bree_2012#
C. Bree, A. Demircan and G. Steinmeyer, Phys. Rev. A 85, 033806 (2012)
Source record · Catalogue · Review register
DOI: 10.1103/physreva.85.033806
Source kind: theory
Recorded technique: The Kramers-Kronig model of bree_2011 (n_2k from (k + 1)-photon PPT ionisation cross sections, nondegenerate absorption at the mean frequency) applied to the n2 dispersion of all noble gases, the saturation of the intensity-dependent index, its wavelength dependence and the radius of convergence of the series.
Materials in structured entries: Ar, He, Kr, Ne, Xe
Dataset quantities: nonlinear_index
Contents: 5 datasets; 0 formulas.
Curation notes#
Defining equations (p. 2-5). n(I) = sum_(k>=0) n_2k I^k (Eq. 1; self coefficients, degenerate case). Eq. (10): n_2k = 2^(k-1) C^(k) / (n0 (n0 eps0 c)^k) Re chi^(2k+1), with C^(k) = (2k + 1)! / (2^(2k) k! (k + 1)!) (Eq. 12); for k = 1, n2 = 3 Re chi^(3) / (4 n0^2 eps0 c). Eq. (11): beta_K = (w0/c) 2^(K-1) C^(K-1) / (n0 (n0 eps0 c)^(K-1)) Im chi^(2K-1); Eq. (13): beta_K = K rho0 hbar w sigma_K. Eq. (16): n_2k(w) = (rho0 hbar c / pi) P int_0^inf (Omega + k w) sigma_(k+1)((Omega + k w)/(k + 1)) / (Omega^2 - w^2) dOmega (the same as bree_2011 Eq. 3). Eq. (18): gamma^(3)(0) = 8 eps0^2 c n2(0) / rho0 ‘using the Lorentz-Lorenz law’ in the far-infrared limit, i.e. n2 = rho0 gamma / (8 eps0^2 c) with n0 = 1: Shelton & Rice’s Taylor (T) convention (p = ... + gamma E^3/6), the relation of the manual page Third-order nonlinearity. Eq. (17) quotes Bishop’s dispersion n2(w) = n2(0) (1 + A w_L^2 + B w_L^4 + ...), w_L^2 = nu w^2 with nu = 12, 6, 4 for THG, ESHG and DFWM, ‘the far-infrared limit n2 ~ chi(3)(0; 0, 0, 0) and the coefficient A do not depend on the nonlinear optical process’ (p. 3). rho0 is not restated; the 2011 paper’s rho_nt = 2.7e19 cm^-3 (‘standard conditions’) is assumed. Ionisation potentials used: 24.59, 21.56, 15.76, 14.00, 12.13 eV; two-photon edges lambda_TPA = 101, 115, 157, 177 and 204 nm (He ... Xe) (p. 4).
Table I (tbl_934361b8054e, image checked): ‘n2 values in cm^2/TW for characteristic wavelength emitted by various laser materials’, 193, 248, 400, 800 and 2000 nm, He ... Xe, printed m(e) = m x 10^e. Extracted as kk_<gas> (5 points each; use = check, a model; its authors state agreement within 20 % of the reference data in the infrared, within 10 % for Ar and Kr from 0.2 to 6 um, p. 4). The 800 nm row equals bree_2011’s Table I Z = 1 column rounded to two digits (5.2, 13, 130, 310, 920 against 5.2, 13.1, 126.8, 306.9, 915.8 x 10^-9 cm^2/TW) and is excluded as a duplicate. Xe at 193 nm lies beyond Xe’s two-photon edge (204 nm) and Xe at 248 nm is near a bound two-photon resonance (measured strongly negative there, Lehmberg et al. 1995, not in the library), which the ionisation-based model does not contain (it has no bound-state resonances): do not trust the UV rows near bound two-photon resonances.
Table II (tbl_150d29e385da, notes only): inversion intensities I_inv (the nontrivial root of sum n_2k I^k = 0) against the plasma clamping intensity I_c (90 fs Gaussian pulses) at 800 nm: He 113/301, Ne 89/204, Ar 49/81, Kr 40/57, Xe 30/37, O2 36/44, N2 50/82 TW/cm^2.
Higher-order Kerr claim (notes only): the saturation and inversion of the index ‘stems from much higher orders’ (for Ar at 800 nm chi(21) and above; chi(5) ... chi(19) do not contribute, p. 7); the series converges for Keldysh gamma > e/2 (Eq. 28); I_inv(lambda) crosses the clamping intensity near 560 nm, so HOKE-dominated filaments are predicted in the infrared. The coefficients n2 ... n32 are in bree_2011’s supplement (not in the library). Status: the saturation follows from using multiphoton-ionisation rates beyond their validity in the KK integral (Wahlstrand et al. 2012, Phys. Rev. Lett. 109, 113904, p. 2-3: with the full rate the KK response is linear in intensity, as measured up to ionisation). Not to be used.
Second copy: Unverified_df851ddaf7be is the WIAS Berlin preprint No. 1651 of this paper (ISSN 0946-8633, ‘submitted: October 6, 2011’; identified from its first page). Its Table 1 prints the same values as 7.8e-9 etc. with one misprint, Kr at 2000 nm ‘2.7e.7’ (journal 2.7(-7)); its Table 2 equals Table II. Not extracted twice.
Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
bree_2012/kk_He#
{
"id": "kk_He",
"material": "He",
"file": "He/bree_2012__kk_He.csv",
"table": "tbl_934361b8054e",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-12,
"abscissa_unit": "nm",
"state": "1atm_0C",
"density": "ideal",
"use": "check",
"excluded_rows": {
"800": "The 800 nm row repeats bree_2011 Table I (Z = 1), rounded; use that one."
},
"parameters": {
"part": "electronic",
"coefficient": "self"
}
}
Table I, n2 in cm^2/TW (printed m(e), stored as me e) at 193, 248, 400, 800, 2000 nm. Kramers-Kronig model; density assumed 2.7e19 cm^-3 as in bree_2011.
bree_2012/kk_Ne#
{
"id": "kk_Ne",
"material": "Ne",
"file": "Ne/bree_2012__kk_Ne.csv",
"table": "tbl_934361b8054e",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-12,
"abscissa_unit": "nm",
"state": "1atm_0C",
"density": "ideal",
"use": "check",
"excluded_rows": {
"800": "The 800 nm row repeats bree_2011 Table I (Z = 1), rounded; use that one."
},
"parameters": {
"part": "electronic",
"coefficient": "self"
}
}
Table I, n2 in cm^2/TW at 193, 248, 400, 800, 2000 nm. Kramers-Kronig model.
bree_2012/kk_Ar#
{
"id": "kk_Ar",
"material": "Ar",
"file": "Ar/bree_2012__kk_Ar.csv",
"table": "tbl_934361b8054e",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-12,
"abscissa_unit": "nm",
"state": "1atm_0C",
"density": "ideal",
"use": "check",
"excluded_rows": {
"800": "The 800 nm row repeats bree_2011 Table I (Z = 1), rounded; use that one."
},
"parameters": {
"part": "electronic",
"coefficient": "self"
}
}
Table I, n2 in cm^2/TW at 193, 248, 400, 800, 2000 nm. Kramers-Kronig model.
bree_2012/kk_Kr#
{
"id": "kk_Kr",
"material": "Kr",
"file": "Kr/bree_2012__kk_Kr.csv",
"table": "tbl_934361b8054e",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-12,
"abscissa_unit": "nm",
"state": "1atm_0C",
"density": "ideal",
"use": "check",
"excluded_rows": {
"800": "The 800 nm row repeats bree_2011 Table I (Z = 1), rounded; use that one."
},
"parameters": {
"part": "electronic",
"coefficient": "self"
}
}
Table I, n2 in cm^2/TW at 193, 248, 400, 800, 2000 nm. Kramers-Kronig model.
bree_2012/kk_Xe#
{
"id": "kk_Xe",
"material": "Xe",
"file": "Xe/bree_2012__kk_Xe.csv",
"table": "tbl_934361b8054e",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-12,
"abscissa_unit": "nm",
"state": "1atm_0C",
"density": "ideal",
"use": "check",
"excluded_rows": {
"800": "The 800 nm row repeats bree_2011 Table I (Z = 1), rounded; use that one.",
"193": "Beyond Xe's two-photon edge (204 nm, p. 4); the model has no bound-state resonances."
},
"parameters": {
"part": "electronic",
"coefficient": "self"
}
}
Table I, n2 in cm^2/TW at 193, 248, 400, 800, 2000 nm. Kramers-Kronig model; the 248 nm value ignores the bound two-photon resonance near which Xe’s measured n2 is negative (Lehmberg et al. 1995, not in the curators’ library).
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.