loriot_2009
===========

V\. Loriot, E\. Hertz, O\. Faucher and B\. Lavorel, Opt\. Express 17, 13429 \(2009\); erratum Opt\. Express 18, 3011 \(2010\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/loriot_2009.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1364/oe\.17\.013429 <https://doi.org/10.1364/oe.17.013429>`__

**Source kind:** measurement

**Recorded technique:** Degenerate pump\-probe transient birefringence \(strong\-field polarization technique\) with a 1 kHz Ti\:sapphire amplifier, 90 fs pulses at 800 nm; pump and probe focused by one f = 20 cm lens, crossing at 4 degrees in a static gas cell; probe polarized at 45 degrees to the pump, crossed analyser, photomultiplier; homodyne detection for n2 \(low intensity\), pure heterodyne detection \(difference of two records with opposite static birefringence\) for the higher orders\. The instantaneous Kerr birefringence is calibrated against the post\-pulse field\-free rotational alignment signal of N2 and O2, computed with Delta alpha\(N2\) = 4\.6 au \(Maroulis\) and Delta alpha\(O2\) = 7\.25 au \(Hertz et al\.\) \(p\. 3\); Ar is calibrated against the N2 alignment signal recorded separately under the same conditions \(p\. 4\)\. n2 measured in 1 bar at room temperature \(Table 1 caption; Fig\. 1 caption\); the higher orders in 100 mbar \(p\. 4\)\.

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

**Dataset quantities:** nonlinear\_index

**Contents:** 6 datasets; 0 formulas.

Curation notes
--------------

The library copy is the authors' submitted manuscript \('Submitted to' on its first pages; validation\.json flags only the missing printed DOI\)\. Its Table 2 values divided by \(j \+ 1\) give exactly the published erratum's table \(loriot\_2010\), so the manuscript's numbers are those the erratum corrects\.

Defining equations \(p\. 3 and p\. 5\)\. Birefringence of the alignment\: Delta n\_rot = \(3 rho / \(4 n0 eps0\)\) Delta alpha \(\<cos^2 theta\> \- 1/3\) \(Eq\. 4\)\. 'The instantaneous Kerr effect produces a variation of the refractive index along the pump polarization axis defined by n\_kerr,par = n2 I'; with n\_kerr,perp = n2 I / 3 the birefringence is Delta n\_kerr = \(2/3\) n2 I \(p\. 3, citing Boyd\)\. The homodyne signal is fitted with Eq\. \(5\), S ~ I\_pr \(x\) \[Delta n\_rot \+ \(2/3\) n2 I\]^2, with a magnitude factor and n2 free\. At high intensity n\_kerr,par = n2 I \+ n4 I^2 \+ \.\.\. \+ n10 I^5 and Delta n\_\(2j\) = 2j/\(2j \+ 1\) n\_\(2j\) I^j \(the generalisation to j \> 2 is the authors'; p\. 5, Eq\. 6\)\. No relation to chi\(3\) or gamma is used; I is the pump intensity in TW/cm^2\.

Convention of the printed n2\: the paper presents it as the Kerr index n = n0 \+ n2 I, but the signal is the index the probe sees because of the pump \(cross\-phase modulation\)\. The authors' erratum \(loriot\_2010, Opt\. Express 18, 3011\) states that the coefficients of Eqs\. \(5\) and \(6\) 'describe therefore the cross\-Kerr refractive index experienced by the probe beam' and that the single\-beam \(self\) value is obtained by 'dividing each cross\-Kerr coefficient n\_2j \.\.\. by \(j \+ 1\)' \(valid when intrapulse alignment is negligible, below 2 % for N2 at 45 TW/cm^2\)\. Loriot et al\. 2011 \(loriot\_2011, p\. 7\) repeat it\: 'n2^cross = 2 x n2, with n2 the standard self\-induced Kerr index'\. The printed values are therefore probe coefficients; the datasets n2\_\* carry the erratum's self values through \[\[errata\]\] \(the paper's own correction\) and are labelled coefficient = self\. Wahlstrand et al\. 2013 \(Phys\. Rev\. A 87, 053801, Table I\) quote exactly the corrected values \(Ar 10\.0 \+\- 0\.9, N2 11 \+\- 2, O2 16\.0 \+\- 3\.5 x 10^\-20 cm^2/W\)\.

Part\. For N2 and O2 the rotational \(alignment\) contribution is separated by fitting the computed alignment response \(Eq\. 5\); what remains is the 'instantaneous electronic' response of the abstract, which for 90 fs pulses also contains any adiabatically following vibrational Raman part and, as Wahlstrand et al\. 2013 \(Table I and p\. 8\) show, the effectively instantaneous rotational\-grating contribution of a degenerate pump\-probe experiment \(their corrected values are N2 8\.4 \+\- 2\.0 and O2 11\.1 \+\- 3\.5 x 10^\-20 cm^2/W\)\. They are recorded as part = instantaneous\. Ar has no rotation\: part = electronic\.

Statistics \(loriot\_2011, p\. 8\)\: Table 1 results from 50, 30 and 8 records at low intensity \(effective I \< 1 TW/cm^2\) in N2, O2 and Ar\. Uncertainty\: 'two standard deviations of the fitted values over a set of experimental records' \(Table 2 caption; the erratum repeats it\); Table 1 prints the same values with no stated level \(Ar 2\.0 \+\- 0\.2 against Table 2's 2\.01 \+\- 0\.19; air 2\.4 \+\- 0\.5 against 2\.4 \+\- 0\.6\)\. The n2 of Table 2 is Table 1's \(p\. 5\: 'We first consider the index n2 as a fixed parameter in Eq\. \(6\) with the values given in Table 1'\)\.

State\: '1 bar' \(Table 1 caption\), 'room temperature' \(Fig\. 1\); the temperature is not stated and 293\.15 K is assumed here\. Fig\. 3 \(and the erratum's Fig\. 1\) caption says 'room temperature and 1 atm'; the tables say 1 bar, which is used\. Wavelength 800 nm, medium not stated\.

Higher\-order Kerr coefficients \(notes only; there is no quantity for them\)\. Table 2 as printed \(probe coefficients; units 10^\-8 cm^4/TW^2, 10^\-9 cm^6/TW^3, 10^\-11 cm^8/TW^4, 10^\-13 cm^10/TW^5; 2 sigma\)\: n4 N2 \-0\.16 \+\- 0\.08, O2 \-1\.55 \+\- 0\.16, Ar \-0\.11 \+\- 0\.31, air \-0\.45 \+\- 0\.9; n6 N2 0\.56 \+\- 0\.06, O2 1\.9 \+\- 0\.2, Ar 1\.6 \+\- 0\.2, air 0\.84 \+\- 0\.09; n8 N2 \-2\.2 \+\- 0\.2, O2 \-10\.5 \+\- 0\.7, Ar \-8\.6 \+\- 0\.5, air \-4\.0 \+\- 0\.3; n10 \(Ar only\) 5\.3 \+\- 0\.3; I\_inv \(n\_kerr,par = 0\) N2 33, O2 19, Ar 26, air 26 TW/cm^2 \(checked against the table image\)\. The erratum's self values are in loriot\_2010\. The claim \(abstract, p\. 5\-6\)\: the Kerr index saturates and becomes negative between 19 and 33 TW/cm^2 \(the erratum moves this to 25\-43 TW/cm^2\), so that the Kerr effect itself defocuses filaments\. Status\: refuted\. Wahlstrand et al\. 2013 \(wahlstrand\_2013, abstract and p\. 8\) reproduce the negative birefringence at high intensity as the plasma\-grating signal of a degenerate pump\-probe experiment \(at the paper's intensities, with the intensity scaled by 1/1\.7\); Wahlstrand et al\. 2012 \(Phys\. Rev\. Lett\. 109, 113904, wahlstrand\_2012b\) find the response of He, Ne, Ar, Kr and Xe 'quadratic in the laser field \.\.\. up to the ionization threshold', and Wahlstrand et al\. 2018 \(Phys\. Rev\. Lett\. 120, 183901\) find it 'approximately quadratic' beyond the ionization threshold in Ar, Kr, Xe, N2 and O2\. The higher\-order coefficients are not to be used\.

Air is skipped \(not a curated species\)\: n2 2\.4 \+\- 0\.6 \(Table 2\), 2\.4 \+\- 0\.5 \(Table 1\), Nibbering's 2\.9 \+\- 0\.4, 10^\-7 cm^2/TW\. The paper's comparison \(p\. 4\)\: consistent with Nibbering for N2, different for O2 and Ar; ref\. 13 \(Neogrady et al\.\) predicts 1\.5\-1\.7 x 10^\-7 cm^2/TW \(gas not stated in the sentence\)\.

**Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets
--------

loriot\_2009/n2\_N2
~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "n2_N2",
     "material": "N2",
     "file": "N2/loriot_2009__n2_N2.csv",
     "table": "tbl_732962a00e08",
     "quantity": "nonlinear_index",
     "unit": "cm2/W",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 100000.0,
       "temperature_k": 293.15
     },
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "2 sigma"
     },
     "parameters": {
       "part": "instantaneous",
       "coefficient": "self",
       "pulse_fs": 90,
       "probe_nm": 800
     }
   }

Table 2 n2 row \(= Table 1 'This work'\), printed 2\.2 \+\- 0\.4 x 10^\-7 cm^2/TW \(the probe, cross\-Kerr coefficient\); the erratum's self value 1\.1 \+\- 0\.2 applied as errata\. 1 bar; 293\.15 K assumed \(room temperature\)\. Rotation fitted out; contains the rotational\-grating part \(see the record's notes\)\.

loriot\_2009/n2\_O2
~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "n2_O2",
     "material": "O2",
     "file": "O2/loriot_2009__n2_O2.csv",
     "table": "tbl_732962a00e08",
     "quantity": "nonlinear_index",
     "unit": "cm2/W",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 100000.0,
       "temperature_k": 293.15
     },
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "2 sigma"
     },
     "parameters": {
       "part": "instantaneous",
       "coefficient": "self",
       "pulse_fs": 90,
       "probe_nm": 800
     }
   }

Table 2 n2 row \(= Table 1 'This work'\), printed 3\.2 \+\- 0\.7 x 10^\-7 cm^2/TW \(the probe, cross\-Kerr coefficient\); the erratum's self value 1\.60 \+\- 0\.35 applied as errata\. 1 bar; 293\.15 K assumed \(room temperature\)\. Rotation fitted out; contains the rotational\-grating part \(see the record's notes\)\.

loriot\_2009/n2\_Ar
~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "n2_Ar",
     "material": "Ar",
     "file": "Ar/loriot_2009__n2_Ar.csv",
     "table": "tbl_732962a00e08",
     "quantity": "nonlinear_index",
     "unit": "cm2/W",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 100000.0,
       "temperature_k": 293.15
     },
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "2 sigma"
     },
     "parameters": {
       "part": "electronic",
       "coefficient": "self",
       "pulse_fs": 90,
       "probe_nm": 800
     }
   }

Table 2 n2 row, printed 2\.01 \+\- 0\.19 x 10^\-7 cm^2/TW \(the probe, cross\-Kerr coefficient; Table 1 prints 2\.0 \+\- 0\.2\); the erratum's self value 1\.00 \+\- 0\.09 applied as errata\. Calibrated against the N2 alignment signal\. 1 bar; 293\.15 K assumed \(room temperature\)\.

loriot\_2009/nibbering\_1997\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "nibbering_1997_N2",
     "material": "N2",
     "file": "N2/loriot_2009__nibbering_1997_N2.csv",
     "table": "tbl_90188e88dc6d",
     "quantity": "nonlinear_index",
     "unit": "cm2/W",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 100000.0,
       "temperature_k": 293.15
     },
     "use": "reproduced",
     "reproduced_from": [
       "nibbering_1997"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "part": "instantaneous",
       "coefficient": "self"
     }
   }

Table 1 row 'n2 \(Ref \[2\]\)'\: Nibbering et al\., J\. Opt\. Soc\. Am\. B 14, 650 \(1997\), quoted in Loriot's units and under Loriot's '1 bar' caption\. Wahlstrand et al\. 2012 \(Table I\) quote the same value as 23 \+\- 3 x 10^\-20 cm^2/W \(sigma 0\.3, not 0\.4, in these units\)\. Use the nibbering\_1997 record\.

loriot\_2009/nibbering\_1997\_O2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "nibbering_1997_O2",
     "material": "O2",
     "file": "O2/loriot_2009__nibbering_1997_O2.csv",
     "table": "tbl_90188e88dc6d",
     "quantity": "nonlinear_index",
     "unit": "cm2/W",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 100000.0,
       "temperature_k": 293.15
     },
     "use": "reproduced",
     "reproduced_from": [
       "nibbering_1997"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "part": "instantaneous",
       "coefficient": "self"
     }
   }

Table 1 row 'n2 \(Ref \[2\]\)'\: Nibbering et al\. \(1997\), quoted under Loriot's '1 bar' caption\. Wahlstrand et al\. 2012 quote 51 \+\- 7 x 10^\-20 cm^2/W\. Use the nibbering\_1997 record\.

loriot\_2009/nibbering\_1997\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "nibbering_1997_Ar",
     "material": "Ar",
     "file": "Ar/loriot_2009__nibbering_1997_Ar.csv",
     "table": "tbl_90188e88dc6d",
     "quantity": "nonlinear_index",
     "unit": "cm2/W",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 100000.0,
       "temperature_k": 293.15
     },
     "use": "reproduced",
     "reproduced_from": [
       "nibbering_1997"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "part": "electronic",
       "coefficient": "self"
     }
   }

Table 1 row 'n2 \(Ref \[2\]\)'\: Nibbering et al\. \(1997\), quoted under Loriot's '1 bar' caption\. Wahlstrand et al\. 2012 quote 14 \+\- 2 x 10^\-20 cm^2/W\. Use the nibbering\_1997 record\.

Formulas
--------

No formulas are recorded.

Corrections
-----------

.. code-block:: text

   [
     {
       "dataset": "n2_N2",
       "row": "n2",
       "column": "value",
       "printed": "2.2",
       "corrected": "1.1",
       "reason": "The printed coefficient is the cross-Kerr index the probe sees (twice the self coefficient for n2), not the single-beam Kerr index n = n0 + n2 I the paper presents it as.",
       "evidence": "The authors' erratum, Opt. Express 18, 3011 (2010) (loriot_2010), Table 1: n2(N2) = 1.1 +- 0.2 x 10^-7 cm^2/TW, obtained by dividing each n_2j by (j + 1) (p. 1); checked on its table image. Also loriot_2011 p. 7 (n2^cross = 2 n2) and Wahlstrand et al. 2013 Table I (11 +- 2 x 10^-20 cm^2/W)."
     },
     {
       "dataset": "n2_N2",
       "row": "n2",
       "column": "sigma",
       "printed": "0.4",
       "corrected": "0.2",
       "reason": "The uncertainty of the cross-Kerr coefficient, halved with it.",
       "evidence": "loriot_2010 Table 1 (table image): 1.1 +- 0.2."
     },
     {
       "dataset": "n2_O2",
       "row": "n2",
       "column": "value",
       "printed": "3.2",
       "corrected": "1.60",
       "reason": "The printed coefficient is the cross-Kerr (probe) index, twice the self coefficient.",
       "evidence": "loriot_2010 Table 1 (table image): n2(O2) = 1.60 +- 0.35 x 10^-7 cm^2/TW; Wahlstrand et al. 2013 Table I quote 16.0 +- 3.5 x 10^-20 cm^2/W."
     },
     {
       "dataset": "n2_O2",
       "row": "n2",
       "column": "sigma",
       "printed": "0.7",
       "corrected": "0.35",
       "reason": "The uncertainty of the cross-Kerr coefficient, halved with it.",
       "evidence": "loriot_2010 Table 1 (table image): 1.60 +- 0.35."
     },
     {
       "dataset": "n2_Ar",
       "row": "n2",
       "column": "value",
       "printed": "2.01",
       "corrected": "1.00",
       "reason": "The printed coefficient is the cross-Kerr (probe) index, twice the self coefficient; 2.01 / 2 = 1.005, printed 1.00 in the erratum.",
       "evidence": "loriot_2010 Table 1 (table image): n2(Ar) = 1.00 +- 0.09 x 10^-7 cm^2/TW; Wahlstrand et al. 2013 Table I quote 10.0 +- 0.9 x 10^-20 cm^2/W."
     },
     {
       "dataset": "n2_Ar",
       "row": "n2",
       "column": "sigma",
       "printed": "0.19",
       "corrected": "0.09",
       "reason": "The uncertainty of the cross-Kerr coefficient, halved with it (0.095, printed 0.09).",
       "evidence": "loriot_2010 Table 1 (table image): 1.00 +- 0.09."
     }
   ]

Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the :doc:`review register </register>` for the checks and decisions.