20 fs bandwidth-limited by the argon pressure; >= 20 fs by evacuating the fibre and stretching), the fibre acting as a spatial filter (M^2 < 1.1); focused to a 1/e2 diameter of ~30 um, imaged on a CCD. Each site exposed to 50 pulses at one fluence; the ablated volume per pulse V_a against on-axis fluence F is linear, and its regression line extrapolated to V_a = 0 gives the threshold F_th (Fig. 2). Ablation depths from light and electron microscopy (Figs. 4-5). In air (sub-10-fs breakdown in vacuum gave the same F_th; note 13).

Materials in structured entries: Corning-7059, SiO2

Dataset quantities: avalanche_coefficient, band_gap, effective_mass, multiphoton_ionization_cross_section

Contents: 8 datasets; 1 formula.

Curation notes#

Journal pages 4076-4079 = pdf pages 1-4. Identity checked against the first page.

WHAT WAS MEASURED (figures). Fig. 3 (p. 4077): F_th of FS and BBS against the pulse duration tau (FWHM) at 780 nm, 5 fs to 5 ps, 50 pulses per site, with the fits of Eq. (1). Error bars ‘represent standard deviations’; ‘the absolute (systematic) error of the measurements is less than +-15%’ (p. 4077; the extraction prints ‘615%’, the ‘6’ being the lost ‘+-’). Not digitised. In the text: ‘we report F_th ~ 1.5 J/cm^2 in fused silica for tau <= 10 fs’ (p. 4076), against Stuart et al.’s prediction of < 0.1 J/cm^2 for tau ~ 10 fs; for tau > 100 fs the FS thresholds agree with Varel et al. (tau > 190 fs) ‘but exceed by approximately a factor of 2 those reported in’ Stuart et al. (stuart_1996), and ‘Starting from the same level at tau >= 1 ps, F_th in BBS becomes by a factor as large as ~3 smaller as compared to FS for tau <= 20 fs’ (p. 4077). The 1.5 J/cm^2 is not recorded as a dataset (it spans 5-10 fs; no single duration). Damage site: the front surface; criterion: extrapolated onset of ablation (zero ablated volume); 50-on-1. Fig. 2: V_a against F at two durations in FS. Figs. 4-5: accumulated ablation depth against the number of pulses at (5 +- 1) J/cm^2 (FS) and (6.2 +- 0.7) J/cm^2 (BBS); per pulse d_a(220 fs) = (170 +- 35) nm and d_a(5 fs) = (200 +- 10) nm for FS, (270 +- 65) and (115 +- 8) nm for BBS, ‘the uncertainties representing a 99% confidence interval’ (p. 4078; no quantity). Fig. 1: an SEM image of a 5-fs crater at 6 F_th.

THE MODEL (Eq. 1, p. 4078), from Stuart et al.: dn/dt = alpha I(t) n(t) + sigma_k I^k, ‘alpha is the avalanche coefficient, and sigma_k is the k-photon absorption cross section with the smallest k satisfying k hbar omega >= Delta’; n_th = 1e21 cm^-3 (‘near the plasma critical density’); chi^2 fits to the F_th data for tau >= 20 fs: ‘alpha_fs = (4 +- 0.6) cm^2/J and sigma_6 = 6 x 10^(8 +- 0.9) cm^-3 ps^-1 (cm^2/TW)^6 for FS and alpha_bbs = (1.2 +- 0.4) cm^2/J and sigma_3 = 7 x 10^(17 +- 0.5) cm^-3 ps^-1 (cm^2/TW)^3 for BBS. The errors given are related to a factor of 2 increase in the chi^2 merit function with respect to its minimum value’ (p. 4078). sigma_k is a rate per unit volume (the equation has no atom density): 6 x 10^8 cm^-3 ps^-1 (cm^2/TW)^6 = 6.0e-52 cm^-3 s^-1 (cm^2/W)^6, and 7e17 cm^-3 ps^-1 (cm^2/TW)^3 = 7e-7 cm^-3 s^-1 (cm^2/W)^3. ‘Whereas alpha_fs is in reasonable agreement with the prediction of the kinetic theory of Stuart et al., sigma_6 and sigma_3 are by some 6 and more than 2 orders of magnitude smaller as compared to the prediction of the Keldysh formula’ (the Keldysh rate evaluated with m_eff = 0.5 m for FS, Fischetti and DiMaria, and m_eff = m for BBS; note 16). Band gaps (p. 4077): ‘Delta_fs ~ 9 eV and Delta_bbs ~ 4 eV’, no source. Keldysh parameter gamma = omega sqrt(2 m Delta)/eE ~ 0.5 for both materials at 5 fs (p. 4078). Photoionised fraction at F = F_th (p. 4079): n_p(500 fs)/n_th ~ 4e-8 and n_p(50 fs)/n_th ~ 1.5e-4 for FS, 0.09 and 0.35 for BBS, so ‘optical breakdown in fused silica is dominated by the avalanche process down to the 10-fs regime, whereas in BBS ... multiphoton ionization takes over for pulse durations below 100 fs’. Note 18: ‘our data ... are inconsistent with a sqrt(I) scaling of the avalanche as proposed’ by Du et al. (du_1994).

CHECK OF THE FIT (computed 2026-09-27): Eq. (1) with the printed alpha and sigma_k, n_th = 1e21 cm^-3, a Gaussian pulse of the stated FWHM and the peak (on-axis) fluence gives F_th(FS) = 1.08, 1.58, 2.17, 3.06, 3.79, 5.60 J/cm^2 at 5, 10, 20, 50, 100, 500 fs (the text’s ~1.5 J/cm^2 at <= 10 fs is reproduced), F_th(BBS) = 0.58, 0.87, 1.41, 1.97, 3.72 J/cm^2 at 10, 20, 50, 100, 500 fs, and photoionised fractions at threshold of 4.7e-4 (50 fs) and 1.8e-7 (500 fs) for FS, 0.40 and 0.073 for BBS, against the printed 1.5e-4, 4e-8, 0.35 and 0.09: the same order of magnitude, not the printed digits (the paper does not state its pulse shape; a sech^2 pulse gives 4.0e-4, 1.45e-7, 0.39 and 0.068); well within sigma_6’s stated factor 10^(+-0.9).

REPRODUCTIONS OF THIS PAPER: schaffer_2001 and jing_2012 (sigma_6 = 6.0e-52 cm^-3 s^-1 (cm^2/W)^6, i.e. this paper’s value converted), couairon_2005 (sigma_6 = 3 x 10^(-67 +- 0.9) s^-1 cm^12/W^6 ‘per atom’, which is not this value divided by an atom density: 6.0e-52/2.1e22 = 2.9e-74; a factor 1e7 apart), jing_2012 (a threshold comparison), dubietis_2019.

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