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 `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1103/PhysRevA\.13\.1095 `__ **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 \, with \ = \(1/2\)\|E\(w,t\)\|^2 the cycle average \(Eqs\. 7b, 15; pp\. 1096\-1097\)\: the same per\-\ 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 \\) 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 \\) = \(pi/2\) 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 :doc:`review register ` for the checks and decisions.