berge_2010#
L. Berge, S. Mauger and S. Skupin, “Multifilamentation of powerful optical pulses in silica”, Phys. Rev. A 81, 013817 (2010)
Source record · Catalogue · Review register
DOI: 10.1103/physreva.81.013817
Source kind: theory
Recorded technique: 3D numerical simulations of multiple filamentation in fused silica at 355 and 1550 nm (extended nonlinear Schrodinger equation with delayed Raman-Kerr response, Keldysh ionization of crystals, Drude plasma, avalanche and recombination, Eqs. 1-3), with a plane-wave modulational-instability analysis (Eqs. 5-9). No measurements.
Materials in structured entries: SiO2
Dataset quantities: atom_density, avalanche_coefficient, band_gap, critical_power, effective_mass, electron_trapping_time, group_delay_dispersion, nonlinear_index, raman_fraction, raman_response_time, refractive_index, third_order_dispersion
Contents: 16 datasets; 2 formulas.
Curation notes#
Journal pages 013817-1 to -10 = PDF pages 1-10. Identity validated.
EVERY VALUE IS A SIMULATION INPUT (recorded assumed, use = check), p. 013817-2: ‘Values for glass dispersion are taken from Ref. [20]’ (Agrawal, Nonlinear Fiber Optics, 3rd ed., 2001); ‘The nonlinear Kerr response includes a Raman-delayed contribution with ratio g varying with the laser wavelength [20,22]’ (Agrawal; Zozulya et al., Phys. Rev. Lett. 82, 1430 (1999)); ‘The Keldysh rate for crystals is employed to model ionization in glass [23], using a reduced (electron-hole) mass of silica equal to 0.635 and considering the ionization potential U_i = 7.8 eV. The initial density of SiO2 molecules is rho_nt = 2.1 x 10^22 cm^-3 and the electron recombination time is set to tau_rec = 150 fs. Besides dispersion coefficients and the constituents of the overall Kerr response Eq. (2), other physical parameters such as the avalanche cross sections sigma have been recalled in Table I.’ Table I’s caption: ‘Kerr indices are taken from Refs. [20,24]’ (ref. 24 is Milam, Appl. Opt. 37, 546 (1998) = milam_1998). The reduced mass, U_i, rho_nt and tau_rec are not attributed.
TABLE I (p. 013817-2, tbl_3463a4cb91f2, image checked): k’’, k’’’, n0, n2, P_cr, g, tau_R, omega_R^-1, sigma at 355 and 1550 nm. The k’’’ row prints ‘fs2/cm’ (image confirmed), dimensionally the unit of k’’; a third-order dispersion is in fs3/cm, recorded so (a misprinted unit, not a value: no erratum mechanism exists for a unit; see the dataset). CHECKS (2026-09-26): P_cr = lambda0^2/(2 pi n0 n2) gives 0.379 MW at 355 nm (printed 0.37) and 12.07 MW at 1550 nm (printed 12). The Drude inverse-bremsstrahlung cross section sigma = e^2 tau_c/(m_e n0 eps0 c (1 + omega0^2 tau_c^2)) (the form of couairon_2005 Eq. 5 and gulley_2012) reproduces both printed sigma with the same collision time, tau_c = 23.13 fs (n0 from Table I, m = m_e); the paper does not state tau_c. The critical density rho_c ~ 1.11 x 10^21/lambda0^2[um] cm^-3 is omega0^2 eps0 m_e/e^2 to 0.4 %.
RAMAN RESPONSE, Eq. (2): R(t) = (1 - g) delta(t) + g theta(t) [(1 + omega_R^2 tau_R^2)/(omega_R tau_R^2)] exp(-t/tau_R) sin(omega_R t); in the modulational instability analysis the Raman part is ‘limited to only 18% of the overall Kerr nonlinearity’ (p. 013817-2). Note that at 355 nm tau_R = 50 fs, at 1550 nm 32 fs.
MODEL RESULTS (not extracted): clamping intensities 15-20 TW/cm2 and peak densities ~4e19 cm^-3 (355 nm, 1 ps), 5.5 TW/cm2 and 5e19 (355 nm, 50 fs), ~20 TW/cm2 and 6e18 (1550 nm, 1 ps), 26-30 TW/cm2 and 7.6-8.8e18 (1550 nm, 50 fs), from Eq. (10); fluences ~2.5 J/cm2 (355 nm, 1 ps), 0.32 (355 nm, 50 fs), 1.5-3 and 0.43 J/cm2 at 1550 nm, compared with ‘damage thresholds of dielectrics’ (refs. 27-28: Tamura et al. 1990; stuart_1996), pp. 013817-3 and -5. Literature quoted in the introduction (not extracted: plasma densities and index changes of other works): 4e19 cm^-3 and 0.4e-3 for 248 nm, 450 fs [17]; 5e-3 at 800 nm; 1.2e-3 at 1558 nm, 870 fs [19].
The Keldysh ‘rate for crystals’ itself is not printed; W(I) enters Eqs. (1) and (3).
Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
berge_2010/gvd#
{
"id": "gvd",
"material": "SiO2",
"file": "SiO2/berge_2010__gvd.csv",
"table": "tbl_3463a4cb91f2",
"quantity": "group_delay_dispersion",
"unit": "fs2/m",
"scale": 100,
"abscissa_unit": "nm",
"use": "check",
"reproduced_from": [
"G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic Press, San Diego, 2001)"
],
"parameters": {
"assumed": true
}
}
Table I k’’, printed in fs2/cm (scale 100 to fs2/m). ‘Values for glass dispersion are taken from Ref. [20]’ (p. 013817-2).
berge_2010/tod#
{
"id": "tod",
"material": "SiO2",
"file": "SiO2/berge_2010__tod.csv",
"table": "tbl_3463a4cb91f2",
"quantity": "third_order_dispersion",
"unit": "fs3/m",
"scale": 100,
"abscissa_unit": "nm",
"use": "check",
"reproduced_from": [
"G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic Press, San Diego, 2001)"
],
"parameters": {
"assumed": true
}
}
Table I k’’’, whose unit is printed ‘fs2/cm’ (image confirmed): a misprint for fs3/cm, the only unit of a third derivative of k in omega that fits the column; recorded as fs3/cm (scale 100 to fs3/m). The unit is an interpretation, not a printed value.
berge_2010/refractive_index#
{
"id": "refractive_index",
"material": "SiO2",
"file": "SiO2/berge_2010__refractive_index.csv",
"table": "tbl_3463a4cb91f2",
"quantity": "refractive_index",
"abscissa_unit": "nm",
"use": "check",
"parameters": {
"assumed": true
}
}
Table I n0, the linear index at the central frequency; source not stated (Agrawal for the dispersion, p. 013817-2).
berge_2010/n2#
{
"id": "n2",
"material": "SiO2",
"file": "SiO2/berge_2010__n2.csv",
"table": "tbl_3463a4cb91f2",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-16,
"abscissa_unit": "nm",
"use": "check",
"reproduced_from": [
"G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic Press, San Diego, 2001)",
"milam_1998"
],
"parameters": {
"part": "total",
"coefficient": "self",
"assumed": true
}
}
Table I n2 (10^-16 cm2/W); ‘Kerr indices are taken from Refs. [20,24]’ (caption). Used as the total Kerr coefficient of Eq. (1), split by g into instantaneous and Raman parts (Eq. 2); which reference gave which wavelength is not said.
berge_2010/critical_power#
{
"id": "critical_power",
"material": "SiO2",
"file": "SiO2/berge_2010__critical_power.csv",
"table": "tbl_3463a4cb91f2",
"quantity": "critical_power",
"unit": "MW",
"abscissa_unit": "nm",
"use": "check",
"parameters": {
"definition": "P_cr = lambda0^2/(2 pi n0 n2) with Table I's n0 and n2"
}
}
Table I P_cr, from P_cr ~ lambda0^2/(2 pi n0 n2) (p. 013817-2). Checked: 0.379 MW at 355 nm (printed 0.37), 12.07 MW at 1550 nm (printed 12) (2026-09-26).
berge_2010/avalanche_cross_section#
{
"id": "avalanche_cross_section",
"material": "SiO2",
"file": "SiO2/berge_2010__avalanche_cross_section.csv",
"table": "tbl_3463a4cb91f2",
"quantity": "avalanche_coefficient",
"unit": "cm2",
"scale": 1e-19,
"abscissa_unit": "nm",
"use": "check",
"parameters": {
"definition": "sigma in d rho/dt = W(I)(rho_nt - rho) + sigma rho I/U_i - rho/tau_rec (Eq. 3), also the plasma absorption term -(sigma/2) rho E of Eq. (1)",
"assumed": true
}
}
Table I sigma (10^-19 cm2), ‘the avalanche cross sections’ (p. 013817-2); the collision time behind them is not stated. Both are the Drude cross section with tau_c = 23.13 fs, m = m_e and Table I’s n0 (source notes; checked 2026-09-26).
berge_2010/raman_fraction_355#
{
"id": "raman_fraction_355",
"material": "SiO2",
"file": "SiO2/berge_2010__raman_fraction_355.csv",
"table": "tbl_3463a4cb91f2",
"quantity": "raman_fraction",
"abscissa": "none",
"use": "check",
"reproduced_from": [
"G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic Press, San Diego, 2001)",
"A. A. Zozulya, S. A. Diddams, A. G. Van Engen and T. S. Clement, Phys. Rev. Lett. 82, 1430 (1999)"
],
"parameters": {
"definition": "g in R(t) = (1 - g) delta(t) + g theta(t) [(1 + omega_R^2 tau_R^2)/(omega_R tau_R^2)] exp(-t/tau_R) sin(omega_R t), Eq. (2)",
"wavelength_nm": 355,
"assumed": true
}
}
Table I g at 355 nm (‘ratio g varying with the laser wavelength [20,22]’).
berge_2010/raman_fraction_1550#
{
"id": "raman_fraction_1550",
"material": "SiO2",
"file": "SiO2/berge_2010__raman_fraction_1550.csv",
"table": "tbl_3463a4cb91f2",
"quantity": "raman_fraction",
"abscissa": "none",
"use": "check",
"reproduced_from": [
"G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic Press, San Diego, 2001)",
"A. A. Zozulya, S. A. Diddams, A. G. Van Engen and T. S. Clement, Phys. Rev. Lett. 82, 1430 (1999)"
],
"parameters": {
"definition": "g in R(t) = (1 - g) delta(t) + g theta(t) [(1 + omega_R^2 tau_R^2)/(omega_R tau_R^2)] exp(-t/tau_R) sin(omega_R t), Eq. (2)",
"wavelength_nm": 1550,
"assumed": true
}
}
Table I g at 1550 nm.
berge_2010/raman_tau_R_355#
{
"id": "raman_tau_R_355",
"material": "SiO2",
"file": "SiO2/berge_2010__raman_tau_R_355.csv",
"table": "tbl_3463a4cb91f2",
"quantity": "raman_response_time",
"unit": "fs",
"abscissa": "none",
"use": "check",
"reproduced_from": [
"G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic Press, San Diego, 2001)",
"A. A. Zozulya, S. A. Diddams, A. G. Van Engen and T. S. Clement, Phys. Rev. Lett. 82, 1430 (1999)"
],
"parameters": {
"constant": "tau_R (decay)",
"model": "R(t) = (1 - g) delta(t) + g theta(t) [(1 + omega_R^2 tau_R^2)/(omega_R tau_R^2)] exp(-t/tau_R) sin(omega_R t)",
"wavelength_nm": 355,
"assumed": true
}
}
Table I tau_R at 355 nm.
berge_2010/raman_tau_R_1550#
{
"id": "raman_tau_R_1550",
"material": "SiO2",
"file": "SiO2/berge_2010__raman_tau_R_1550.csv",
"table": "tbl_3463a4cb91f2",
"quantity": "raman_response_time",
"unit": "fs",
"abscissa": "none",
"use": "check",
"reproduced_from": [
"G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic Press, San Diego, 2001)",
"A. A. Zozulya, S. A. Diddams, A. G. Van Engen and T. S. Clement, Phys. Rev. Lett. 82, 1430 (1999)"
],
"parameters": {
"constant": "tau_R (decay)",
"model": "R(t) = (1 - g) delta(t) + g theta(t) [(1 + omega_R^2 tau_R^2)/(omega_R tau_R^2)] exp(-t/tau_R) sin(omega_R t)",
"wavelength_nm": 1550,
"assumed": true
}
}
Table I tau_R at 1550 nm.
berge_2010/raman_inverse_omega_R_355#
{
"id": "raman_inverse_omega_R_355",
"material": "SiO2",
"file": "SiO2/berge_2010__raman_inverse_omega_R_355.csv",
"table": "tbl_3463a4cb91f2",
"quantity": "raman_response_time",
"unit": "fs",
"abscissa": "none",
"use": "check",
"reproduced_from": [
"G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic Press, San Diego, 2001)",
"A. A. Zozulya, S. A. Diddams, A. G. Van Engen and T. S. Clement, Phys. Rev. Lett. 82, 1430 (1999)"
],
"parameters": {
"constant": "1/omega_R (oscillation)",
"model": "R(t) = (1 - g) delta(t) + g theta(t) [(1 + omega_R^2 tau_R^2)/(omega_R tau_R^2)] exp(-t/tau_R) sin(omega_R t)",
"wavelength_nm": 355,
"assumed": true
}
}
Table I omega_R^-1 at 355 nm.
berge_2010/raman_inverse_omega_R_1550#
{
"id": "raman_inverse_omega_R_1550",
"material": "SiO2",
"file": "SiO2/berge_2010__raman_inverse_omega_R_1550.csv",
"table": "tbl_3463a4cb91f2",
"quantity": "raman_response_time",
"unit": "fs",
"abscissa": "none",
"use": "check",
"reproduced_from": [
"G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic Press, San Diego, 2001)",
"A. A. Zozulya, S. A. Diddams, A. G. Van Engen and T. S. Clement, Phys. Rev. Lett. 82, 1430 (1999)"
],
"parameters": {
"constant": "1/omega_R (oscillation)",
"model": "R(t) = (1 - g) delta(t) + g theta(t) [(1 + omega_R^2 tau_R^2)/(omega_R tau_R^2)] exp(-t/tau_R) sin(omega_R t)",
"wavelength_nm": 1550,
"assumed": true
}
}
Table I omega_R^-1 at 1550 nm.
berge_2010/model_band_gap#
{
"id": "model_band_gap",
"material": "SiO2",
"table": "text",
"quantity": "band_gap",
"unit": "eV",
"abscissa": "none",
"use": "check",
"parameters": {
"kind": "assumed",
"assumed": true
}
}
1 inline points in the source record.
p. 013817-2: ‘considering the ionization potential U_i = 7.8 eV’ in the Keldysh rate for crystals; no source cited.
berge_2010/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. 013817-2: ‘using a reduced (electron-hole) mass of silica equal to 0.635’; no source cited.
berge_2010/model_molecule_density#
{
"id": "model_molecule_density",
"material": "SiO2",
"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. 013817-2: ‘The initial density of SiO2 molecules is rho_nt = 2.1 x 10^22 cm^-3’.
berge_2010/model_recombination_time#
{
"id": "model_recombination_time",
"material": "SiO2",
"table": "text",
"quantity": "electron_trapping_time",
"unit": "fs",
"abscissa": "none",
"use": "check",
"parameters": {
"assumed": true
}
}
1 inline points in the source record.
p. 013817-2: ‘the electron recombination time is set to tau_rec = 150 fs’; no source cited.
Formulas#
berge_2010/propagation_model#
{
"id": "propagation_model",
"material": "SiO2",
"equation": "Eqs. (1)-(3), p. 013817-2",
"printed": "dz E = (i/(2k0)) T^-1 nabla_perp^2 E + i D E - i (k0/(2 n0^2 rho_c)) T^-1 rho E - (sigma/2) rho E - U_i W(I)(rho_nt - rho)/(2I) E + i (omega0/c) n2 T int R(t - t')|E(t')|^2 dt' E (1); R(t) = (1 - g) delta(t) + g theta(t) [(1 + omega_R^2 tau_R^2)/(omega_R tau_R^2)] exp(-t/tau_R) sin(omega_R t) (2); dt rho = W(I)(rho_nt - rho) + sigma rho I/U_i - rho/tau_rec (3)",
"variable": "E: envelope with I = |E|^2; T = 1 + (i/omega0) dt; D = sum_{n>=2} (k^(n)/n!)(i dt)^n; rho_c ~ 1.11e21/lambda0^2[um] cm^-3; W(I) the Keldysh rate for crystals",
"coefficients": {
"U_i": "7.8 eV",
"reduced_mass": "0.635",
"rho_nt": "2.1e22 cm^-3",
"tau_rec": "150 fs"
},
"check": "P_cr and sigma of Table I checked (see the datasets); W(I) is not printed."
}
The input pulse is a second-order supergaussian in x and y with I0 = 2 pi P_in/[P_cr Gamma^2(5/4)] (Eq. 4).
berge_2010/clamping_estimate#
{
"id": "clamping_estimate",
"material": "SiO2",
"equation": "Eq. (10), p. 013817-5",
"printed": "W(I) = 2 rho_c n0 n2 I / (Delta T rho_nt)",
"variable": "Delta T: the duration of the pulse after the first ionization front; I the clamping intensity",
"coefficients": {
"rho_nt": "2.1e22 cm^-3"
},
"check": "Not reproduced: W(I) is not printed."
}
The balance of Kerr focusing and plasma defocusing used to estimate the clamping intensity and peak density.
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.