bree_2012 ========= C\. Bree, A\. Demircan and G\. Steinmeyer, Phys\. Rev\. A 85, 033806 \(2012\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1103/physreva\.85\.033806 `__ **Source kind:** theory **Recorded technique:** The Kramers\-Kronig model of bree\_2011 \(n\_2k from \(k \+ 1\)\-photon PPT ionisation cross sections, nondegenerate absorption at the mean frequency\) applied to the n2 dispersion of all noble gases, the saturation of the intensity\-dependent index, its wavelength dependence and the radius of convergence of the series\. **Materials in structured entries:** Ar, He, Kr, Ne, Xe **Dataset quantities:** nonlinear\_index **Contents:** 5 datasets; 0 formulas. Curation notes -------------- Defining equations \(p\. 2\-5\)\. n\(I\) = sum\_\(k\>=0\) n\_2k I^k \(Eq\. 1; self coefficients, degenerate case\)\. Eq\. \(10\)\: n\_2k = 2^\(k\-1\) C^\(k\) / \(n0 \(n0 eps0 c\)^k\) Re chi^\(2k\+1\), with C^\(k\) = \(2k \+ 1\)\! / \(2^\(2k\) k\! \(k \+ 1\)\!\) \(Eq\. 12\); for k = 1, n2 = 3 Re chi^\(3\) / \(4 n0^2 eps0 c\)\. Eq\. \(11\)\: beta\_K = \(w0/c\) 2^\(K\-1\) C^\(K\-1\) / \(n0 \(n0 eps0 c\)^\(K\-1\)\) Im chi^\(2K\-1\); Eq\. \(13\)\: beta\_K = K rho0 hbar w sigma\_K\. Eq\. \(16\)\: n\_2k\(w\) = \(rho0 hbar c / pi\) P int\_0^inf \(Omega \+ k w\) sigma\_\(k\+1\)\(\(Omega \+ k w\)/\(k \+ 1\)\) / \(Omega^2 \- w^2\) dOmega \(the same as bree\_2011 Eq\. 3\)\. Eq\. \(18\)\: gamma^\(3\)\(0\) = 8 eps0^2 c n2\(0\) / rho0 'using the Lorentz\-Lorenz law' in the far\-infrared limit, i\.e\. n2 = rho0 gamma / \(8 eps0^2 c\) with n0 = 1\: Shelton & Rice's Taylor \(T\) convention \(p = \.\.\. \+ gamma E^3/6\), the relation of the manual page Third\-order nonlinearity\. Eq\. \(17\) quotes Bishop's dispersion n2\(w\) = n2\(0\) \(1 \+ A w\_L^2 \+ B w\_L^4 \+ \.\.\.\), w\_L^2 = nu w^2 with nu = 12, 6, 4 for THG, ESHG and DFWM, 'the far\-infrared limit n2 ~ chi\(3\)\(0; 0, 0, 0\) and the coefficient A do not depend on the nonlinear optical process' \(p\. 3\)\. rho0 is not restated; the 2011 paper's rho\_nt = 2\.7e19 cm^\-3 \('standard conditions'\) is assumed\. Ionisation potentials used\: 24\.59, 21\.56, 15\.76, 14\.00, 12\.13 eV; two\-photon edges lambda\_TPA = 101, 115, 157, 177 and 204 nm \(He \.\.\. Xe\) \(p\. 4\)\. Table I \(tbl\_934361b8054e, image checked\)\: 'n2 values in cm^2/TW for characteristic wavelength emitted by various laser materials', 193, 248, 400, 800 and 2000 nm, He \.\.\. Xe, printed m\(e\) = m x 10^e\. Extracted as kk\_\ \(5 points each; use = check, a model; its authors state agreement within 20 % of the reference data in the infrared, within 10 % for Ar and Kr from 0\.2 to 6 um, p\. 4\)\. The 800 nm row equals bree\_2011's Table I Z = 1 column rounded to two digits \(5\.2, 13, 130, 310, 920 against 5\.2, 13\.1, 126\.8, 306\.9, 915\.8 x 10^\-9 cm^2/TW\) and is excluded as a duplicate\. Xe at 193 nm lies beyond Xe's two\-photon edge \(204 nm\) and Xe at 248 nm is near a bound two\-photon resonance \(measured strongly negative there, Lehmberg et al\. 1995, not in the library\), which the ionisation\-based model does not contain \(it has no bound\-state resonances\)\: do not trust the UV rows near bound two\-photon resonances\. Table II \(tbl\_150d29e385da, notes only\)\: inversion intensities I\_inv \(the nontrivial root of sum n\_2k I^k = 0\) against the plasma clamping intensity I\_c \(90 fs Gaussian pulses\) at 800 nm\: He 113/301, Ne 89/204, Ar 49/81, Kr 40/57, Xe 30/37, O2 36/44, N2 50/82 TW/cm^2\. Higher\-order Kerr claim \(notes only\)\: the saturation and inversion of the index 'stems from much higher orders' \(for Ar at 800 nm chi\(21\) and above; chi\(5\) \.\.\. chi\(19\) do not contribute, p\. 7\); the series converges for Keldysh gamma \> e/2 \(Eq\. 28\); I\_inv\(lambda\) crosses the clamping intensity near 560 nm, so HOKE\-dominated filaments are predicted in the infrared\. The coefficients n2 \.\.\. n32 are in bree\_2011's supplement \(not in the library\)\. Status\: the saturation follows from using multiphoton\-ionisation rates beyond their validity in the KK integral \(Wahlstrand et al\. 2012, Phys\. Rev\. Lett\. 109, 113904, p\. 2\-3\: with the full rate the KK response is linear in intensity, as measured up to ionisation\)\. Not to be used\. Second copy\: Unverified\_df851ddaf7be is the WIAS Berlin preprint No\. 1651 of this paper \(ISSN 0946\-8633, 'submitted\: October 6, 2011'; identified from its first page\)\. Its Table 1 prints the same values as 7\.8e\-9 etc\. with one misprint, Kr at 2000 nm '2\.7e\.7' \(journal 2\.7\(\-7\)\); its Table 2 equals Table II\. Not extracted twice\. **Recorded bibliographic identity status:** VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- bree\_2012/kk\_He ~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "kk_He", "material": "He", "file": "He/bree_2012__kk_He.csv", "table": "tbl_934361b8054e", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-12, "abscissa_unit": "nm", "state": "1atm_0C", "density": "ideal", "use": "check", "excluded_rows": { "800": "The 800 nm row repeats bree_2011 Table I (Z = 1), rounded; use that one." }, "parameters": { "part": "electronic", "coefficient": "self" } } Table I, n2 in cm^2/TW \(printed m\(e\), stored as me e\) at 193, 248, 400, 800, 2000 nm\. Kramers\-Kronig model; density assumed 2\.7e19 cm^\-3 as in bree\_2011\. bree\_2012/kk\_Ne ~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "kk_Ne", "material": "Ne", "file": "Ne/bree_2012__kk_Ne.csv", "table": "tbl_934361b8054e", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-12, "abscissa_unit": "nm", "state": "1atm_0C", "density": "ideal", "use": "check", "excluded_rows": { "800": "The 800 nm row repeats bree_2011 Table I (Z = 1), rounded; use that one." }, "parameters": { "part": "electronic", "coefficient": "self" } } Table I, n2 in cm^2/TW at 193, 248, 400, 800, 2000 nm\. Kramers\-Kronig model\. bree\_2012/kk\_Ar ~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "kk_Ar", "material": "Ar", "file": "Ar/bree_2012__kk_Ar.csv", "table": "tbl_934361b8054e", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-12, "abscissa_unit": "nm", "state": "1atm_0C", "density": "ideal", "use": "check", "excluded_rows": { "800": "The 800 nm row repeats bree_2011 Table I (Z = 1), rounded; use that one." }, "parameters": { "part": "electronic", "coefficient": "self" } } Table I, n2 in cm^2/TW at 193, 248, 400, 800, 2000 nm\. Kramers\-Kronig model\. bree\_2012/kk\_Kr ~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "kk_Kr", "material": "Kr", "file": "Kr/bree_2012__kk_Kr.csv", "table": "tbl_934361b8054e", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-12, "abscissa_unit": "nm", "state": "1atm_0C", "density": "ideal", "use": "check", "excluded_rows": { "800": "The 800 nm row repeats bree_2011 Table I (Z = 1), rounded; use that one." }, "parameters": { "part": "electronic", "coefficient": "self" } } Table I, n2 in cm^2/TW at 193, 248, 400, 800, 2000 nm\. Kramers\-Kronig model\. bree\_2012/kk\_Xe ~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "kk_Xe", "material": "Xe", "file": "Xe/bree_2012__kk_Xe.csv", "table": "tbl_934361b8054e", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-12, "abscissa_unit": "nm", "state": "1atm_0C", "density": "ideal", "use": "check", "excluded_rows": { "800": "The 800 nm row repeats bree_2011 Table I (Z = 1), rounded; use that one.", "193": "Beyond Xe's two-photon edge (204 nm, p. 4); the model has no bound-state resonances." }, "parameters": { "part": "electronic", "coefficient": "self" } } Table I, n2 in cm^2/TW at 193, 248, 400, 800, 2000 nm\. Kramers\-Kronig model; the 248 nm value ignores the bound two\-photon resonance near which Xe's measured n2 is negative \(Lehmberg et al\. 1995, not in the curators' library\)\. 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.