bischel_1986b#

W. K. Bischel and M. J. Dyer, “Wavelength dependence of the absolute Raman gain coefficient for the Q(1) transition in H2”, J. Opt. Soc. Am. B 3, 677 (1986)

Source record · Catalogue · Review register

DOI: 10.1364/josab.3.000677

Source kind: measurement

Recorded technique: Pulsed pump / cw probe Raman gain (and inverse Raman absorption) on the Q(1) line of normal H2 at 298 K in a 62 cm cell, collimated collinear beams, both lasers single frequency: 532 nm pump (single-frequency doubled YAG, 20 ns) with a 683 nm ring dye probe; 594 nm pulsed dye pump with the 476.5 nm Ar+ probe (inverse Raman, giving the gain at 477 nm); 307 nm (doubled dye) pump with the 351.4 nm Ar+ probe. Pump area from a scanned 0.1 mm aperture (Eq. 1), gain from the time integral of ln(S/S0) (Eq. 3); corrections for the laser linewidth, the pump intensity (inverse Raman) and the density (477 nm, 12.3 amagat), measurements at 20 amagat otherwise (pp. 677-680).

Materials in structured entries: H2

Dataset quantities: dephasing_time, raman_gain, raman_line_shift, raman_shift, raman_transition_polarizability

Contents: 8 datasets; 5 formulas.

Curation notes#

Journal pages 677-682 = PDF pages 1-6 (page n of the PDF is p. 676 + n). Identity checked on the first page. Source id bischel_1986b: bischel_1986 is the same authors’ Phys. Rev. A 33, 3113 (1986) (Ref. 14 here), curated in another extraction.

TABLE 1 (p. 680), ‘Comparison of Measured and Calculated Q(1) Gain Coefficients at 298 K’, gamma in 10^-9 cm/W against the pump wavelength (nm): this work at 532 (2.5 +- 0.4), 477 (3.5 +- 0.3) and 308 (6.6 +- 0.8); previous work at 694 (1.5 +- 0.8, Ref. 8, Bloembergen et al.), 530 (1.8 +- 0.4, Ref. 10, Venkin et al.), 353 (5.0 +- 0.5, Ref. 12, Komine, personal communication) and 265 (5.5 +- 1.6, no footnote: Venkin et al. measured at 530 and 265 nm, p. 677); Eq. (11) at all seven. ‘The error bars listed are our best estimate of the absolute uncertainty in the measured values. They were obtained by adding the standard deviation calculated from the scatter in the data to a reasonable estimate of the systematic error in the measurement technique’ (p. 680): level not stated. The text gives the UV pump as 307 nm (pp. 677, 678, 681) where Table 1 prints 308; Eq. (11) gives 7.05 at 308 nm and 7.09 at 307 nm against the printed 7.06, so 308 is the wavelength of the calculated column. Wavelengths are nominal laser lines (air or vacuum not stated; the difference is below the printed precision). Measured values are the high-density limit: the 532 and 308 nm data at 20 amagat need no density correction, the 477 nm value (inverse Raman at 12.3 amagat) was raised 4 % to the high-density limit (p. 680). The 477 nm and 308 nm values include the laser-linewidth correction (+15 to 30 %, p. 679-680); the 477 nm value is extrapolated to zero pump fluence (Fig. 4).

STATE of the gain datasets (the quantity requires one): recorded as { 21.82 atm, 298 K }, the ideal-gas pressure of 20 amagat at 298 K (the density of the 532 and 308 nm measurements; the temperature of Table 1’s caption). The values are the high-density limit, independent of the density (Eq. 11; p. 681). The previous-work rows carry the same state for comparison only: their own conditions are not given here.

FORMULAS (p. 681): Eq. (11), the room-temperature gain in wavelength, density and temperature (through Delta nu); Eq. (5), the cross section of Bischel and Black (Ref. 20); Eq. (8), the linewidth (reproduced from Ref. 14 = bischel_1986); Eqs. (9)-(10), the line shift. Eq. (11) reproduces Table 1’s calculated column to <= 0.25 % (all seven wavelengths, vacuum or air alike; checked 2026-09-26). Its constant 9.37e6 follows from Eqs. (4) and (5) with R = 0.99, K_B = 0.658, Delta nu = 52 rho MHz and 1 amagat = 2.6868e19 cm^-3: 9.43e6 (0.6 % above; the paper does not give its constants).

TEXT VALUES: the transition polarizabilities ‘alpha_01 = 1.11 x 10^-25 cm^3 and gamma_01 = 0.951 x 10^-25 cm^3 for lambda_p = 500 nm’ (Ref. 22, W. Huo, personal communication, 1983), used for the polarization correction R = 0.99 of Eq. (6) to Eq. (7) (p. 681; the Q-branch average sum_J f_J b_JJ = 0.321 at 298 K) - the datasets alpha01_H2 and gamma01_H2, reproduced; the zero-density transition frequency ‘nu_r(0) = 4155.25 +- 0.01 cm^-1’ (Refs. 28-31, p. 681) - shift_H2, reproduced; the shift coefficient ‘At 298 K, we have measured C = -96 MHz/amagat’ (Ref. 14) - line_shift_H2, reproduced from bischel_1986; ‘D = 0.174 MHz amagat^-2’ (Ref. 26, Murray and Javan, curated as murray_1972: their Q_1(0) coefficient, see the formula) in the formula line_shift_eq9; ‘T2 = 6.1 nsec amagat’ (from Refs. 13-16, p. 679) - T2_H2, reproduced; ‘the room-temperature value of 52 MHz/amagat for the Raman linewidth’ (p. 681, Eq. (8) at 298 K, 51.8 rounded). Also: the dye-laser calibration, ‘For a H2 density of 12.1 amagats, we measured an effective linewidth of 860 MHz where the true linewidth is 650 MHz’ (p. 678), and ‘the Raman linewidth of 1055 MHz at a density of 20 amagats’ (p. 680): both from Eq. (8), not new measurements.

FWHM: ‘Delta nu is the full width at half-maximum Raman linewidth in hertz’ (Eq. 4, p. 680); Eq. (8) is ‘a best-fit formula for the FWHM Raman linewidth Delta nu in megahertz at any temperature and density (rho < 100 amagats)’, including Dicke narrowing (309/rho in MHz amagat) (p. 681).

H2 is normal hydrogen at 298 K (‘K_B ... equal to 0.658 at 298 K for the J = 1 level in H2’, p. 681). Ref. 8 is printed ‘IEEE J. Quantum Electron. QE-3, 197 (1976)’ (Ottusch and Rockwell cite it as 1967): kept as printed.

Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets#

bischel_1986b/gain_H2#

{
  "id": "gain_H2",
  "material": "H2",
  "file": "H2/bischel_1986b__gain_H2.csv",
  "table": "tbl_33f36ba412af",
  "quantity": "raman_gain",
  "unit": "cm/W",
  "scale": 1e-09,
  "abscissa_unit": "nm",
  "state": {
    "pressure_atm": 21.82,
    "temperature_k": 298.0
  },
  "density": "ideal",
  "use": "primary",
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "transition": "v=0-1 Q(1)"
  }
}

Table 1 (p. 680), ‘This Work’: the measured steady-state high-density-limit gain of H2 Q(1) at 298 K against the pump wavelength (532 nm gain, 477 nm from inverse Raman absorption, 308 nm gain), sigma the printed +- (the scatter’s standard deviation plus an estimate of the systematic error, level not stated). State: 20 amagat at 298 K (see the record’s notes).

bischel_1986b/gain_previous_H2#

{
  "id": "gain_previous_H2",
  "material": "H2",
  "file": "H2/bischel_1986b__gain_previous_H2.csv",
  "table": "tbl_33f36ba412af",
  "quantity": "raman_gain",
  "unit": "cm/W",
  "scale": 1e-09,
  "abscissa_unit": "nm",
  "state": {
    "pressure_atm": 21.82,
    "temperature_k": 298.0
  },
  "density": "ideal",
  "use": "reproduced",
  "reproduced_from": [
    "N. Bloembergen, G. Bret, P. Lallemand, A. Pine and P. Simova, IEEE J. Quantum Electron. QE-3, 197 (1976) (year as printed)",
    "G. V. Venkin, L. L. Kulyuk and D. I. Maleev, Kvantovaya Elektron. (Moscow) 2, 2475 (1975) [Sov. J. Quantum Electron. 5, 1348 (1976)]",
    "H. Komine, Northrop Research and Technology Center (personal communication, 1983)"
  ],
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "transition": "v=0-1 Q(1)"
  }
}

Table 1 (p. 680), ‘Previous Work’: 694 nm (a, Ref. 8, broadband ruby laser, ‘~50%’ quoted error, p. 677), 530 nm (b, Ref. 10), 353 nm (c, Ref. 12, unpublished), 265 nm (no footnote; Ref. 10’s quadrupled line, p. 677). Conditions (density, temperature) not given here; the state is the table’s for comparison only.

bischel_1986b/gain_eq11_H2#

{
  "id": "gain_eq11_H2",
  "material": "H2",
  "file": "H2/bischel_1986b__gain_eq11_H2.csv",
  "table": "tbl_33f36ba412af",
  "quantity": "raman_gain",
  "unit": "cm/W",
  "scale": 1e-09,
  "abscissa_unit": "nm",
  "state": {
    "pressure_atm": 21.82,
    "temperature_k": 298.0
  },
  "density": "ideal",
  "use": "check",
  "parameters": {
    "transition": "v=0-1 Q(1)"
  }
}

Table 1 (p. 680), gamma_cal from Eq. (11) at 298 K in the high-density limit (Delta nu = 52 rho MHz), reproduced by the formula gain_eq11 to <= 0.25 %.