liu_2005#

Y. Liu, H. Jiang, Q. Sun, Z. Wu, H. Yang, and Q. Gong, “Different tendencies of breakdown threshold on pulse duration in the subpicosecond regime in fused silica”, J. Opt. A: Pure Appl. Opt. 7, 198-203 (2005)

Source record · Catalogue · Review register

DOI: 10.1088/1464-4258/7/4/008

Source kind: measurement

Recorded technique: Single-shot laser-induced breakdown inside bulk fused silica (polished, 10 x 5 x 3 mm^3; grade not stated) at 800 nm, pulse durations 240 fs to 2.5 ps (compressor grating), each site irradiated once. The spatially filtered beam underfills (by ~3) a 0.4 or 0.85 NA objective; the beam radius omega after the objective and its distance d to the focus measured by knife edge give the effective NA = omega/(omega^2 + d^2)^0.5 = 0.126 and 0.255 (focal radii ~2.0 and 0.95 um for a Gaussian beam). Breakdown detected by imaging the plasma luminescence from the side onto a cooled CCD (Princeton Instruments TE/CCD-512/SB, a filter blocking 800 nm), the threshold being the lowest input energy giving a plasma image (p. 199). Depths 6, 170 and 300 um (+-5 um); the detailed data at 300 um. Simulated with a 3-D nonlinear envelope equation (Eq. 1: diffraction, GVD, Kerr, plasma absorption and defocusing, multiphoton absorption) coupled to an electron-density rate equation (Eq. 2: avalanche and multiphoton ionization, no recombination) solved by an ADI method.

Materials in structured entries: SiO2

Dataset quantities: atom_density, band_gap, damage_threshold_energy, electron_collision_time, multiphoton_ionization_cross_section, nonlinear_index

Contents: 6 datasets; 1 formula.

Curation notes#

Journal pages 198-203 = pdf pages 2-7 (journal page = 196 + pdf page; pdf page 1 is the IOP download cover). Identity checked against the first page.

WHAT WAS MEASURED. Fig. 2 (p. 200): the threshold energy against pulse duration (240 fs - 2.5 ps) at 300 um depth for effective NA 0.126 (squares) and 0.255 (triangles): with NA 0.126 the threshold rises for pulses shorter than 700 fs; with NA 0.255 it keeps decreasing from 2.5 ps to 240 fs (figure only, not digitised). The depth changed the threshold by at most 10 % without changing the trend (p. 200). The one threshold printed in the text: Fig. 1’s example, NA 0.255, 400 fs, ‘For E_in = 0.17 uJ, an image of pure noise is obtained while for E_in = 0.18 uJ a clear image of the plasma can be seen. Therefore the threshold in this case can be defined as 0.18 uJ with an error of 0.01 uJ’ (p. 199): dataset threshold_energy_400fs (the depth of this example is not stated). The energies are the input pulse energies (E_in).

THE MODEL AND ITS INPUTS (p. 200; assumed, datasets check): Eq. (1), (i 2k d/dz + nabla_perp^2) eps = k k’’ d^2 eps/d xi^2 - 2 k k0 n2 |eps|^2 eps - i k sigma (1 + i omega0 tau_c) rho eps - i k beta^(K) |eps|^(2K-2) eps, with n2 = 3.54 x 10^-16 cm^2/W (Ref. 17, Sudrie et al., Phys. Rev. Lett. 89, 186601 (2002)), beta^(K) = K hbar omega0 sigma_K rho_at; ‘A band gap potential E_g = 9 eV of the material yields the K = 6 required for the ionization and the multiphoton ionization (MPI) coefficient sigma_K = 9.8 x 10^-70 s^-1 cm^12 W^-6’ (Ref. 17); the inverse-bremsstrahlung cross section sigma = k e^2 tau_c / omega0 m_e eps0 (1 + (omega0 tau_c)^2) = 1.55 x 10^-18 cm^2 with tau_c = 2.33 x 10^-14 s (Ref. 17); ‘The critical plasma density rho_c, and the background atom density, rho_at = 2.1 x 10^21 cm^-3, are in the ratio rho_at/rho_c ~ 12’ (Ref. 18, Ward and Berge 2003). Eq. (2): d rho/d xi = sigma/(n0^2 E_g) rho |eps|^2 + sigma_K rho_at |eps|^(2K) (|eps|^2 the intensity); rho_0 = 1.0 x 10^8 cm^-3 initial electrons (Ref. 8, Tien et al. 1999); recombination omitted (a test with it changed little). The MPI term is used ‘not expressed by Keldysh’s formula ... because the adiabaticity parameter gamma >> 1 in our experiments’. k’’ and n0 are not given.

CHECKS (computed 2026-09-27). rho_c = eps0 m_e omega0^2/e^2 = 1.742e21 cm^-3 at 800 nm, so rho_at/rho_c ~ 12 requires rho_at = 2.1e22 cm^-3 (12.06), not the printed 2.1e21 (1.21): erratum (couairon_2005, the same group’s model inputs, prints rho_at = 2.1e22). The printed sigma = 1.55e-18 cm^2 is not reproduced by its own formula with tau_c = 2.33e-14 s: with k = n0 omega0/c and n0 = 1.45 it gives 1.19e-18 cm^2 (1.55e-18 needs tau_c ~ 1.8e-14 s); not decidable, no erratum. sigma_K = 9.8e-70 against couairon_2005’s 9.6e-70 s^-1 cm^12/W^6 for the same Keldysh limit.

THRESHOLD DENSITIES (model results, notes only). The simulated plasma density saturates below 1e19 cm^-3 (p. 200); with rho_th = 1.8e19 and 1.45e19 cm^-3 the NA 0.126 thresholds rise below 1000 and 550 fs, with 1.3e19 they are flat after 500 fs, with 1.0e19 they keep decreasing (Fig. 3a); the experiment matches rho_th = 1.45e19 cm^-3 (NA 0.126) and 6.11e19 cm^-3 (NA 0.255), the integrated densities agreeing to 6 % (p. 201); for NA 0.126 the 300 and 700 fs density curves cross at 1.4e19 cm^-3; for NA 0.255 slight saturation above 5.6e19 cm^-3 at 300 fs (p. 202). The rise at loose focusing is attributed to plasma defocusing (Figs. 4-6). Figs. 3-6 are figures only.

FINDING (the NA). The paper prints ‘effective NA = 0.225’ once (p. 202, in the discussion of Fig. 6) and 0.255 everywhere else (abstract, p. 199, Figs. 1-4 captions): a misprint in this paper, which hamam_2018 carries into its tables.

REPRODUCTIONS OF THIS PAPER. hamam_2018 Table 2 attributes its threshold intensities and powers against pulse width to this paper, but this paper prints no intensities and no table (Fig. 2 gives input energies only): hamam_2018’s values are its own conversion of Fig. 2 (listed for review; hamam_2018 is another extraction’s record).

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