bree_2011#
C. Bree, A. Demircan and G. Steinmeyer, Phys. Rev. Lett. 106, 183902 (2011)
Source record · Catalogue · Review register
DOI: 10.1103/physrevlett.106.183902
Source kind: theory
Recorded technique: Kerr coefficients n_2k computed by a Kramers-Kronig transform of (k + 1)-photon ionisation cross sections from a modified PPT (Keldysh) theory (Eq. 1), with the nondegenerate absorption approximated by the degenerate one at the mean frequency (Eq. 2); a one-parameter model (the ionisation potential) for the noble gases, extended to O2 and N2 with Talebpour’s effective charge (Z_eff = 0.53 and 0.9; curated as talebpour_1999).
Materials in structured entries: Ar, He, Kr, Ne, O2, Xe
Dataset quantities: nonlinear_index
Contents: 11 datasets; 0 formulas.
Curation notes#
Defining equations. Eq. (3), p. 2: n_2k(w) = (hbar c rho_nt / pi) P int_0^inf (Omega + k w) sigma_(k+1)((Omega + k w)/(k + 1)) / (Omega^2 - w^2) dOmega (P: Cauchy principal value); the K-photon absorption coefficient Delta alpha_K(w) = K hbar w rho_nt sigma_K I^(K-1), ‘with a particle density rho_nt = 2.7 x 10^19 cm^-3 corresponding to standard conditions’ (p. 1, checked on the page image). The index is n = n0 + n2 I + n4 I^2 + ... (p. 1 and Fig. 3), a single-beam (self) coefficient. The companion paper bree_2012 (Eq. 10) gives the relation to chi: n_2k = 2^(k-1) C^(k) / (n0 (n0 eps0 c)^k) Re chi^(2k+1), C^(k) = (2k + 1)!/(2^(2k) k! (k + 1)!), and gamma^(3)(0) = 8 eps0^2 c n2(0) / rho0 (Eq. 18).
Table I (tbl_3d9fe63acf83; JSON cells, no CSV; equal to the table image): n2 in 10^-8 cm^2/TW of the neutral atoms at 800 nm (Z = 1) and in the static limit, of the singly charged ions (Z = 2: skipped, not curated species), and ‘Experimental data (rightmost column) as compiled from [18,21] and corrected for the dispersion of the DFWM process with Eq. (13) in [20]’ ([18] Bishop & Pipin, J. Chem. Phys. 91, 3549 (1989); [21] Shelton & Rice, Chem. Rev. 94, 3 (1994); [20] Bree et al., IEEE J. Quantum Electron. 46, 433 (2010), not in the library). The model columns are datasets kk_<gas> (rows 800nm and static, use = check: a semi-empirical model whose authors quote agreement of 26 % (He), 15 % (Ne, Kr, Xe) and better (Ar) with reference data, p. 2); the reference column is refs_<gas> (reproduced).
The reference column is the static limit: the text compares the model’s long-wavelength He value 4.8 x 10^-9 cm^2/TW with ‘3.8 x 10^-9 cm^2/TW that was derived in [18]’ (p. 2), and the column equals gamma0 x 8.911e-23 cm^2/W per au (N gamma_T / (8 eps0^2 c) at the Loschmidt density), with gamma0 = 43.104 (He), 108 (Ne), 1167 (Ar), 2600 (Kr), 6888 au (Xe) as tabulated from Shelton & Rice and Bishop & Pipin: 0.3841, 0.962, 10.399, 23.17, 61.38 against 0.38, 0.96, 10.40, 23.17, 61.39 (checked 2026-09-26). So it is gamma0 in Shelton & Rice’s T convention converted to n2 at 1 atm and 0 C, whatever ‘corrected for the dispersion of the DFWM process’ means.
Other values in the text: O2 long-wavelength limit n2(w -> 0) = 0.7 x 10^-7 cm^2/TW from the model with Z_eff = 0.53 (dataset kk_static_O2), ‘which agrees excellently with the electronic contribution of n2 = 0.746 x 10^-7 cm^2/TW computed in [28]’ (Hellwarth, Pennington & Henesian, Phys. Rev. A 41, 2766 (1990); record hellwarth_1990; not duplicated here) (p. 3, page image checked). He: the n2 maximum is about 4 x 10^-8 cm^2/TW near 100 nm, the zero crossing at 85 nm, negative up to 50.4 nm (p. 2); Ar: about 10^-7 cm^2/TW in the infrared, zero crossing at 140 nm (p. 2). Neutral Ar against Ar+ with ionisation: ‘from n2 = 1.3 x 10^-7 cm^2/W at p = 0 to n2 = 0.6 x 10^-7 cm^2 at p = 1’ (p. 4): the units are misprinted (cm^2/TW, as Table I’s 12.68 and 6.14 x 10^-8 show); text only, nothing extracted.
Higher-order Kerr claim (notes only): the model gives n4 of Ar with an infrared limit of 2 x 10^-12 cm^4/TW^2, 12 times higher at 240 nm, negative below 210 nm (p. 3; page image checked), positive n_2k up to n18 at 800 nm and negative beyond, and an Ar index that saturates near 42 TW/cm^2 and inverts at 49 TW/cm^2 (Loriot: 30 and 34), with inversion intensities of 112, 89, 40 and 30 TW/cm^2 for He, Ne, Kr, Xe (p. 3); a negative n4 at 800 nm (Loriot’s -0.36 +- 1.03 x 10^-9 cm^4/TW^2) ‘appears to be incompatible’ with the model. The coefficients n2 ... n32 are in the supplement, not in the library. Status: the premise (MPI-rate expansion as the absorption in the KK integral) is criticised by Wahlstrand et al. 2012 (Phys. Rev. Lett. 109, 113904, p. 2-3), who show that with the full ionisation rate the KK response stays linear in I up to ionisation and that the MPI model ‘strongly overestimates’ the low-frequency absorption at high intensity, ‘the source of the saturation and inversion calculated in [12,13]’. The n2 (k = 1) values are not affected by that criticism; the higher orders are not to be used.
Wavelengths: 800 nm, medium not stated (vacuum assumed).
Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
bree_2011/kk_He#
{
"id": "kk_He",
"material": "He",
"file": "He/bree_2011__kk_He.csv",
"table": "tbl_3d9fe63acf83",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-20,
"abscissa_unit": "nm",
"state": "1atm_0C",
"density": "ideal",
"use": "check",
"parameters": {
"part": "electronic",
"coefficient": "self"
}
}
Table I, Z = 1 (800 nm) and n2(w -> 0) (static) columns, 10^-8 cm^2/TW = 10^-20 cm^2/W, at rho_nt = 2.7e19 cm^-3 (‘standard conditions’, read as 1 atm and 0 C with the rounded Loschmidt number). Kramers-Kronig model, not a measurement. The model’s 800 nm row is repeated (rounded) in bree_2012 Table I.
bree_2011/kk_Ne#
{
"id": "kk_Ne",
"material": "Ne",
"file": "Ne/bree_2011__kk_Ne.csv",
"table": "tbl_3d9fe63acf83",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-20,
"abscissa_unit": "nm",
"state": "1atm_0C",
"density": "ideal",
"use": "check",
"parameters": {
"part": "electronic",
"coefficient": "self"
}
}
Table I, Z = 1 (800 nm) and static columns; Kramers-Kronig model at rho_nt = 2.7e19 cm^-3.
bree_2011/kk_Ar#
{
"id": "kk_Ar",
"material": "Ar",
"file": "Ar/bree_2011__kk_Ar.csv",
"table": "tbl_3d9fe63acf83",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-20,
"abscissa_unit": "nm",
"state": "1atm_0C",
"density": "ideal",
"use": "check",
"parameters": {
"part": "electronic",
"coefficient": "self"
}
}
Table I, Z = 1 (800 nm) and static columns; Kramers-Kronig model at rho_nt = 2.7e19 cm^-3.
bree_2011/kk_Kr#
{
"id": "kk_Kr",
"material": "Kr",
"file": "Kr/bree_2011__kk_Kr.csv",
"table": "tbl_3d9fe63acf83",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-20,
"abscissa_unit": "nm",
"state": "1atm_0C",
"density": "ideal",
"use": "check",
"parameters": {
"part": "electronic",
"coefficient": "self"
}
}
Table I, Z = 1 (800 nm) and static columns; Kramers-Kronig model at rho_nt = 2.7e19 cm^-3.
bree_2011/kk_Xe#
{
"id": "kk_Xe",
"material": "Xe",
"file": "Xe/bree_2011__kk_Xe.csv",
"table": "tbl_3d9fe63acf83",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-20,
"abscissa_unit": "nm",
"state": "1atm_0C",
"density": "ideal",
"use": "check",
"parameters": {
"part": "electronic",
"coefficient": "self"
}
}
Table I, Z = 1 (800 nm) and static columns; Kramers-Kronig model at rho_nt = 2.7e19 cm^-3.
bree_2011/kk_static_O2#
{
"id": "kk_static_O2",
"material": "O2",
"table": "text",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-19,
"abscissa_unit": "nm",
"state": "1atm_0C",
"density": "ideal",
"use": "check",
"parameters": {
"part": "electronic",
"coefficient": "self"
}
}
1 inline points in the source record.
Text p. 3: ‘For oxygen, our theory yields a long-wavelength limit n2(w -> 0) = 0.7 x 10^-7 cm^2/TW’ (page image checked), with Talebpour’s Z_eff = 0.53; rho_nt = 2.7e19 cm^-3 as for the atoms (assumed: the O2 density is not restated).
bree_2011/refs_He#
{
"id": "refs_He",
"material": "He",
"file": "He/bree_2011__refs_He.csv",
"table": "tbl_3d9fe63acf83",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-20,
"abscissa_unit": "nm",
"state": "1atm_0C",
"density": "ideal",
"use": "reproduced",
"reproduced_from": [
"bishop_1989",
"shelton_1994"
],
"parameters": {
"part": "electronic",
"coefficient": "self"
}
}
Table I ‘Refs. [18,21]’ column: the static gamma0 of the reference literature converted to n2 at the Loschmidt density (0.3841 from 43.104 au; see the record’s notes). He is presumably Bishop & Pipin’s value [18]; the paper does not say which reference gives which gas.
bree_2011/refs_Ne#
{
"id": "refs_Ne",
"material": "Ne",
"file": "Ne/bree_2011__refs_Ne.csv",
"table": "tbl_3d9fe63acf83",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-20,
"abscissa_unit": "nm",
"state": "1atm_0C",
"density": "ideal",
"use": "reproduced",
"reproduced_from": [
"shelton_1994",
"bishop_1989"
],
"parameters": {
"part": "electronic",
"coefficient": "self"
}
}
Table I ‘Refs. [18,21]’ column: static gamma0 (108 au) converted to n2 at the Loschmidt density (see the record’s notes).
bree_2011/refs_Ar#
{
"id": "refs_Ar",
"material": "Ar",
"file": "Ar/bree_2011__refs_Ar.csv",
"table": "tbl_3d9fe63acf83",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-20,
"abscissa_unit": "nm",
"state": "1atm_0C",
"density": "ideal",
"use": "reproduced",
"reproduced_from": [
"shelton_1994",
"bishop_1989"
],
"parameters": {
"part": "electronic",
"coefficient": "self"
}
}
Table I ‘Refs. [18,21]’ column: static gamma0 (1167 au) converted to n2 at the Loschmidt density (see the record’s notes).
bree_2011/refs_Kr#
{
"id": "refs_Kr",
"material": "Kr",
"file": "Kr/bree_2011__refs_Kr.csv",
"table": "tbl_3d9fe63acf83",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-20,
"abscissa_unit": "nm",
"state": "1atm_0C",
"density": "ideal",
"use": "reproduced",
"reproduced_from": [
"shelton_1994",
"bishop_1989"
],
"parameters": {
"part": "electronic",
"coefficient": "self"
}
}
Table I ‘Refs. [18,21]’ column: static gamma0 (2600 au) converted to n2 at the Loschmidt density (see the record’s notes).
bree_2011/refs_Xe#
{
"id": "refs_Xe",
"material": "Xe",
"file": "Xe/bree_2011__refs_Xe.csv",
"table": "tbl_3d9fe63acf83",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-20,
"abscissa_unit": "nm",
"state": "1atm_0C",
"density": "ideal",
"use": "reproduced",
"reproduced_from": [
"shelton_1994",
"bishop_1989"
],
"parameters": {
"part": "electronic",
"coefficient": "self"
}
}
Table I ‘Refs. [18,21]’ column: static gamma0 (6888 au) converted to n2 at the Loschmidt density (see the record’s notes).
Formulas#
No formulas are recorded.
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.