lehmberg_1976#
R. H. Lehmberg, J. Reintjes and R. C. Eckardt, “Negative nonlinear susceptibility of cesium vapor around 1.06 um”, Phys. Rev. A 13, 1095 (1976)
Source record · Catalogue · Review register
Source kind: measurement
Recorded technique: Theory: the third-order density-matrix solution for the instantaneous n2 of an atomic vapour (Eq. 8) plus the inertial population terms (Eqs. 7b, 11, 20), evaluated for Cs at 1.064 um in a three-level model (6s, 6p, 7s; Eqs. 18, 24) and in full to 8s, 8p and 6d with L-S splitting (Eq. 8), dipole matrix elements from Heavens’s line strengths. Measurement: self-defocusing of single 35 ps (FWHM) mode-locked Nd:YAG pulses at 1.064 um, about 6 GW/cm2, linear and circular polarisation, in a 100 cm Cs cell at N = 0.08-0.32 x 10^17 cm^-3 (reservoir 260-305 C, cell 460 C); output energy profiles fitted at their half-maximum points by a paraxial constant-shape Gaussian beam model with measured a0, rho0 and P(t), n2 free (Eqs. 26, 27; pp. 1099-1100).
Materials in structured entries: None recorded.
Dataset quantities: None recorded.
Contents: 0 datasets; 0 formulas.
Curation notes#
Notes only: caesium is not an optmat material. Identity checked on the first page: Lehmberg, Reintjes and Eckardt, Phys. Rev. A 13 (No. 3, March 1976), 1095-1103; PDF pages 1-9 = journal pp. 1095-1103, PDF page 10 repeats Fig. 3. The library’s title reads ‘1.06 mm’ (OCR); the paper’s is 1.06 um. This is Ref. [8] of lehmberg_1995, the source of that paper’s Eqs. (1) and (3).
WHAT IT ESTABLISHES. The field is E(t) = (1/2) e E(w,t) exp(-iwt) + c.c. (Eq. 2) and the instantaneous index is delta n = n2 <E^2>, with <E^2> = (1/2)|E(w,t)|^2 the cycle average (Eqs. 7b, 15; pp. 1096-1097): the same per-<E^2> n2 as lehmberg_1995’s delta n = (1/2) n2 |E|^2 (Gaussian esu). Eq. (8) (p. 1096) gives n2 = (2 pi N / hbar) sum_beta [|P-_beta|^2/(w_beta0 - 2w) + |P+_beta|^2/(w_beta0 + 2w) + |Q_beta|^2/w_beta0] - 2 pi N [Q_0 sum_alpha R_alpha + (|P-_0|^2 - |P+_0|^2)/(2 hbar w)], with P-_beta = sum_alpha (e.mu_beta,alpha)(e.mu_alpha,0)/[hbar(w_alpha0 - w)] (Eq. 9a). Its first term is the near-two-photon-resonant chi(3). The three-level form (Eq. 18b) is n2 = n20 - n10, n20 = 2 pi N mu21^2 mu10^2/[hbar^3 (w10 - w)^2 (w20 - 2w)]; Eq. (23) splits it into the two-photon ‘polarization’ term and the coherent (adiabatic-following) population term. For circular light the s-s two-photon term vanishes (Eq. 24, n2 = -n10, p. 1098). The real two-photon population q_2 is fourth order and left out ‘unless w20 - 2w is comparable to the atomic linewidth’ (p. 1097); the inertial terms (Eq. 20, integrals over <E^2>) matter only when the pulse is not short against Gamma10^-1.
COMPARISON WITH OEP 8 EQ. (9). At degenerate frequencies OEP 8’s kernel (its Eq. 2) is M = 2 P-, so |P-|^2 = |M|^2/4 and the two-photon term is n2 = (pi/2) N |M|^2/(E_f - 2 hbar w) = (pi/2) N gamma_res with gamma_res = R_f/(Omega_f - 2w), R_f = |M|^2/hbar: OEP 8’s Eq. (9) at Gamma -> 0, given n2(esu, per <E^2>) = (pi/2) N gamma_T (Taylor gamma, Gaussian). Checked numerically (computed): the printed |mu10| = 3.16 and |mu21| = 2.92 au, 6p at 11547 cm^-1, lambda = 1.064 um and w20 - 2w = -261 cm^-1 give n20, n10, n21 = -2.364, 0.3364, -0.2561 x 10^-30 N esu (printed -2.36, 0.335, -0.256; p. 1099) with 1 au of gamma = 5.0367 x 10^-40 esu, and Table I’s three-level column (-2.70, -0.335) is n20 - n10 and -n10.
NUMBERS (Cs, 1.064 um; Table I, p. 1098, tbl_ae66cf80eb7f, n2/N in 10^-30 esu): measured -1.5 +- 0.02 (linear, a: integral terms ignored), -1.4 +- 0.2 (b: divided by 1 + eta, eta = 0.08), circular -0.35 +- 0.04 and -0.26 +- 0.03 (eta = 0.36); calculated -2.70 and -0.335 (three-level), -2.62 and -0.525 (Eq. 8); Miles and Harris -0.66 (linear). The measurement is 0.53 of the full calculation for linear light; the authors put the gap on N (vapour-pressure tables, perhaps 2 times too high) or P(t), and on Heavens’s oscillator strengths (about 5 % high, so the theory up to 10 % high); the ratio linear/circular, free of N, agrees within 8 % (5.4 against 5.0; p. 1101). Gamma10^-1 about 80 ps at 0.32 x 10^17 cm^-3 (p. 1099; Chen and Phelps, Ref. 25).
DOUBT. Table I prints the linear value of column a as ‘-1.5 +- 0.02’ (checked on the page image), against +- 0.2 in column b after only an 8 % adjustment: probably a misprint for +- 0.2. No value is taken, so no erratum.
NOT TAKEN (no material): every number above; the Cs dimer absorption (sigma_D about 4 x 10^-16 cm^2, Eq. 29) and the two- and four-photon absorption estimates quoted from Miles and Harris and Morton (p. 1101). The paper has no noble-gas data. The noble-gas use is the equation and its convention (OEP 8, Q1); the register entry records the 6p[1/2]0 strength that lehmberg_1995’s own Eq. (3) implies through it.
Register: TC-997.
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
No datasets are recorded.
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.