reichert_2015
=============

M\. Reichert, P\. Zhao, J\. M\. Reed, T\. R\. Ensley, D\. J\. Hagan and E\. W\. Van Stryland, "Beam deflection measurement of bound\-electronic and rotational nonlinear refraction in molecular gases", Opt\. Express 23, 22224 \(2015\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/reichert_2015.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1364/OE\.23\.022224 <https://doi.org/10.1364/OE.23.022224>`__

**Source kind:** measurement

**Recorded technique:** Polarization\-resolved beam deflection \(excite\-probe\)\: 800\-nm, 83\-fs excitation \(w\_e = 177 um\) and a 650\-nm white\-light\-continuum probe \(40 nm FWHM, 265 fs, w\_0,p = 60 um\) crossing at \<= 1 degree in ambient laboratory air; the probe's deflection measured by a quadrant photodiode versus delay \(to 2 ns\)\. Probe at 0, 90 and 54\.7 degrees \(the magic angle removes the rotational part\)\. The interaction length \(6\.5 cm\) is not characterized and is fitted\: the electronic part is measured relative to the rotational revivals, whose size is fixed by literature Delta alpha values \(self\-reference\)\. CS2 vapour \(1250\-nm excitation, 950\-nm probe\) likewise \(pp\. 22227\-22233\)\.

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

**Dataset quantities:** polarizability\_anisotropy, rotational\_constant

**Contents:** 10 datasets; 0 formulas.

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

Journal pages 22224\-22237 = PDF pages 1\-14\. Identity checked against the first page\.

NOTHING CURATED IS MEASURED\. The only n2 is of ambient AIR\: n2,el\(air\) = \(10 \+\- 2\) x 10^\-24 m2/W \(magic angle, 800 nm, 83 fs; p\. 22233\), with Table 2 comparing Wahlstrand et al\. \[48\] 7\.9 \+\- 1\.0, Liu and Chin \[49\] 9\.6 and a Shelton\-and\-Rice\-based 9\.1 \(1e\-24 m2/W\), and an air\-averaged gamma \(1\.25 \+\- 0\.20\) x 10^\-62 C^4 m^4/J^3 \(the text says \+\- 0\.10\) = \(10\.1 \+\- 2\.0\) x 10^\-37 esu against 0\.78 gamma\(N2\) \+ 0\.21 gamma\(O2\) \+ 0\.01 gamma\(Ar\) with N = 2\.5e19 cm^\-3\. Air is not curated\: not extracted\. CS2 \(not curated\)\: gamma\(gas\) = \(19 \+\- 4\) x 10^\-62 C^4 m^4/J^3, B and D of three species \(Table 3\), not extracted\.

DEFINING EQUATIONS \(SI; pp\. 22227\-22228\)\. Eq\. \(1\)\: Delta n\_rot\(t\) = \[N Delta alpha / \(2 eps0 n0\)\] \(\<cos^2 theta\(t\)\> \- 1/3\)\. Eq\. \(2\)\: Delta n\(t\) = 2 n2,el I\_e\(t\) \+ \(c N / 4\) \(Delta alpha\)^2 sum\_J T\_J int I\_e\(t'\) sin\(omega\_\(J,J\-2\)\(t \- t'\)\) exp\(\-Gamma\_\(J,J\-2\)\(t \- t'\)\) dt', T\_J = \(2 / 15 hbar\) J\(J \- 1\)/\(2J \- 1\) \(rho\_JJ \- rho\_\(J\-2,J\-2\)\) \(Eq\. \(3\)\); 'The factor of 2 in the first term arises from interference of the two beams doubling the phase change \[32\]' \(nondegenerate probe; absent from the rotational term\)\: n2,el is the SELF coefficient\. Eq\. \(4\)\: mu = mu\(0\) \+ alpha E \+ beta E^2 \+ gamma E^3, the field being E0\(omega\) cos\(k\.r \- omega t\) \(no 1/2 or 1/6\: the perturbation\-series convention\)\. Eq\. \(5\)\: n2,el = \[3 N / \(4 eps0^2 c n0 n0,e\)\] f\(3\) Re\<gamma\>, f\(3\) = \[\(n0^2 \+ 2\)/3\]^2 \[\(n0,e^2 \+ 2\)/3\]^2 the Lorentz\-Lorenz local\-field factor \(~1 in dilute gases\)\. Eq\. \(8\)\: Delta n\_el / Delta n\_rot proportional to gamma / \(Delta alpha\)^2\. Eqs\. \(9\)\-\(11\)\: Delta n\(0\) = Delta n\_el \+ Delta n\_rot, Delta n\(90\) = Delta n\_el/3 \- Delta n\_rot/2, Delta n\(54\.7\) = 5 Delta n\_el / 9\.

TABLE 1 \(p\. 22232; image checked; extracted by tools/extract/reichert\_2015\.py\)\: Delta alpha \(1e\-40 F m2\) N2 0\.77, O2 1\.21, marked '\[35\]' = Bridge and Buckingham, Proc\. R\. Soc\. London A 295, 334 \(1966\) \(not in the library\)\: values used, not measured \(the fit of the air revivals 'gives a good determination of the ratio Delta alpha\(O2\)/Delta alpha\(N2\), that agrees well with the values in \[35\]', p\. 22230\)\. Recorded as reproduced, unit 'SI' \(F m2 = C m2/V\), no stated wavelength \(abscissa 'not stated'\)\. Fitted constants\: 14N2 B = 1\.9896\(2\) cm^\-1, D = 5\.9\(6\) x 10^\-6 cm^\-1 \(Raman\: 1\.989574\(12\), 5\.76\(3\)\); 16O2 B = 1\.4377\(2\), D = 5\.1\(5\) \(1\.437682\(9\), 4\.852\(12\)\)\: now extracted \(2026\-09\-26\) as the B\_fit\_\*, D\_fit\_\* datasets \(check\) and the Raman columns as reproductions\. J\-dependent dephasing rates in Fig\. 4 only\. The group velocity in air uses n0,e = 1\.000275 \(Ciddor\)\.

TABLE 1 B AND D \(p\. 22232; image and text layer checked\)\. The table's column marks a and b have no footnote in the paper; the text says\: 'The values of B and D found from fitting are given in Table 1 for each molecule, which shows a comparison to Raman scattering measurements \[41\]' \(p\. 22232\), \[41\] = A\. Weber, 'High\-resolution rotational Raman spectra of gases', in Raman Spectroscopy of Gases and Liquids \(Springer, 1979\), curated as weber\_1979 \(Chap\. 3, Table 3\.2\)\. So a = this work \(the fit of the Fourier\-transformed air revivals to 300 ps, Fig\. 3, with Eq\. \(2\) and centrifugal distortion\), b = Weber's Raman values\. The digits in parentheses are the uncertainty in the last digit\(s\) \(level not stated\)\. The fitted constants are effective values of the v = 0 rotational ladder of each molecule in ambient air \(~1 atm, room temperature\); for O2 the model counts 'only odd J values' \(p\. 22231\) and does not mention the electron\-spin \(fine\-structure\) splitting\. The 14N2 Raman column is digit\-identical to bendtsen\_1974's pure rotational B\_0 and D \(Table VII\), so it is recorded as reproduced from bendtsen\_1974 \(through Weber\); the 16O2 column's original is not identified \(reproduced from Weber\)\. The fitted values agree with the Raman ones well within their stated uncertainties\: B\(N2\) 1\.9896\(2\) against 1\.989574 \(\+0\.13 of the stated 0\.0002\), B\(O2\) 1\.4377\(2\) against 1\.437682 \(\+0\.09\), D\(N2\) 5\.9\(6\) against 5\.76, D\(O2\) 5\.1\(5\) against 4\.852 \(both within 0\.5 of theirs\)\.

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

Datasets
--------

reichert\_2015/dalpha\_bridge\_buckingham\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dalpha_bridge_buckingham_N2",
     "material": "N2",
     "file": "N2/reichert_2015__dalpha_bridge_buckingham_N2.csv",
     "table": "tbl_f40cb41739d3",
     "quantity": "polarizability_anisotropy",
     "unit": "SI",
     "scale": 1e-40,
     "abscissa_unit": "nm",
     "use": "reproduced",
     "reproduced_from": [
       "N. J. Bridge and A. D. Buckingham, Proc. R. Soc. Lond. A 295, 334 (1966)"
     ]
   }

Table 1, Delta alpha '0\.77 \[35\]' in 1e\-40 F m2 \(SI polarizability, C m2/V\)\. The self\-reference of the measurement, not a result\. Wavelength not stated\.

reichert\_2015/dalpha\_bridge\_buckingham\_O2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dalpha_bridge_buckingham_O2",
     "material": "O2",
     "file": "O2/reichert_2015__dalpha_bridge_buckingham_O2.csv",
     "table": "tbl_f40cb41739d3",
     "quantity": "polarizability_anisotropy",
     "unit": "SI",
     "scale": 1e-40,
     "abscissa_unit": "nm",
     "use": "reproduced",
     "reproduced_from": [
       "N. J. Bridge and A. D. Buckingham, Proc. R. Soc. Lond. A 295, 334 (1966)"
     ]
   }

Table 1, Delta alpha '1\.21 \[35\]' in 1e\-40 F m2\. As dalpha\_bridge\_buckingham\_N2\.

reichert\_2015/B\_fit\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "B_fit_N2",
     "material": "N2",
     "file": "N2/reichert_2015__B_fit_N2.csv",
     "table": "tbl_f40cb41739d3",
     "quantity": "rotational_constant",
     "unit": "cm-1",
     "abscissa": "label",
     "use": "check",
     "parameters": {
       "constant": "B",
       "vibrational_state_v": 0
     },
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table 1 \(p\. 22232\), column 'B \(cm\-1\)a'\: 1\.9896\(2\), fitted to the rotational Raman spectrum \(Fourier transform of the beam\-deflection signal\) of 14N2 in ambient air; the \(2\) is the uncertainty in the last digit, level not stated\. An effective v = 0 constant\.

reichert\_2015/D\_fit\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "D_fit_N2",
     "material": "N2",
     "file": "N2/reichert_2015__D_fit_N2.csv",
     "table": "tbl_f40cb41739d3",
     "quantity": "rotational_constant",
     "unit": "cm-1",
     "scale": 1e-06,
     "abscissa": "label",
     "use": "check",
     "parameters": {
       "constant": "D",
       "vibrational_state_v": 0
     },
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table 1 \(p\. 22232\), column 'D \(10\-6 cm\-1\)a'\: 5\.9\(6\) x 1e\-6 cm^\-1, fitted as B\_fit\_N2; level not stated\.

reichert\_2015/B\_fit\_O2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "B_fit_O2",
     "material": "O2",
     "file": "O2/reichert_2015__B_fit_O2.csv",
     "table": "tbl_f40cb41739d3",
     "quantity": "rotational_constant",
     "unit": "cm-1",
     "abscissa": "label",
     "use": "check",
     "parameters": {
       "constant": "B",
       "vibrational_state_v": 0
     },
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table 1 \(p\. 22232\), column 'B \(cm\-1\)a'\: 1\.4377\(2\) for 16O2, fitted as B\_fit\_N2 \(the O2 spin splitting not modelled\); level not stated\.

reichert\_2015/D\_fit\_O2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "D_fit_O2",
     "material": "O2",
     "file": "O2/reichert_2015__D_fit_O2.csv",
     "table": "tbl_f40cb41739d3",
     "quantity": "rotational_constant",
     "unit": "cm-1",
     "scale": 1e-06,
     "abscissa": "label",
     "use": "check",
     "parameters": {
       "constant": "D",
       "vibrational_state_v": 0
     },
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table 1 \(p\. 22232\), column 'D \(10\-6 cm\-1\)a'\: 5\.1\(5\) x 1e\-6 cm^\-1 for 16O2; level not stated\.

reichert\_2015/B\_raman\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "B_raman_N2",
     "material": "N2",
     "file": "N2/reichert_2015__B_raman_N2.csv",
     "table": "tbl_f40cb41739d3",
     "quantity": "rotational_constant",
     "unit": "cm-1",
     "abscissa": "label",
     "use": "reproduced",
     "reproduced_from": [
       "bendtsen_1974",
       "weber_1979"
     ],
     "parameters": {
       "constant": "B",
       "vibrational_state_v": 0
     },
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table 1 \(p\. 22232\), column 'B \(cm\-1\)b', the Raman comparison value \[41\] \(Weber 1979\)\: 1\.989574\(12\), digit\-identical with bendtsen\_1974 Table VII's pure rotational B\_0 \(its original\)\.

reichert\_2015/D\_raman\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "D_raman_N2",
     "material": "N2",
     "file": "N2/reichert_2015__D_raman_N2.csv",
     "table": "tbl_f40cb41739d3",
     "quantity": "rotational_constant",
     "unit": "cm-1",
     "scale": 1e-06,
     "abscissa": "label",
     "use": "reproduced",
     "reproduced_from": [
       "bendtsen_1974",
       "weber_1979"
     ],
     "parameters": {
       "constant": "D",
       "vibrational_state_v": 0
     },
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table 1 \(p\. 22232\), column 'D \(10\-6 cm\-1\)b' \[41\]\: 5\.76\(3\), bendtsen\_1974 Table VII's pure rotational D\.

reichert\_2015/B\_raman\_O2
~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "B_raman_O2",
     "material": "O2",
     "file": "O2/reichert_2015__B_raman_O2.csv",
     "table": "tbl_f40cb41739d3",
     "quantity": "rotational_constant",
     "unit": "cm-1",
     "abscissa": "label",
     "use": "reproduced",
     "reproduced_from": [
       "R. J. Butcher, D. V. Willetts and W. J. Jones, Proc. R. Soc. A324, 231 (1971)",
       "weber_1979"
     ],
     "parameters": {
       "constant": "B",
       "vibrational_state_v": 0
     },
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table 1 \(p\. 22232\), column 'B \(cm\-1\)b' \[41\]\: 1\.437682\(9\) for 16O2\: Weber's Table 3\.2 \(weber\_1979 table3\_2\_B0\_O2\_butcher, p\. 88\) prints it as \[3\.17a\] R\. J\. Butcher, D\. V\. Willetts and W\. J\. Jones, Proc\. R\. Soc\. A324, 231 \(1971\), the original \(not in the library\); digit\-identical\. hajigeorgiou\_2013's B\_0 is 1\.437674521 \(Table III\) and 1\.43767602 \(Table I, from Yu et al\.\)\: 6\-8e\-6 cm^\-1 below, within 1 sigma of the \(9\)\.

reichert\_2015/D\_raman\_O2
~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "D_raman_O2",
     "material": "O2",
     "file": "O2/reichert_2015__D_raman_O2.csv",
     "table": "tbl_f40cb41739d3",
     "quantity": "rotational_constant",
     "unit": "cm-1",
     "scale": 1e-06,
     "abscissa": "label",
     "use": "reproduced",
     "reproduced_from": [
       "R. J. Butcher, D. V. Willetts and W. J. Jones, Proc. R. Soc. A324, 231 (1971)",
       "weber_1979"
     ],
     "parameters": {
       "constant": "D",
       "vibrational_state_v": 0
     },
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table 1 \(p\. 22232\), column 'D \(10\-6 cm\-1\)b' \[41\]\: 4\.852\(12\) for 16O2 \(weber\_1979 table3\_2\_D0\_O2\_butcher, from \[3\.17a\] Butcher et al\. 1971, digit\-identical\), against hajigeorgiou\_2013's D\_0 4\.839482 \(Table III\) and 4\.8405146 \(Table I\)\: 1\.0 sigma of the \(12\) below\.

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.