bree_2011 ========= C\. Bree, A\. Demircan and G\. Steinmeyer, Phys\. Rev\. Lett\. 106, 183902 \(2011\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1103/physrevlett\.106\.183902 `__ **Source kind:** theory **Recorded technique:** Kerr coefficients n\_2k computed by a Kramers\-Kronig transform of \(k \+ 1\)\-photon ionisation cross sections from a modified PPT \(Keldysh\) theory \(Eq\. 1\), with the nondegenerate absorption approximated by the degenerate one at the mean frequency \(Eq\. 2\); a one\-parameter model \(the ionisation potential\) for the noble gases, extended to O2 and N2 with Talebpour's effective charge \(Z\_eff = 0\.53 and 0\.9; curated as talebpour\_1999\)\. **Materials in structured entries:** Ar, He, Kr, Ne, O2, Xe **Dataset quantities:** nonlinear\_index **Contents:** 11 datasets; 0 formulas. Curation notes -------------- Defining equations\. Eq\. \(3\), p\. 2\: n\_2k\(w\) = \(hbar c rho\_nt / pi\) P int\_0^inf \(Omega \+ k w\) sigma\_\(k\+1\)\(\(Omega \+ k w\)/\(k \+ 1\)\) / \(Omega^2 \- w^2\) dOmega \(P\: Cauchy principal value\); the K\-photon absorption coefficient Delta alpha\_K\(w\) = K hbar w rho\_nt sigma\_K I^\(K\-1\), 'with a particle density rho\_nt = 2\.7 x 10^19 cm^\-3 corresponding to standard conditions' \(p\. 1, checked on the page image\)\. The index is n = n0 \+ n2 I \+ n4 I^2 \+ \.\.\. \(p\. 1 and Fig\. 3\), a single\-beam \(self\) coefficient\. The companion paper bree\_2012 \(Eq\. 10\) gives the relation to chi\: n\_2k = 2^\(k\-1\) C^\(k\) / \(n0 \(n0 eps0 c\)^k\) Re chi^\(2k\+1\), C^\(k\) = \(2k \+ 1\)\!/\(2^\(2k\) k\! \(k \+ 1\)\!\), and gamma^\(3\)\(0\) = 8 eps0^2 c n2\(0\) / rho0 \(Eq\. 18\)\. Table I \(tbl\_3d9fe63acf83; JSON cells, no CSV; equal to the table image\)\: n2 in 10^\-8 cm^2/TW of the neutral atoms at 800 nm \(Z = 1\) and in the static limit, of the singly charged ions \(Z = 2\: skipped, not curated species\), and 'Experimental data \(rightmost column\) as compiled from \[18,21\] and corrected for the dispersion of the DFWM process with Eq\. \(13\) in \[20\]' \(\[18\] Bishop & Pipin, J\. Chem\. Phys\. 91, 3549 \(1989\); \[21\] Shelton & Rice, Chem\. Rev\. 94, 3 \(1994\); \[20\] Bree et al\., IEEE J\. Quantum Electron\. 46, 433 \(2010\), not in the library\)\. The model columns are datasets kk\_\ \(rows 800nm and static, use = check\: a semi\-empirical model whose authors quote agreement of 26 % \(He\), 15 % \(Ne, Kr, Xe\) and better \(Ar\) with reference data, p\. 2\); the reference column is refs\_\ \(reproduced\)\. The reference column is the static limit\: the text compares the model's long\-wavelength He value 4\.8 x 10^\-9 cm^2/TW with '3\.8 x 10^\-9 cm^2/TW that was derived in \[18\]' \(p\. 2\), and the column equals gamma0 x 8\.911e\-23 cm^2/W per au \(N gamma\_T / \(8 eps0^2 c\) at the Loschmidt density\), with gamma0 = 43\.104 \(He\), 108 \(Ne\), 1167 \(Ar\), 2600 \(Kr\), 6888 au \(Xe\) as tabulated from Shelton & Rice and Bishop & Pipin\: 0\.3841, 0\.962, 10\.399, 23\.17, 61\.38 against 0\.38, 0\.96, 10\.40, 23\.17, 61\.39 \(checked 2026\-09\-26\)\. So it is gamma0 in Shelton & Rice's T convention converted to n2 at 1 atm and 0 C, whatever 'corrected for the dispersion of the DFWM process' means\. Other values in the text\: O2 long\-wavelength limit n2\(w \-\> 0\) = 0\.7 x 10^\-7 cm^2/TW from the model with Z\_eff = 0\.53 \(dataset kk\_static\_O2\), 'which agrees excellently with the electronic contribution of n2 = 0\.746 x 10^\-7 cm^2/TW computed in \[28\]' \(Hellwarth, Pennington & Henesian, Phys\. Rev\. A 41, 2766 \(1990\); record hellwarth\_1990; not duplicated here\) \(p\. 3, page image checked\)\. He\: the n2 maximum is about 4 x 10^\-8 cm^2/TW near 100 nm, the zero crossing at 85 nm, negative up to 50\.4 nm \(p\. 2\); Ar\: about 10^\-7 cm^2/TW in the infrared, zero crossing at 140 nm \(p\. 2\)\. Neutral Ar against Ar\+ with ionisation\: 'from n2 = 1\.3 x 10^\-7 cm^2/W at p = 0 to n2 = 0\.6 x 10^\-7 cm^2 at p = 1' \(p\. 4\)\: the units are misprinted \(cm^2/TW, as Table I's 12\.68 and 6\.14 x 10^\-8 show\); text only, nothing extracted\. Higher\-order Kerr claim \(notes only\)\: the model gives n4 of Ar with an infrared limit of 2 x 10^\-12 cm^4/TW^2, 12 times higher at 240 nm, negative below 210 nm \(p\. 3; page image checked\), positive n\_2k up to n18 at 800 nm and negative beyond, and an Ar index that saturates near 42 TW/cm^2 and inverts at 49 TW/cm^2 \(Loriot\: 30 and 34\), with inversion intensities of 112, 89, 40 and 30 TW/cm^2 for He, Ne, Kr, Xe \(p\. 3\); a negative n4 at 800 nm \(Loriot's \-0\.36 \+\- 1\.03 x 10^\-9 cm^4/TW^2\) 'appears to be incompatible' with the model\. The coefficients n2 \.\.\. n32 are in the supplement, not in the library\. Status\: the premise \(MPI\-rate expansion as the absorption in the KK integral\) is criticised by Wahlstrand et al\. 2012 \(Phys\. Rev\. Lett\. 109, 113904, p\. 2\-3\), who show that with the full ionisation rate the KK response stays linear in I up to ionisation and that the MPI model 'strongly overestimates' the low\-frequency absorption at high intensity, 'the source of the saturation and inversion calculated in \[12,13\]'\. The n2 \(k = 1\) values are not affected by that criticism; the higher orders are not to be used\. Wavelengths\: 800 nm, medium not stated \(vacuum assumed\)\. **Recorded bibliographic identity status:** VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- bree\_2011/kk\_He ~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "kk_He", "material": "He", "file": "He/bree_2011__kk_He.csv", "table": "tbl_3d9fe63acf83", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-20, "abscissa_unit": "nm", "state": "1atm_0C", "density": "ideal", "use": "check", "parameters": { "part": "electronic", "coefficient": "self" } } Table I, Z = 1 \(800 nm\) and n2\(w \-\> 0\) \(static\) columns, 10^\-8 cm^2/TW = 10^\-20 cm^2/W, at rho\_nt = 2\.7e19 cm^\-3 \('standard conditions', read as 1 atm and 0 C with the rounded Loschmidt number\)\. Kramers\-Kronig model, not a measurement\. The model's 800 nm row is repeated \(rounded\) in bree\_2012 Table I\. bree\_2011/kk\_Ne ~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "kk_Ne", "material": "Ne", "file": "Ne/bree_2011__kk_Ne.csv", "table": "tbl_3d9fe63acf83", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-20, "abscissa_unit": "nm", "state": "1atm_0C", "density": "ideal", "use": "check", "parameters": { "part": "electronic", "coefficient": "self" } } Table I, Z = 1 \(800 nm\) and static columns; Kramers\-Kronig model at rho\_nt = 2\.7e19 cm^\-3\. bree\_2011/kk\_Ar ~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "kk_Ar", "material": "Ar", "file": "Ar/bree_2011__kk_Ar.csv", "table": "tbl_3d9fe63acf83", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-20, "abscissa_unit": "nm", "state": "1atm_0C", "density": "ideal", "use": "check", "parameters": { "part": "electronic", "coefficient": "self" } } Table I, Z = 1 \(800 nm\) and static columns; Kramers\-Kronig model at rho\_nt = 2\.7e19 cm^\-3\. bree\_2011/kk\_Kr ~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "kk_Kr", "material": "Kr", "file": "Kr/bree_2011__kk_Kr.csv", "table": "tbl_3d9fe63acf83", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-20, "abscissa_unit": "nm", "state": "1atm_0C", "density": "ideal", "use": "check", "parameters": { "part": "electronic", "coefficient": "self" } } Table I, Z = 1 \(800 nm\) and static columns; Kramers\-Kronig model at rho\_nt = 2\.7e19 cm^\-3\. bree\_2011/kk\_Xe ~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "kk_Xe", "material": "Xe", "file": "Xe/bree_2011__kk_Xe.csv", "table": "tbl_3d9fe63acf83", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-20, "abscissa_unit": "nm", "state": "1atm_0C", "density": "ideal", "use": "check", "parameters": { "part": "electronic", "coefficient": "self" } } Table I, Z = 1 \(800 nm\) and static columns; Kramers\-Kronig model at rho\_nt = 2\.7e19 cm^\-3\. bree\_2011/kk\_static\_O2 ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "kk_static_O2", "material": "O2", "table": "text", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-19, "abscissa_unit": "nm", "state": "1atm_0C", "density": "ideal", "use": "check", "parameters": { "part": "electronic", "coefficient": "self" } } 1 inline points in the source record. Text p\. 3\: 'For oxygen, our theory yields a long\-wavelength limit n2\(w \-\> 0\) = 0\.7 x 10^\-7 cm^2/TW' \(page image checked\), with Talebpour's Z\_eff = 0\.53; rho\_nt = 2\.7e19 cm^\-3 as for the atoms \(assumed\: the O2 density is not restated\)\. bree\_2011/refs\_He ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "refs_He", "material": "He", "file": "He/bree_2011__refs_He.csv", "table": "tbl_3d9fe63acf83", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-20, "abscissa_unit": "nm", "state": "1atm_0C", "density": "ideal", "use": "reproduced", "reproduced_from": [ "bishop_1989", "shelton_1994" ], "parameters": { "part": "electronic", "coefficient": "self" } } Table I 'Refs\. \[18,21\]' column\: the static gamma0 of the reference literature converted to n2 at the Loschmidt density \(0\.3841 from 43\.104 au; see the record's notes\)\. He is presumably Bishop & Pipin's value \[18\]; the paper does not say which reference gives which gas\. bree\_2011/refs\_Ne ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "refs_Ne", "material": "Ne", "file": "Ne/bree_2011__refs_Ne.csv", "table": "tbl_3d9fe63acf83", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-20, "abscissa_unit": "nm", "state": "1atm_0C", "density": "ideal", "use": "reproduced", "reproduced_from": [ "shelton_1994", "bishop_1989" ], "parameters": { "part": "electronic", "coefficient": "self" } } Table I 'Refs\. \[18,21\]' column\: static gamma0 \(108 au\) converted to n2 at the Loschmidt density \(see the record's notes\)\. bree\_2011/refs\_Ar ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "refs_Ar", "material": "Ar", "file": "Ar/bree_2011__refs_Ar.csv", "table": "tbl_3d9fe63acf83", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-20, "abscissa_unit": "nm", "state": "1atm_0C", "density": "ideal", "use": "reproduced", "reproduced_from": [ "shelton_1994", "bishop_1989" ], "parameters": { "part": "electronic", "coefficient": "self" } } Table I 'Refs\. \[18,21\]' column\: static gamma0 \(1167 au\) converted to n2 at the Loschmidt density \(see the record's notes\)\. bree\_2011/refs\_Kr ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "refs_Kr", "material": "Kr", "file": "Kr/bree_2011__refs_Kr.csv", "table": "tbl_3d9fe63acf83", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-20, "abscissa_unit": "nm", "state": "1atm_0C", "density": "ideal", "use": "reproduced", "reproduced_from": [ "shelton_1994", "bishop_1989" ], "parameters": { "part": "electronic", "coefficient": "self" } } Table I 'Refs\. \[18,21\]' column\: static gamma0 \(2600 au\) converted to n2 at the Loschmidt density \(see the record's notes\)\. bree\_2011/refs\_Xe ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "refs_Xe", "material": "Xe", "file": "Xe/bree_2011__refs_Xe.csv", "table": "tbl_3d9fe63acf83", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-20, "abscissa_unit": "nm", "state": "1atm_0C", "density": "ideal", "use": "reproduced", "reproduced_from": [ "shelton_1994", "bishop_1989" ], "parameters": { "part": "electronic", "coefficient": "self" } } Table I 'Refs\. \[18,21\]' column\: static gamma0 \(6888 au\) converted to n2 at the Loschmidt density \(see the record's notes\)\. 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.