rosasco_1986 ============ G\. J\. Rosasco and W\. S\. Hurst, J\. Opt\. Soc\. Am\. B 3, 1251 \(1986\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1364/josab\.3\.001251 `__ **Source kind:** measurement **Recorded technique:** cw phase\-modulated stimulated Raman spectroscopy \(optical\-heterodyne\-detected Raman\-induced Kerr effect\) as in rosasco\_1985\: Kr\-ion pump \(14779 cm^\-1, 10 MHz\), ring\-dye probe \(17751 cm^\-1, 1 MHz\), 45\-pass cell; 5 % D2 in H2 \(the D2 Q\(3\), Q\(4\) lines as internal standard\) at 1\.0\-6\.0 atm, bracketed by two 5 % D2 in He runs that calibrate the mirror contribution; ideal\-gas densities, pressure and temperature to 0\.1 %\. **Materials in structured entries:** D2, H2, He **Dataset quantities:** nonlinear\_susceptibility **Contents:** 5 datasets; 0 formulas. Curation notes -------------- The electronic hyperpolarizability of H2 from its nonresonant optical \(ac\) Kerr constant, and a dispersion comparison of H2's electronic hyperpolarizability from ac Kerr, dc Kerr, THG, FISHG and CARS \(Fig\. 4, figure only\)\. Definitions \(Appendix A, p\. 1255\)\: \(A1\) P\_1,i = D chi\_ijkl\(\-w1, w2, w3, w4\) E\_2,j E\_3,k E\_4,l with D = 6, 3, 1 and Fourier components \(as rosasco\_1985\); \(A2\) Hellwarth's representation 24 chi\_ijkl = \[sigma \+ 2A \+ B \+ B\] delta delta \+ \.\.\.; sigma the electronic hyperpolarizability, A and B the nuclear \(vibrational, rotational\) terms, \(A3\)\-\(A10\); the measured nonresonant chi^N = 2 sigma/24 \+ 2 B\(0\)/24 \+ chi\_R\(2A\+B\)^OR \(Eq\. \(6\)\), with the far\-off\-resonance Raman sums \(A12\) and the reorientation term \(A13\) 2B\(0\)/24 = \(2/24\) \(1/15\) \(N/k\_B T\) gamma\_0^2 \(1 \- R\_0 \+ 8 R\_0^2/15 \+ \.\.\.\), gamma\_0 the optical polarizability anisotropy \(Bridge and Buckingham 1966, not in the library\)\. Eq\. \(11\), p\. 1253\: '\[3 sigma/24\]\_1 amagat, cgs = N0 gamma/24 = 5\.639 x 10^\-22 gamma\_AU' with gamma in atomic units \(checked\: 2\.687e19/24 x 5\.0367e\-40 esu/au = 5\.639e\-22\), gamma the Taylor \(Shelton\) gamma\. So gamma\_T \(au\) = \(3 sigma/24\)/5\.639e\-22 = 1\.5 \(2 sigma/24\)/5\.639e\-22\. Result \(p\. 1253\)\: chi\_0^N/\(A\_0 N\_0\) = 0\.0137 \(\+0\.0003, \-0\.0005\) \(Eq\. \(7\), the range from the mirror model\), A\_0 N\_0 = 461\.4 x 10^\-19 esu \(rosasco\_1985 Eq\. \(47\)\); with the computed 2B\(0\)/24 and off\-resonant Raman terms of Table 1 this gives 2 sigma/24 = 2\.966 x 10^\-19 esu for H2\. \(Recomputing chi\_0^N from Table 1's components, 2\.966 \+ 2\.722 \+ 0\.665 \- 0\.00547 = 6\.348 x 10^\-19 = 0\.01376 A\_0 N\_0, which rounds to 0\.0138, not the printed 0\.0137\: a rounding question only\.\) The reference susceptibility 'is believed to have an uncertainty of \+\-5 %' \(p\. 1251\); Table 1 note a\: 'Estimated errors for most of the values given in this table are \+\-5 %\. These results assume the pump \(14779 cm^\-1\) and probe \(17751 cm^\-1\) frequencies employed in this work\.' Table 1 rows not extracted \(computed corrections, a mixture of the A and B terms, not one 'part'\)\: chi\_R\(2A\+B\)^OR sums H2 0\.665 \(Sum' over omega \- Omega, excluding the resonant Q branch\) and \-0\.00547 \(omega \+ Omega\), D2 0\.0834 and \-0\.00275; chi\_R\(2A\-B\)^OR sums H2 0\.663 and \+0\.00471, D2 0\.0516 and \+0\.00243 \(the last row prints B\(omega \- Omega\) inside a sum over omega \+ Omega, image checked\: presumably a misprint; the H2 0\.663 cell carries a stray prime on its footnote f\); A\_0 N\_0 \(D2\) 461\.4\. Dispersion \(pp\. 1253\-1254\)\: Owyoung's and Hellwarth's chi^NRE\(\-w1, w2, w3, w4\) proportional to chi\(w1\) chi\(w2\) chi\(w3\) chi\(w4\) \(Eq\. \(8\)\), with one pole\: chi^NRE proportional to chi\_0 \[1 \+ k \(w^2\)\_eff\] \(Eq\. \(9\)\), \(w^2\)\_eff = w1^2 \+ w2^2 \+ w3^2 \+ w4^2 \(Eq\. \(10\)\); dc Kerr, FISHG and THG dispersion rates in the ratio 1\:3\:6 \(Dawes, Finn\)\. No coefficients are given \(the Fig\. 4 line is Mizrahi and Shelton's\)\: no formula recorded\. In Fig\. 4 the dc\-KE value of rosasco\_1985 Table IV is corrected by \+3 % for far\-off\-resonance Raman terms, the CARS value is Lundeen et al\.'s D2 scaled by Mizrahi and Shelton's H2\:D2 ratio, the THG value Ward and New's; the paper speculates the dc Kerr value 'may be approximately 20 % low'\. Wavelengths\: the pump is given as 14779 cm^\-1 \(vacuum wavenumber, as printed; the Kr\-ion 676\.4 nm line\), recorded with wavelength\_unit cm\-1; the probe 17751 cm^\-1 is in parameters\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- rosasco\_1986/sigma\_H2 ~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "sigma_H2", "material": "H2", "file": "H2/rosasco_1986__sigma_H2.csv", "table": "tbl_1142277dccf1", "quantity": "nonlinear_susceptibility", "unit": "esu (per amagat)", "scale": 1e-19, "abscissa_unit": "cm-1", "use": "primary", "uncertainty": { "relative": 0.05, "level": "not stated" }, "parameters": { "process": "kerr", "convention": "rosasco_1985_hellwarth", "part": "electronic", "probe_cm1": 17751 } } Table 1 \(p\. 1254\), 10^\-19 esu at 1 amagat and 296 K \(per amagat, N0 = Loschmidt's number; no state\), Hellwarth's convention of rosasco\_1985 \(2 sigma/24 = N0 gamma\_T/36\)\: 2 sigma/24 of H2, 'determined in this work' \(note b\)\: the electronic part of the measured ac Kerr constant, chi\_0^N minus the computed 2B\(0\)/24 \(2\.722\) and off\-resonant Raman terms\. Nondegenerate optical Kerr chi\(\-w, w, W, \-W\), pump 14779 cm^\-1, probe 17751 cm^\-1\. \+\-5 % \(note a; the level is not stated\)\. Electronic \(the paper\: 'the electronic hyperpolarizability'\), separated by subtraction of the calculated reorientation and Raman terms\. rosasco\_1986/sigma\_D2 ~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "sigma_D2", "material": "D2", "file": "D2/rosasco_1986__sigma_D2.csv", "table": "tbl_1142277dccf1", "quantity": "nonlinear_susceptibility", "unit": "esu (per amagat)", "scale": 1e-19, "abscissa_unit": "cm-1", "use": "check", "parameters": { "process": "kerr", "convention": "rosasco_1985_hellwarth", "part": "electronic", "probe_cm1": 17751 } } Table 1 \(p\. 1254\), 10^\-19 esu at 1 amagat and 296 K \(per amagat, N0 = Loschmidt's number; no state\), Hellwarth's convention of rosasco\_1985 \(2 sigma/24 = N0 gamma\_T/36\)\: 2 sigma/24 of D2, 'From the H2 value and the ratio of H2/D2 of ~1\.02; see Ref\. 13' \(note c, Mizrahi and Shelton 1985, mizrahi\_1985\_h2d2\)\: derived, not measured \(2\.966/1\.02 = 2\.908\)\. Electronic\. rosasco\_1986/sigma\_He ~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "sigma_He", "material": "He", "file": "He/rosasco_1986__sigma_He.csv", "table": "tbl_1142277dccf1", "quantity": "nonlinear_susceptibility", "unit": "esu (per amagat)", "scale": 1e-19, "abscissa_unit": "cm-1", "use": "reproduced", "reproduced_from": [ "rosasco_1985", "ward_1969" ], "parameters": { "process": "kerr", "convention": "rosasco_1985_hellwarth", "part": "electronic" } } Table 1 \(p\. 1254\), 10^\-19 esu at 1 amagat and 296 K \(per amagat, N0 = Loschmidt's number; no state\), Hellwarth's convention of rosasco\_1985 \(2 sigma/24 = N0 gamma\_T/36\)\: 2 sigma/24 of He, 'Value from Ref\. 14 \[Ward and New\], as reported in Ref\. 6 \[rosasco\_1985\]' \(note d\)\: 1\.5 x 0\.178 = 0\.267 = rosasco\_1985's He reference \(0\.0267 x 10^\-18\) in 3 sigma/24; ultimately the Sitz and Yaris theory Ward and New normalize to\. Used to model the D2\:He calibration runs\. Electronic\. The wavelength column holds this paper's pump \(the value's own frequency is Ward and New's\)\. rosasco\_1986/reorientation\_H2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "reorientation_H2", "material": "H2", "file": "H2/rosasco_1986__reorientation_H2.csv", "table": "tbl_1142277dccf1", "quantity": "nonlinear_susceptibility", "unit": "esu (per amagat)", "scale": 1e-19, "abscissa_unit": "cm-1", "use": "check", "parameters": { "process": "kerr", "convention": "rosasco_1985_hellwarth", "part": "rotational", "temperature_k": 296 } } Table 1 \(p\. 1254\), 10^\-19 esu at 1 amagat and 296 K \(per amagat, N0 = Loschmidt's number; no state\), Hellwarth's convention of rosasco\_1985 \(2 sigma/24 = N0 gamma\_T/36\)\: 2B\(0\)/24 of H2 = 2\.722, the molecular\-reorientation \(orientational\) term of the ac Kerr constant, 'Calculated from Eq\. \(A13\) and the anisotropy values from Ref\. 8' \(Bridge and Buckingham 1966; note e\), at 296 K \(it scales as 1/T\)\. Computed, not measured\. Rotational\. rosasco\_1986/reorientation\_D2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "reorientation_D2", "material": "D2", "file": "D2/rosasco_1986__reorientation_D2.csv", "table": "tbl_1142277dccf1", "quantity": "nonlinear_susceptibility", "unit": "esu (per amagat)", "scale": 1e-19, "abscissa_unit": "cm-1", "use": "check", "parameters": { "process": "kerr", "convention": "rosasco_1985_hellwarth", "part": "rotational", "temperature_k": 296 } } Table 1 \(p\. 1254\), 10^\-19 esu at 1 amagat and 296 K \(per amagat, N0 = Loschmidt's number; no state\), Hellwarth's convention of rosasco\_1985 \(2 sigma/24 = N0 gamma\_T/36\)\: 2B\(0\)/24 of D2 = 2\.827, the molecular\-reorientation \(orientational\) term of the ac Kerr constant, 'Calculated from Eq\. \(A13\) and the anisotropy values from Ref\. 8' \(Bridge and Buckingham 1966; note e\), at 296 K \(it scales as 1/T\)\. Computed, not measured\. Rotational\. 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 :doc:`review register ` for the checks and decisions.