ottusch_1988#
J. J. Ottusch and D. A. Rockwell, “Measurement of Raman gain coefficients of hydrogen, deuterium, and methane”, IEEE J. Quantum Electron. 24, 2076 (1988)
Source record · Catalogue · Review register
DOI: 10.1109/3.8545
Source kind: measurement
Recorded technique: Small-signal steady-state Raman gain at a 532 nm pump (frequency-doubled single-mode phase-conjugate Nd:YAG, 35 ns FWHM): a backward-Raman oscillator generates the Stokes seed, which is amplified with the pump in an 18.5 cm amplifier cell holding the same gas at the same pressure; calorimeters on the pump, the input and the amplified seed; the gain from the slope of E_S/E_S0 against E_P with the measured area and time overlap integrals, Eqs. (1)-(3) (pp. 2076-2078). Also the gain against the amplifier density with the oscillator fixed at 61 amagat (Fig. 5).
Materials in structured entries: CH4, D2, H2
Dataset quantities: raman_cross_section, raman_gain
Contents: 11 datasets; 6 formulas.
Curation notes#
Journal pages 2076-2080 = PDF pages 1-5 (page n of the PDF is p. 2075 + n). Identity checked on the first page.
DUPLICATE COPY: the library’s Ottusch_1988_MeasurementRamanGain_ec9131 is the same article from a different PDF file (sha256 ec91313e... against 86cd3d06...): the text is identical but for metadata and a footnote’s position, Table II’s cells are identical, and Table I (its tbl_fb338ba08905) differs only by a misread ‘D_3 Q(2)’ for ‘D_2 Q(2)’. Not extracted twice (compared 2026-09-26).
TABLE I (p. 2077), ‘Spectroscopic parameters used in Raman gain calculation’ (all taken from others): Stokes wavelength 683 (H2 Q(1)), 633 (D2 Q(2)), 630 nm (CH4 nu1); Delta N 0.66 N_TOT, 0.38 N_TOT, N_TOT; the linewidth laws (footnote a: ‘FWHM, rho in amagats’), in MHz: H2 309/rho + 51.8 rho [12], D2 101/rho + 120 rho [16], [17], CH4 8220 + 384 rho [13] (the formulas linewidth_H2, linewidth_D2, linewidth_CH4); dsigma/dOmega (cm^2 sr^-1) 0.81e-30, 0.79e-30, 2.7e-30 [18] (Bischel and Black 1983), the datasets dsigma_*. ‘The values we use for Delta N, Delta nu, and dsigma/dOmega are essentially the same as those used by Hanna et al. [14] (hanna_1986), with the exception that more recently measured expressions for Delta nu have been used for CH4 and D2’ (p. 2077). The H2 law is cited to [12] = Bischel and Dyer, J. Opt. Soc. Am. B 3, 677 (1986) (bischel_1986b, Eq. 8 at 298 K), itself reproducing Bischel and Dyer, Phys. Rev. A 33, 3113 (1986) (bischel_1986).
LINEWIDTH LAWS (for review and solprop): FWHM, in MHz, rho in amagat (Table I footnote a, image checked). The 1/rho terms are the Dicke-narrowing terms (H2, D2), in MHz amagat; the CH4 constant 8220 MHz is the width of the unresolved Q branch at zero density, not a collision width. Temperature not stated (room temperature).
TABLE II (p. 2079), ‘Comparison of calculated and measured Raman gain coefficients at lambda_P = 532 nm’, cm/GW: H2 Q(1) at 60 amagat: calculated 2.86, this work 2.64 +- 0.20, previous 2.5 +- 0.4 (bischel_1986b); D2 Q(2) at 60 amagat: 0.55, 0.45 +- 0.05; CH4 nu1 at 115 amagat: 1.28, 1.26 +- 0.10, previous 1.2 (Lopert, Ph.D. dissertation, Univ. California, Davis, 1983). ‘The uncertainties result mainly from imperfect shot-to-shot repeatability of the IR source and are estimated from the scatter in the values of the gain slope produced by several independent measurements’ (p. 2078): level not stated. ‘The measured Raman gain coefficients listed in Table II are uncorrected for the small, but finite, spectral bandwidth of the seed beam ... we judge the possible underestimation of the true Raman gain to be no more than 8 percent for H2, 4 percent for D2, and 6 percent for CH4’ (p. 2079). The D2 gain ‘is lower by more than a factor of 2 than the corresponding value reported by Hanna et al.’, who claim a factor-of-two accuracy (pp. 2078-2079). The previous-work column is a reproduction (use = “reproduced”); the calculated column Eq. (4) (use = “check”).
THE STATE of a gain (the quantity requires one): the gains are at the printed density (amagat, the abscissa); the measurement temperature is not stated (room temperature). The state is recorded as { 60 (or 115) atm, 273.15 K }, the ideal-gas state at 0 C with that density in amagat, so that it encodes the printed density exactly, not a measured pressure (a second curator’s decision: a gain against density needs no pressure).
REPRODUCTION (2026-09-26): Eq. (4), g = (2 lambda_S^2/h nu_S)(Delta N/pi Delta nu) dsigma/dOmega, with Table I’s parameters and N_TOT = rho x 2.6868e19 cm^-3 gives 2.827 (H2, printed 2.86), 0.546 (D2, 0.55) and 1.276 cm/GW (CH4, 1.28): within 1.2 %.
LINE SHIFTS (Fig. 5 caption, p. 2079; reproduced, formulas shift_H2 and shift_D2): ‘for H2 nu_A,S - nu(rho = 0) = -96 rho + 0.17 rho^2 [12], [20] and for D2 nu_A,S - nu(rho = 0) = -50 rho [20] (nu in MHz, rho in amagats)’. Fig. 5 (gain against amplifier density, oscillator at 61 amagat) is a figure only.
ISOTOPOLOGUES: natural H2 and D2 (normal: the J = 1 and J = 2 fractions 0.66 and 0.38 of Table I are room-temperature populations); 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#
ottusch_1988/dsigma_H2#
{
"id": "dsigma_H2",
"material": "H2",
"file": "H2/ottusch_1988__dsigma_H2.csv",
"table": "tbl_6fef6b554123",
"quantity": "raman_cross_section",
"unit": "cm2/sr",
"scale": 1e-30,
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"bischel_1983"
],
"parameters": {
"transition": "v=0-1 Q(1)"
}
}
Table I (p. 2077), dsigma/dOmega of H2 Q(1) used in Eq. (4) at the 532 nm pump, footnote e: [18] Bischel and Black (bischel_1983, re-pointed 2026-09-27). Polarization and definition not restated here. Bischel and Black print no value at 532 nm: their H2 fit (Table 1) gives 8.59e-31 cm2/sr for the Q branch (8.51e-31 with bischel_1986b’s R = 0.99 for Q(1)), 6 % above this 0.81e-30.
ottusch_1988/dsigma_D2#
{
"id": "dsigma_D2",
"material": "D2",
"file": "D2/ottusch_1988__dsigma_D2.csv",
"table": "tbl_6fef6b554123",
"quantity": "raman_cross_section",
"unit": "cm2/sr",
"scale": 1e-30,
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"bischel_1983"
],
"parameters": {
"transition": "v=0-1 Q(2)"
}
}
Table I (p. 2077), dsigma/dOmega of D2 Q(2) at the 532 nm pump, footnote e: [18] (bischel_1983, re-pointed 2026-09-27). Hanna et al.’s value at 0.53 um is 8.0e-36 m^2/sr as printed (8.0e-35 corrected, hanna_1986), i.e. 0.80e-30 cm^2/sr: the same. Bischel and Black print no value at 532 nm: their D2 Q-branch fit (Table 1) gives 7.38e-31 cm2/sr, 7 % below this 0.79e-30.
ottusch_1988/dsigma_CH4#
{
"id": "dsigma_CH4",
"material": "CH4",
"file": "CH4/ottusch_1988__dsigma_CH4.csv",
"table": "tbl_6fef6b554123",
"quantity": "raman_cross_section",
"unit": "cm2/sr",
"scale": 1e-30,
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"bischel_1983"
],
"parameters": {
"transition": "nu1 Q branch"
}
}
Table I (p. 2077), dsigma/dOmega of the CH4 nu1 Q branch at the 532 nm pump, footnote e: [18] (bischel_1983, re-pointed 2026-09-27). Bischel and Black print no value at 532 nm: their CH4 fit (Table 1, with the shift 2917 cm-1) gives 2.78e-30 cm2/sr, 3 % above this 2.7e-30.
ottusch_1988/gain_H2#
{
"id": "gain_H2",
"material": "H2",
"file": "H2/ottusch_1988__gain_H2.csv",
"table": "tbl_963e1d09eaae",
"quantity": "raman_gain",
"unit": "cm/GW",
"abscissa": "density",
"abscissa_unit": "amagat",
"state": {
"pressure_atm": 60.0,
"temperature_k": 273.15
},
"density": "ideal",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"transition": "v=0-1 Q(1)",
"pump_nm": 532
}
}
Table II (p. 2079), this work: the measured steady-state gain of H2 Q(1) at the 532 nm pump and 60 amagat (sigma: the printed +-, estimated from the scatter of independent gain slopes, level not stated; uncorrected for the seed bandwidth, possibly low by up to 8 %). The state encodes the printed density (see the record’s notes); the temperature (room) is not stated.
ottusch_1988/gain_D2#
{
"id": "gain_D2",
"material": "D2",
"file": "D2/ottusch_1988__gain_D2.csv",
"table": "tbl_963e1d09eaae",
"quantity": "raman_gain",
"unit": "cm/GW",
"abscissa": "density",
"abscissa_unit": "amagat",
"state": {
"pressure_atm": 60.0,
"temperature_k": 273.15
},
"density": "ideal",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"transition": "v=0-1 Q(2)",
"pump_nm": 532
}
}
Table II (p. 2079), this work: the measured gain of D2 Q(2) at 532 nm and 60 amagat; the authors ‘could find no reported direct measurement of the gain coefficient for deuterium’ (p. 2076); possibly low by up to 4 % (seed bandwidth). State as for gain_H2.
ottusch_1988/gain_CH4#
{
"id": "gain_CH4",
"material": "CH4",
"file": "CH4/ottusch_1988__gain_CH4.csv",
"table": "tbl_963e1d09eaae",
"quantity": "raman_gain",
"unit": "cm/GW",
"abscissa": "density",
"abscissa_unit": "amagat",
"state": {
"pressure_atm": 115.0,
"temperature_k": 273.15
},
"density": "ideal",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"transition": "nu1 Q branch",
"pump_nm": 532
}
}
Table II (p. 2079), this work: the measured gain of the CH4 nu1 Q branch at 532 nm and 115 amagat (the library cells read ‘CH_3’, the image prints CH4); possibly low by up to 6 % (seed bandwidth). State as for gain_H2, at 115 amagat.
ottusch_1988/gain_calc_H2#
{
"id": "gain_calc_H2",
"material": "H2",
"file": "H2/ottusch_1988__gain_calc_H2.csv",
"table": "tbl_963e1d09eaae",
"quantity": "raman_gain",
"unit": "cm/GW",
"abscissa": "density",
"abscissa_unit": "amagat",
"state": {
"pressure_atm": 60.0,
"temperature_k": 273.15
},
"density": "ideal",
"use": "check",
"parameters": {
"transition": "v=0-1 Q(1)",
"pump_nm": 532
}
}
Table II (p. 2079), ‘Calculated’ by Eq. (4) with Table I’s parameters (reproduced to 1.2 %: 2.827 against 2.86).
ottusch_1988/gain_calc_D2#
{
"id": "gain_calc_D2",
"material": "D2",
"file": "D2/ottusch_1988__gain_calc_D2.csv",
"table": "tbl_963e1d09eaae",
"quantity": "raman_gain",
"unit": "cm/GW",
"abscissa": "density",
"abscissa_unit": "amagat",
"state": {
"pressure_atm": 60.0,
"temperature_k": 273.15
},
"density": "ideal",
"use": "check",
"parameters": {
"transition": "v=0-1 Q(2)",
"pump_nm": 532
}
}
Table II (p. 2079), ‘Calculated’ by Eq. (4) (reproduced: 0.546 against 0.55).
ottusch_1988/gain_calc_CH4#
{
"id": "gain_calc_CH4",
"material": "CH4",
"file": "CH4/ottusch_1988__gain_calc_CH4.csv",
"table": "tbl_963e1d09eaae",
"quantity": "raman_gain",
"unit": "cm/GW",
"abscissa": "density",
"abscissa_unit": "amagat",
"state": {
"pressure_atm": 115.0,
"temperature_k": 273.15
},
"density": "ideal",
"use": "check",
"parameters": {
"transition": "nu1 Q branch",
"pump_nm": 532
}
}
Table II (p. 2079), ‘Calculated’ by Eq. (4) (reproduced: 1.276 against 1.28).
ottusch_1988/gain_previous_H2#
{
"id": "gain_previous_H2",
"material": "H2",
"file": "H2/ottusch_1988__gain_previous_H2.csv",
"table": "tbl_963e1d09eaae",
"quantity": "raman_gain",
"unit": "cm/GW",
"abscissa": "density",
"abscissa_unit": "amagat",
"state": {
"pressure_atm": 60.0,
"temperature_k": 273.15
},
"density": "ideal",
"use": "reproduced",
"reproduced_from": [
"bischel_1986b"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"transition": "v=0-1 Q(1)",
"pump_nm": 532
}
}
Table II (p. 2079), ‘Previous Work’ footnote a: [12], Bischel and Dyer’s 532 nm value 2.5 +- 0.4 (x 10^-9 cm/W there, measured at 20 amagat, 298 K, the high-density limit), placed on the 60 amagat row.
ottusch_1988/gain_previous_CH4#
{
"id": "gain_previous_CH4",
"material": "CH4",
"file": "CH4/ottusch_1988__gain_previous_CH4.csv",
"table": "tbl_963e1d09eaae",
"quantity": "raman_gain",
"unit": "cm/GW",
"abscissa": "density",
"abscissa_unit": "amagat",
"state": {
"pressure_atm": 115.0,
"temperature_k": 273.15
},
"density": "ideal",
"use": "reproduced",
"reproduced_from": [
"R. B. Lopert, Measured stimulated Raman gain in methane, Ph.D. dissertation, Univ. California, Davis (1983)"
],
"parameters": {
"transition": "nu1 Q branch",
"pump_nm": 532
}
}
Table II (p. 2079), ‘Previous Work’ footnote b: [13], Lopert’s methane gain, no uncertainty printed.
Formulas#
ottusch_1988/linewidth_H2#
{
"id": "linewidth_H2",
"material": "H2",
"equation": "Table I, p. 2077",
"printed": "Delta nu = 309/rho + 51.8 rho (MHz; FWHM, rho in amagats)",
"variable": "rho: the density of H2 in amagat",
"state": "room temperature (not stated; Bischel and Dyer's 298 K)",
"density": "unknown",
"range": "not stated (Bischel and Dyer: rho < 100 amagat)",
"coefficients": {
"A_MHz_amagat": "309",
"B_MHz_per_amagat": "51.8"
},
"check": "At 60 amagat, 3113 MHz, which with Table I's other parameters reproduces the calculated H2 gain 2.86 cm/GW to 1.2 % (2026-09-26). Identical to bischel_1986b Eq. (8) at T = 298 K."
}
The Q(1) FWHM with the Dicke term 309/rho (MHz amagat), reproduced from [12] (bischel_1986b, Eq. 8), originally Bischel and Dyer, Phys. Rev. A 33, 3113 (1986) (bischel_1986). Not solprop’s H2 source (solprop takes 309 and 52.2 from bischel_1986 Table I).
ottusch_1988/linewidth_D2#
{
"id": "linewidth_D2",
"material": "D2",
"equation": "Table I, p. 2077",
"printed": "Delta nu = 101/rho + 120 rho (MHz; FWHM, rho in amagats)",
"variable": "rho: the density of D2 in amagat",
"state": "room temperature (not stated)",
"density": "unknown",
"range": "not stated",
"coefficients": {
"A_MHz_amagat": "101",
"B_MHz_per_amagat": "120"
},
"check": "At 60 amagat, 7202 MHz, which reproduces the calculated D2 gain 0.55 cm/GW to 0.7 % (2026-09-26)."
}
The D2 Q(2) FWHM with the Dicke term 101/rho (MHz amagat), from [16] D. A. Russell and W. B. Roh, J. Mol. Spectrosc. 124, 240 (1987) (russell_1987) and [17] K. C. Smyth, G. J. Rosasco and W. S. Hurst, J. Chem. Phys. 87, 1001 (1987) (smyth_1987); which coefficient comes from which is not said. Against the originals (checked 2026-09-27): 101 MHz amagat is Russell and Roh’s Q(2) Dicke term, (4 pi nu^2/c) D_0 with D_0 = 0.901 cm2 amagat/s (their Table I) and nu = 2987 cm-1: 3.370e-3 cm-1 amagat = 101.0 MHz amagat; 120 MHz/amagat lies between Russell and Roh’s FWHM a(Q(2)) = 3.91e-3 cm-1/amagat = 117.2 MHz/amagat and twice Smyth et al.’s HWHM gamma(Q(2)) = 2 x 2.06e-3 cm-1/amagat = 123.5 MHz/amagat, and equals their mean (120.4) to the printed digits (an inference). Both originals are room-temperature measurements; the FWHM of this law is consistent with both (Smyth et al.’s are half widths). solprop’s D2 vibrational linewidth is this law: inverse_density 1.01e8 (Hz amagat) and density 1.20e8 (Hz/amagat), FWHM: the same numbers.
ottusch_1988/linewidth_CH4#
{
"id": "linewidth_CH4",
"material": "CH4",
"equation": "Table I, p. 2077",
"printed": "Delta nu = 8220 + 384 rho (MHz; FWHM, rho in amagats)",
"variable": "rho: the density of CH4 in amagat",
"state": "room temperature (not stated)",
"density": "unknown",
"range": "not stated",
"coefficients": {
"constant_MHz": "8220",
"B_MHz_per_amagat": "384"
},
"check": "At 115 amagat, 52380 MHz, which reproduces the calculated CH4 gain 1.28 cm/GW to 0.3 % (2026-09-26)."
}
The CH4 nu1 Q-branch FWHM from [13] R. B. Lopert, Ph.D. dissertation (UC Davis, 1983), not in the library. The constant 8220 MHz (0.274 cm-1) is the unresolved Q-branch width at zero density. solprop’s CH4 vibrational linewidth is this law: constant 8.22e9 Hz, density 3.84e8 Hz/amagat, FWHM (solprop: ‘its constant term is not a verified isolated-molecule lifetime’). Hanna et al. used Taira et al.’s 0.32 + 0.012p cm-1 instead (hanna_1986).
ottusch_1988/shift_H2#
{
"id": "shift_H2",
"material": "H2",
"equation": "Fig. 5 caption, p. 2079",
"printed": "nu_A,S - nu(rho = 0) = -96 rho + 0.17 rho^2 (nu in MHz, rho in amagats)",
"variable": "rho: the density of H2 in amagat",
"state": "room temperature (not stated)",
"density": "unknown",
"range": "not stated",
"coefficients": {
"C_MHz_per_amagat": "-96",
"D_MHz_per_amagat2": "0.17"
},
"check": "Not reproducible here (Fig. 5 is a figure); the same numbers as bischel_1986b Eq. (9) (C = -96 MHz/amagat at 298 K, D = 0.174 MHz amagat^-2 from Murray and Javan)."
}
The collisional shift of H2 Q(1), reproduced from [12] (bischel_1986b) and [20] J. R. Murray and A. Javan, J. Mol. Spectrosc. 42, 1 (1972), curated as murray_1972 (2026-09-27); used for the theoretical curves of Fig. 5. The 0.17 MHz/amagat^2 is Murray and Javan’s Q_1(0) quadratic coefficient (0.0058e-3 cm-1/amagat^2 = 0.174), carried over from bischel_1986b; their Q_1(1) value is 0.0045e-3 = 0.135 MHz/amagat^2.
ottusch_1988/shift_D2#
{
"id": "shift_D2",
"material": "D2",
"equation": "Fig. 5 caption, p. 2079",
"printed": "nu_A,S - nu(rho = 0) = -50 rho (nu in MHz, rho in amagats)",
"variable": "rho: the density of D2 in amagat",
"state": "room temperature (not stated)",
"density": "unknown",
"range": "not stated",
"coefficients": {
"C_MHz_per_amagat": "-50"
},
"check": "Not reproducible here (Fig. 5 is a figure). Against the original (murray_1972, 2026-09-27): its Table III linear-fit a for D2 Q_1(2), -1.7 +- 0.3 x 10^-3 cm-1/amagat at 25 C, is -51.0 MHz/amagat (x 29.98): this -50 to 2 %."
}
The collisional shift of D2 Q(2), reproduced from [20] Murray and Javan (1972), curated as murray_1972 (2026-09-27).
ottusch_1988/gain_eq4#
{
"id": "gain_eq4",
"material": "H2",
"equation": "Eq. (4), p. 2077",
"printed": "g = (2 lambda_S^2/(h nu_S)) (Delta N/(pi Delta nu)) (dsigma/dOmega)",
"variable": "lambda_S, nu_S: the Stokes wavelength and frequency; Delta N the population difference; Delta nu the FWHM of the gain profile; dsigma/dOmega the differential cross section",
"state": "as the parameters",
"density": "unknown",
"range": "steady state, small signal",
"coefficients": {
"factor": "2"
},
"check": "With Table I's parameters and rho x 2.6868e19 cm^-3 reproduces Table II's calculated gains to 1.2 % (H2), 0.7 % (D2) and 0.3 % (CH4) (2026-09-26)."
}
The plane-wave steady-state peak gain [12] (bischel_1986b Eq. 4), for H2, D2 and CH4 alike (the material key names the first). Hanna et al.’s Eq. (1) is the same law in angular frequencies.
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.