lehmberg_1995
=============

R\. H\. Lehmberg, C\. J\. Pawley, A\. V\. Deniz, M\. Klapisch and Y\. Leng, "Two\-photon resonantly\-enhanced negative nonlinear refractive index in xenon at 248 nm", Opt\. Commun\. 121, 78 \(1995\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/lehmberg_1995.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1016/0030\-4018\(95\)00433\-9 <https://doi.org/10.1016/0030-4018%2895%2900433-9>`__

**Source kind:** measurement

**Recorded technique:** Measurement\: a KrF\-amplified 248\.4 nm pulse of about 10 ps \(Fig\. 4\: '10 ps KrF beam'; a dye oscillator, distributed\-feedback dye laser, BBO doubling, a KrF discharge amplifier, a spatial filter; p\. 81\), linearly polarised, about 2 GW/cm2, through a 4\.6 m cell of Xe, CO2 or both between CaF2 windows; the output fluence profiles fitted by a paraxial propagation code \(the incident beam's measured profile and phase curvature, the windows and air paths included\) with n2 free, at each pressure, and the pressure dependence's linear fit scaled to 760 Torr and 300 K \(Figs\. 10b, 12b\)\. Xe directly from self\-defocusing up to 266 Torr; Xe also as n2\(CO2\) from CO2 self\-focusing times the ratio n2\(Xe\)/n2\(CO2\) from a cancellation experiment \(129 Torr of Xe added to 1260 Torr of CO2\)\. Calculation \(Xe\)\: the sum over states of Eq\. \(1\) \(and its two\-photon\-resonant term alone, Eq\. 3\), dipole matrix elements from a parametric\-potential relativistic atomic\-structure calculation fitted to 36 measured levels \(rms 700 cm^\-1\), all J = 1 odd states to 9s, 9d and two\-photon states to 9p, 5f, no continuum \(p\. 80\)\.

**Materials in structured entries:** CO2, Xe

**Dataset quantities:** nonlinear\_index\_field

**Contents:** 4 datasets; 0 formulas.

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

Journal pp\. 78\-88 = PDF pages 1\-11\. Identity checked against the first page\.

WHAT IS TAKEN\. Table 1 \(p\. 87, tbl\_30b21d3fcab2; cells checked against the image\), at 760 Torr and 300 K and 248\.4 nm, in 10^\-14 esu\: Xe calculated \-1\.54 \+\- 0\.30, Xe by self\-defocusing \-2\.06 \+\- 0\.14, Xe by CO2 compensation \-1\.82 \+\- 0\.08, CO2 by self\-focusing \+0\.160 \+\- 0\.007\. Not taken\: air \(Ref\. \[2\]\) and fused silica \(Ref\. \[1\]\), other papers' values\. The text's combined Xe value, \-\(1\.97 \+\- 0\.23\) x 10^\-14 esu \(p\. 87\), is the two measurements combined and is not a separate dataset\.

THE DEFINITION\. 'Applying the usual definition delta n = \(1/2\) n2 \|E\|^2, where \.\.\. E is the slowly\-varying complex laser field amplitude' \(p\. 79\)\: \(1/2\)\|E\|^2 is the mean square of the real field, so n2 is per \<E^2\> \(nonlinear\_index\_field, definition '\<E^2\>'\)\. In intensity units n2\(cm2/W\) = 4 pi 10^7 n2\(esu\) / \(c n0\) = 4\.19e\-3 n2\(esu\) \(computed, n0 = 1, c in cm/s\)\: the combined \-1\.97e\-14 esu is \-8\.25e\-21 m2/W\. nibbering\_1997 \(Table 1, Ref\. 8\) reproduces Xe as \-963 \+\- 112 e\-23 m2/W, 1\.17 times that and 1\.12 times the self\-defocusing value; its conversion is not stated \(TC\-854\)\.

DOUBTS\. Above 266 Torr the self\-defocusing fits fail \(Fig\. 11\), perhaps from Xe2 dimers \(about 0\.6 % at 1 atm\); the 760 Torr values are extrapolated linearly from lower pressures\. The temperature was about 20 C \(p\. 85\), the values scaled to 300 K\. Fig\. 12's caption prints 'n2\(Xe\) = \(2\.35 \+\- 0\.12\) x 10^\-15 esu' for a CO2 shot\: it means n2\(CO2\) \(the panel and the text\)\.

TWO\-PHOTON DATA\. The 6p\[1/2\]\_0 resonance at 249\.6 nm 'has been studied by several authors \[4\-7\]' \(p\. 78\); its two\-photon excitation cross section is in kroll\_1990 \(S\. Kröll and W\. Bischel, Phys\. Rev\. A 41, 1340 \(1990\), Ref\. \[5\]\), from which the Appendix estimates the resonantly enhanced three\-photon ionisation of atomic Xe as negligible here \(no number printed; p\. 88\)\. Not taken\: the Appendix's upper limit on the two\-photon excitation rate of the Xe2 dimer at 248\.4 nm, W \< 3\.7e5 I^2 s^\-1 \(I in GW/cm^2\), estimated from Gornik et al\.'s spectra \(Ref\. \[4\]\), and the photoionisation cross section of the excited dimer levels, 4e\-18 \(printed 'cm^\-1', for cm^2\), quoted from Ref\. \[22\] \(p\. 88\)\: a bound and a quoted value, neither of the atom\.

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

Datasets
--------

lehmberg\_1995/calculated\_Xe
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "calculated_Xe",
     "material": "Xe",
     "file": "Xe/lehmberg_1995__calculated_Xe.csv",
     "table": "tbl_30b21d3fcab2",
     "quantity": "nonlinear_index_field",
     "unit": "esu",
     "scale": 1e-14,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_k": 300.0
     },
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "definition": "<E^2>: delta n = (1/2) n2 |E|^2, E the complex amplitude (p. 79)",
       "part": "total",
       "coefficient": "self",
       "polarization": "linear",
       "pulse_fs": 10000,
       "method": "sum over states, Eq. (1); parametric-potential relativistic matrix elements, no continuum"
     }
   }

Table 1 \(p\. 87\), row 'Xe \(Eqs\. \(1\) or \(3\)\)'\: the ab initio n2 of xenon at 248\.4 nm, 760 Torr, 300 K, 10^\-14 esu; Eqs\. \(1\) and \(3\) give \-1\.536 and \-1\.539 \(p\. 80\), the error from \+\-7 % in the dipole matrix elements\. Negative\: 248\.4 nm lies just above the two\-photon resonance with 6p\[1/2\]\_0 at 249\.6 nm \(80119 cm^\-1\)\.

lehmberg\_1995/defocusing\_Xe
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "defocusing_Xe",
     "material": "Xe",
     "file": "Xe/lehmberg_1995__defocusing_Xe.csv",
     "table": "tbl_30b21d3fcab2",
     "quantity": "nonlinear_index_field",
     "unit": "esu",
     "scale": 1e-14,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_k": 300.0
     },
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "definition": "<E^2>: delta n = (1/2) n2 |E|^2, E the complex amplitude (p. 79)",
       "part": "total",
       "coefficient": "self",
       "polarization": "linear",
       "pulse_fs": 10000,
       "technique": "self-defocusing: output fluence profiles fitted by a propagation code, up to 266 Torr"
     }
   }

Table 1 \(p\. 87\), row 'Xe \(self\-defocusing exp\.\)'\: the linear fit of n2 against pressure up to 266 Torr \(Fig\. 10b\) scaled to 760 Torr and 300 K, 10^\-14 esu\. Near the two\-photon resonance at 249\.6 nm\.

lehmberg\_1995/compensation\_Xe
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "compensation_Xe",
     "material": "Xe",
     "file": "Xe/lehmberg_1995__compensation_Xe.csv",
     "table": "tbl_30b21d3fcab2",
     "quantity": "nonlinear_index_field",
     "unit": "esu",
     "scale": 1e-14,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_k": 300.0
     },
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "definition": "<E^2>: delta n = (1/2) n2 |E|^2, E the complex amplitude (p. 79)",
       "part": "total",
       "coefficient": "self",
       "polarization": "linear",
       "pulse_fs": 10000,
       "technique": "compensation of CO2 self-focusing by Xe, scaled by n2(CO2)"
     }
   }

Table 1 \(p\. 87\), row 'Xe \(CO\_2 compensation exp\.\)'\: n2\(CO2\) from CO2 self\-focusing times n2\(Xe\)/n2\(CO2\) from the cancellation of CO2's self\-focusing by added Xe, 760 Torr and 300 K, 10^\-14 esu; 'unaffected by either profile broadening or high Xe pressure effects' \(p\. 86\)\.

lehmberg\_1995/focusing\_CO2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "focusing_CO2",
     "material": "CO2",
     "file": "CO2/lehmberg_1995__focusing_CO2.csv",
     "table": "tbl_30b21d3fcab2",
     "quantity": "nonlinear_index_field",
     "unit": "esu",
     "scale": 1e-14,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_k": 300.0
     },
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "definition": "<E^2>: delta n = (1/2) n2 |E|^2, E the complex amplitude (p. 79)",
       "part": "total",
       "coefficient": "self",
       "polarization": "linear",
       "pulse_fs": 10000,
       "technique": "whole-beam self-focusing: output fluence profiles fitted by a propagation code"
     }
   }

Table 1 \(p\. 87\), row 'CO\_2 \(self\-focusing exp\.\)'\: \+0\.160 \+\- 0\.007 x 10^\-14 esu at 248\.4 nm, 760 Torr, 300 K, from whole\-beam self\-focusing fits \(Fig\. 12; its caption's 'n2\(Xe\)' means CO2\)\. Includes the molecule's rotational part at 10 ps\.

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.