jukna_2018#
V. Jukna, N. Garejev, G. Tamosauskas and A. Dubietis, “Role of external focusing geometry in supercontinuum generation in bulk solid-state media”, J. Opt. Soc. Am. B 36, A54 (2019)
Source record · Catalogue · Review register
Source kind: measurement
Recorded technique: Supercontinuum generation in a 4-mm sapphire plate by 210-fs, 1.3-um pulses (OPA signal stretched by a 9-nm interference filter, up to 6 uJ), focused by an f = +100 mm lens (23 um FWHM spot) on the input face or 1 mm inside; spectra 0.2-1.8 um with Si and Ge detectors; filament-induced luminescence photographed from the side. Simulated with a unidirectional nonparaxial propagation equation (Eqs. 1-3) and a photoionization-avalanche-recombination rate equation (Eq. 4).
Materials in structured entries: Al2O3
Dataset quantities: atom_density, avalanche_coefficient, band_gap, electron_collision_time, electron_trapping_time, nonlinear_index, refractive_index
Contents: 7 datasets; 1 formula.
Curation notes#
Journal pages A54-A60 = PDF pages 1-7; ‘published 20 December 2018’ in the February 2019 issue (vol. 36, no. 2): the source id keeps the library’s 2018, the citation the volume year 2019. Identity validated.
MEASURED (no curated quantity): supercontinuum threshold 2 uJ with the focus on the input face and 1.48 uJ with the focus 1 mm inside, where the continuum is suppressed between 2.0 and 2.5 uJ and recovers above 2.5 uJ (pp. A55-A56); the continuum spans 470 nm - 1.8 um at the 1e-5 level; the luminescence band of sapphire peaks at 325 nm, attributed to 11-photon absorption ‘assuming its bandgap of 9.9 eV and photon energy of 0.95 eV’ (p. A55; 9.9/0.954 = 10.4, so 11 photons: checked 2026-09-26). Polarization and crystal orientation (c-axis) not stated.
SIMULATION INPUTS (pp. A56-A57, datasets assumed): ‘n0 = 1.75 and n2 = 3.1 x 10^-16 cm2/W [29] are the linear and nonlinear refractive indices of sapphire, respectively; sigma = 1.9 x 10^-21 m2 is the cross section for inverse Bremsstrahlung; tau_c = 1 fs is the effective electron collision time; rho_nt = 2.35 x 10^22 cm^-3 is the density of neutral molecules’; ‘The intensity-dependent photoionization rate W was calculated from Keldysh’s theory with electron-hole mass ratio m* = 1 and assuming bandgap of sapphire U_g = 9.9 eV [28]’; ‘tau_rec = 100 ps [30] is the free electron recombination time’; n(omega) ‘from a Sellmeier equation [28]’ (Weber, Handbook of Optical Materials, CRC 2002; the formula is not printed). Ref. 29 is Major et al., Opt. Lett. 29, 602 (2004); ref. 30 Guizard et al., Europhys. Lett. 29, 401 (1995). The ‘electron-hole mass ratio m* = 1’ is ambiguous (a mass in electron masses, or a ratio of the electron and hole masses): not recorded as a dataset. The Kerr response of Eq. (2) is instantaneous (no Raman term). Simulated input: 210 fs, 30-um FWHM Gaussian beam, flat phase at the focus.
CHECK (2026-09-26): the Drude cross section e^2 tau_c/(m_e n0 eps0 c (1 + omega0^2 tau_c^2)) at 1.3 um with tau_c = 1 fs and n0 = 1.75 is 1.957e-21 m2; printed 1.9e-21 m2 (truncated rather than rounded, or a slightly different n0 or mass).
REPRODUCES: silva_2012 (ref. 13) and dubietis_2019’s review (ref. 1, Lith. J. Phys. 2017 version) are cited for context only.
Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
jukna_2018/model_refractive_index#
{
"id": "model_refractive_index",
"material": "Al2O3",
"table": "text",
"quantity": "refractive_index",
"abscissa_unit": "nm",
"use": "check",
"parameters": {
"assumed": true
}
}
1 inline points in the source record.
p. A56: ‘n0 = 1.75 ... the linear ... refractive index of sapphire’ at the 1.3-um carrier (the dispersion itself from a Sellmeier equation of ref. 28). Axis not stated.
jukna_2018/model_n2#
{
"id": "model_n2",
"material": "Al2O3",
"table": "text",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"abscissa_unit": "nm",
"use": "check",
"reproduced_from": [
"A. Major, F. Yoshino, I. Nikolakakos, J. S. Aitchison and P. W. E. Smith, Opt. Lett. 29, 602 (2004)"
],
"parameters": {
"part": "unknown",
"coefficient": "self",
"assumed": true
}
}
1 inline points in the source record.
p. A56: ‘n2 = 3.1 x 10^-16 cm2/W [29]’, used as the instantaneous Kerr coefficient of Eq. (2) at 1.3 um. Axis and polarization not stated.
jukna_2018/model_avalanche_cross_section#
{
"id": "model_avalanche_cross_section",
"material": "Al2O3",
"table": "text",
"quantity": "avalanche_coefficient",
"unit": "m2",
"abscissa_unit": "nm",
"use": "check",
"parameters": {
"definition": "sigma in eps0^-1 J = n0 c [sigma (1 + i omega0 tau_c) rho + ...] E (Eq. 3) and the avalanche term (sigma/U_g)|E|^2 rho (1 - rho/rho_nt) of Eq. (4)",
"assumed": true
}
}
1 inline points in the source record.
p. A56: ‘sigma = 1.9 x 10^-21 m2 is the cross section for inverse Bremsstrahlung’; the Drude value for tau_c = 1 fs, n0 = 1.75 is 1.957e-21 m2 (source notes).
jukna_2018/model_collision_time#
{
"id": "model_collision_time",
"material": "Al2O3",
"table": "text",
"quantity": "electron_collision_time",
"unit": "fs",
"abscissa": "none",
"use": "check",
"parameters": {
"assumed": true
}
}
1 inline points in the source record.
p. A56: ‘tau_c = 1 fs is the effective electron collision time’; no source.
jukna_2018/model_molecule_density#
{
"id": "model_molecule_density",
"material": "Al2O3",
"table": "text",
"quantity": "atom_density",
"unit": "cm-3",
"abscissa": "none",
"use": "check",
"parameters": {
"counts": "molecules",
"assumed": true
}
}
1 inline points in the source record.
p. A56: ‘rho_nt = 2.35 x 10^22 cm^-3 is the density of neutral molecules’; no source.
jukna_2018/model_band_gap#
{
"id": "model_band_gap",
"material": "Al2O3",
"table": "text",
"quantity": "band_gap",
"unit": "eV",
"abscissa": "none",
"use": "check",
"reproduced_from": [
"M. J. Weber, Handbook of Optical Materials (CRC Press, 2002)"
],
"parameters": {
"kind": "assumed",
"assumed": true
}
}
1 inline points in the source record.
p. A57: ‘assuming bandgap of sapphire U_g = 9.9 eV [28]’, the gap of the Keldysh rate; also used for the 11-photon count of the luminescence (p. A55).
jukna_2018/model_recombination_time#
{
"id": "model_recombination_time",
"material": "Al2O3",
"table": "text",
"quantity": "electron_trapping_time",
"unit": "ps",
"abscissa": "none",
"use": "check",
"reproduced_from": [
"S. Guizard, P. Martin, P. Daguzan, G. Petite, P. Audebert, J. P. Geindre, A. Dos Santos and A. Antonnetti, Europhys. Lett. 29, 401 (1995)"
],
"parameters": {
"assumed": true
}
}
1 inline points in the source record.
p. A57: ‘tau_rec = 100 ps [30] is the free electron recombination time’.
Formulas#
jukna_2018/propagation_model#
{
"id": "propagation_model",
"material": "Al2O3",
"equation": "Eqs. (1)-(4), pp. A56-A57",
"printed": "dE^/dz = i (sqrt(k^2(omega) - k_perp^2) - k0 - k0' omega) E^ + i (omega/(2 n(omega) c)) eps0^-1 (P^ + i J^/omega) (1); eps0^-1 P = 2 n0 n2 |E|^2 E (2); eps0^-1 J = n0 c [sigma (1 + i omega0 tau_c) rho + (W U_g/|E|^2)(1 - rho/rho_nt)] E (3); d rho/dt = W (1 - rho/rho_nt) + (sigma/U_g) |E|^2 rho (1 - rho/rho_nt) - rho/tau_rec (4)",
"variable": "E^(omega, k_perp, z): the envelope's spectrum; W the Keldysh photoionization rate",
"coefficients": {
"n0": "1.75",
"n2": "3.1e-16 cm^2/W",
"sigma": "1.9e-21 m^2",
"tau_c": "1 fs",
"rho_nt": "2.35e22 cm^-3",
"U_g": "9.9 eV",
"m_star": "1 ('electron-hole mass ratio')",
"tau_rec": "100 ps"
},
"reproduced_from": [
"A. Couairon, E. Brambilla, T. Corti, D. Majus, O. de J. Ramirez-Gongora and M. Kolesik, Eur. Phys. J. Spec. Top. 199, 5 (2011)"
],
"check": "sigma: 1.957e-21 m2 from the Drude formula with tau_c = 1 fs, n0 = 1.75 at 1.3 um (printed 1.9e-21) (2026-09-26)."
}
The photoionization term of Eq. (4) is W (1 - rho/rho_nt), a rate per volume already (as printed).
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.