shelton_1985_sf6#
D. P. Shelton and V. Mizrahi, Chem. Phys. Lett. 120, 318 (1985)
Source record · Catalogue · Review register
DOI: 10.1016/0009-2614(85)87065-2
Source kind: measurement
Recorded technique: Electric-field-induced second-harmonic generation (ESHG) with periodic phase matching: a cw dye or argon-ion laser (0.3-2.0 W) weakly focused through a cell whose electrodes (spacing 2.69 mm) reverse the static field every coherence length, the gas density being adjusted to phase match (1-6 atm); sample SF6 (99.99 %) and reference N2 (99.9995 %); densities from pressure and temperature by the virial equation of state (virial corrections about 2 % for SF6, Dymond and Smith) (pp. 1-2).
Materials in structured entries: N2, SF6
Dataset quantities: hyperpolarizability, hyperpolarizability_ratio, phase_match_density_ratio
Contents: 4 datasets; 1 formula.
Curation notes#
The paper’s aim is the hyperpolarizability gamma; its by-product, the ratio Delta alpha_SF6 / Delta alpha_N2 with Delta alpha = alpha(2 omega) - alpha(omega), ‘is just proportional to the phase match density rho measured’ (table note a), i.e. it is the phase-match density ratio rho_N2 / rho_SF6. As in shelton_1990 the printed number is filed under N2 as gas with SF6 as reference_material (the package’s quantity is rho_gas / rho_reference); parameters.sample_gas and shelton_reference_gas keep the paper’s roles.
Wavelengths: the fundamental, 670.0, 650.0, 620.0 nm (dye laser) and 514.5, 488.0, 457.9 nm (argon-ion lines as usually quoted in air); the paper does not say, and standard air is assumed (as the later papers of the series state, shelton_1986_ch4 and shelton_1986_co2).
Uncertainty: +-0.003 per ratio (level not stated); ‘the accuracy of the overall measurement is chiefly determined by photon-counting statistics’ (p. 2). The gamma values (Table 1, fit gamma = A(1 + B nu^2), A = 8.21e-62 C^4 m^4 J^-3, B = 8.44e-10 cm^2) are hyperpolarizabilities and are not extracted. The 694.3 nm row holds only Ward and Miller’s gamma.
The same ratio at 1064 and 1319 nm is in shelton_1990 (density_N2_over_SF6).
THIRD-ORDER DATA (added 2026-09-26; supersedes the remark above that the gamma values are not extracted). gamma(-2 omega; omega, omega, 0), the ESHG gamma of Shelton’s series (Taylor-series convention, SI C^4 m^4 J^-3; shelton_1990 and shelton_1994 reproduce these values), measured relative to N2 and put on an absolute scale with Mizrahi & Shelton’s smoothed N2 curve (ref [10]). The authors note (p. 319): ‘The values at lambda = 514.5 nm in ref. [6] [shelton_1982] are systematically low by 1.5% [10]; when corrected, gamma_SF6 from ref. [6] coincides with the value reported here.’ Fit (p. 319): gamma = A (1 + B nu^2), formula below (nu the fundamental wavenumber, not nu_L^2). Relations between processes (pp. 319-320): gamma^elec = gamma_0^elec [1 + C (omega/omega_0)^2] (Eq. 2) with C^THG : C^ESHG : C^Kerr = 6 : 3 : 1 (Eq. 3, Dawes; Finn); the measured gamma^THG/gamma^ESHG of SF6 at 694.3 nm is 1.14 +- 0.07 (Elliott & Ward; Ward & Elliott) against 1.15 predicted from this dispersion, while gamma^ESHG/gamma^Kerr is measured 0.65 +- 0.06 against 1.11 predicted, attributed to vibrational contributions to the Kerr gamma (ratios between processes: no quantity; recorded here only). For H2 gamma_0^vib/gamma_0^elec = 0.28 is quoted from Mizrahi & Shelton (to be published).
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
shelton_1985_sf6/density_N2_over_SF6#
{
"id": "density_N2_over_SF6",
"material": "N2",
"file": "N2/shelton_1985_sf6__density_N2_over_SF6.csv",
"table": "tbl_72ec8b2e57c2",
"quantity": "phase_match_density_ratio",
"abscissa_unit": "nm",
"wavelength_medium": "standard_air",
"density": "real",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"reference_material": "SF6",
"harmonic": 2,
"process": "ESHG (electric-field-induced second-harmonic generation), periodic phase matching",
"definition": "rho_gas / rho_reference_gas at equal wave-vector mismatch |Delta k| = (4 pi / lambda) |n(2w) - n(w)|; to first order in density = [alpha_ref(2w) - alpha_ref(w)] / [alpha_gas(2w) - alpha_gas(w)]; lambda = fundamental",
"sample_gas": "SF6",
"shelton_reference_gas": "N2",
"printed_as": "Delta alpha_SF6 / Delta alpha_N2"
}
}
Table 1, Delta alpha_SF6 / Delta alpha_N2 = rho_N2 / rho_SF6 as printed, six fundamental wavelengths 457.9-670.0 nm.
shelton_1985_sf6/gamma_SF6_over_N2#
{
"id": "gamma_SF6_over_N2",
"material": "SF6",
"file": "SF6/shelton_1985_sf6__gamma_SF6_over_N2.csv",
"table": "tbl_72ec8b2e57c2",
"quantity": "hyperpolarizability_ratio",
"unit": "1",
"abscissa_unit": "nm",
"wavelength_medium": "standard_air",
"use": "check",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"reference_material": "N2",
"process": "eshg",
"convention": "T",
"part": "total"
}
}
Table 1 (p. 319): gamma_SF6/gamma_N2 by ESHG, as printed (Eq. 1: gamma_A/gamma_B = (S_A/S_B)^(1/2) (rho_A n_A / rho_B n_B)^-1, n = (n_0^4 n_omega^(2+zeta) n_2omega)^(1/6)). The raw measurement behind gamma_SF6. ‘The accuracy of the overall measurement is chiefly determined by photon-counting statistics’; the 457.9 nm error is large for lack of a filter (p. 319).
shelton_1985_sf6/gamma_SF6#
{
"id": "gamma_SF6",
"material": "SF6",
"file": "SF6/shelton_1985_sf6__gamma_SF6.csv",
"table": "tbl_72ec8b2e57c2",
"quantity": "hyperpolarizability",
"unit": "SI",
"scale": 1e-62,
"abscissa_unit": "nm",
"wavelength_medium": "standard_air",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"process": "eshg",
"convention": "T",
"part": "total"
}
}
Table 1 (p. 319): gamma_SF6 in 1e-62 C^4 m^4 J^-3, ‘Obtained using the smoothed results given in ref. [10]’ for gamma_N2 (Mizrahi & Shelton, then to be published; the N2 ESHG curve of mizrahi_1985_arn2o2, itself calibrated against He); ‘The error bars given for gamma_SF6 include allowance for +-0.4% uncertainty in the calibration values of gamma_N2’ (p. 319). Total ESHG gamma; ‘The nu^2 dependence seen in these experiments substantiates the usual assumption that vibrational contributions to gamma are negligible at optical frequencies for ESHG’ (pp. 319-320; shelton_1988 later finds gamma^v_ESHG ~ -3e-62, not negligible). shelton_1990 Table III(b) reproduces these on its new He calibration (e.g. 98.2e-63 against 9.75e-62 at 670 nm).
shelton_1985_sf6/gamma_SF6_ward_miller#
{
"id": "gamma_SF6_ward_miller",
"material": "SF6",
"file": "SF6/shelton_1985_sf6__gamma_SF6_ward_miller.csv",
"table": "tbl_72ec8b2e57c2",
"quantity": "hyperpolarizability",
"unit": "SI",
"scale": 1e-62,
"abscissa_unit": "nm",
"wavelength_medium": "standard_air",
"use": "reproduced",
"reproduced_from": [
"ward_1979"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"process": "eshg",
"convention": "T",
"part": "total"
}
}
Table 1 row 694.3 nm, note c): ‘From ref. [12]’ (Ward & Miller 1979), ESHG, as converted by the authors.
Formulas#
shelton_1985_sf6/fit#
{
"id": "fit",
"material": "SF6",
"equation": "text, p. 319",
"printed": "gamma = A (1 + B nu^2); A = (8.21 +- 0.09) x 10^-62 C^4 m^4 J^-3 and B = (8.44 +- 0.03) x 10^-10 cm^2, where nu is in cm^-1",
"variable": "nu: vacuum wavenumber of the fundamental in cm^-1 (not nu_L^2: for ESHG nu_L^2 = 6 nu^2, so B corresponds to Shelton & Rice's A = B/6 = 1.41e-10 cm^2)",
"process": "eshg",
"convention": "T",
"part": "total",
"range": "457.9-694.3 nm (Table 1, including Ward & Miller's 694.3 nm point: 'the results are also presented graphically in fig. 1')",
"coefficients": {
"A": "8.21e-62",
"B": "8.44e-10"
},
"coefficient_units": {
"A": "C^4 m^4 J^-3",
"B": "cm^2"
},
"calibration": "N2: Mizrahi & Shelton's smoothed gamma_N2 (ref [10]), on the old He calibration",
"check": "Gives 9.753e-62 at 670.0 nm (14921 cm^-1 from the air wavelength) and 10.826e-62 at 514.5 nm against 9.75 +- 0.07 and 10.84 +- 0.04. Checked 2026-09-26."
}
Weighted least-squares straight line against nu^2; A and B uncertainties as printed. Superseded by shelton_1990’s refit (gamma_0 = 89.10e-63, A = 0.500e-10, B = 2.124e-20 against nu_L^2, including 1064 and 1319 nm).
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.