gulley_2012#
J. R. Gulley, S. W. Winkler, W. M. Dennis, C. M. Liebig and R. Stoian, “Interaction of ultrashort-laser pulses with induced undercritical plasmas in fused silica”, Phys. Rev. A 85, 013808 (2012)
Source record · Catalogue · Review register
DOI: 10.1103/physreva.85.013808
Source kind: measurement
Recorded technique: 800-nm Ti:sapphire amplifiers (120-150 fs, 1 kHz; the text’s pulse is 140 fs FWHM) focused by a 25-cm lens onto the front surface of a 200-um fused-silica plate in air; beam profiles before and after the sample, multi-SHG-FROG of the transmitted pulse; the sample was not translated (~1e7 pulses per site). Simulated with a 3+1D nonlinear Schrodinger equation (Eq. 1) with Drude dispersion corrections, coupled to Rethfeld’s multiple rate equation with Keldysh photoionization, from the measured beam profile and FROG field.
Materials in structured entries: SiO2
Dataset quantities: band_gap, damage_threshold_energy, damage_threshold_fluence, effective_mass, electron_collision_time, electron_trapping_time, group_delay_dispersion, nonlinear_index, raman_fraction, raman_response_time, refractive_index
Contents: 13 datasets; 1 formula.
Curation notes#
Journal pages 013808-1 to -10 = PDF pages 1-10. Identity validated.
MEASURED DAMAGE (text, p. 013808-3): ‘These damage thresholds are summarized as follows: 60 uJ (5.1 J/cm2) for Secs. IV A and IV B, 45 uJ (3.8 J/cm2) for Sec. IV C 2, and 55 uJ (4.7 J/cm2) for Sec. IV C 3.’ ‘The multishot damage threshold was determined in the experiment, by visual inspection, to be 60 uJ (5.1 J/cm2). Since the sample was not translated in the experiment the surface was exposed to multiple (~10^7) pulses of the same energy ... lowering the damage threshold by approximately 25%. [35] The single-shot optical damage threshold is therefore expected to be around 80 uJ (6.8 J/cm2).’ The fluences are ‘peak single-shot fluence on the front sample surface’ (p. 013808-3); all five pairs share the ratio E/F = 1.18e-5 cm2 (checked 2026-09-26), one spot size. The Sec. IV C 2 and IV C 3 values are ‘destruction thresholds’ in the FROG series, the second with the laser of the Laboratoire Hubert Curien (p. 013808-9); ‘some of the subsections have different damage threshold measurements, as some were measured under different experimental conditions’ (p. 013808-3), which are not detailed further. Site: the front surface (the beam focused onto it; the simulations put the single-shot damage there too). No uncertainty stated. Grade not stated.
SIMULATION INPUTS: ‘All other numerical parameters for the computer simulation (summarized in Table I) were taken from Ref. [19]’ (Winkler et al., Appl. Phys. A 84, 413 (2006); p. 013808-3), so Table I’s values are reproduced from ref. 19 and assumed. Table I (p. 013808-3, tbl_763380c3ceb4, image checked): lambda 800 nm; R(tau) = [(tau_1^2 + tau_2^2)/(tau_1 tau_2^2)] exp(-tau/tau_2) sin(tau/tau_1) with tau_1 = 32 fs, tau_2 = 12.2 fs; f_r = 0.18; n0 = 1.45; k_2 = ‘361 fs^2 W^-1’; n2 = 2.48 x 10^-16 cm2 W^-1; U = 9 eV; m_e = 9.1 x 10^-31 kg; tau_c ‘Multiple values used’. Text (p. 013808-2): the Keldysh rate ‘with a reduced electron-hole mass of half the electron rest mass’; ‘a recombination time of 150 fs [19,34]’ (Winkler 2006; Wu, Chowdhury and Xu, Phys. Rev. B 72, 085128 (2005)); the damage criterion of the simulation, a free-electron density above 1e21 cm^-3 anywhere (p. 013808-3).
FINDINGS. (1) k_2’s unit is printed ‘fs^2 W^-1’ in the image: impossible for a GVD coefficient (fs^2 per length); the same number, 361, is couairon_2005’s k’’ at 800 nm in fs2/cm, and it is recorded as fs2/cm (an interpretation). (2) R(tau): as printed, tau_2 = 12.2 fs is the decay time and tau_1 = 32 fs the oscillation period parameter, the reverse of couairon_2005 (sin(t/12 fs) exp(-t/32 fs)) and berge_2010 (tau_R 32 fs decay at 1550 nm); either the definition or the values are swapped relative to the others: not resolvable from this paper, recorded as printed. (3) The critical power is written P_cr = lambda^2/(8 pi n0 n2) (p. 013808-4), a quarter of the usual lambda^2/(2 pi n0 n2) (0.71 against 2.83 MW with Table I’s values; computed 2026-09-26); no value is printed. (4) The absorption cross section sigma = e^2 tau_c/[m_e n0 eps0 c (1 + omega0^2 tau_c^2)] peaks at tau_c = 1/omega0 = 0.425 fs (printed ‘approximately tau_c = 0.42 fs’, p. 013808-4; checked).
THE COLLISION TIME: Fig. 2 gives the simulated single-shot threshold against tau_c; ‘Since the single-shot threshold is estimated from experiment to be 80 uJ (6.8 J/cm2) Fig. 2 suggests an approximate collision time of the order of 10 fs ... Therefore a 10-fs collision time is assumed hereafter’ (p. 013808-4); these simulations then predict a single-shot threshold of 80-85 uJ (6.8-7.2 J/cm2) (p. 013808-6). With G = 1 the simulated threshold ‘never exceeds 30 uJ (2.5 J/cm2)’.
TABLE II (p. 013808-9, tbl_f6dc38765622) is scrambled in the library; transcribed from the image in the script (checked against the scrambled characters). FROG retrieval diagnostics, not material data: pulse energy (uJ), trace dimensions, G_error, OC: 1, 256 x 128, 0.00319, 0.0115; 10, 0.00417, 0.0135; 17, 0.0036, 0.0105; 25, 0.0041, 0.008; 35, 0.00623, 0.01; 46, 0.0051, 0.011; 50, 0.00536, 0.0095; 55, 0.0062, 0.01 (all 256 x 128).
FIGURES ONLY: Fig. 2 (simulated thresholds against tau_c, three curves), Figs. 3-11 (plasma densities, beam profiles, FROG traces and fields).
Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
gulley_2012/damage_fluence#
{
"id": "damage_fluence",
"material": "SiO2",
"table": "text",
"quantity": "damage_threshold_fluence",
"unit": "J/cm2",
"abscissa": "duration",
"abscissa_unit": "fs",
"use": "primary",
"parameters": {
"site": "surface",
"criterion": "visible damage (visual inspection) of the front surface",
"shots": "~1e7 (sample not translated, 1 kHz)",
"wavelength_nm": 800
}
}
3 inline points in the source record.
p. 013808-3, the three measured thresholds as peak fluence on the front surface (rows: the sections they belong to). IV A: multishot (~1e7 pulses, sample not translated), ‘by visual inspection’. IV C 2 and IV C 3: ‘destruction threshold’ of the FROG series (IV C 3 with the Saint-Etienne laser); conditions otherwise not detailed. The duration is the text’s 140 fs FWHM (the lasers give 120-150 fs).
gulley_2012/damage_energy#
{
"id": "damage_energy",
"material": "SiO2",
"table": "text",
"quantity": "damage_threshold_energy",
"unit": "uJ",
"abscissa": "duration",
"abscissa_unit": "fs",
"use": "primary",
"parameters": {
"site": "surface",
"criterion": "visible damage (visual inspection) of the front surface",
"shots": "~1e7 (sample not translated, 1 kHz)",
"wavelength_nm": 800
}
}
3 inline points in the source record.
p. 013808-3, the same thresholds as pulse energies (see damage_fluence); focusing by a 25-cm lens onto the front surface, NA not stated.
gulley_2012/single_shot_estimate#
{
"id": "single_shot_estimate",
"material": "SiO2",
"table": "text",
"quantity": "damage_threshold_fluence",
"unit": "J/cm2",
"abscissa": "duration",
"abscissa_unit": "fs",
"use": "check",
"parameters": {
"site": "surface",
"criterion": "estimated single-shot threshold",
"shots": 1,
"wavelength_nm": 800
}
}
1 inline points in the source record.
p. 013808-3: ‘The single-shot optical damage threshold is therefore expected to be around 80 uJ (6.8 J/cm2)’, the multishot 60 uJ raised by the ~25 % incubation lowering of Schaffer et al. (ref. 35, Proc. SPIE 3451, 2 (1998)): an estimate, not a measurement.
gulley_2012/model_band_gap#
{
"id": "model_band_gap",
"material": "SiO2",
"file": "SiO2/gulley_2012__band_gap.csv",
"table": "tbl_763380c3ceb4",
"quantity": "band_gap",
"unit": "eV",
"abscissa": "none",
"use": "check",
"reproduced_from": [
"S. W. Winkler, I. M. Burakov, R. Stoian, N. M. Bulgakova, A. Husakou, A. Mermillod-Blondin, A. Rosenfeld, D. Ashkenasi and I. V. Hertel, Appl. Phys. A 84, 413 (2006)"
],
"parameters": {
"kind": "assumed",
"assumed": true
}
}
Table I, U ‘Band gap energy’ 9 eV; taken from ref. 19 (source notes).
gulley_2012/model_refractive_index#
{
"id": "model_refractive_index",
"material": "SiO2",
"file": "SiO2/gulley_2012__refractive_index.csv",
"table": "tbl_763380c3ceb4",
"quantity": "refractive_index",
"abscissa_unit": "nm",
"use": "check",
"reproduced_from": [
"S. W. Winkler, I. M. Burakov, R. Stoian, N. M. Bulgakova, A. Husakou, A. Mermillod-Blondin, A. Rosenfeld, D. Ashkenasi and I. V. Hertel, Appl. Phys. A 84, 413 (2006)"
],
"parameters": {
"assumed": true
}
}
Table I n0 = 1.45 at the 800-nm peak wavelength.
gulley_2012/model_gvd#
{
"id": "model_gvd",
"material": "SiO2",
"file": "SiO2/gulley_2012__gvd.csv",
"table": "tbl_763380c3ceb4",
"quantity": "group_delay_dispersion",
"unit": "fs2/m",
"scale": 100,
"abscissa_unit": "nm",
"use": "check",
"reproduced_from": [
"S. W. Winkler, I. M. Burakov, R. Stoian, N. M. Bulgakova, A. Husakou, A. Mermillod-Blondin, A. Rosenfeld, D. Ashkenasi and I. V. Hertel, Appl. Phys. A 84, 413 (2006)"
],
"parameters": {
"assumed": true
}
}
Table I k_2 = 361, unit printed ‘fs^2 W^-1’ (image confirmed), impossible for a GVD: read as fs2/cm (scale 100 to fs2/m), the unit of the same value in couairon_2005 at 800 nm. An interpretation of a misprinted unit.
gulley_2012/model_n2#
{
"id": "model_n2",
"material": "SiO2",
"file": "SiO2/gulley_2012__n2.csv",
"table": "tbl_763380c3ceb4",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-16,
"abscissa_unit": "nm",
"use": "check",
"reproduced_from": [
"S. W. Winkler, I. M. Burakov, R. Stoian, N. M. Bulgakova, A. Husakou, A. Mermillod-Blondin, A. Rosenfeld, D. Ashkenasi and I. V. Hertel, Appl. Phys. A 84, 413 (2006)"
],
"parameters": {
"part": "total",
"coefficient": "self",
"assumed": true
}
}
Table I n2 = 2.48 x 10^-16 cm2 W^-1, the total Kerr coefficient of Eq. (1), split into (1 - f_r) instantaneous and f_r Raman parts.
gulley_2012/model_raman_fraction#
{
"id": "model_raman_fraction",
"material": "SiO2",
"file": "SiO2/gulley_2012__raman_fraction.csv",
"table": "tbl_763380c3ceb4",
"quantity": "raman_fraction",
"abscissa": "none",
"use": "check",
"reproduced_from": [
"S. W. Winkler, I. M. Burakov, R. Stoian, N. M. Bulgakova, A. Husakou, A. Mermillod-Blondin, A. Rosenfeld, D. Ashkenasi and I. V. Hertel, Appl. Phys. A 84, 413 (2006)"
],
"parameters": {
"definition": "f_r in Eq. (1): i(k0 n2/n0)(1 - f_r) T I A + i(k0 n2/n0) f_r T [int R(tau - tau') I(tau') dtau'] A",
"assumed": true
}
}
Table I f_r, ‘Raman fraction of nonlinear polarization’.
gulley_2012/model_raman_tau_1#
{
"id": "model_raman_tau_1",
"material": "SiO2",
"file": "SiO2/gulley_2012__raman_tau_1.csv",
"table": "tbl_763380c3ceb4",
"quantity": "raman_response_time",
"unit": "fs",
"abscissa": "none",
"use": "check",
"reproduced_from": [
"S. W. Winkler, I. M. Burakov, R. Stoian, N. M. Bulgakova, A. Husakou, A. Mermillod-Blondin, A. Rosenfeld, D. Ashkenasi and I. V. Hertel, Appl. Phys. A 84, 413 (2006)"
],
"parameters": {
"constant": "tau_1 (in sin(tau/tau_1), as printed)",
"model": "R(tau) = [(tau_1^2 + tau_2^2)/(tau_1 tau_2^2)] exp(-tau/tau_2) sin(tau/tau_1)",
"assumed": true
}
}
Table I tau_1 = 32 fs; in the printed R(tau) it is the oscillation parameter, sin(tau/tau_1), the reverse of couairon_2005’s assignment (source notes, finding 2).
gulley_2012/model_raman_tau_2#
{
"id": "model_raman_tau_2",
"material": "SiO2",
"file": "SiO2/gulley_2012__raman_tau_2.csv",
"table": "tbl_763380c3ceb4",
"quantity": "raman_response_time",
"unit": "fs",
"abscissa": "none",
"use": "check",
"reproduced_from": [
"S. W. Winkler, I. M. Burakov, R. Stoian, N. M. Bulgakova, A. Husakou, A. Mermillod-Blondin, A. Rosenfeld, D. Ashkenasi and I. V. Hertel, Appl. Phys. A 84, 413 (2006)"
],
"parameters": {
"constant": "tau_2 (in exp(-tau/tau_2), as printed)",
"model": "R(tau) = [(tau_1^2 + tau_2^2)/(tau_1 tau_2^2)] exp(-tau/tau_2) sin(tau/tau_1)",
"assumed": true
}
}
Table I tau_2 = 12.2 fs; in the printed R(tau) it is the decay time, exp(-tau/tau_2) (source notes, finding 2).
gulley_2012/model_reduced_mass#
{
"id": "model_reduced_mass",
"material": "SiO2",
"table": "text",
"quantity": "effective_mass",
"unit": "m_e",
"abscissa": "none",
"use": "check",
"parameters": {
"carrier": "reduced",
"assumed": true
}
}
1 inline points in the source record.
p. 013808-2: the Keldysh rate ‘with a reduced electron-hole mass of half the electron rest mass’. The Drude cross section of Table I uses the free-electron mass m_e.
gulley_2012/model_recombination_time#
{
"id": "model_recombination_time",
"material": "SiO2",
"table": "text",
"quantity": "electron_trapping_time",
"unit": "fs",
"abscissa": "none",
"use": "check",
"reproduced_from": [
"S. W. Winkler, I. M. Burakov, R. Stoian, N. M. Bulgakova, A. Husakou, A. Mermillod-Blondin, A. Rosenfeld, D. Ashkenasi and I. V. Hertel, Appl. Phys. A 84, 413 (2006)",
"A. Q. Wu, I. H. Chowdhury and X. Xu, Phys. Rev. B 72, 085128 (2005)"
],
"parameters": {
"assumed": true
}
}
1 inline points in the source record.
p. 013808-2: ‘we also assume an exponential loss of free carriers from the conduction band with a recombination time of 150 fs [19,34]’.
gulley_2012/model_collision_time#
{
"id": "model_collision_time",
"material": "SiO2",
"table": "text",
"quantity": "electron_collision_time",
"unit": "fs",
"abscissa": "none",
"use": "check",
"parameters": {
"assumed": true
}
}
1 inline points in the source record.
p. 013808-4: chosen by matching the simulated single-shot threshold (Fig. 2) to the estimated 80 uJ: ‘Fig. 2 suggests an approximate collision time of the order of 10 fs ... Therefore a 10-fs collision time is assumed hereafter’. An order-of-magnitude, model-dependent choice.
Formulas#
gulley_2012/propagation_model#
{
"id": "propagation_model",
"material": "SiO2",
"equation": "Eq. (1), p. 013808-2, and Table I",
"printed": "dA/dz = (i/(2k0)) T^-1 nabla_perp^2 A + i D_b A + i (k0 n2/n0)(1 - f_r) T I A + i (k0 n2/n0) f_r T [int_-inf^tau dtau' R(tau - tau') I(tau')] A - (W_PI U/(2I)) A - (sigma/2)(1 + i omega0 tau_c) G^-1 [rho A]; I = (1/2) n0 c eps0 |A|^2; D_b = sum_{m>=2} (k_m/m!)(i d_tau)^m; T = 1 + (i/omega0) d_tau; G = 1 + (i/omega0) g d_tau; g = (-i omega0 tau_c)/(1 - i omega0 tau_c); sigma = e^2 tau_c/(m_e n0 eps0 c (1 + omega0^2 tau_c^2)); R(tau) = [(tau_1^2 + tau_2^2)/(tau_1 tau_2^2)] exp(-tau/tau_2) sin(tau/tau_1)",
"variable": "A: complex field envelope, E = (1/2) A exp[i(k0 z - omega0 t)] + c.c.; tau = t - z k_1; rho the free-carrier density from Rethfeld's multiple rate equation (rethfeld_2004)",
"coefficients": {
"tau_1": "32 fs",
"tau_2": "12.2 fs",
"f_r": "0.18",
"n0": "1.45",
"k_2": "361 (unit printed fs^2 W^-1)",
"n2": "2.48e-16 cm^2/W",
"U": "9 eV",
"tau_c": "10 fs (chosen)",
"tau_rec": "150 fs"
},
"reproduced_from": [
"J. R. Gulley and W. M. Dennis, Phys. Rev. A 81, 033818 (2010)"
],
"check": "sigma peaks at tau_c = 1/omega0 = 0.425 fs at 800 nm (printed 'approximately tau_c = 0.42 fs'); at tau_c = 10 fs, sigma = 1.32e-18 cm2 (computed, not printed) (2026-09-26)."
}
The Drude dispersion operator G is the paper’s subject (ref. 30); only the GVD term of D_b is kept. P_cr is written lambda^2/(8 pi n0 n2) in the self-focusing length z_sf = pi w_xy^2/(lambda sqrt(P/P_cr - 1)) (p. 013808-4; source notes, finding 3).
Corrections#
No dataset errata are recorded in this source record.
Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the review register for the checks and decisions.