wahlstrand_2012#

J. K. Wahlstrand, Y.-H. Cheng and H. M. Milchberg, “Absolute measurement of the transient optical nonlinearity in N2, O2, N2O, and Ar”, Phys. Rev. A 85, 043820 (2012)

Source record · Catalogue · Review register

DOI: 10.1103/PhysRevA.85.043820

Source kind: measurement

Recorded technique: Single-shot supercontinuum spectral interferometry (SSSI): a 40-fs, 800-nm (1.55 eV) Ti:sapphire pump and a chirped supercontinuum probe (generated in SF6, usable bandwidth 120 nm, group-delay dispersion 1750 fs^2) copropagate through a thin gas flow (laser-drilled flattened tube, outer thickness 475 um, L_eff = 418 um) in a vacuum chamber; the probe phase shift Delta Phi(x, t) is extracted from the spectral interferogram (1000 shots averaged). The pump spot (29 um x 27 um) is measured from the Kerr phase along two perpendicular slices (Dove prism). L_eff comes from a folded wave-front interferometer at 635 nm on the N2 flow; the other gases are measured in the backfilled chamber at about 90 Torr and referenced to the N2 flow-tube measurement (effective length 4.41 mm at 90 Torr). Probe parallel and perpendicular to the pump separate the instantaneous and rotational parts (pp. 2-3).

Materials in structured entries: Ar, N2, N2O, O2

Dataset quantities: nonlinear_index, polarizability_anisotropy

Contents: 19 datasets; 0 formulas.

Curation notes#

Journal pages 043820-1 to -5 = PDF pages 1-5. Identity checked against the first page. Air is not curated; no air value is given here anyway.

DEFINING EQUATIONS (quoted; Gaussian units throughout). Eq. (1), p. 043820-1: ‘The total nonlinear index of refraction, to second order in the field or first order in the laser intensity, is Delta n(t) = n2 I(t) + int R(t - t’) I(t’) dt’’, with I(t) the laser intensity and R(t) the (rotational, plus a small adiabatic bond-stretch) Raman response. Eq. (2), p. 1: Delta Phi(x, t) = k0 int Delta n dz = k0 Delta n_atm(x, t) int P(z)/P0 dz = k0 Delta n_atm(x, t) L_eff, with k0 the average vacuum wavenumber of the chirped probe over the overlap and Delta n_atm ‘the change in refractive index at atmospheric pressure P0’. Separation (pp. 2-3): Delta Phi_par = Delta Phi_inst + Delta Phi_rot, Delta Phi_perp = Delta Phi_inst/3 - Delta Phi_rot/2, so Delta Phi_inst = 3(Delta Phi_par + 2 Delta Phi_perp)/5 and Delta Phi_rot = 2(Delta Phi_par - 3 Delta Phi_perp)/5. Long-pulse limit (p. 3): n2,long = n2 - [8 pi N (Delta alpha)^2 / (15 n0^2 c^2 hbar B)] sum_j [j(j - 1)/(2j - 1)^2] (rho_j/(2j + 1) - rho_(j-2)/(2j - 3)), rho_j the thermal (nuclear-spin weighted) populations; B = 2.0 (N2), 1.44 (O2), 0.41 cm^-1 (N2O). The paper states no relation between n2 and chi(3) or gamma (it only defines Delta alpha = alpha_par - alpha_perp, the linear polarizabilities along and across the bond axis, p. 1).

SELF OR PROBE COEFFICIENT. Eq. (1) writes the probe’s index as n2 I, with no factor 2, and the paper does not discuss the cross-phase factor. The tabulated n2 is nevertheless the SELF coefficient: (i) the same group’s PRL (wahlstrand_2012b, which calibrates ‘as in [this paper]’) writes Delta n = 2 n2 I and gives the same Ar value, 9.7 +- 1.2; (ii) wahlstrand_2013 (p. 7) says its calculations ‘provide theoretical justification for the analysis performed in’ this paper, the only difference between the probe’s and the self index being the factor 2 of the bound electronic part, and compares these values with Loriot’s erratum-corrected self coefficients; (iii) zahedpour_2015 (p. 5795) writes the probe index as 2 n2 I + int R, citing this paper. Recorded as coefficient = ‘self’ (TC-276).

PART. The instantaneous part is attributed to the electronic response: the adiabatic bond-stretch (vibrational) contribution, which the 40-fs pulse cannot separate, is estimated ~30 times smaller than the measured instantaneous phase in N2 and O2 (p. 3, citing Zheltikov’s response function and Shelton and Rice’s < 10 %). The molecular values are therefore recorded as ‘electronic_vibrational’ (Ar: ‘electronic’); the rotational part is removed by the polarization analysis, not by the pulse duration. For pulses longer than ~80 fs the instantaneous and rotational responses merge (Fig. 3, 40-100 fs, N2).

REFERENCE STATE. ‘absolute values of Kerr nonlinearity at 1 atm’ (p. 2); no temperature is stated for the reduction (the density-matrix code of note [23] uses 300 K; n2/n2,long is for ‘atmospheric density and room temperature’). Recorded as 101325 Pa and 290.9 K (decided 2026-09-26, TC-316; the other sources’ unstated temperatures are 293.15 K). The absolute scale rests on L_eff from Delta phi = k0 (n0 - 1) L_eff = 1.16 rad with n0 - 1 = 2.795e-4 for N2 at 633 nm and 1 atm (Clergent et al. 1999, now clergent_1999); optmat’s default N2 model gives that refractivity at 101325 Pa and about 291 K (2.795e-4 lies between 2.822e-4 at 288.15 K and 2.773e-4 at 293.15 K; computed 2026-09-26; at 632.8 nm in standard air the fit/N2 model gives 2.795e-4 at 290.88 K), so the effective reference density is that of N2 at 290.9 K, 1 atm: +0.7 % against 293.15 K. The group’s own n2 are recorded at that state. The ORIGIN of 2.795e-4 (clergent_1999, checked 2026-09-26): it is Clergent et al.’s Table 5 value for N2, (n - 1) x 10^6 = 279.5 +- 0.8 at 632.8 nm, 101.325 kPa and 293.15 K (mu p/T with mu = 808.8 +- 1.2 x 1e-9 K/Pa). At that state optmat’s N2 model gives 277.33e-6, so the value is +0.78 % above the fit; Clergent’s Ar and CO2 are likewise +0.56 % and +0.50 % above optmat’s models (a common calibration offset of that measurement, about twice its stated 0.3 %). Two readings follow: if Clergent’s absolute value were right, the n2 would refer to N2 at 293.15 K, 1 atm (the state of Clergent’s value; the group states no temperature); if optmat’s N2 model is right (Clergent’s offset is common to all three gases, which suggests a calibration error of that measurement), the phase calibration refers to the density of N2 at 290.9 K, 1 atm, as recorded here, and the n2 are 0.78 % above what the same measurement gives at 293.15 K. No value is changed here.

WAVELENGTHS. Pump 800 nm (1.55 eV, p. 1), vacuum assumed. Probe: supercontinuum, n2 and Delta alpha showed ‘no measurable variation, to within error ... over the central probe wavelength range of 550-635 nm’; for a probe at 580 nm the n2 at 800 nm is overestimated ‘by less than 3 %’ (power-series dispersion, Shelton and Rice / Bishop; p. 4). probe_nm = 580 is recorded.

UNCERTAINTY (p. 3): ‘The largest source of uncertainty is the peak intensity ... the uncertainty values given in Table I are the absolute error; the relative contribution between n2 and Delta alpha was measured much more precisely ... Ratios of values between gases are also more precise than the absolute error given’. Level not stated.

TABLE I (p. 3). The library’s cells file has merged all rows into one garbled row; the values are entered inline, read from the table image and confirmed in the pdf text layer (pdftotext, page 3). Columns: n2 (1e-20 cm2/W) this work, Nibbering et al. [10], Loriot et al. [16], Shelton and Rice [25]; Delta alpha (1e-25 cm3) this work and Lin et al. [26]; n2/n2,long this work (Ar blank; N2 0.23, O2 0.14, N2O 0.04: a derived ratio, not extracted, there is no quantity for it). The Shelton and Rice column (Ar 10.4, N2 8.1, O2 8.7) is not tabulated as n2 in Shelton and Rice; how it was computed is not stated.

TEXT (not extracted). Pulse-width study in N2 40-100 fs at constant energy (Fig. 3); the nonlinear response, instantaneous and rotational, is linear in intensity up to the ionization threshold for every gas (p. 2). Peak intensities (Fig. 2): Ar 41, N2 45, O2 14, N2O 28 TW/cm2. No higher-order Kerr terms are measured here.

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