hellwarth_1975#
R. Hellwarth, J. Cherlow and T.-T. Yang, “Origin and frequency dependence of nonlinear optical susceptibilities of glasses”, Phys. Rev. B 11, 964-967 (1975)
Source record · Catalogue · Review register
Source kind: measurement
Recorded technique: Absolute spontaneous Raman-scattering cross sections (90-degree scattering, the 514-nm argon-ion line, a double monochromator calibrated with a quartz-iodine standard lamp, absolute scale by comparison with the 992-cm^-1 line of liquid benzene, known to 3 % (Kato and Takuma), with index corrections), polarized and depolarized, of five glasses (Fig. 1): Homosil fused quartz (Amersil, Inc.), LSO (American Optical Co.), ED-4 (Owens Illinois, Inc.), SF-7 and LaSF-7 (Schott). Through the Born-Oppenheimer form of the third-order polarization (Eqs. 1-2), the fluctuation-dissipation relation (Eq. 6) and Kramers-Kronig (Eqs. 7-8), the zero-frequency nuclear transforms B0 and A0 + B0; combined with Owyoung’s intensity-induced polarization change (IIPC) sigma + 2 B0 at 694 nm (Eq. 3; Ref. 1) to give the electronic sigma, the self-focusing index n2 (Eq. 9) and its electronic fraction f_e (Table I). Room temperature (not stated).
Materials in structured entries: ED-4, LSO, LaSF-7, SF-7, SiO2
Dataset quantities: nonlinear_index_field, nonlinear_susceptibility, raman_fraction
Contents: 22 datasets; 0 formulas.
Curation notes#
Journal pages 964-967 = pdf pages 1-4 (journal page = 963 + pdf page). Identity checked against the first page (title, authors, Phys. Rev. B 11, No. 2; received 3 June 1974). Table I read on the page image (pdf p. 4, 150 dpi) cell by cell: the library’s cells (tbl_aa2b556d00dc, JSON only) are all as printed.
DEFINITIONS (Gaussian esu throughout, pp. 964-965). Eq. (1): the electronic part of P^(3), (1/2) sigma E(t) E^2(t), instantaneous, ‘for frequencies well below the electronic band gap’; sigma independent of temperature at fixed density. Eq. (2): the nuclear part, E(t) int ds a(t - s) E^2(s) + int ds E(s) b(t - s) E(t).E(s), ‘By “Raman scattering” we mean inelastic light scattering from all nuclear motions, vibrations, rotations, librations, etc., except macroscopic density fluctuations’; electrostriction and heating are excluded. A_Delta, B_Delta = int dt a(t), b(t) e^(i Delta t); A0, B0 their values at Delta = 0. Eq. (3): the IIPC rotation theta = pi omega z <E^2(t)> (sigma + 2 B0) cos 2 phi/8 n c. Eqs. (4)-(5): the Raman power gains g_par = (2 pi omega F^2/n c) Im(A + B), g_perp = (pi omega F^2/n c) Im B, F the pump amplitude. Eq. (6): Im B_Delta = (pi c^4/hbar nu omega^3) d^2 sigma_perp/d Omega d Delta (1 - e^(-hbar Delta/kT)), and A_Delta from (1/2) sigma_par - sigma_perp; d^2 sigma_i/d Omega d Delta ‘the fraction of incident photons ... scattered per unit distance into solid angle d Omega and angular frequency range d Delta’. Eq. (8): B0 = (2 c^4/hbar nu) int_0^inf (d Delta/omega^3 Delta) d^2 sigma_perp/d Omega d Delta (1 - e^(-hbar Delta/kT)), ‘and similarly for A0’. Eq. (9), p. 967: ‘Since the change in refractive index for linear polarization is defined as n2 <E^2(t)>, ... n2 = pi(3 sigma/2 + 2 A0 + 2 B0)/n’. f_e ‘according to (9), is [1 + 4(B0 + A0)/(3 sigma)]^-1’ (p. 967). In stolen_1989’s notation N_2R f(t) = (2 pi/n)[a(t) + b(t)] (its p. 1165), so the nuclear share of Eq. (9)’s n2 is that paper’s alpha = N_2R/N_20.
TABLE I (tbl_aa2b556d00dc, p. 967; tools/extract/hellwarth_1975.py). ‘Nonlinear polarization parameters defined in text as derived from our Raman data and intensity-induced polarization change (IIPC) measurements. From these are derived the self-focusing index n2 of Eq. (9) and the fraction f_e of it that is electronic in origin. All quantities are in esu.’ Columns: n; 10^16 B0 (a, this work); 10^16 (A0 + B0) (a); 10^15 (sigma + 2 B0) (b, ‘References 1 and 12’); 10^15 sigma; 10^14 n2 [Eq. (4)]; 10^14 n2 (Meas.); f_e (%). All five glasses are clean rows and all are recorded. Per glass: sigma (nonlinear_susceptibility, convention hellwarth_sigma, part electronic, primary), sigma + 2 B0 (the same quantity, part electronic_vibrational, reproduced from Owyoung), n2 of Eq. (9) (nonlinear_index_field, part electronic_vibrational, primary); fused quartz’s and ED-4’s measured n2 (reproduced). B0, A0 + B0 and f_e have no quantity (weber_1978 does the same with Heiman and Hellwarth’s A0, B0 and f_e) and stay in the printed cells: B0 = 14 +- 2, 28 +- 3, 26 +- 3, 210 +- 20, 380 +- 40 (10^-16 esu); A0 + B0 = 57 +- 6, 70 +- 7, 68 +- 7, 315 +- 30, 540 +- 50 (10^-16 esu); f_e = 79 +- 3, 81 +- 3, 85 +- 3, 79 +- 3, 71 +- 3 % (fused quartz, LSO, ED-4, SF-7, LaSF-7). The column header ‘10^14 n2 [Eq. (4)]’ is printed so (image checked); the caption and the text make it Eq. (9) (Eq. (4) is the gain): a header slip, not a value.
CHECKS (computed 2026-09-28, all five rows). sigma = (sigma + 2 B0) - 2 B0: 28.2, 40.4, 51.8, 160.0, 176.0 (printed 28, 40, 52, 160, 176). Eq. (9) with the printed sigma, A0 + B0 and n: 11.49, 15.29, 18.45, 57.69, 60.55 (printed 11, 15, 18, 58, 61). f_e = [1 + 4(A0 + B0)/(3 sigma)]^-1: 78.65, 81.08, 85.15, 79.21, 70.97 % (printed 79, 81, 85, 79, 71). Every derived column is reproduced to its printed digits.
THE NUCLEAR SHARE (computed, not printed). 1 - f_e = 0.21 +- 0.03 for fused quartz (0.2135 from the printed cells: 2 pi (A0 + B0)/n = 2.45e-14 esu of n2 = 11.49e-14 esu), 0.19 (LSO), 0.15 (ED-4), 0.21 (SF-7), 0.29 (LaSF-7). The fraction is of the long-pulse (monochromatic, Delta = 0) n2 for linear polarization, n = n0 + n2 <E^2>, in the Born-Oppenheimer limit, with electrostriction and heating excluded. boling_1978 (p. 604) quotes these as ‘nuclear contributions of 29, 21, 15, 19, and 21 percent’ for LaSF-7, SF-7, ED-4, LSO and fused silica. The paper warns (p. 966) that ‘our values for A_Delta and B_Delta are up to 10% to 20% larger than their values in the long-wavelength (BO) limit’: with A0 and B0 scaled by 0.9 or 0.8 (and sigma re-deduced from the IIPC) fused quartz’s nuclear share becomes 0.19 or 0.17. For comparison: stolen_1989 estimates 0.18 ‘From Raman-scattering cross-section and gain measurements’ (its Refs. 6 = this paper, 16 = stolen_1973); weber_1978’s Table 3 gives f_e = 0.74 for SiO2 from Heiman and Hellwarth’s later parameters (a nuclear share of 0.26).
UNCERTAINTY (p. 966). ‘The estimated absolute uncertainty of the curves of Fig. 1 is about +-10% for the polarized spectra and slightly greater for the depolarized spectra’, mostly calibration, so ‘the errors are probably not smoothed out by the integrating procedure and carry over to the values of B0 and A0 + B0’. Integration tails < 1 %; the spectrum below 20 cm^-1 assumed linear to zero (truncating at 20 cm^-1 changed the results by < 1 %). Dispersion: A and B may be 10-20 % above their long-wavelength values; a 647-nm check in fused quartz gave the same scattering relative to benzene. The table’s +- have no stated level.
FOOTNOTES AND REFERENCES (a doubt, not corrected). Table I’s footnotes c ‘Reference 9’, d ‘Reference 8’, e ‘Reference 7’ (measured n2) do not fit the reference list: Ref. 9 is Bliss, Speck and Simmons (unpublished), but Ref. 8 is Stolen and Ippen’s Raman-gain letter (printed ‘Appl. Phys. Lett. 22, 275 (1973)’; the letter begins on p. 276) and Ref. 7 Kato and Takuma’s benzene cross section, neither an n2 measurement; footnote b’s ‘Reference 12’ is Udagawa et al.’s benzene-vapour Raman paper, not an IIPC measurement. The text names three n2 measurements: Bliss et al. (Ref. 9) and Moran et al. (Ref. 10), ‘both made at 1.06 um’, with which the predictions ‘are seen to be consistent’, and Levenson (Ref. 4, three-wave mixing near 525 nm), ‘about 30% lower’ than whose values the predictions are. The numbers fit that reading if c is Levenson’s (fused quartz 11 against 18, ED-4 18 against 26: 39 % and 31 % lower) and d, e Bliss’s and Moran’s (ED-4 15 and 15 against 18); but the paper does not say so, and the footnote letters are recorded as printed. The measured n2 are reproduced values of uncertain origin and wavelength (‘not stated’).
TEXT (notes only). The polarized cross sections of fused quartz ‘yield Raman gains in (4) about 20% greater than those reported by Stolen and Ippen, but within their limits of error’ (p. 965; stolen_1973). For benzene, sigma ~ 0.1 B0 (Ref. 4) and McComb’s Kerr dispersion gives B0 rising 4 % +- 3 % from 647 to 514 nm (p. 966). The complex A_nu and B_nu at all nu were to appear in NBS Special Publication ‘Damage in Laser Materials: 1974’ (not in the library). Fig. 1 (the differential cross sections, 10^-10 cm^-1 sr^-1 per cm^-1, 0-1300 cm^-1; fused quartz’s polarized peak about 2.2 near 440 cm^-1, read by eye) is not digitised.
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
hellwarth_1975/sigma_SiO2#
{
"id": "sigma_SiO2",
"material": "SiO2",
"file": "SiO2/hellwarth_1975__sigma_SiO2.csv",
"table": "tbl_aa2b556d00dc",
"quantity": "nonlinear_susceptibility",
"unit": "esu",
"scale": 1e-15,
"abscissa_unit": "nm",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"process": "kerr",
"convention": "hellwarth_sigma",
"part": "electronic",
"technique": "IIPC (Owyoung) minus 2 B0 from absolute spontaneous Raman cross sections (this work)",
"grade": "Homosil",
"form": "bulk"
}
}
Table I (p. 967), ‘Fused quartz’, column ‘10^15 sigma’: the electronic coefficient of Eq. (1), P = (1/2) sigma E E^2, deduced as Owyoung’s IIPC sigma + 2 B0 (694 nm) minus twice this paper’s B0 (514-nm Raman spectra, Eq. 8); taken as frequency independent below the gap, recorded at the IIPC’s 694 nm. Sample: Homosil fused quartz (Amersil, Inc.). sigma the printed +- (level not stated). Not independent of the same row’s n2 (Eq. 9 uses it).
hellwarth_1975/iipc_SiO2#
{
"id": "iipc_SiO2",
"material": "SiO2",
"file": "SiO2/hellwarth_1975__iipc_SiO2.csv",
"table": "tbl_aa2b556d00dc",
"quantity": "nonlinear_susceptibility",
"unit": "esu",
"scale": 1e-15,
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"A. Owyoung, IEEE J. Quantum Electron. 9, 1064 (1973); A. Owyoung, Nat. Bur. Stds. Spec. Publ. No. 387 (U. S. GPO, Washington, D. C., 1973); A. Owyoung, R. W. Hellwarth, and N. George, Phys. Rev. B 5, 628 (1972) (Ref. 1; Table I footnote b, 'References 1 and 12')"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"process": "kerr",
"convention": "hellwarth_sigma",
"part": "electronic_vibrational",
"technique": "intensity-induced polarization change (ellipse rotation), Owyoung",
"polarization": "elliptical (ellipse rotation)",
"grade": "Homosil",
"form": "bulk"
}
}
Table I (p. 967), ‘Fused quartz’, column ‘10^15 (sigma + 2 B0)’, footnote b: Owyoung’s intensity-induced polarization change (ellipse rotation, Eq. 3), ‘taken at 694 nm’ (p. 966). The combination sigma + 2 B0 in the normalisation of Eqs. (1)-(2) (B0 the zero-frequency transform of the anisotropic nuclear kernel b(t)); 24 c1122 in Maker-Terhune terms (hellwarth_1990 Eq. 17). sigma the printed +- (level not stated). Footnote b’s ‘Reference 12’ is Udagawa et al.’s benzene-vapour Raman paper (source notes).
hellwarth_1975/n2_SiO2#
{
"id": "n2_SiO2",
"material": "SiO2",
"file": "SiO2/hellwarth_1975__n2_SiO2.csv",
"table": "tbl_aa2b556d00dc",
"quantity": "nonlinear_index_field",
"unit": "esu",
"scale": 1e-14,
"abscissa_unit": "nm",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"definition": "n = n0 + n2 <E^2(t)>, <E^2(t)> the time average of the square of the real field, for linear polarization (p. 967)",
"part": "electronic_vibrational",
"coefficient": "self",
"technique": "Eq. (9) from sigma (IIPC) and A0 + B0 (spontaneous Raman), long-wavelength limit",
"polarization": "linear",
"grade": "Homosil",
"form": "bulk"
}
}
Table I (p. 967), ‘Fused quartz’, column ‘10^14 n2 [Eq. (4)]’ (the header’s ‘Eq. (4)’ is Eq. (9); the caption and the text say Eq. (9), Eq. (4) is the Raman gain): n2 = pi(3 sigma/2 + 2 A0 + 2 B0)/n, the index change n2 <E^2(t)> of a monochromatic beam for linear polarization in the Born-Oppenheimer (long-wavelength) limit, electronic plus nuclear, without electrostriction and heating; ‘depend mainly on Owyoung’s data’ (p. 967). Wavelength not stated (a prediction for ‘optical’ frequencies, compared with 1.06-um measurements). Its electronic fraction f_e is in the printed cells (source notes). sigma the printed +- (level not stated).
hellwarth_1975/sigma_LSO#
{
"id": "sigma_LSO",
"material": "LSO",
"file": "LSO/hellwarth_1975__sigma_LSO.csv",
"table": "tbl_aa2b556d00dc",
"quantity": "nonlinear_susceptibility",
"unit": "esu",
"scale": 1e-15,
"abscissa_unit": "nm",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"process": "kerr",
"convention": "hellwarth_sigma",
"part": "electronic",
"technique": "IIPC (Owyoung) minus 2 B0 from absolute spontaneous Raman cross sections (this work)",
"form": "bulk"
}
}
Table I (p. 967), ‘LSO glass’, column ‘10^15 sigma’: the electronic coefficient of Eq. (1), P = (1/2) sigma E E^2, deduced as Owyoung’s IIPC sigma + 2 B0 (694 nm) minus twice this paper’s B0 (514-nm Raman spectra, Eq. 8); taken as frequency independent below the gap, recorded at the IIPC’s 694 nm. Sample: LSO (American Optical Co.). sigma the printed +- (level not stated). Not independent of the same row’s n2 (Eq. 9 uses it).
hellwarth_1975/iipc_LSO#
{
"id": "iipc_LSO",
"material": "LSO",
"file": "LSO/hellwarth_1975__iipc_LSO.csv",
"table": "tbl_aa2b556d00dc",
"quantity": "nonlinear_susceptibility",
"unit": "esu",
"scale": 1e-15,
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"A. Owyoung, IEEE J. Quantum Electron. 9, 1064 (1973); A. Owyoung, Nat. Bur. Stds. Spec. Publ. No. 387 (U. S. GPO, Washington, D. C., 1973); A. Owyoung, R. W. Hellwarth, and N. George, Phys. Rev. B 5, 628 (1972) (Ref. 1; Table I footnote b, 'References 1 and 12')"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"process": "kerr",
"convention": "hellwarth_sigma",
"part": "electronic_vibrational",
"technique": "intensity-induced polarization change (ellipse rotation), Owyoung",
"polarization": "elliptical (ellipse rotation)",
"form": "bulk"
}
}
Table I (p. 967), ‘LSO glass’, column ‘10^15 (sigma + 2 B0)’, footnote b: Owyoung’s intensity-induced polarization change (ellipse rotation, Eq. 3), ‘taken at 694 nm’ (p. 966). The combination sigma + 2 B0 in the normalisation of Eqs. (1)-(2) (B0 the zero-frequency transform of the anisotropic nuclear kernel b(t)); 24 c1122 in Maker-Terhune terms (hellwarth_1990 Eq. 17). sigma the printed +- (level not stated). Footnote b’s ‘Reference 12’ is Udagawa et al.’s benzene-vapour Raman paper (source notes).
hellwarth_1975/n2_LSO#
{
"id": "n2_LSO",
"material": "LSO",
"file": "LSO/hellwarth_1975__n2_LSO.csv",
"table": "tbl_aa2b556d00dc",
"quantity": "nonlinear_index_field",
"unit": "esu",
"scale": 1e-14,
"abscissa_unit": "nm",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"definition": "n = n0 + n2 <E^2(t)>, <E^2(t)> the time average of the square of the real field, for linear polarization (p. 967)",
"part": "electronic_vibrational",
"coefficient": "self",
"technique": "Eq. (9) from sigma (IIPC) and A0 + B0 (spontaneous Raman), long-wavelength limit",
"polarization": "linear",
"form": "bulk"
}
}
Table I (p. 967), ‘LSO glass’, column ‘10^14 n2 [Eq. (4)]’ (the header’s ‘Eq. (4)’ is Eq. (9); the caption and the text say Eq. (9), Eq. (4) is the Raman gain): n2 = pi(3 sigma/2 + 2 A0 + 2 B0)/n, the index change n2 <E^2(t)> of a monochromatic beam for linear polarization in the Born-Oppenheimer (long-wavelength) limit, electronic plus nuclear, without electrostriction and heating; ‘depend mainly on Owyoung’s data’ (p. 967). Wavelength not stated (a prediction for ‘optical’ frequencies, compared with 1.06-um measurements). Its electronic fraction f_e is in the printed cells (source notes). sigma the printed +- (level not stated).
hellwarth_1975/sigma_ED-4#
{
"id": "sigma_ED-4",
"material": "ED-4",
"file": "ED-4/hellwarth_1975__sigma_ED-4.csv",
"table": "tbl_aa2b556d00dc",
"quantity": "nonlinear_susceptibility",
"unit": "esu",
"scale": 1e-15,
"abscissa_unit": "nm",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"process": "kerr",
"convention": "hellwarth_sigma",
"part": "electronic",
"technique": "IIPC (Owyoung) minus 2 B0 from absolute spontaneous Raman cross sections (this work)",
"form": "bulk"
}
}
Table I (p. 967), ‘ED-4 glass’, column ‘10^15 sigma’: the electronic coefficient of Eq. (1), P = (1/2) sigma E E^2, deduced as Owyoung’s IIPC sigma + 2 B0 (694 nm) minus twice this paper’s B0 (514-nm Raman spectra, Eq. 8); taken as frequency independent below the gap, recorded at the IIPC’s 694 nm. Sample: ED-4 (Owens Illinois, Inc.). sigma the printed +- (level not stated). Not independent of the same row’s n2 (Eq. 9 uses it).
hellwarth_1975/iipc_ED-4#
{
"id": "iipc_ED-4",
"material": "ED-4",
"file": "ED-4/hellwarth_1975__iipc_ED-4.csv",
"table": "tbl_aa2b556d00dc",
"quantity": "nonlinear_susceptibility",
"unit": "esu",
"scale": 1e-15,
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"A. Owyoung, IEEE J. Quantum Electron. 9, 1064 (1973); A. Owyoung, Nat. Bur. Stds. Spec. Publ. No. 387 (U. S. GPO, Washington, D. C., 1973); A. Owyoung, R. W. Hellwarth, and N. George, Phys. Rev. B 5, 628 (1972) (Ref. 1; Table I footnote b, 'References 1 and 12')"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"process": "kerr",
"convention": "hellwarth_sigma",
"part": "electronic_vibrational",
"technique": "intensity-induced polarization change (ellipse rotation), Owyoung",
"polarization": "elliptical (ellipse rotation)",
"form": "bulk"
}
}
Table I (p. 967), ‘ED-4 glass’, column ‘10^15 (sigma + 2 B0)’, footnote b: Owyoung’s intensity-induced polarization change (ellipse rotation, Eq. 3), ‘taken at 694 nm’ (p. 966). The combination sigma + 2 B0 in the normalisation of Eqs. (1)-(2) (B0 the zero-frequency transform of the anisotropic nuclear kernel b(t)); 24 c1122 in Maker-Terhune terms (hellwarth_1990 Eq. 17). sigma the printed +- (level not stated). Footnote b’s ‘Reference 12’ is Udagawa et al.’s benzene-vapour Raman paper (source notes).
hellwarth_1975/n2_ED-4#
{
"id": "n2_ED-4",
"material": "ED-4",
"file": "ED-4/hellwarth_1975__n2_ED-4.csv",
"table": "tbl_aa2b556d00dc",
"quantity": "nonlinear_index_field",
"unit": "esu",
"scale": 1e-14,
"abscissa_unit": "nm",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"definition": "n = n0 + n2 <E^2(t)>, <E^2(t)> the time average of the square of the real field, for linear polarization (p. 967)",
"part": "electronic_vibrational",
"coefficient": "self",
"technique": "Eq. (9) from sigma (IIPC) and A0 + B0 (spontaneous Raman), long-wavelength limit",
"polarization": "linear",
"form": "bulk"
}
}
Table I (p. 967), ‘ED-4 glass’, column ‘10^14 n2 [Eq. (4)]’ (the header’s ‘Eq. (4)’ is Eq. (9); the caption and the text say Eq. (9), Eq. (4) is the Raman gain): n2 = pi(3 sigma/2 + 2 A0 + 2 B0)/n, the index change n2 <E^2(t)> of a monochromatic beam for linear polarization in the Born-Oppenheimer (long-wavelength) limit, electronic plus nuclear, without electrostriction and heating; ‘depend mainly on Owyoung’s data’ (p. 967). Wavelength not stated (a prediction for ‘optical’ frequencies, compared with 1.06-um measurements). Its electronic fraction f_e is in the printed cells (source notes). sigma the printed +- (level not stated).
hellwarth_1975/sigma_SF-7#
{
"id": "sigma_SF-7",
"material": "SF-7",
"file": "SF-7/hellwarth_1975__sigma_SF-7.csv",
"table": "tbl_aa2b556d00dc",
"quantity": "nonlinear_susceptibility",
"unit": "esu",
"scale": 1e-15,
"abscissa_unit": "nm",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"process": "kerr",
"convention": "hellwarth_sigma",
"part": "electronic",
"technique": "IIPC (Owyoung) minus 2 B0 from absolute spontaneous Raman cross sections (this work)",
"form": "bulk"
}
}
Table I (p. 967), ‘SF-7 glass’, column ‘10^15 sigma’: the electronic coefficient of Eq. (1), P = (1/2) sigma E E^2, deduced as Owyoung’s IIPC sigma + 2 B0 (694 nm) minus twice this paper’s B0 (514-nm Raman spectra, Eq. 8); taken as frequency independent below the gap, recorded at the IIPC’s 694 nm. Sample: SF-7 (Schott). sigma the printed +- (level not stated). Not independent of the same row’s n2 (Eq. 9 uses it).
hellwarth_1975/iipc_SF-7#
{
"id": "iipc_SF-7",
"material": "SF-7",
"file": "SF-7/hellwarth_1975__iipc_SF-7.csv",
"table": "tbl_aa2b556d00dc",
"quantity": "nonlinear_susceptibility",
"unit": "esu",
"scale": 1e-15,
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"A. Owyoung, IEEE J. Quantum Electron. 9, 1064 (1973); A. Owyoung, Nat. Bur. Stds. Spec. Publ. No. 387 (U. S. GPO, Washington, D. C., 1973); A. Owyoung, R. W. Hellwarth, and N. George, Phys. Rev. B 5, 628 (1972) (Ref. 1; Table I footnote b, 'References 1 and 12')"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"process": "kerr",
"convention": "hellwarth_sigma",
"part": "electronic_vibrational",
"technique": "intensity-induced polarization change (ellipse rotation), Owyoung",
"polarization": "elliptical (ellipse rotation)",
"form": "bulk"
}
}
Table I (p. 967), ‘SF-7 glass’, column ‘10^15 (sigma + 2 B0)’, footnote b: Owyoung’s intensity-induced polarization change (ellipse rotation, Eq. 3), ‘taken at 694 nm’ (p. 966). The combination sigma + 2 B0 in the normalisation of Eqs. (1)-(2) (B0 the zero-frequency transform of the anisotropic nuclear kernel b(t)); 24 c1122 in Maker-Terhune terms (hellwarth_1990 Eq. 17). sigma the printed +- (level not stated). Footnote b’s ‘Reference 12’ is Udagawa et al.’s benzene-vapour Raman paper (source notes).
hellwarth_1975/n2_SF-7#
{
"id": "n2_SF-7",
"material": "SF-7",
"file": "SF-7/hellwarth_1975__n2_SF-7.csv",
"table": "tbl_aa2b556d00dc",
"quantity": "nonlinear_index_field",
"unit": "esu",
"scale": 1e-14,
"abscissa_unit": "nm",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"definition": "n = n0 + n2 <E^2(t)>, <E^2(t)> the time average of the square of the real field, for linear polarization (p. 967)",
"part": "electronic_vibrational",
"coefficient": "self",
"technique": "Eq. (9) from sigma (IIPC) and A0 + B0 (spontaneous Raman), long-wavelength limit",
"polarization": "linear",
"form": "bulk"
}
}
Table I (p. 967), ‘SF-7 glass’, column ‘10^14 n2 [Eq. (4)]’ (the header’s ‘Eq. (4)’ is Eq. (9); the caption and the text say Eq. (9), Eq. (4) is the Raman gain): n2 = pi(3 sigma/2 + 2 A0 + 2 B0)/n, the index change n2 <E^2(t)> of a monochromatic beam for linear polarization in the Born-Oppenheimer (long-wavelength) limit, electronic plus nuclear, without electrostriction and heating; ‘depend mainly on Owyoung’s data’ (p. 967). Wavelength not stated (a prediction for ‘optical’ frequencies, compared with 1.06-um measurements). Its electronic fraction f_e is in the printed cells (source notes). sigma the printed +- (level not stated).
hellwarth_1975/sigma_LaSF-7#
{
"id": "sigma_LaSF-7",
"material": "LaSF-7",
"file": "LaSF-7/hellwarth_1975__sigma_LaSF-7.csv",
"table": "tbl_aa2b556d00dc",
"quantity": "nonlinear_susceptibility",
"unit": "esu",
"scale": 1e-15,
"abscissa_unit": "nm",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"process": "kerr",
"convention": "hellwarth_sigma",
"part": "electronic",
"technique": "IIPC (Owyoung) minus 2 B0 from absolute spontaneous Raman cross sections (this work)",
"form": "bulk"
}
}
Table I (p. 967), ‘LASF-7 glass’, column ‘10^15 sigma’: the electronic coefficient of Eq. (1), P = (1/2) sigma E E^2, deduced as Owyoung’s IIPC sigma + 2 B0 (694 nm) minus twice this paper’s B0 (514-nm Raman spectra, Eq. 8); taken as frequency independent below the gap, recorded at the IIPC’s 694 nm. Sample: LaSF-7 (Schott). sigma the printed +- (level not stated). Not independent of the same row’s n2 (Eq. 9 uses it).
hellwarth_1975/iipc_LaSF-7#
{
"id": "iipc_LaSF-7",
"material": "LaSF-7",
"file": "LaSF-7/hellwarth_1975__iipc_LaSF-7.csv",
"table": "tbl_aa2b556d00dc",
"quantity": "nonlinear_susceptibility",
"unit": "esu",
"scale": 1e-15,
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"A. Owyoung, IEEE J. Quantum Electron. 9, 1064 (1973); A. Owyoung, Nat. Bur. Stds. Spec. Publ. No. 387 (U. S. GPO, Washington, D. C., 1973); A. Owyoung, R. W. Hellwarth, and N. George, Phys. Rev. B 5, 628 (1972) (Ref. 1; Table I footnote b, 'References 1 and 12')"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"process": "kerr",
"convention": "hellwarth_sigma",
"part": "electronic_vibrational",
"technique": "intensity-induced polarization change (ellipse rotation), Owyoung",
"polarization": "elliptical (ellipse rotation)",
"form": "bulk"
}
}
Table I (p. 967), ‘LASF-7 glass’, column ‘10^15 (sigma + 2 B0)’, footnote b: Owyoung’s intensity-induced polarization change (ellipse rotation, Eq. 3), ‘taken at 694 nm’ (p. 966). The combination sigma + 2 B0 in the normalisation of Eqs. (1)-(2) (B0 the zero-frequency transform of the anisotropic nuclear kernel b(t)); 24 c1122 in Maker-Terhune terms (hellwarth_1990 Eq. 17). sigma the printed +- (level not stated). Footnote b’s ‘Reference 12’ is Udagawa et al.’s benzene-vapour Raman paper (source notes).
hellwarth_1975/n2_LaSF-7#
{
"id": "n2_LaSF-7",
"material": "LaSF-7",
"file": "LaSF-7/hellwarth_1975__n2_LaSF-7.csv",
"table": "tbl_aa2b556d00dc",
"quantity": "nonlinear_index_field",
"unit": "esu",
"scale": 1e-14,
"abscissa_unit": "nm",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"definition": "n = n0 + n2 <E^2(t)>, <E^2(t)> the time average of the square of the real field, for linear polarization (p. 967)",
"part": "electronic_vibrational",
"coefficient": "self",
"technique": "Eq. (9) from sigma (IIPC) and A0 + B0 (spontaneous Raman), long-wavelength limit",
"polarization": "linear",
"form": "bulk"
}
}
Table I (p. 967), ‘LASF-7 glass’, column ‘10^14 n2 [Eq. (4)]’ (the header’s ‘Eq. (4)’ is Eq. (9); the caption and the text say Eq. (9), Eq. (4) is the Raman gain): n2 = pi(3 sigma/2 + 2 A0 + 2 B0)/n, the index change n2 <E^2(t)> of a monochromatic beam for linear polarization in the Born-Oppenheimer (long-wavelength) limit, electronic plus nuclear, without electrostriction and heating; ‘depend mainly on Owyoung’s data’ (p. 967). Wavelength not stated (a prediction for ‘optical’ frequencies, compared with 1.06-um measurements). Its electronic fraction f_e is in the printed cells (source notes). sigma the printed +- (level not stated).
hellwarth_1975/n2_measured_SiO2#
{
"id": "n2_measured_SiO2",
"material": "SiO2",
"file": "SiO2/hellwarth_1975__n2_measured_SiO2.csv",
"table": "tbl_aa2b556d00dc",
"quantity": "nonlinear_index_field",
"unit": "esu",
"scale": 1e-14,
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"Table I footnote c, 'Reference 9': E. R. Bliss, D. R. Speck, and W. W. Simmons (unpublished), as numbered; the text suggests M. D. Levenson, IEEE J. Quantum Electron. QE-10, 110 (1974) (source notes)"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"definition": "n = n0 + n2 <E^2(t)>, for linear polarization (p. 967), as the paper compares it",
"part": "unknown",
"coefficient": "self",
"technique": "not stated (a measurement of another laboratory)"
}
}
Table I (p. 967), ‘Fused quartz’, column ‘10^14 n2 (Meas.)’: ‘18 ± 3’ with footnote c (‘Reference 9’, Bliss et al., unpublished, 1.06 um per the text). The paper calls its predictions (11 +- 1) ‘consistent’ with Bliss et al. and Moran et al. and ‘about 30% lower’ than Levenson’s (near 525 nm), which fits this value better; the footnote numbering is doubtful (source notes). Wavelength and part not stated. sigma the printed +- (level not stated).
hellwarth_1975/n2_measured_ED-4#
{
"id": "n2_measured_ED-4",
"material": "ED-4",
"file": "ED-4/hellwarth_1975__n2_measured_ED-4.csv",
"table": "tbl_aa2b556d00dc",
"quantity": "nonlinear_index_field",
"unit": "esu",
"scale": 1e-14,
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"Table I footnote c, 'Reference 9': E. R. Bliss, D. R. Speck, and W. W. Simmons (unpublished)",
"Table I footnote d, 'Reference 8': the reference list's Ref. 8 is R. H. Stolen and E. P. Ippen, Appl. Phys. Lett. 22, 275 [276] (1973), which has no n2 (not identifiable; source notes)",
"Table I footnote e, 'Reference 7': the reference list's Ref. 7 is Y. Kato and H. Takuma, J. Opt. Soc. Am. 61, 347 (1971), which has no n2 (not identifiable; source notes)"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"definition": "n = n0 + n2 <E^2(t)>, for linear polarization (p. 967), as the paper compares it",
"part": "unknown",
"coefficient": "self",
"technique": "not stated (measurements of other laboratories)"
}
}
Table I (p. 967), ‘ED-4 glass’, column ‘10^14 n2 (Meas.)’: three values under a brace, ‘26 ± 3 c’, ‘15 ± 2 d’, ‘15 ± 3 e’ (rows c, d, e by footnote letter; image checked). The footnote numbers do not match the reference list (source notes); the text’s three n2 measurements are Bliss et al. and Moran et al. (1.06 um) and Levenson (near 525 nm). Wavelength and part not stated. sigma the printed +- (level not stated).
hellwarth_1975/nuclear_fraction_SiO2#
{
"id": "nuclear_fraction_SiO2",
"material": "SiO2",
"file": "SiO2/hellwarth_1975__nuclear_fraction_SiO2.csv",
"table": "tbl_aa2b556d00dc",
"quantity": "raman_fraction",
"unit": "1",
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"definition": "1 - f_e: the nuclear (Raman) share of the long-pulse n2 of Eq. (9), n2 = pi (3 sigma/2 + 2 A0 + 2 B0)/n, for linear polarization; f_e as printed in Table I",
"form": "bulk"
}
}
Table I (p. 967), ‘Fused quartz’, column ‘f_e (%)’: the electronic fraction of the long-pulse, long-wavelength n2 of Eq. (9) for linear polarization, f_e = [1 + 4(A0 + B0)/(3 sigma)]^-1, recorded as its complement 1 - f_e, the share of every nuclear (Raman) motion (the script subtracts the printed whole percent from 100; the +- kept, level not stated; TC-694). From absolute spontaneous Raman cross sections (this work) and Owyoung’s IIPC; the paper warns that A0 and B0 may be 10-20 % above their long-wavelength values (p. 967).
hellwarth_1975/nuclear_fraction_LSO#
{
"id": "nuclear_fraction_LSO",
"material": "LSO",
"file": "LSO/hellwarth_1975__nuclear_fraction_LSO.csv",
"table": "tbl_aa2b556d00dc",
"quantity": "raman_fraction",
"unit": "1",
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"definition": "1 - f_e: the nuclear (Raman) share of the long-pulse n2 of Eq. (9), n2 = pi (3 sigma/2 + 2 A0 + 2 B0)/n, for linear polarization; f_e as printed in Table I",
"form": "bulk"
}
}
Table I (p. 967), ‘LSO glass’, column ‘f_e (%)’: the electronic fraction of the long-pulse, long-wavelength n2 of Eq. (9) for linear polarization, f_e = [1 + 4(A0 + B0)/(3 sigma)]^-1, recorded as its complement 1 - f_e, the share of every nuclear (Raman) motion (the script subtracts the printed whole percent from 100; the +- kept, level not stated; TC-694). From absolute spontaneous Raman cross sections (this work) and Owyoung’s IIPC; the paper warns that A0 and B0 may be 10-20 % above their long-wavelength values (p. 967).
hellwarth_1975/nuclear_fraction_ED-4#
{
"id": "nuclear_fraction_ED-4",
"material": "ED-4",
"file": "ED-4/hellwarth_1975__nuclear_fraction_ED-4.csv",
"table": "tbl_aa2b556d00dc",
"quantity": "raman_fraction",
"unit": "1",
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"definition": "1 - f_e: the nuclear (Raman) share of the long-pulse n2 of Eq. (9), n2 = pi (3 sigma/2 + 2 A0 + 2 B0)/n, for linear polarization; f_e as printed in Table I",
"form": "bulk"
}
}
Table I (p. 967), ‘ED-4 glass’, column ‘f_e (%)’: the electronic fraction of the long-pulse, long-wavelength n2 of Eq. (9) for linear polarization, f_e = [1 + 4(A0 + B0)/(3 sigma)]^-1, recorded as its complement 1 - f_e, the share of every nuclear (Raman) motion (the script subtracts the printed whole percent from 100; the +- kept, level not stated; TC-694). From absolute spontaneous Raman cross sections (this work) and Owyoung’s IIPC; the paper warns that A0 and B0 may be 10-20 % above their long-wavelength values (p. 967).
hellwarth_1975/nuclear_fraction_SF-7#
{
"id": "nuclear_fraction_SF-7",
"material": "SF-7",
"file": "SF-7/hellwarth_1975__nuclear_fraction_SF-7.csv",
"table": "tbl_aa2b556d00dc",
"quantity": "raman_fraction",
"unit": "1",
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"definition": "1 - f_e: the nuclear (Raman) share of the long-pulse n2 of Eq. (9), n2 = pi (3 sigma/2 + 2 A0 + 2 B0)/n, for linear polarization; f_e as printed in Table I",
"form": "bulk"
}
}
Table I (p. 967), ‘SF-7 glass’, column ‘f_e (%)’: the electronic fraction of the long-pulse, long-wavelength n2 of Eq. (9) for linear polarization, f_e = [1 + 4(A0 + B0)/(3 sigma)]^-1, recorded as its complement 1 - f_e, the share of every nuclear (Raman) motion (the script subtracts the printed whole percent from 100; the +- kept, level not stated; TC-694). From absolute spontaneous Raman cross sections (this work) and Owyoung’s IIPC; the paper warns that A0 and B0 may be 10-20 % above their long-wavelength values (p. 967).
hellwarth_1975/nuclear_fraction_LaSF-7#
{
"id": "nuclear_fraction_LaSF-7",
"material": "LaSF-7",
"file": "LaSF-7/hellwarth_1975__nuclear_fraction_LaSF-7.csv",
"table": "tbl_aa2b556d00dc",
"quantity": "raman_fraction",
"unit": "1",
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"definition": "1 - f_e: the nuclear (Raman) share of the long-pulse n2 of Eq. (9), n2 = pi (3 sigma/2 + 2 A0 + 2 B0)/n, for linear polarization; f_e as printed in Table I",
"form": "bulk"
}
}
Table I (p. 967), ‘LASF-7 glass’, column ‘f_e (%)’: the electronic fraction of the long-pulse, long-wavelength n2 of Eq. (9) for linear polarization, f_e = [1 + 4(A0 + B0)/(3 sigma)]^-1, recorded as its complement 1 - f_e, the share of every nuclear (Raman) motion (the script subtracts the printed whole percent from 100; the +- kept, level not stated; TC-694). From absolute spontaneous Raman cross sections (this work) and Owyoung’s IIPC; the paper warns that A0 and B0 may be 10-20 % above their long-wavelength values (p. 967).
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.