pigeon_2016
===========

J\. J\. Pigeon, S\. Ya\. Tochitsky, E\. C\. Welch and C\. Joshi, Opt\. Lett\. 41, 3924 \(2016\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/pigeon_2016.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1364/ol\.41\.003924 <https://doi.org/10.1364/ol.41.003924>`__

**Source kind:** measurement

**Recorded technique:** Collinear nondegenerate four\-wave mixing of a dual\-line CO2\-laser beat wave \(10P20 at 10\.59 um and 10R16 at 10\.27 um, 882 GHz beat, 200 MW, 197 \+\- 21 ps FWHM, 1 Hz; UCLA Neptune laboratory\) focused by a 2\.5 m NaCl lens \(600 um 1/e^2 spot, elliptical\) into a 2 m gas cell \(25 cm interaction length\); first Stokes sideband \(10\.9 um\) isolated by grating and monochromator and measured with a cooled HgCdTe detector; background from the same pressure of He \(about 20 times smaller nonlinearity\); quantitative data at \<= 380 Torr of high\-purity gas \(dry air \< 3 ppm water\) to avoid collisional ionisation \(breakdown fluorescence above 630 Torr\); peak intensity about 15 GW/cm^2\.

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

**Dataset quantities:** nonlinear\_index

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

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

Defining equation \(p\. 2\)\: the first\-Stokes energy W\_10\.9 = k\_10\.9^2 n2,eff^2 W\_10\.6^2 W\_10\.3 A\_10\.9 / \(sqrt\(3\) tau^2\) \(int\_0^L dz / \(pi a b\)^\(3/2\)\)^2 \(Eq\. 1\), 'assuming perfect phase\-matching, negligible pump depletion, and a linear relationship between n2 and pressure'; k the wavenumber, A the \(iris\-defined, 4 mm\) area of the Stokes beam, tau the pulse length, a and b the beam axes; sqrt\(3\) because the sideband is sqrt\(3\) shorter than the pump\. n2,eff is taken from the difference of the sample and He slopes of W\_10\.9 against W\_10\.6^2 W\_10\.3 \(Fig\. 4\)\. The effective index is 'n2,eff = n2,electronic \+ n2,molecular' \(p\. 2\)\: with 200 ps pulses the rotational \(Rayleigh, Delta J = 0\) response is adiabatic, so part = total; the paper checks that the nearest Raman line \(N2 J = 4 \-\> 2 at 840 GHz, 42 GHz from the beat\) adds no resonant contribution \(p\. 2\)\. The index is the single\-beam n in n = n0 \+ n2 I implied by the FWM formula \(coefficient = self; the formula's normalisation is the paper's\)\. Uncertainty \(p\. 3\)\: least\-squares slopes of sample and background, pulse length and the beam integral, dominated by the slope fits \(level not stated\)\.

Table 1 \(tbl\_a7c0c0dc1804, 'Scaled to Atmospheric Pressure'; image checked\)\: n2,eff in 10^\-19 cm^2/W\. The pressure scaling from \<= 380 Torr is linear \(the paper's assumption\); the temperature is not stated\: 101325 Pa and 293\.15 K are assumed\. The wavelength column is labelled 10\.6 um \(the pumps are 10\.59 and 10\.27 um\)\. The 0\.8 um column is Nibbering et al\. \(J\. Opt\. Soc\. Am\. B 14, 650, 1997; ref\. 11\) and the 2\.4 um column is 'Calculated from measurements in Zahedpour et al\. using n2,eff = n2 \+ n2,rot' \(ref\. 13, Opt\. Lett\. 40, 5794, 2015; footnote b, '\+' read from the page image\)\: both long\-pulse \(total\) effective values chosen to compare with the 200 ps measurement \(as pigeon\_2018 says, p\. 4\)\. Nibbering's 0\.8 um values quoted here \(N2 3 \+\- 0\.7, O2 8 \+\- 2\.2\) are not the instantaneous ones Loriot and Wahlstrand quote from the same paper \(2\.3 and 5\.1\), consistent with Nibbering's long\-pulse \(inertial\) values; check against nibbering\_1997\. Air \(5\.0 \+\- 0\.9 at 10\.6 um; 4 \+\- 1\.1 at 0\.8 um 'calculated from measurements of N2, O2, and Ar', footnote a\) is skipped\.

Other gases \(p\. 4\)\: Kr and Xe gave symmetric FWM spectra with lower yield; no signal above noise in Ar\. Their values are in pigeon\_2018\. The asymmetric \(red\) FWM spectrum of air shows rotational Raman scattering matters for 200 ps, 10 um pulses\.

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

Datasets
--------

pigeon\_2016/fwm\_N2
~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "fwm_N2",
     "material": "N2",
     "file": "N2/pigeon_2016__fwm_N2.csv",
     "table": "tbl_a7c0c0dc1804",
     "quantity": "nonlinear_index",
     "unit": "cm2/W",
     "scale": 1e-19,
     "abscissa_unit": "um",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_k": 293.15
     },
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "part": "total",
       "coefficient": "self",
       "pulse_fs": 197000
     }
   }

Table 1, 10\.6 um column\: n2,eff \(electronic plus molecular, 200 ps\) scaled linearly from \<= 380 Torr to atmospheric pressure; 293\.15 K assumed\.

pigeon\_2016/fwm\_O2
~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "fwm_O2",
     "material": "O2",
     "file": "O2/pigeon_2016__fwm_O2.csv",
     "table": "tbl_a7c0c0dc1804",
     "quantity": "nonlinear_index",
     "unit": "cm2/W",
     "scale": 1e-19,
     "abscissa_unit": "um",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_k": 293.15
     },
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "part": "total",
       "coefficient": "self",
       "pulse_fs": 197000
     }
   }

Table 1, 10\.6 um column\: n2,eff \(electronic plus molecular, 200 ps\) scaled linearly to atmospheric pressure \(the O2 data of Fig\. 4 were taken at 250 Torr\); 293\.15 K assumed\.

pigeon\_2016/nibbering\_1997\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "nibbering_1997_N2",
     "material": "N2",
     "file": "N2/pigeon_2016__nibbering_1997_N2.csv",
     "table": "tbl_a7c0c0dc1804",
     "quantity": "nonlinear_index",
     "unit": "cm2/W",
     "scale": 1e-19,
     "abscissa_unit": "um",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_k": 293.15
     },
     "use": "reproduced",
     "reproduced_from": [
       "nibbering_1997"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "part": "total",
       "coefficient": "self"
     }
   }

Table 1, 0\.8 um column \(ref\. 11, Nibbering et al\. 1997\)\: a long\-pulse \(total\) value; the state is Pigeon's 'atmospheric pressure'\. Use the nibbering\_1997 record\.

pigeon\_2016/nibbering\_1997\_O2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "nibbering_1997_O2",
     "material": "O2",
     "file": "O2/pigeon_2016__nibbering_1997_O2.csv",
     "table": "tbl_a7c0c0dc1804",
     "quantity": "nonlinear_index",
     "unit": "cm2/W",
     "scale": 1e-19,
     "abscissa_unit": "um",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_k": 293.15
     },
     "use": "reproduced",
     "reproduced_from": [
       "nibbering_1997"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "part": "total",
       "coefficient": "self"
     }
   }

Table 1, 0\.8 um column \(ref\. 11, Nibbering et al\. 1997\)\: a long\-pulse \(total\) value\. Use the nibbering\_1997 record\.

pigeon\_2016/zahedpour\_2015\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "zahedpour_2015_N2",
     "material": "N2",
     "file": "N2/pigeon_2016__zahedpour_2015_N2.csv",
     "table": "tbl_a7c0c0dc1804",
     "quantity": "nonlinear_index",
     "unit": "cm2/W",
     "scale": 1e-19,
     "abscissa_unit": "um",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_k": 293.15
     },
     "use": "reproduced",
     "reproduced_from": [
       "zahedpour_2015"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "part": "total",
       "coefficient": "self"
     }
   }

Table 1, 2\.4 um column, footnote b\: computed by Pigeon et al\. from Zahedpour et al\.'s \(2015\) n2 and n2,rot as n2,eff = n2 \+ n2,rot \(the long\-pulse sum\), not printed by Zahedpour\. Use the zahedpour\_2015 record\.

pigeon\_2016/zahedpour\_2015\_O2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "zahedpour_2015_O2",
     "material": "O2",
     "file": "O2/pigeon_2016__zahedpour_2015_O2.csv",
     "table": "tbl_a7c0c0dc1804",
     "quantity": "nonlinear_index",
     "unit": "cm2/W",
     "scale": 1e-19,
     "abscissa_unit": "um",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_k": 293.15
     },
     "use": "reproduced",
     "reproduced_from": [
       "zahedpour_2015"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "part": "total",
       "coefficient": "self"
     }
   }

Table 1, 2\.4 um column, footnote b\: n2 \+ n2,rot computed by Pigeon et al\. from Zahedpour et al\. \(2015\)\. Use the zahedpour\_2015 record\.

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 </register>` for the checks and decisions.