hamam_2018#

K. A. Hamam and Y. E. E.-D. Gamal, “Numerical analysis of breakdown dynamics dependence on pulse width in laser-induced damage in fused silica: Role of optical system”, Results Phys. 9, 725 (2018)

Source record · Catalogue · Review register

DOI: 10.1016/j.rinp.2018.03.042

Source kind: theory

Recorded technique: Rate-equation model of the conduction-electron density in fused silica (Keldysh photoionization, Drude avalanche, diffusion and recombination losses, Eq. 2), solved with fourth-order Runge-Kutta for Gaussian pulses in space and time, and compared with the bulk breakdown thresholds that Liu et al. (2005) measured at 800 nm, 240 fs - 2.5 ps, with two focusing conditions (effective NA 0.126 and 0.255; focal radii 2.0 and 0.95 um), single pulse per site. The measured thresholds are reproduced in Tables 1 and 2; the breakdown criterion of the model is n_cr ~ 1.45e19 cm^-3 (from Liu et al.).

Materials in structured entries: SiO2

Dataset quantities: band_gap, critical_power, damage_threshold_intensity, effective_mass, electron_trapping_time, nonlinear_index, refractive_index

Contents: 8 datasets; 3 formulas.

Curation notes#

Journal pages 725-733 = PDF pages 1-9. Identity validated (DOI printed).

THE THRESHOLDS ARE LIU ET AL.’S. ‘The model is applied to investigate the threshold intensity dependence on laser pulse width in the experimental measurements that are given by Liu et al. (2005)’ (abstract); Table 2’s note: ‘Laser power calculated corresponding to the measured threshold intensity given by Liu et al., (2005) for the two numerical apertures NA = 0.126 and 0.255.’ Both datasets are therefore reproduced (Liu et al. is not in the library). Liu’s experiment as described here (pp. 725-726): Ti:sapphire, 800 nm, FWHM 240 fs - 2.5 ps, a 10 x 5 x 3 mm3 fused-silica block, ‘each location of the sample only once’ (single shot), a CCD behind a filter that blocks the 800-nm light; the effective NA = w/(w^2 + d^2)^0.5 from the knife-edge beam radius w after the objective and the distance d to the focus; the objectives under-filled by about 3; focal radii (FWHM, ‘estimated’) 2.0 and 0.95 um. The damage criterion of the measurement is not stated here. Tables 1-2 list nine durations, 250 fs - 2.2 ps, not the ‘240 fs - 2.5 ps’ of the text.

NA 0.225 OR 0.255 (finding). Table 1 and Table 2 head the second condition ‘NA = 0.225’ (image checked); the abstract, the text (pp. 726-728) and the captions of Figs. 1-12 give 0.255. Recorded as 0.255, with the table heading noted.

TABLE 2’s POWER COLUMN (not extracted: no quantity). Printed P (W), NA 0.126: 5.68E04, 2.93E04, 1.83E04, 1,13E04 (decimal comma, image checked), 9.33E03, 9.63E03, 8.83E03, 9.70E03, 9.75E03; NA 0.225/0.255: 4.05E04, 2.55E04, 1.55E04, 1.20E04, 1.04E04, 8.33E03, 7.95E03, 8.40E03, 8.45E03. Check (2026-09-26): P/I_th = 7.86e-9 cm2 (NA 0.126, except the first row, 7.43e-9) and 7.09e-9 cm2 (NA 0.255), not pi w0^2 for the stated radii (1.26e-7 and 2.84e-8 cm2): how P was calculated is not reproduced. The powers are compared with P_cr = 2.19e6 W to argue that self-focusing is negligible (p. 727).

TABLE 1’s KELDYSH PARAMETER (not extracted: no quantity). Check (2026-09-26): every printed gamma is sqrt(2) = 1.414 times Eq. (1) evaluated with the stated eps_eff = 9.0 eV and m’ = m/2 (to 4 digits), i.e. the table used m’ = m_e (or a field convention differing by 2 in I); except the NA 0.225 row at 2.05E-12 s, printed 7.696 where its I_th = 1.185E12 gives 7.97 (7.696 would need I = 1.27e12). gamma > 3 throughout: multiphoton regime.

MODEL INPUTS (pp. 726-727; datasets where a quantity exists): eps_eff = eps_g = 9.0 eV (‘Following the values of gamma shown in Table 1, eps_eff is taken to be = 9.0 eV (the energy gap for fused silica)’); ‘m’ is the reduced mass and is approximate ~m/2 [2]’; Z0 = 377 Ohm; the momentum scattering rate ‘1/tau_m(eps) = 10^14 - 10^16 s^-1’, ‘adopted ... by others Arnold Cartier and de Maria [22]’ (a range: no dataset); M ~ 9.98 x 10^-26 kg in Eq. (5) (no quantity); the recombination time tau_rec = R^-1 = 1.5 x 10^-13 s, ‘an empirical value for fused silica ... [23,24]’; the breakdown criterion n_cr ~ 1.45e19 cm^-3 [2]; for P_cr: n_r = 1.454, n2 = 3.2 x 10^-16 cm2/W [25,26], giving P_cr = 2.19 x 10^6 W (checked: 2.189e6 W, 2026-09-26). In Eq. (6) the Rayleigh length z_R = n_r pi w0^2 / lambda0; z_R = 2.35e-3 cm (NA 0.126) and 5.313e-4 cm (NA 0.255) (pp. 729-730).

MODEL RESULTS (figures only): calculated threshold against pulse width compared with Liu’s (Fig. 1), electron density and ionization rate against time (Figs. 2-4), their spatial variation (Figs. 5-12). Table 3 (tbl_9f0fb5be3f74): the electron density at the end of the pulse with and without losses (1.45e19 v 1.435e19 ... 1.2536e19 cm^-3), a model diagnostic, not extracted. Text: I_th at r = z = 0 is 3.51e12 W/cm2 for 395 fs, NA 0.126 (p. 730), model value.

Reference [10] (Schaffer et al. 2001, schaffer_2001) is cited for the practical NA limit 0.5.

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

Datasets#

hamam_2018/threshold_NA0126#

{
  "id": "threshold_NA0126",
  "material": "SiO2",
  "file": "SiO2/hamam_2018__threshold_NA0126.csv",
  "table": "tbl_5037c0738f9f",
  "quantity": "damage_threshold_intensity",
  "unit": "W/cm2",
  "abscissa": "duration",
  "abscissa_unit": "s",
  "use": "reproduced",
  "reproduced_from": [
    "liu_2005"
  ],
  "parameters": {
    "site": "bulk",
    "criterion": "not stated here (Liu et al.'s single-shot observation with a CCD)",
    "shots": 1,
    "wavelength_nm": 800,
    "numerical_aperture": 0.126
  }
}

Table 2, ‘Beam spot size = 2.0 (um)’ column I_th (the same values as Table 1). Liu et al.’s measured bulk breakdown thresholds (source notes); pulse FWHM as the abscissa. Grade of the fused silica not stated.

hamam_2018/threshold_NA0255#

{
  "id": "threshold_NA0255",
  "material": "SiO2",
  "file": "SiO2/hamam_2018__threshold_NA0255.csv",
  "table": "tbl_5037c0738f9f",
  "quantity": "damage_threshold_intensity",
  "unit": "W/cm2",
  "abscissa": "duration",
  "abscissa_unit": "s",
  "use": "reproduced",
  "reproduced_from": [
    "liu_2005"
  ],
  "parameters": {
    "site": "bulk",
    "criterion": "not stated here (Liu et al.'s single-shot observation with a CCD)",
    "shots": 1,
    "wavelength_nm": 800,
    "numerical_aperture": "0.255 (text, abstract, Figs. 1-12; Tables 1-2 print 0.225)"
  }
}

Table 2, ‘Beam spot size = 0.95 (um)’ column I_th. The tables head this condition ‘NA = 0.225’, the text and captions 0.255 (source notes).