hanna_1986 ========== D\. C\. Hanna, D\. J\. Pointer and D\. J\. Pratt, "Stimulated Raman scattering of picosecond light pulses in hydrogen, deuterium, and methane", IEEE J\. Quantum Electron\. 22, 332 \(1986\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1109/jqe\.1986\.1072945 `__ **Source kind:** measurement **Recorded technique:** Stimulated Raman scattering thresholds of about 100 ps pulses \(mode\-locked, Q\-switched Nd\:YAG at 1\.06 um, about 70 ps at 0\.53 um after doubling; also a mode\-locked dye laser near 560 nm\) in H2, D2 and CH4 at 30 atm, in 0\.5 and 1 m cells \(tight focusing\) and in fused\-silica capillaries of 200 um bore, 40 and 78 cm long \(pp\. 332\-335\)\. The measured quantities are threshold energies \(1 % conversion, Tables II\-III\); the Raman parameters of Table I are calculated from published cross sections and linewidths \(Eqs\. 1\-2, p\. 332\-333\)\. **Materials in structured entries:** CH4, D2, H2 **Dataset quantities:** dephasing\_time, raman\_cross\_section, raman\_gain, raman\_linewidth, raman\_shift **Contents:** 14 datasets; 1 formula. Curation notes -------------- Journal pages 332\-336 = PDF pages 1\-5 \(page n of the PDF is p\. 331 \+ n\)\. Identity checked on the first page \(IEEE J\. Quantum Electron\. QE\-22, No\. 2\)\. NOTHING IN TABLE I IS MEASURED HERE\. Table I \(p\. 333\), 'Steady\-state Raman gain g\_R and dephasing time T2, both calculated at 30 atm pressure'\: \- dsigma/dOmega \(m^2/sr, the intensity definition\: 'defined here in terms of the ratio of scattered and incident intensities', p\. 332; \(dsigma/dOmega\)\_photons = \(omega\_p/ omega\_s\)\(dsigma/dOmega\)\_intensity\)\: for H2 and CH4 converted by Eq\. \(2\) from Schrotter and Klockner's tabulated relative normalized cross sections \[17\] \(curated as schrotter\_1979, Table 4\.2\) to the pumps used, with a single intermediate level at nu\_ig = 90000 cm\-1 \(H2, D2\) or 70000 cm\-1 \(CH4\) \[18\] \(p\. 333\); for D2 '\* Scaled from the measured value at 694nm reported by Devir \[22\]'\. Reproduced \(converted\), use = "reproduced"\. \- g\_R \(m/W\)\: calculated by Eq\. \(1\), g\_R = 16 pi^2 c^2 Delta N dsigma/dOmega/\(n\_s^2 hbar omega\_s^3 Delta omega\_R\), Delta omega\_R the FWHM linewidth \(angular frequency\), Delta N = N\_tot \(CH4, the Q branch unresolved at 30 atm\), 0\.66 N\_tot \(H2, J = 1\) and 0\.38 N\_tot \(D2, J = 2\) \[21\] \(p\. 333\)\. The paper's own calculation\: use = "check"\. \- T2 \(ps\) = 2/Delta omega\_R \(p\. 333\), from the linewidths below at 30 atm\: use = "check"\. \- the shifts \(4155, 2987, 2917 cm\-1\) as printed, source not stated \(use = "check"\)\. solprop's D2 vibrational frequency cites this paper\: 2987 cm\-1\. The pump wavelengths are printed as 1\.06 um \(9,391 cm\-1\) and 0\.53 um \(18,782 cm\-1\), nominal Nd\:YAG values; the abscissa is the printed um value \(1/9391 cm = 1\.0648 um\)\. LINEWIDTHS USED \(p\. 333, reproduced; quoted\)\: 'Delta omega\_R is the Raman linewidth \(angular frequency, FWHM\)' \(p\. 332\)\. 'For CH4, Delta nu\_R = 0\.32 \+ 0\.012p cm\-1 where p is in atmospheres \[19\] \(Taira, Ide and Takuma, Chem\. Phys\. Lett\. 91, 299 \(1982\)\); for H2 and D2 \[Q\(1\) and Q\(2\) transitions, respectively\] since we operate at pressures where the linewidth is proportional to pressure \(\>10 atmospheres\) we use the line broadening coefficients of 51 MHz/atm \[16\], and 70 MHz/atm \[20\], respectively' \(\[16\] Bischel and Black 1983 with Owyoung 1983; \[20\] Murray and Javan, J\. Mol\. Spectrosc\. 42, 1 \(1972\)\)\. The H2 and D2 coefficients are the datasets linewidth\_H2 and linewidth\_D2, the CH4 law the formula linewidth\_CH4; all three are FWHM as this paper uses them \(the cited papers are not in the library\: their own FWHM/HWHM statements are unchecked\)\. Temperature not stated \(room temperature\)\. Since 2026\-09\-27 \[20\] is curated \(murray\_1972\)\: its widths are FWHM in its own words, and its D2 Q\_1\(2\) coefficient, 2\.2e\-3 cm\-1/amagat, does not give 70 MHz/atm \(see linewidth\_D2\)\. REPRODUCTION \(2026\-09\-26, scratch\)\: T2 = 2/Delta omega\_R gives 208\.0 ps \(H2, 51 MHz/atm x 30\), 151\.6 ps \(D2, printed 150\) and 15\.6 ps \(CH4, printed 16\)\. Eq\. \(1\) with n\_s = 1 reproduces the printed g\_R to 1\-4 % \(H2 0\.960 and 1\.019, D2 0\.962 at 1\.06 um, CH4 0\.991 and 0\.996 of the printed values\) only with N\_tot the density of 30 atm at 273\.15 K \(30 amagat\); at 293\-300 K the calculation falls 5\-13 % below\. The temperature is not stated\: the state 30 atm, 273\.15 K is this inference, not a printed statement\. D2 at 0\.53 um is off by a factor 10\.5 with the printed cross section\: see the erratum\. ERRATUM \(D2, 0\.53 um cross section\)\: printed 8\.0 x 10^\-36, read 8\.0 x 10^\-35\. Both D2 values are scaled from one Devir value by Eq\. \(2\); the ratio of Eq\. \(2\) between the two pumps is \(15795/6404\)^4 x \[\(1/71218 \+ 1/105795\)/\(1/80609 \+ 1/96404\)\]^2 = 37\.0 x 1\.064 = 39\.4, so 2\.0e\-36 at 1\.06 um gives 7\.9e\-35 at 0\.53 um; and Eq\. \(1\) with the printed g\_R = 1\.0e\-11 m/W needs 8\.4e\-35 \(at 30 amagat\)\. The printed g\_R ratio 0\.53/1\.06 um \(2\.7\) matches H2's \(2\.85\) and CH4's \(2\.6\)\. The table image was checked\: it prints 10^\-36\. TABLES II AND III \(pp\. 334\-335; notes only, no quantity\)\: measured and calculated threshold energies \(1 % conversion to the first Stokes\) for tight focusing \(Table II\) and capillary waveguides \(Table III\), 30 atm, with the geometry \(l/b, l, l\_eff\) and pulse length of each; measured and calculated agree to within a factor of two \(p\. 334\)\. E\.g\. CH4 in a 0\.78 m capillary at 0\.53 um\: measured 14 uJ \(T\_p = 67 ps\), calculated 13 uJ\. Dye\-laser pumped CH4 \(35 cm cell, l/b ~ 10\)\: thresholds 120, 170 and 200 uJ at 30, 20 and 15 atm \(p\. 335\)\. Fig\. 2\: D2 threshold energy against pressure \(a figure only\)\. ISOTOPOLOGUES\: natural H2 and D2 \(normal hydrogen and deuterium\: the J = 1 and J = 2 fractions 0\.66 and 0\.38 are room\-temperature populations \[21\]\); 12CH4\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- hanna\_1986/shift\_H2 ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "shift_H2", "material": "H2", "file": "H2/hanna_1986__shift_H2.csv", "table": "tbl_555a4008bd8a", "quantity": "raman_shift", "unit": "cm-1", "abscissa": "label", "use": "check", "parameters": { "transition": "v=0-1 Q(1)" } } Table I \(p\. 333\), 'Shift 4155cm\-1' of H2 Q\(1\), as used in the calculation; source not stated\. hanna\_1986/shift\_D2 ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "shift_D2", "material": "D2", "file": "D2/hanna_1986__shift_D2.csv", "table": "tbl_555a4008bd8a", "quantity": "raman_shift", "unit": "cm-1", "abscissa": "label", "use": "check", "parameters": { "transition": "v=0-1 Q(2)" } } Table I \(p\. 333\), 'Shift 2987cm\-1' of D2 Q\(2\), as used in the calculation; source not stated\. solprop's D2 vibrational frequency \(2987\.0 cm\-1\) cites this paper\. hanna\_1986/shift\_CH4 ~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "shift_CH4", "material": "CH4", "file": "CH4/hanna_1986__shift_CH4.csv", "table": "tbl_555a4008bd8a", "quantity": "raman_shift", "unit": "cm-1", "abscissa": "label", "use": "check", "parameters": { "transition": "nu1 Q branch" } } Table I \(p\. 333\), 'Shift 2917cm\-1' of the CH4 \(nu1\) Q branch, as used in the calculation; source not stated\. hanna\_1986/dsigma\_H2 ~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "dsigma_H2", "material": "H2", "file": "H2/hanna_1986__dsigma_H2.csv", "table": "tbl_555a4008bd8a", "quantity": "raman_cross_section", "unit": "m2/sr", "abscissa_unit": "um", "use": "reproduced", "reproduced_from": [ "schrotter_1979" ], "parameters": { "transition": "v=0-1 Q(1)" } } Table I \(p\. 333\), dsigma/dOmega of H2 Q\(1\) at the pumps 1\.06 and 0\.53 um \(nominal\), converted by Eq\. \(2\) from Schrotter and Klockner's relative normalized cross sections \(nu\_ig = 90000 cm\-1\); intensity definition \(p\. 332\)\. Checked against the original \(schrotter\_1979 Table 4\.2\)\: Eq\. \(2\) with Sigma\_j = 3\.45 at 514\.5 nm \(sigma\_H2\_b, Fouche and Chang\) gives 1\.23e\-36 and 7\.93e\-35 m^2/sr \(printed 1\.2e\-36 and 7\.9e\-35\); the values back out Sigma\_j = 3\.38\-3\.44 \(from 514\.5 nm\) or 3\.41\-3\.47 \(from 488 nm\), so Hanna et al\. used H2's 514\.5 nm value 3\.45\. hanna\_1986/dsigma\_D2 ~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "dsigma_D2", "material": "D2", "file": "D2/hanna_1986__dsigma_D2.csv", "table": "tbl_555a4008bd8a", "quantity": "raman_cross_section", "unit": "m2/sr", "abscissa_unit": "um", "use": "reproduced", "reproduced_from": [ "A. D. Devir, J. Appl. Phys. 49, 3110 (1978)" ], "parameters": { "transition": "v=0-1 Q(2)" } } Table I \(p\. 333\), dsigma/dOmega of D2 Q\(2\) at 1\.06 and 0\.53 um, '\* Scaled from the measured value at 694nm reported by Devir \[22\]' \(by Eq\. 2, nu\_ig = 90000 cm\-1\); intensity definition\. The 0\.53 um value is printed 8\.0 x 10^\-36, corrected to 8\.0 x 10^\-35 by the erratum\. hanna\_1986/dsigma\_CH4 ~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "dsigma_CH4", "material": "CH4", "file": "CH4/hanna_1986__dsigma_CH4.csv", "table": "tbl_555a4008bd8a", "quantity": "raman_cross_section", "unit": "m2/sr", "abscissa_unit": "um", "use": "reproduced", "reproduced_from": [ "schrotter_1979" ], "parameters": { "transition": "nu1 Q branch" } } Table I \(p\. 333\), dsigma/dOmega of the CH4 nu1 Q branch at 1\.06 and 0\.53 um, converted by Eq\. \(2\) from Schrotter and Klockner \(nu\_ig = 70000 cm\-1\); intensity definition\. Checked against the original \(schrotter\_1979 Table 4\.2\)\: the printed values back out Sigma\_j = 8\.86 \(1\.06 um\) and 8\.53 \(0\.53 um\) from 514\.5 nm, or 9\.02 and 8\.68 from 488 nm; Table 4\.2's CH4 values are 9\.1, 8\.7 and 9\.3 at 515 nm and 6\.8, 9\.2 and 8\.7 at 488 nm \(mean of all thirteen 8\.55, Table 4\.4's 8\.56\)\. Consistent to 2\-4 %, but no single printed Sigma\_j reproduces both pumps \(the one\-digit rounding of 7\.0 and 2\.7 allows 1\-2 %\)\. hanna\_1986/gain\_H2 ~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gain_H2", "material": "H2", "file": "H2/hanna_1986__gain_H2.csv", "table": "tbl_555a4008bd8a", "quantity": "raman_gain", "unit": "m/W", "abscissa_unit": "um", "state": { "pressure_atm": 30.0, "temperature_k": 273.15 }, "density": "ideal", "use": "check", "parameters": { "transition": "v=0-1 Q(1)" } } Table I \(p\. 333\), steady\-state g\_R of H2 Q\(1\) at 30 atm, calculated by Eq\. \(1\) with dsigma\_H2, Delta N = 0\.66 N\_tot and the FWHM 51 MHz/atm x 30 atm\. The temperature is not stated\: 273\.15 K is inferred \(Eq\. \(1\) reproduces the printed values to 1\-4 % only with the 30 atm, 0 C density; the record's notes\)\. hanna\_1986/gain\_D2 ~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gain_D2", "material": "D2", "file": "D2/hanna_1986__gain_D2.csv", "table": "tbl_555a4008bd8a", "quantity": "raman_gain", "unit": "m/W", "abscissa_unit": "um", "state": { "pressure_atm": 30.0, "temperature_k": 273.15 }, "density": "ideal", "use": "check", "parameters": { "transition": "v=0-1 Q(2)" } } Table I \(p\. 333\), steady\-state g\_R of D2 Q\(2\) at 30 atm, Eq\. \(1\) with dsigma\_D2, Delta N = 0\.38 N\_tot and the FWHM 70 MHz/atm x 30 atm\. Temperature inferred as for gain\_H2\. hanna\_1986/gain\_CH4 ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gain_CH4", "material": "CH4", "file": "CH4/hanna_1986__gain_CH4.csv", "table": "tbl_555a4008bd8a", "quantity": "raman_gain", "unit": "m/W", "abscissa_unit": "um", "state": { "pressure_atm": 30.0, "temperature_k": 273.15 }, "density": "ideal", "use": "check", "parameters": { "transition": "nu1 Q branch" } } Table I \(p\. 333\), steady\-state g\_R of the CH4 Q branch at 30 atm, Eq\. \(1\) with dsigma\_CH4, Delta N = N\_tot and the FWHM 0\.32 \+ 0\.012 x 30 = 0\.68 cm\-1\. Temperature inferred as for gain\_H2\. hanna\_1986/T2\_H2 ~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "T2_H2", "material": "H2", "file": "H2/hanna_1986__T2_H2.csv", "table": "tbl_555a4008bd8a", "quantity": "dephasing_time", "unit": "ps", "abscissa": "pressure", "abscissa_unit": "atm", "use": "check", "parameters": { "transition": "v=0-1 Q(1)" } } Table I \(p\. 333\), T2 = 2/Delta omega\_R of H2 Q\(1\) at 30 atm from the FWHM coefficient 51 MHz/atm \(reproduced 208\.0 ps\)\. Calculated, not measured\. hanna\_1986/T2\_D2 ~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "T2_D2", "material": "D2", "file": "D2/hanna_1986__T2_D2.csv", "table": "tbl_555a4008bd8a", "quantity": "dephasing_time", "unit": "ps", "abscissa": "pressure", "abscissa_unit": "atm", "use": "check", "parameters": { "transition": "v=0-1 Q(2)" } } Table I \(p\. 333\), T2 = 2/Delta omega\_R of D2 Q\(2\) at 30 atm from 70 MHz/atm \(reproduced 151\.6 ps, printed 150\)\. Calculated\. hanna\_1986/T2\_CH4 ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "T2_CH4", "material": "CH4", "file": "CH4/hanna_1986__T2_CH4.csv", "table": "tbl_555a4008bd8a", "quantity": "dephasing_time", "unit": "ps", "abscissa": "pressure", "abscissa_unit": "atm", "use": "check", "parameters": { "transition": "nu1 Q branch" } } Table I \(p\. 333\), T2 = 2/Delta omega\_R of the CH4 Q branch at 30 atm from 0\.32 \+ 0\.012p cm\-1 \(reproduced 15\.6 ps, printed 16\)\. Calculated\. hanna\_1986/linewidth\_H2 ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "linewidth_H2", "material": "H2", "table": "text", "quantity": "raman_linewidth", "unit": "MHz/atm", "abscissa": "none", "use": "reproduced", "reproduced_from": [ "W. K. Bischel and G. Black, in Excimer Lasers, C. K. Rhodes, H. Egger and H. Plummer, Eds. (American Institute of Physics, New York, 1983), pp. 181-187; A. Owyoung, Opt. Lett. 2, 91 (1983)" ], "parameters": { "transition": "v=0-1 Q(1)", "width": "fwhm", "perturber": "self" } } 1 inline points in the source record. p\. 333\: 'for H2 and D2 \[Q\(1\) and Q\(2\) transitions, respectively\] since we operate at pressures where the linewidth is proportional to pressure \(\>10 atmospheres\) we use the line broadening coefficients of 51 MHz/atm \[16\], and 70 MHz/atm \[20\]'\. Used as the FWHM Delta omega\_R/2 pi \('Delta omega\_R is the Raman linewidth \(angular frequency, FWHM\)', p\. 332\)\. No Dicke term \(A/rho\) is used\: the law is linear, for p \> 10 atm\. Temperature not stated \(room temperature\)\. hanna\_1986/linewidth\_D2 ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "linewidth_D2", "material": "D2", "table": "text", "quantity": "raman_linewidth", "unit": "MHz/atm", "abscissa": "none", "use": "reproduced", "reproduced_from": [ "murray_1972" ], "parameters": { "transition": "v=0-1 Q(2)", "width": "fwhm", "perturber": "self" } } 1 inline points in the source record. p\. 333, as linewidth\_H2\: the D2 Q\(2\) broadening coefficient 70 MHz/atm \[20\], used as the FWHM, linear in pressure above 10 atm, no Dicke term\. Temperature not stated\. Re\-pointed to murray\_1972 \(2026\-09\-27\)\: its Table II D2 Q\_1\(2\) is 2\.2 \+\- 0\.2 x 10^\-3 cm\-1 per amagat at 25 C \(FWHM in its words\) = 66\.0 MHz/amagat, i\.e\. 60\.4 MHz/atm at 25 C \(1 atm = 0\.916 amagat\)\: 70 MHz/atm does not follow from it \(it is within the error only as MHz/amagat, 66 \+\- 6\); how Hanna et al\. converted is not said\. Formulas -------- hanna\_1986/linewidth\_CH4 ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "linewidth_CH4", "material": "CH4", "equation": "text, p. 333", "printed": "Delta nu_R = 0.32 + 0.012p cm-1 where p is in atmospheres", "variable": "p: the pressure of CH4 in atm", "state": "not stated (room temperature)", "density": "unknown", "range": "not stated here (Taira et al.'s title: 1-50 atm)", "coefficients": { "constant_cm1": "0.32", "slope_cm1_per_atm": "0.012" }, "check": "At 30 atm, 0.68 cm-1, whose T2 = 2/(2 pi c Delta nu) = 15.6 ps reproduces Table I's 16 ps (2026-09-26)." } The CH4 nu1 Q\-branch linewidth \(FWHM, as this paper uses it for Delta omega\_R\), reproduced from Y\. Taira, K\. Ide and H\. Takuma, Chem\. Phys\. Lett\. 91, 299 \(1982\) \[19\] \(not in the library\)\: a model input\. The constant term is the unresolved Q\-branch width at zero pressure, not a collision width\. Corrections ----------- .. code-block:: text [ { "dataset": "dsigma_D2", "row": "0.53 um pump", "column": "value", "printed": "8.0e-36", "corrected": "8.0e-35", "reason": "Both D2 values are scaled by Eq. (2) from one 694 nm value (Devir); Eq. (2) makes the 0.53 um value 39.4 times the 1.06 um one (2.0e-36 -> 7.9e-35), and Eq. (1) with the printed g_R = 1.0e-11 m/W needs 8.4e-35 m^2/sr. The exponent -36 is a misprint for -35.", "evidence": "Table I image checked: '8.0x10-36*'. Ratio of Eq. (2) between the pumps: (15795/6404)^4 x [(1/71218 + 1/105795)/(1/80609 + 1/96404)]^2 = 37.0 x 1.064 = 39.4; H2's printed ratio (66) and CH4's (39) are of the same order, D2's printed 4.0 is not; the printed g_R ratio 0.53/1.06 um of D2 (2.7) matches H2 (2.85) and CH4 (2.6). Recomputed 2026-09-26." } ] 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.