shelton_1982#

D. P. Shelton and A. D. Buckingham, Phys. Rev. A 26, 2787 (1982)

Source record · Catalogue · Review register

Source kind: measurement

Recorded technique: Electric-field-induced second-harmonic generation (ESHG) with periodic phase matching, cw argon-ion laser (about 1 W), 158 electrode pairs (N = 79, spacing l = 1.27 mm) in a stainless-steel cell, confocal parameter z0 = 9.2 cm; the gas density is adjusted to the peak of the phase-matching curve, located to better than 0.1 % in density; density from pressure (Budenberg dead-weight tester, or mercury manometer) and temperature (platinum resistance thermometer) by the virial equation of state with second and third virial coefficients (Dymond and Smith); measurements near 20 C (pp. 2789-2792).

Materials in structured entries: Ar, CH4, CO2, H2, He, N2, SF6

Dataset quantities: hyperpolarizability

Contents: 9 datasets; 0 formulas.

Curation notes#

NO DATASETS: the linear-dispersion content is the optimum phase-matching density rho_opt at a fixed wave-vector mismatch |Delta k|_opt = 2465.0 +- 0.5 m^-1 (Table II note b, Table III note b), with Delta k = (4 pi/lambda_w)(n_w - n_2w) = -(2 pi/(lambda_w eps0))(alpha_2w - alpha_w) rho (Eq. (5)), so (alpha_2w - alpha_w) is proportional to 1/rho_opt. The vocabulary has no quantity for a phase-match density at a stated |Delta k| (FORMAT NEED: e.g. ‘phase_match_density’, unit mol/m3, with parameters.delta_k_per_m and harmonic; phase_mismatch_per_density would need 1/rho, not the printed number, and no ratio is printed). The values are transcribed here from the library tables (CSV cells; the images agree).

Table II (tbl_09cd9a18fa27), at 514.5 nm, rho_opt (mol m^-3) at |Delta k|_opt = 2465.0 +- 0.5 m^-1: He 4690 +- 3, Ar 236.8 +- 0.2, H2 322.7 +- 0.2, N2 220.7 +- 0.2, CO2 125.32 +- 0.02, CH4 98.97 +- 0.02, SF6 127.7 +- 0.4 (CH3F 121.6, CHF3 174.9, CF4 220.8: not curated species); rho_3K (third spatial harmonic of the electrode field, Eq. (12)) at |Delta k_3K|_opt = 7412.4 +- 1.5 m^-1: CH4 297.9 +- 0.2 (CH3F 367 +- 1).

Table III (tbl_e6603d44b34e), rho_He and rho_CH4 (mol m^-3) at |Delta k|_opt = 2465.0 m^-1: 694.3 nm He 11620 +- 12 (note d: ‘From Ref. 1’), CH4 270 +- 3 (note e: ‘From Ref. 4’); 514.5 nm He 4690 +- 3, CH4 98.97 +- 0.02; 501.7 nm 4346 +- 2, 90.71 +- 0.08; 496.5 nm 4205 +- 2, 87.51 +- 0.02; 488.0 nm 3987 +- 2, 82.26 +- 0.04; 476.5 nm 3698 +- 2, 75.75 +- 0.07; 457.9 nm 3265 +- 2, 65.58 +- 0.07. The 694.3 nm values are other authors’ (Ref. 1: R. S. Finn and J. F. Ward, Phys. Rev. Lett. 26, 285 (1971); Ref. 4: C. K. Miller and J. F. Ward, Phys. Rev. A 16, 1179 (1977)), apparently converted to this |Delta k|; the paper does not say how.

Wavelengths: the argon-ion lines are printed at their standard air wavelengths (514.5, 501.7, 496.5, 488.0, 476.5, 457.9 nm; ruby 694.3 nm), although Eq. (1) defines lambda_w as a vacuum wavelength (shelton_1986 prints the vacuum values 514.7, 496.6, 488.1, 476.6).

Accuracy: the phase-match density limited ‘by the accuracy of the virial corrections, the gauge calibration, the sample purity, and the reproducibility of the peak-position determination’ (p. 2792); the +- are those of the tables, level not stated. The ratios of these densities between two gases at one wavelength (e.g. rho_He/rho_CH4) would be phase_match_density_ratio data; they are not printed, so they are not stored.

Not extracted: Table I (phase-matching peak parameters, theory), the hyperpolarizabilities gamma, beta and gamma rho_opt (Tables II, III).

THIRD-ORDER DATA (added 2026-09-26; the “NO DATASETS” and “Not extracted” remarks above predate it and concern the linear data). Definitions (p. 2788): the second-harmonic power is Eq. (3), with the nonlinear susceptibility of the gas chi_NL = (1/4) [(n_omega^2 + 2)/3]^2 [(n_2omega^2 + 2)/3] [mu^(0) beta/3 k_B T + gamma] rho (Eq. 4), rho the number density, beta and gamma ‘the appropriate components of the first and second hyperpolarizability tensors’ (all fields parallel), the static field E^(0) cos(Kz); the same gamma (Taylor-series convention, SI C^4 m^4 J^-3) as shelton_1990. Ratios: R = [gamma + mu beta/3kT]_A / [...]_B = (S_A/S_B)^(1/2) (n_B rho_B)/(n_A rho_A) (Eq. 13, p. 2792; the printed Eq. 13 shows no square root on the signal ratio, but Eq. (6) makes the power quadratic in chi_NL and the text says ‘only the phase-matching density and the square root of the second-harmonic signal need to be measured’ (p. 2792); the tabulated gammas are unaffected). Calibration: gamma_He of Sitz & Yaris (ref 18), 2.950e-63 C^4 m^4 J^-3 at 514.5 nm (Table II note d) and Table III’s values at the other lines; ‘the correct values of the hyperpolarizabilities could be recovered from the values in Table II by multiplying by the ratio of the new and old values of gamma_He’ (p. 2792). Uncertainties exclude the He calibration (~1 %). Nondipolar molecules measured near 20 C; CH3F and CHF3 (dipolar, 20-170 C) are not curated. Parts: the atoms electronic; the molecules total ESHG gamma. Datasets: table2_<gas> (Ar, H2, N2, CO2, SF6 at 514.5 nm; CH4’s Table II value is table3_CH4’s 514.5 nm row), table3_CH4 (six lines), table3_CH4_miller_ward (694.3 nm, reproduced), table3_He_calc (the calibrant, reproduced), and text_He_absolute (the direct absolute measurement, 2.7 +- 0.5e-63 at 514.5 nm, p. 2791). Also from the text (p. 2791): the illustrative He parameters omega_1 = 3.9e16 rad/s, alpha_0 = 2.3e-41 C^2 m^2 J^-1, gamma_0 = 2.8e-63 C^4 m^4 J^-3 (from Bogaard & Orr, ref 15; not extracted). A text slip: p. 2797 prints |Delta k|_opt = 0.9965 (pi/l) = 2456.0 +- 0.5 m^-1 while Tables II and III give 2465.0 +- 0.5 m^-1; 0.9965 pi / 1.27 mm = 2465.0 m^-1, so the text’s 2456.0 transposes two digits (the tables are right). Later correction by the same group (shelton_1985_sf6, p. 319): ‘The values at lambda = 514.5 nm in ref. [6] [this paper] are systematically low by 1.5% [10]’ (ref [10]: Mizrahi & Shelton, then to be published); not applied here (the Table II values are as printed).

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_1982/table2_Ar#

{
  "id": "table2_Ar",
  "material": "Ar",
  "file": "Ar/shelton_1982__table2_Ar.csv",
  "table": "tbl_09cd9a18fa27",
  "quantity": "hyperpolarizability",
  "unit": "SI",
  "scale": 1e-63,
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "primary",
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "eshg",
    "convention": "T",
    "part": "electronic"
  }
}

Table II (p. 2793): 10^63 gamma (C^4 m^4 J^-3) measured by ESHG at 514.5 nm, the ratio to He times the calibrant, near 20 C. Calibrated against gamma_He = 2.950e-63 C^4 m^4 J^-3 at 514.5 nm, ‘Calculated value from Ref. 18’ (Sitz & Yaris 1968; Table II note d); ‘Error estimates exclude the uncertainty of gamma_He used for calibration’ (note a), ‘thought to be about 1%’ (p. 2792). Shelton & Rice 1994 rescale such values to Bishop & Pipin’s He.

shelton_1982/table2_H2#

{
  "id": "table2_H2",
  "material": "H2",
  "file": "H2/shelton_1982__table2_H2.csv",
  "table": "tbl_09cd9a18fa27",
  "quantity": "hyperpolarizability",
  "unit": "SI",
  "scale": 1e-63,
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "primary",
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "eshg",
    "convention": "T",
    "part": "total"
  }
}

shelton_1982/table2_N2#

{
  "id": "table2_N2",
  "material": "N2",
  "file": "N2/shelton_1982__table2_N2.csv",
  "table": "tbl_09cd9a18fa27",
  "quantity": "hyperpolarizability",
  "unit": "SI",
  "scale": 1e-63,
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "primary",
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "eshg",
    "convention": "T",
    "part": "total"
  }
}

shelton_1982/table2_CO2#

{
  "id": "table2_CO2",
  "material": "CO2",
  "file": "CO2/shelton_1982__table2_CO2.csv",
  "table": "tbl_09cd9a18fa27",
  "quantity": "hyperpolarizability",
  "unit": "SI",
  "scale": 1e-63,
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "primary",
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "eshg",
    "convention": "T",
    "part": "total"
  }
}

shelton_1982/table2_SF6#

{
  "id": "table2_SF6",
  "material": "SF6",
  "file": "SF6/shelton_1982__table2_SF6.csv",
  "table": "tbl_09cd9a18fa27",
  "quantity": "hyperpolarizability",
  "unit": "SI",
  "scale": 1e-63,
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "primary",
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "eshg",
    "convention": "T",
    "part": "total"
  }
}

shelton_1982/table3_CH4#

{
  "id": "table3_CH4",
  "material": "CH4",
  "file": "CH4/shelton_1982__table3_CH4.csv",
  "table": "tbl_e6603d44b34e",
  "quantity": "hyperpolarizability",
  "unit": "SI",
  "scale": 1e-63,
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "primary",
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "eshg",
    "convention": "T",
    "part": "total"
  }
}

Table III (p. 2793): gamma_CH4 by ESHG at the six argon-ion lines 514.5-457.9 nm (the 514.5 nm value is also Table II’s). Calibrated against gamma_He = 2.950e-63 C^4 m^4 J^-3 at 514.5 nm, and at each wavelength the calculated gamma_He of the same table (table3_He_calc), ‘Calculated value from Ref. 18’ (Sitz & Yaris 1968; Table II note d); ‘Error estimates exclude the uncertainty of gamma_He used for calibration’ (note a), ‘thought to be about 1%’ (p. 2792). Shelton & Rice 1994 rescale such values to Bishop & Pipin’s He. Note c: ‘Error estimates exclude the uncertainty of gamma_He’. The authors see a resonance-like feature at 20140 cm^-1 (width ~200 cm^-1, Fig. 5), attributed tentatively to the Delta v = 8 CH-stretch overtone (20520 cm^-1 expected): measured Delta gamma^res/gamma^nonres = +5e-2 against a calculated 1e-10 (pp. 2795-2796). Later ESHG work (shelton_1986_ch4) is the reference for CH4’s dispersion.

shelton_1982/table3_CH4_miller_ward#

{
  "id": "table3_CH4_miller_ward",
  "material": "CH4",
  "file": "CH4/shelton_1982__table3_CH4_miller_ward.csv",
  "table": "tbl_e6603d44b34e",
  "quantity": "hyperpolarizability",
  "unit": "SI",
  "scale": 1e-63,
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "C. K. Miller and J. F. Ward, Phys. Rev. A 16, 1179 (1977)"
  ],
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "eshg",
    "convention": "T",
    "part": "total"
  }
}

Table III note e: the 694.3 nm gamma_CH4 = 196 +- 2 is ‘From Ref. 4’ (Miller & Ward 1977), presumably rescaled to the same He calculation (not stated).

shelton_1982/table3_He_calc#

{
  "id": "table3_He_calc",
  "material": "He",
  "file": "He/shelton_1982__table3_He_calc.csv",
  "table": "tbl_e6603d44b34e",
  "quantity": "hyperpolarizability",
  "unit": "SI",
  "scale": 1e-63,
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "P. Sitz and R. Yaris, J. Chem. Phys. 49, 3546 (1968)"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "eshg",
    "convention": "T",
    "part": "electronic"
  }
}

Table III note a: 10^63 gamma_He for ESHG, ‘Calculated values from Ref. 18 [Sitz & Yaris 1968]; assumed in calibrating the gamma_CH4 measurements’ (694.3-457.9 nm). The old He calibration: Bishop & Pipin’s later curve (shelton_1990 Table II in SI, with its C corrected) gives 2.990e-63 at 514.5 nm (19431 cm^-1), 1.3 % above Sitz & Yaris’s 2.950 (computed here, not a statement of the paper).

shelton_1982/text_He_absolute#

{
  "id": "text_He_absolute",
  "material": "He",
  "table": "text",
  "quantity": "hyperpolarizability",
  "unit": "SI",
  "scale": 1e-63,
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "primary",
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "eshg",
    "convention": "T",
    "part": "electronic"
  }
}

1 inline points in the source record.

p. 2791: ‘Our experimentally determined value of gamma_He at 514.5 nm is 2.7 +- 0.5 x 10^-63 C^4 m^4 J^-3 in agreement with the computed value of 2.95 +- 0.03 x 10^-63’ (Sitz & Yaris). An absolute ESHG measurement from Eqs. (4) and (6), with the factors (2m - 1)/m ~ 2 for the ~30 longitudinal laser modes and 1.14^2 for the cos Kz component of the electrode field (Eq. 12).

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.