shelton_1986_ch4 ================ D\. P\. Shelton, Phys\. Rev\. A 34, 304 \(1986\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1103/physreva\.34\.304 `__ **Source kind:** measurement **Recorded technique:** ESHG with periodic phase matching as in shelton\_1985\_sf6 \(electrode spacing 2\.69 mm, 0\.9\-5\.9 atm at 20\-27 C\), cw dye or argon\-ion laser, 0\.3\-3\.0 W; dye\-laser wavelengths set with a 1 m spectrometer calibrated by Na and Ne lamps; sample CH4 \(99\.97 %\) and reference N2 \(99\.999 %\) in triplets ABA or coupled triplets; densities from the virial equation of state \(p\. 1\)\. **Materials in structured entries:** CH4, N2 **Dataset quantities:** hyperpolarizability, hyperpolarizability\_ratio, phase\_match\_density\_ratio **Contents:** 8 datasets; 3 formulas. Curation notes -------------- The by\-product ratio Delta alpha\_CH4 / Delta alpha\_N2 \(Delta alpha = alpha\(2 omega\) \- alpha\(omega\)\) 'is just proportional to rho^\-1, the inverse phase\-match density' \(p\. 1\)\: it is rho\_N2 / rho\_CH4, filed under N2 with CH4 as reference\_material as in shelton\_1990\. Table I gives the air wavelength \(note a\) and the vacuum wavenumber \(note b\) of the fundamental; the wavenumber is the abscissa, the air wavelength the row id\. Uncertainty \(p\. 1\)\: 'The accuracy of the polarizability dispersion ratio has been given as \+\-0\.20%, a conservative estimate based on the absolute pressure\-gauge accuracy of \+\-0\.15%\. If the gauge is linear, the dispersion ratio accuracy will instead be set by the \+\-0\.03% density ratio reproducibility\. The correct value for the error bar is probably intermediate'; Table I note c\: 'The tabulated error bars may be too pessimistic by as much as a factor of 7\.' The tabulated \+\- are kept as printed \(level not stated\)\. The gamma values, the gamma fits \(Fig\. 1\) and Table II \(other processes\) are hyperpolarizabilities and are not extracted\. Refractive indices for the local\-field factors were 'calculated from tables' \(Landolt\-Bornstein\)\. THIRD\-ORDER DATA \(added 2026\-09\-26; supersedes the remark above that the gamma values are not extracted\)\. gamma is the ESHG \\_zzzz \(fields parallel\) of Shelton's series \(Taylor convention, SI C^4 m^4 J^\-3\), calibrated on the old He value \(Sitz & Yaris, 42\.6 au static\) through Mizrahi & Shelton's N2/He ratio \(Eqs\. 2, 3, as in shelton\_1986\_co2\); the A, B, C of the fits below are against nu^2 of the fundamental, not nu\_L^2\. The electronic dispersion of all processes is written gamma^e\(\-omega\_s; omega\_1, omega\_2, omega\_3\) = gamma^e\(0; 0, 0, 0\)\(1 \+ C omega\_L^2\) \(Eqs\. 4\-5\)\. Part\: the author compares ESHG, dc Kerr, FWM and THG and, with Elliott & Ward's estimate that the vibrational part is '3% or less for dc Kerr and an order of magnitude smaller still for ESHG', concludes that 'the vibrational contribution to gamma\_CH4 is negligible' \(p\. 307; shelton\_1990 later finds the 1319 nm ESHG point 12 sigma below this curve, attributed to gamma^vR\)\. No vibrational\-overtone resonance is seen at the 0\.1 % level, contrary to shelton\_1982's suggestion \(p\. 307\)\. **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\_1986\_ch4/density\_N2\_over\_CH4 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "density_N2_over_CH4", "material": "N2", "file": "N2/shelton_1986_ch4__density_N2_over_CH4.csv", "table": "tbl_9090f1c5cfc2", "quantity": "phase_match_density_ratio", "abscissa_unit": "cm-1", "wavelength_medium": "vacuum", "density": "real", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "reference_material": "CH4", "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": "CH4", "shelton_reference_gas": "N2", "printed_as": "Delta alpha_CH4 / Delta alpha_N2" } } Table I, Delta alpha\_CH4 / Delta alpha\_N2 = rho\_N2 / rho\_CH4 as printed, 12 fundamentals 476\.5\-671\.7 nm \(air\), abscissa the printed vacuum wavenumber\. shelton\_1986\_ch4/gamma\_CH4\_over\_N2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gamma_CH4_over_N2", "material": "CH4", "file": "CH4/shelton_1986_ch4__gamma_CH4_over_N2.csv", "table": "tbl_9090f1c5cfc2", "quantity": "hyperpolarizability_ratio", "unit": "1", "abscissa_unit": "cm-1", "use": "check", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "reference_material": "N2", "process": "eshg", "convention": "T", "part": "total" } } Table I \(p\. 305\)\: gamma\_CH4/gamma\_N2 by ESHG as printed \(Eq\. 1 as in shelton\_1986\_co2\), 12 wavelengths 476\.5\-671\.7 nm \(row\: air wavelength; abscissa\: vacuum wavenumber\)\. 'The accuracy of the ratio is about \+\-0\.3%, while the reproducibility is about \+\-0\.1%' \(p\. 304\)\. The raw measurement behind gamma\_CH4\. shelton\_1986\_ch4/gamma\_CH4 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gamma_CH4", "material": "CH4", "file": "CH4/shelton_1986_ch4__gamma_CH4.csv", "table": "tbl_9090f1c5cfc2", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-63, "abscissa_unit": "cm-1", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "eshg", "convention": "T", "part": "total" } } Table I column d \(p\. 305\)\: gamma\_CH4 in 1e\-63 C^4 m^4 J^\-3, 'Obtained using Refs\. 13 and 19 for calibration' \(Mizrahi & Shelton's gamma\_N2/gamma\_He = 20\.30 \[1 \+ 6\.55e\-10 nu^2\] and Sitz & Yaris's gamma\_He = 42\.6 au \[1 \+ 2\.94e\-10 nu^2\], 1 au = 6\.2360e\-65; see shelton\_1986\_co2's formulas calibration\_\*\)\. '\+\-0\.4% due to the gamma\_N2/gamma\_He calibration' is included in the error bars; the ~1 % uncertainty of gamma\_He is not \(p\. 305\)\. The old He calibration; shelton\_1990 Table III\(c\) reproduces these rescaled \(e\.g\. 206\.76 against 204\.1 at 671\.7 nm\)\. Total ESHG gamma; the author concludes that 'the vibrational contribution to gamma\_CH4 is negligible' \(p\. 307\)\. shelton\_1986\_ch4/gamma\_CH4\_miller\_ward ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gamma_CH4_miller_ward", "material": "CH4", "file": "CH4/shelton_1986_ch4__gamma_CH4_miller_ward.csv", "table": "tbl_9090f1c5cfc2", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-63, "abscissa_unit": "cm-1", "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 I last column, note e\: 'From Ref\. 20' \(Miller & Ward 1977\), 694\.3 nm\: 195 \+\- 2 \(shelton\_1982 Table III prints the same measurement as 196 \+\- 2; the conversions differ\)\. shelton\_1986\_ch4/gamma\_CH4\_shelton\_1982 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gamma_CH4_shelton_1982", "material": "CH4", "file": "CH4/shelton_1986_ch4__gamma_CH4_shelton_1982.csv", "table": "tbl_9090f1c5cfc2", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-63, "abscissa_unit": "cm-1", "use": "reproduced", "reproduced_from": [ "shelton_1982" ], "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "eshg", "convention": "T", "part": "total" } } Table I last column, note f\: 'From Ref\. 12' \(Shelton & Buckingham 1982, Table III\), as printed there\. The previous results 'agree well with the curve fitted to the present results', but their 'error bars had been underestimated by about a factor of 2 or more' \(pp\. 306\-307\)\. shelton\_1986\_ch4/table2\_dc\_kerr ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_dc_kerr", "material": "CH4", "file": "CH4/shelton_1986_ch4__table2_dc_kerr.csv", "table": "tbl_0ba11cfe8ccf", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-63, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "reproduced", "reproduced_from": [ "buckingham_1969" ], "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "dc_kerr", "convention": "T", "part": "total" } } Table II \(p\. 306\)\: 'Hyperpolarizability of CH4 measured by several nonlinear\-optical processes', 1e\-63 C^4 m^4 J^\-3, converted by the author with '1 esu = 7\.4279 x 10^\-25 C^4 m^4 J^\-3' \(note b; 6 x the au ratio, Ward's chi = gamma/6\)\. nu\_L^2 printed 4\.99, 8\.64, 8\.64, 14\.47, 24\.88 x 10^8 cm^\-2\. Note c\: gamma\(\-omega; 0, 0, omega\), from Ref\. 21 \(Buckingham & Orr 1969\)\. About 10 % above the ESHG\-predicted line \(p\. 307\)\. Re\-pointed to buckingham\_1969 \(now in the library\)\: digit\-identical with its 10^60 gamma\(CH4\) = 0\.180 \+\- 0\.009 C^4 m^4 J^\-3 \(p\. 677\), whose error is the stated 5 % absolute accuracy\. shelton\_1986\_ch4/table2\_cars ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_cars", "material": "CH4", "file": "CH4/shelton_1986_ch4__table2_cars.csv", "table": "tbl_0ba11cfe8ccf", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-63, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "reproduced", "reproduced_from": [ "G. Hauchecorne, F. Kerherve and G. Mayer, J. Phys. (Paris) 32, 47 (1971)", "W. G. Rado, Appl. Phys. Lett. 11, 123 (1967)", "lundeen_1983" ], "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "cars", "convention": "T", "part": "total", "stokes_nm": "975, 975, 683 (rows in order)" } } Table II \(p\. 306\)\: 'Hyperpolarizability of CH4 measured by several nonlinear\-optical processes', 1e\-63 C^4 m^4 J^\-3, converted by the author with '1 esu = 7\.4279 x 10^\-25 C^4 m^4 J^\-3' \(note b; 6 x the au ratio, Ward's chi = gamma/6\)\. nu\_L^2 printed 4\.99, 8\.64, 8\.64, 14\.47, 24\.88 x 10^8 cm^\-2\. FWM gamma\(\-2 omega\_1 \+ omega\_2; omega\_1, omega\_1, \-omega\_2\) \(CARS\-type\)\. Rows\: note d, from Ref\. 22 \(Hauchecorne et al\. 1971\), 694 and 975 nm; note e, 'From Ref\. 23 \[Rado 1967\], as corrected and given in Ref\. 24 \[Lundeen et al\.\], but with their vibrational correction removed', 694 and 975 nm; note f, 'From Ref\. 24, with their vibrational correction removed', 532 and 683 nm\. Abscissa\: the pump wavelength; the Stokes \(975, 975, 683 nm\) in parameters\. 'The FWM results are in good agreement with' the ESHG\-predicted line \(p\. 307\)\. shelton\_1986\_ch4/table2\_thg ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_thg", "material": "CH4", "file": "CH4/shelton_1986_ch4__table2_thg.csv", "table": "tbl_0ba11cfe8ccf", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-63, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "reproduced", "reproduced_from": [ "ward_1984" ], "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "thg", "convention": "T", "part": "total" } } Table II \(p\. 306\)\: 'Hyperpolarizability of CH4 measured by several nonlinear\-optical processes', 1e\-63 C^4 m^4 J^\-3, converted by the author with '1 esu = 7\.4279 x 10^\-25 C^4 m^4 J^\-3' \(note b; 6 x the au ratio, Ward's chi = gamma/6\)\. nu\_L^2 printed 4\.99, 8\.64, 8\.64, 14\.47, 24\.88 x 10^8 cm^\-2\. Note g\: gamma\(\-3 omega; omega, omega, omega\), from Ref\. 25 \(Ward & Elliott, cited as J\. Chem\. Phys\. 80, 1002 \(1984\); the paper starts on p\. 1003\), 694\.3 nm\. About 10 % below the ESHG\-predicted line \(p\. 307\)\. Formulas -------- shelton\_1986\_ch4/ratio\_fit ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "ratio_fit", "material": "CH4", "equation": "Fig. 2 caption, p. 3", "printed": "Delta alpha_CH4 / Delta alpha_N2 = A (1 + B nu^2 + C nu^4); A = 2.1029, B = 0.916 x 10^-10 cm^2, C = 1.69 x 10^-20 cm^4", "variable": "nu: vacuum wavenumber of the fundamental in cm^-1", "range": "14883-20981 cm^-1 (476.5-671.7 nm)", "coefficients": { "A": "2.1029", "B": "0.916e-10", "C": "1.69e-20" }, "check": "As printed (page image checked) it lies 0.016 below the data at 14883 cm^-1 and 0.063 below at 20981 cm^-1, outside every error bar. With C = 16.9 x 10^-20 cm^4 it reproduces all twelve points to within 0.0018 (the error bars are 0.0043-0.0046): C is misprinted by a factor of 10 (read 16.9 x 10^-20). Checked 2026-09-25." } A fit of the dispersion ratio, not of the refractive index\. A straight line in nu^2 also passes through all the error bars \(p\. 3\)\. shelton\_1986\_ch4/gamma\_fit\_quadratic ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gamma_fit_quadratic", "material": "CH4", "equation": "Fig. 1 caption, p. 305", "printed": "gamma = A(1 + B nu^2 + C nu^4); A = 149.1 x 10^-63 C^4 m^4 J^-3, B = 14.70 x 10^-10 cm^2 and C = 89.1 x 10^-20 cm^4, where nu is given in cm^-1", "variable": "nu: vacuum wavenumber of the fundamental in cm^-1 (not nu_L^2)", "process": "eshg", "convention": "T", "part": "total", "range": "14883-20981 cm^-1 (476.5-671.7 nm, Table I column d)", "coefficients": { "A": "149.1e-63", "B": "14.70e-10", "C": "89.1e-20" }, "coefficient_units": { "A": "C^4 m^4 J^-3", "B": "cm^2", "C": "cm^4" }, "calibration": "old He (Sitz & Yaris) via N2 (Eqs. 2, 3)", "check": "Gives 204.17 at 14883 cm^-1 and 271.33 at 20981 cm^-1 against 204.1 +- 0.9 and 271.0 +- 1.8. Checked 2026-09-26." } Least\-squares fit to the 12 present values; 'the scatter of data points about the quadratic curve is in better agreement with the statistical estimate of the measurement reproducibility' than a straight line \(p\. 305\)\. shelton\_1986\_ch4/gamma\_fit\_linear ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gamma_fit_linear", "material": "CH4", "equation": "Fig. 1 caption, p. 305", "printed": "gamma = A'(1 + B' nu^2) with A' = 136.3 x 10^-63 C^4 m^4 J^-3 and B' = 22.31 x 10^-10 cm^2", "variable": "nu: vacuum wavenumber of the fundamental in cm^-1 (not nu_L^2)", "process": "eshg", "convention": "T", "part": "total", "range": "14883-20981 cm^-1", "coefficients": { "A": "136.3e-63", "B": "22.31e-10" }, "coefficient_units": { "A": "C^4 m^4 J^-3", "B": "cm^2" }, "calibration": "old He (Sitz & Yaris) via N2 (Eqs. 2, 3)", "check": "Gives 203.66 at 14883 cm^-1 and 270.16 at 20981 cm^-1 (within the error bars of 204.1 +- 0.9 and 271.0 +- 1.8). Checked 2026-09-26." } 'A straight\-line least squares fitted to the data will also pass through all the error bars'; the line used, as gamma^e\(0\)\(1 \+ C omega\_L^2\), for the comparison with the other processes \(Fig\. 4\)\. Superseded by shelton\_1990 Table IV \(161\.5e\-63, A = 1\.532e\-10, B = 4\.334e\-20 against nu\_L^2\)\. 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 :doc:`review register ` for the checks and decisions.