reichert_2015#
M. Reichert, P. Zhao, J. M. Reed, T. R. Ensley, D. J. Hagan and E. W. Van Stryland, “Beam deflection measurement of bound-electronic and rotational nonlinear refraction in molecular gases”, Opt. Express 23, 22224 (2015)
Source record · Catalogue · Review register
DOI: 10.1364/OE.23.022224
Source kind: measurement
Recorded technique: Polarization-resolved beam deflection (excite-probe): 800-nm, 83-fs excitation (w_e = 177 um) and a 650-nm white-light-continuum probe (40 nm FWHM, 265 fs, w_0,p = 60 um) crossing at <= 1 degree in ambient laboratory air; the probe’s deflection measured by a quadrant photodiode versus delay (to 2 ns). Probe at 0, 90 and 54.7 degrees (the magic angle removes the rotational part). The interaction length (6.5 cm) is not characterized and is fitted: the electronic part is measured relative to the rotational revivals, whose size is fixed by literature Delta alpha values (self-reference). CS2 vapour (1250-nm excitation, 950-nm probe) likewise (pp. 22227-22233).
Materials in structured entries: N2, O2
Dataset quantities: polarizability_anisotropy, rotational_constant
Contents: 10 datasets; 0 formulas.
Curation notes#
Journal pages 22224-22237 = PDF pages 1-14. Identity checked against the first page.
NOTHING CURATED IS MEASURED. The only n2 is of ambient AIR: n2,el(air) = (10 +- 2) x 10^-24 m2/W (magic angle, 800 nm, 83 fs; p. 22233), with Table 2 comparing Wahlstrand et al. [48] 7.9 +- 1.0, Liu and Chin [49] 9.6 and a Shelton-and-Rice-based 9.1 (1e-24 m2/W), and an air-averaged gamma (1.25 +- 0.20) x 10^-62 C^4 m^4/J^3 (the text says +- 0.10) = (10.1 +- 2.0) x 10^-37 esu against 0.78 gamma(N2) + 0.21 gamma(O2) + 0.01 gamma(Ar) with N = 2.5e19 cm^-3. Air is not curated: not extracted. CS2 (not curated): gamma(gas) = (19 +- 4) x 10^-62 C^4 m^4/J^3, B and D of three species (Table 3), not extracted.
DEFINING EQUATIONS (SI; pp. 22227-22228). Eq. (1): Delta n_rot(t) = [N Delta alpha / (2 eps0 n0)] (<cos^2 theta(t)> - 1/3). Eq. (2): Delta n(t) = 2 n2,el I_e(t) + (c N / 4) (Delta alpha)^2 sum_J T_J int I_e(t’) sin(omega_(J,J-2)(t - t’)) exp(-Gamma_(J,J-2)(t - t’)) dt’, T_J = (2 / 15 hbar) J(J - 1)/(2J - 1) (rho_JJ - rho_(J-2,J-2)) (Eq. (3)); ‘The factor of 2 in the first term arises from interference of the two beams doubling the phase change [32]’ (nondegenerate probe; absent from the rotational term): n2,el is the SELF coefficient. Eq. (4): mu = mu(0) + alpha E + beta E^2 + gamma E^3, the field being E0(omega) cos(k.r - omega t) (no 1/2 or 1/6: the perturbation-series convention). Eq. (5): n2,el = [3 N / (4 eps0^2 c n0 n0,e)] f(3) Re<gamma>, f(3) = [(n0^2 + 2)/3]^2 [(n0,e^2 + 2)/3]^2 the Lorentz-Lorenz local-field factor (~1 in dilute gases). Eq. (8): Delta n_el / Delta n_rot proportional to gamma / (Delta alpha)^2. Eqs. (9)-(11): Delta n(0) = Delta n_el + Delta n_rot, Delta n(90) = Delta n_el/3 - Delta n_rot/2, Delta n(54.7) = 5 Delta n_el / 9.
TABLE 1 (p. 22232; image checked; extracted by tools/extract/reichert_2015.py): Delta alpha (1e-40 F m2) N2 0.77, O2 1.21, marked ‘[35]’ = Bridge and Buckingham, Proc. R. Soc. London A 295, 334 (1966) (not in the library): values used, not measured (the fit of the air revivals ‘gives a good determination of the ratio Delta alpha(O2)/Delta alpha(N2), that agrees well with the values in [35]’, p. 22230). Recorded as reproduced, unit ‘SI’ (F m2 = C m2/V), no stated wavelength (abscissa ‘not stated’). Fitted constants: 14N2 B = 1.9896(2) cm^-1, D = 5.9(6) x 10^-6 cm^-1 (Raman: 1.989574(12), 5.76(3)); 16O2 B = 1.4377(2), D = 5.1(5) (1.437682(9), 4.852(12)): now extracted (2026-09-26) as the B_fit_*, D_fit_* datasets (check) and the Raman columns as reproductions. J-dependent dephasing rates in Fig. 4 only. The group velocity in air uses n0,e = 1.000275 (Ciddor).
TABLE 1 B AND D (p. 22232; image and text layer checked). The table’s column marks a and b have no footnote in the paper; the text says: ‘The values of B and D found from fitting are given in Table 1 for each molecule, which shows a comparison to Raman scattering measurements [41]’ (p. 22232), [41] = A. Weber, ‘High-resolution rotational Raman spectra of gases’, in Raman Spectroscopy of Gases and Liquids (Springer, 1979), curated as weber_1979 (Chap. 3, Table 3.2). So a = this work (the fit of the Fourier-transformed air revivals to 300 ps, Fig. 3, with Eq. (2) and centrifugal distortion), b = Weber’s Raman values. The digits in parentheses are the uncertainty in the last digit(s) (level not stated). The fitted constants are effective values of the v = 0 rotational ladder of each molecule in ambient air (~1 atm, room temperature); for O2 the model counts ‘only odd J values’ (p. 22231) and does not mention the electron-spin (fine-structure) splitting. The 14N2 Raman column is digit-identical to bendtsen_1974’s pure rotational B_0 and D (Table VII), so it is recorded as reproduced from bendtsen_1974 (through Weber); the 16O2 column’s original is not identified (reproduced from Weber). The fitted values agree with the Raman ones well within their stated uncertainties: B(N2) 1.9896(2) against 1.989574 (+0.13 of the stated 0.0002), B(O2) 1.4377(2) against 1.437682 (+0.09), D(N2) 5.9(6) against 5.76, D(O2) 5.1(5) against 4.852 (both within 0.5 of theirs).
Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
reichert_2015/dalpha_bridge_buckingham_N2#
{
"id": "dalpha_bridge_buckingham_N2",
"material": "N2",
"file": "N2/reichert_2015__dalpha_bridge_buckingham_N2.csv",
"table": "tbl_f40cb41739d3",
"quantity": "polarizability_anisotropy",
"unit": "SI",
"scale": 1e-40,
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"N. J. Bridge and A. D. Buckingham, Proc. R. Soc. Lond. A 295, 334 (1966)"
]
}
Table 1, Delta alpha ‘0.77 [35]’ in 1e-40 F m2 (SI polarizability, C m2/V). The self-reference of the measurement, not a result. Wavelength not stated.
reichert_2015/dalpha_bridge_buckingham_O2#
{
"id": "dalpha_bridge_buckingham_O2",
"material": "O2",
"file": "O2/reichert_2015__dalpha_bridge_buckingham_O2.csv",
"table": "tbl_f40cb41739d3",
"quantity": "polarizability_anisotropy",
"unit": "SI",
"scale": 1e-40,
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"N. J. Bridge and A. D. Buckingham, Proc. R. Soc. Lond. A 295, 334 (1966)"
]
}
Table 1, Delta alpha ‘1.21 [35]’ in 1e-40 F m2. As dalpha_bridge_buckingham_N2.
reichert_2015/B_fit_N2#
{
"id": "B_fit_N2",
"material": "N2",
"file": "N2/reichert_2015__B_fit_N2.csv",
"table": "tbl_f40cb41739d3",
"quantity": "rotational_constant",
"unit": "cm-1",
"abscissa": "label",
"use": "check",
"parameters": {
"constant": "B",
"vibrational_state_v": 0
},
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table 1 (p. 22232), column ‘B (cm-1)a’: 1.9896(2), fitted to the rotational Raman spectrum (Fourier transform of the beam-deflection signal) of 14N2 in ambient air; the (2) is the uncertainty in the last digit, level not stated. An effective v = 0 constant.
reichert_2015/D_fit_N2#
{
"id": "D_fit_N2",
"material": "N2",
"file": "N2/reichert_2015__D_fit_N2.csv",
"table": "tbl_f40cb41739d3",
"quantity": "rotational_constant",
"unit": "cm-1",
"scale": 1e-06,
"abscissa": "label",
"use": "check",
"parameters": {
"constant": "D",
"vibrational_state_v": 0
},
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table 1 (p. 22232), column ‘D (10-6 cm-1)a’: 5.9(6) x 1e-6 cm^-1, fitted as B_fit_N2; level not stated.
reichert_2015/B_fit_O2#
{
"id": "B_fit_O2",
"material": "O2",
"file": "O2/reichert_2015__B_fit_O2.csv",
"table": "tbl_f40cb41739d3",
"quantity": "rotational_constant",
"unit": "cm-1",
"abscissa": "label",
"use": "check",
"parameters": {
"constant": "B",
"vibrational_state_v": 0
},
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table 1 (p. 22232), column ‘B (cm-1)a’: 1.4377(2) for 16O2, fitted as B_fit_N2 (the O2 spin splitting not modelled); level not stated.
reichert_2015/D_fit_O2#
{
"id": "D_fit_O2",
"material": "O2",
"file": "O2/reichert_2015__D_fit_O2.csv",
"table": "tbl_f40cb41739d3",
"quantity": "rotational_constant",
"unit": "cm-1",
"scale": 1e-06,
"abscissa": "label",
"use": "check",
"parameters": {
"constant": "D",
"vibrational_state_v": 0
},
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table 1 (p. 22232), column ‘D (10-6 cm-1)a’: 5.1(5) x 1e-6 cm^-1 for 16O2; level not stated.
reichert_2015/B_raman_N2#
{
"id": "B_raman_N2",
"material": "N2",
"file": "N2/reichert_2015__B_raman_N2.csv",
"table": "tbl_f40cb41739d3",
"quantity": "rotational_constant",
"unit": "cm-1",
"abscissa": "label",
"use": "reproduced",
"reproduced_from": [
"bendtsen_1974",
"weber_1979"
],
"parameters": {
"constant": "B",
"vibrational_state_v": 0
},
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table 1 (p. 22232), column ‘B (cm-1)b’, the Raman comparison value [41] (Weber 1979): 1.989574(12), digit-identical with bendtsen_1974 Table VII’s pure rotational B_0 (its original).
reichert_2015/D_raman_N2#
{
"id": "D_raman_N2",
"material": "N2",
"file": "N2/reichert_2015__D_raman_N2.csv",
"table": "tbl_f40cb41739d3",
"quantity": "rotational_constant",
"unit": "cm-1",
"scale": 1e-06,
"abscissa": "label",
"use": "reproduced",
"reproduced_from": [
"bendtsen_1974",
"weber_1979"
],
"parameters": {
"constant": "D",
"vibrational_state_v": 0
},
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table 1 (p. 22232), column ‘D (10-6 cm-1)b’ [41]: 5.76(3), bendtsen_1974 Table VII’s pure rotational D.
reichert_2015/B_raman_O2#
{
"id": "B_raman_O2",
"material": "O2",
"file": "O2/reichert_2015__B_raman_O2.csv",
"table": "tbl_f40cb41739d3",
"quantity": "rotational_constant",
"unit": "cm-1",
"abscissa": "label",
"use": "reproduced",
"reproduced_from": [
"R. J. Butcher, D. V. Willetts and W. J. Jones, Proc. R. Soc. A324, 231 (1971)",
"weber_1979"
],
"parameters": {
"constant": "B",
"vibrational_state_v": 0
},
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table 1 (p. 22232), column ‘B (cm-1)b’ [41]: 1.437682(9) for 16O2: Weber’s Table 3.2 (weber_1979 table3_2_B0_O2_butcher, p. 88) prints it as [3.17a] R. J. Butcher, D. V. Willetts and W. J. Jones, Proc. R. Soc. A324, 231 (1971), the original (not in the library); digit-identical. hajigeorgiou_2013’s B_0 is 1.437674521 (Table III) and 1.43767602 (Table I, from Yu et al.): 6-8e-6 cm^-1 below, within 1 sigma of the (9).
reichert_2015/D_raman_O2#
{
"id": "D_raman_O2",
"material": "O2",
"file": "O2/reichert_2015__D_raman_O2.csv",
"table": "tbl_f40cb41739d3",
"quantity": "rotational_constant",
"unit": "cm-1",
"scale": 1e-06,
"abscissa": "label",
"use": "reproduced",
"reproduced_from": [
"R. J. Butcher, D. V. Willetts and W. J. Jones, Proc. R. Soc. A324, 231 (1971)",
"weber_1979"
],
"parameters": {
"constant": "D",
"vibrational_state_v": 0
},
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table 1 (p. 22232), column ‘D (10-6 cm-1)b’ [41]: 4.852(12) for 16O2 (weber_1979 table3_2_D0_O2_butcher, from [3.17a] Butcher et al. 1971, digit-identical), against hajigeorgiou_2013’s D_0 4.839482 (Table III) and 4.8405146 (Table I): 1.0 sigma of the (12) below.
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.