liu_1979
========

P\. Liu, R\. Yen, and N\. Bloembergen, "Two\-photon absorption coefficients in uv window and coating materials", Appl\. Opt\. 18, 1015\-1018 \(1979\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/liu_1979.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1364/ao\.18\.001015 <https://doi.org/10.1364/ao.18.001015>`__

**Source kind:** measurement

**Recorded technique:** The set\-up of liu\_1978 \(Ref\. 3\)\: single 30\-ps \(average\) pulses from a mode\-locked Nd\:YAG oscillator, amplified, frequency\-tripled \(355 nm\) or quadrupled \(266 nm\), separated by a dispersive prism; energy transmission against peak input intensity of a Gaussian beam, fitted with Eq\. \(8\) \(reflection R and linear absorption alpha included; R from the low\-intensity transmission, 'The published data on the index of refraction of these materials in this region are quite limited', p\. 1017\), with the tau\-A pulse normalisation \(Eqs\. 11\-13\)\. New\: an automatic data acquisition with an HP 9820A calculator and cascaded sample\-and\-hold circuits \(Figs\. 1\-2\)\: 'the transmission can be measured with a standard deviation of 0\.4%\. At a maximum intensity level of few GW/cm2 and sample thickness of 5 mm, two\-photon absorption coefficients of a few times 10^\-6 cm/MW can be measured' \(p\. 1017\)\. Bulk single crystals about 5 mm thick, oriented by x\-ray diffraction\: SrF2, BaF2, CdF2 from Optovac, MgF2 from Harshaw, LiYF4 from Sanders Associates; fused silica\. Linear polarization \(the polarization dependence studied by rotating the crystal; circular light by a quartz quarter\-wave plate\)\.

**Materials in structured entries:** BaF2, CdF2, LiYF4, MgF2, SiO2, SrF2

**Dataset quantities:** band\_gap, two\_photon\_absorption\_coefficient

**Contents:** 15 datasets; 0 formulas.

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

Journal pages 1015\-1018 = pdf pages 1\-4 \(journal page = 1014 \+ pdf page\)\. Identity checked against the first page\. The last page mixes the journal's meetings calendar with the references\.

DEFINITION OF beta\: as liu\_1978, the two\-photon coefficient of dI/dz = \-alpha I \- beta I^2 with the surface reflection removed \(Eqs\. 7\-10\); Eq\. \(2\), gamma\_N = N hbar omega W/I^N; Eqs\. \(4\)\-\(6\) relate beta to chi''\(3\) for \[100\], \[110\] and circular polarization \(as liu\_1978's Eqs\. 6\-8\)\. beta in cm/MW \(Table I\)\.

TABLE I \(tbl\_14fb6f23a7e6, p\. 1017; image checked, all cells agree\)\. beta at 355 and 266 nm and the band gap\. Upper bounds \('\<'\) are kept as excluded datasets\. The uncertainties\: footnote b \(fused silica\) 'The uncertainty shown here only counts the scattering of the data\. For absolute value, a systematic uncertainty \+\-43% should be added'; text \(p\. 1017\)\: 'The main uncertainty in the absolute value \.\.\. is from the calibrations and the saturation of the conversion efficiency in the tau A technique\. It was estimated to be \+\-43%\. However, the uncertainty in the relative values \.\.\. is quite small\. It is due to the scattering of the data points and ranges from \+\-5% to \+\-20%\.' Recorded\: relative = the printed %, systematic\_relative = 0\.43, level not stated\. Detection limit\: 'In materials with band gaps larger than 2 hbar omega, the nonlinear absorption is below the detection limit of 3 x 10^\-6 cm/MW' \(abstract\)\.

FUSED SILICA AT 266 NM \(p\. 1017\)\: 'The two\-photon absorption coefficient of fused silica at 266 nm is measured to be 1\.7 x 10^\-5 \+\- 20% cm/MW\. Previously it was reported to be on the verge of the earlier detection limit of 4\.5 x 10^\-5 cm/MW' \(liu\_1978's Table II value, recorded there as check\)\. This value supersedes it\.

BAND GAPS\. 'Band gaps are listed when available' \(footnote a\); no source is given in the table\. The text \(p\. 1017\)\: 'BaF2, with a published band gap of 9\.06 eV \(Ref\. 13\: W\. H\. Strelow \[Strehlow\] and E\. L\. Cook, J\. Phys\. Chem\. Ref\. Data 2, 163 \(1973\)\), does not show two\-photon absorption at 266 nm, and no band gap information of SrF2 is available\. Apparently, accurate measurements of band gaps in these materials are needed\.' SrF2's gap is printed '?' \(not recorded\); CdF2 '~6' and LiYF4 '~11' are approximate \(the tilde stays in printed\)\. taylor\_1988 quotes this paper's doubt about BaF2's gap\.

CdF2 \(p\. 1017\)\: 'our CdF2 sample displayed a two\-photon absorption coefficient, which is highly frequency dependent\. It increased by a factor of 38 in going from 355 nm to 266 nm' \(1\.60e\-3/4\.17e\-5 = 38\.4, computed\)\. 'Our CdF2 sample had a low intensity transmission of 83% at 355 nm and 63% at 266 nm, which is much higher than the published data' \(Ref\. 12\)\.

POLARIZATION \(p\. 1017\)\: at 266 nm in NaCl, for light along \[001\] polarized along \[100\] or \[110\], and for circular light, 'no change in the two\-photon absorption coefficient is observed' \(no value printed\)\: the isotropy condition 2 chi''\_xxyy \+ chi''\_xyyx = chi''\_xxxx holds and chi''\_xyyx is small; 'Similar results have been observed in RbI at 355 nm'\. \(liu\_1978 found circular light smaller in RbI\.\)

KELDYSH FORMULA\. Eqs\. \(1\)\-\(3\) \(p\. 1015\) repeat liu\_1978's Eqs\. \(3\)\-\(4\) with the exponent printed exp\[2\<Delta/hbar omega \+ 1\>\(2 \- Delta/E\_g\)\] \(equal to liu\_1978's exp\[2N\(1 \- e^2E^2/4m\*omega^2E\_g\)\] to first order\) and without the leading omega in Eq\. \(1\); no new parameters are fitted here\. See liu\_1978 \(formula keldysh\_gamma\_n\)\.

FIGURES \(not digitised\)\. Fig\. 1\: block diagram of the data acquisition\. Fig\. 2\: its circuits\.

REPRODUCTIONS OF THIS PAPER\: taylor\_1988 \(the 266\-nm column with liu\_1978\), brimacombe\_1989 \(fused silica 1\.7e\-5 cm/MW\), dragomir\_2002 \(Table 1\: fused silica 1\.7e\-11 cm/W, 30 ps\), couairon\_2005\.

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

Datasets
--------

liu\_1979/beta\_266\_SiO2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "beta_266_SiO2",
     "material": "SiO2",
     "file": "SiO2/liu_1979__beta_266_SiO2.csv",
     "table": "tbl_14fb6f23a7e6",
     "quantity": "two_photon_absorption_coefficient",
     "unit": "cm/MW",
     "abscissa_unit": "nm",
     "use": "primary",
     "uncertainty": {
       "relative": 0.2,
       "systematic_relative": 0.43,
       "level": "not stated"
     },
     "parameters": {
       "technique": "energy transmission against peak intensity of single 30-ps pulses (tau-A normalisation, automated acquisition)",
       "pulse_fs": 30000,
       "polarization": "linear",
       "form": "bulk"
     }
   }

Table I \(p\. 1017\) and the text \(p\. 1017\), 'Fused silica'\: 1\.7e\-5 cm/MW \+\- 20 % \(the scatter only, footnote b\), plus the \+\-43 % systematic uncertainty\. Supersedes liu\_1978's 4\.5e\-5 \(its detection limit\)\. Grade not stated\.

liu\_1979/beta\_355\_CdF2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "beta_355_CdF2",
     "material": "CdF2",
     "file": "CdF2/liu_1979__beta_355_CdF2.csv",
     "table": "tbl_14fb6f23a7e6",
     "quantity": "two_photon_absorption_coefficient",
     "unit": "cm/MW",
     "abscissa_unit": "nm",
     "use": "primary",
     "uncertainty": {
       "relative": 0.15,
       "systematic_relative": 0.43,
       "level": "not stated"
     },
     "parameters": {
       "technique": "energy transmission against peak intensity of single 30-ps pulses (tau-A normalisation, automated acquisition)",
       "pulse_fs": 30000,
       "polarization": "linear",
       "form": "bulk"
     }
   }

Table I \(p\. 1017\), 'CdF2'\: 4\.17e\-5 cm/MW \+\- 15 % \(relative\), plus the \+\-43 % systematic uncertainty\. Optovac crystal about 5 mm thick; orientation not stated\. Low\-intensity transmission 83 % at 355 nm\.

liu\_1979/beta\_266\_CdF2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "beta_266_CdF2",
     "material": "CdF2",
     "file": "CdF2/liu_1979__beta_266_CdF2.csv",
     "table": "tbl_14fb6f23a7e6",
     "quantity": "two_photon_absorption_coefficient",
     "unit": "cm/MW",
     "abscissa_unit": "nm",
     "use": "primary",
     "uncertainty": {
       "relative": 0.05,
       "systematic_relative": 0.43,
       "level": "not stated"
     },
     "parameters": {
       "technique": "energy transmission against peak intensity of single 30-ps pulses (tau-A normalisation, automated acquisition)",
       "pulse_fs": 30000,
       "polarization": "linear",
       "form": "bulk"
     }
   }

Table I \(p\. 1017\), 'CdF2'\: 1\.60e\-3 cm/MW \+\- 5 % \(relative\), plus the \+\-43 % systematic uncertainty; 'comparable with that of the alkali\-halides' \(abstract\), 38 times the 355\-nm value\. Low\-intensity transmission 63 % at 266 nm\.

liu\_1979/beta\_355\_MgF2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "beta_355_MgF2",
     "material": "MgF2",
     "file": "MgF2/liu_1979__beta_355_MgF2.csv",
     "table": "tbl_14fb6f23a7e6",
     "quantity": "two_photon_absorption_coefficient",
     "unit": "cm/MW",
     "abscissa_unit": "nm",
     "use": "excluded",
     "parameters": {
       "technique": "energy transmission against peak intensity of single 30-ps pulses (tau-A normalisation, automated acquisition)",
       "pulse_fs": 30000,
       "polarization": "linear",
       "form": "bulk"
     }
   }

Table I \(p\. 1017\)\: printed as an upper bound \('\<6\.2 × 10\-6', i\.e\. \< 6\.2e\-6 cm/MW\); 'In materials with band gaps larger than 2 hbar omega, the nonlinear absorption is below the detection limit' \(abstract\)\. Not a measured beta\. Harshaw crystal; orientation not stated\.

liu\_1979/beta\_266\_MgF2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "beta_266_MgF2",
     "material": "MgF2",
     "file": "MgF2/liu_1979__beta_266_MgF2.csv",
     "table": "tbl_14fb6f23a7e6",
     "quantity": "two_photon_absorption_coefficient",
     "unit": "cm/MW",
     "abscissa_unit": "nm",
     "use": "excluded",
     "parameters": {
       "technique": "energy transmission against peak intensity of single 30-ps pulses (tau-A normalisation, automated acquisition)",
       "pulse_fs": 30000,
       "polarization": "linear",
       "form": "bulk"
     }
   }

Table I \(p\. 1017\)\: printed as an upper bound \('\<2\.8 × 10\-6', i\.e\. \< 2\.8e\-6 cm/MW\); 'In materials with band gaps larger than 2 hbar omega, the nonlinear absorption is below the detection limit' \(abstract\)\. Not a measured beta\. Harshaw crystal; orientation not stated\.

liu\_1979/beta\_355\_SrF2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "beta_355_SrF2",
     "material": "SrF2",
     "file": "SrF2/liu_1979__beta_355_SrF2.csv",
     "table": "tbl_14fb6f23a7e6",
     "quantity": "two_photon_absorption_coefficient",
     "unit": "cm/MW",
     "abscissa_unit": "nm",
     "use": "excluded",
     "parameters": {
       "technique": "energy transmission against peak intensity of single 30-ps pulses (tau-A normalisation, automated acquisition)",
       "pulse_fs": 30000,
       "polarization": "linear",
       "form": "bulk"
     }
   }

Table I \(p\. 1017\)\: printed as an upper bound \('\<5\.7 × 10\-6', i\.e\. \< 5\.7e\-6 cm/MW\); 'In materials with band gaps larger than 2 hbar omega, the nonlinear absorption is below the detection limit' \(abstract\)\. Not a measured beta\. Optovac crystal; orientation not stated\.

liu\_1979/beta\_266\_SrF2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "beta_266_SrF2",
     "material": "SrF2",
     "file": "SrF2/liu_1979__beta_266_SrF2.csv",
     "table": "tbl_14fb6f23a7e6",
     "quantity": "two_photon_absorption_coefficient",
     "unit": "cm/MW",
     "abscissa_unit": "nm",
     "use": "excluded",
     "parameters": {
       "technique": "energy transmission against peak intensity of single 30-ps pulses (tau-A normalisation, automated acquisition)",
       "pulse_fs": 30000,
       "polarization": "linear",
       "form": "bulk"
     }
   }

Table I \(p\. 1017\)\: printed as an upper bound \('\<5\.4 × 10\-6', i\.e\. \< 5\.4e\-6 cm/MW\); 'In materials with band gaps larger than 2 hbar omega, the nonlinear absorption is below the detection limit' \(abstract\)\. Not a measured beta\. Optovac crystal; orientation not stated\.

liu\_1979/beta\_355\_BaF2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "beta_355_BaF2",
     "material": "BaF2",
     "file": "BaF2/liu_1979__beta_355_BaF2.csv",
     "table": "tbl_14fb6f23a7e6",
     "quantity": "two_photon_absorption_coefficient",
     "unit": "cm/MW",
     "abscissa_unit": "nm",
     "use": "excluded",
     "parameters": {
       "technique": "energy transmission against peak intensity of single 30-ps pulses (tau-A normalisation, automated acquisition)",
       "pulse_fs": 30000,
       "polarization": "linear",
       "form": "bulk"
     }
   }

Table I \(p\. 1017\)\: printed as an upper bound \('\<3\.6 × 10\-6', i\.e\. \< 3\.6e\-6 cm/MW\); 'In materials with band gaps larger than 2 hbar omega, the nonlinear absorption is below the detection limit' \(abstract\)\. Not a measured beta\. Optovac crystal; orientation not stated\.

liu\_1979/beta\_266\_BaF2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "beta_266_BaF2",
     "material": "BaF2",
     "file": "BaF2/liu_1979__beta_266_BaF2.csv",
     "table": "tbl_14fb6f23a7e6",
     "quantity": "two_photon_absorption_coefficient",
     "unit": "cm/MW",
     "abscissa_unit": "nm",
     "use": "excluded",
     "parameters": {
       "technique": "energy transmission against peak intensity of single 30-ps pulses (tau-A normalisation, automated acquisition)",
       "pulse_fs": 30000,
       "polarization": "linear",
       "form": "bulk"
     }
   }

Table I \(p\. 1017\)\: printed as an upper bound \('\<4\.0 × 10\-6', i\.e\. \< 4\.0e\-6 cm/MW\); 'In materials with band gaps larger than 2 hbar omega, the nonlinear absorption is below the detection limit' \(abstract\)\. Not a measured beta\. Optovac crystal; orientation not stated\.

liu\_1979/beta\_266\_LiYF4
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "beta_266_LiYF4",
     "material": "LiYF4",
     "file": "LiYF4/liu_1979__beta_266_LiYF4.csv",
     "table": "tbl_14fb6f23a7e6",
     "quantity": "two_photon_absorption_coefficient",
     "unit": "cm/MW",
     "abscissa_unit": "nm",
     "use": "excluded",
     "parameters": {
       "technique": "energy transmission against peak intensity of single 30-ps pulses (tau-A normalisation, automated acquisition)",
       "pulse_fs": 30000,
       "polarization": "linear",
       "form": "bulk"
     }
   }

Table I \(p\. 1017\)\: printed as an upper bound \('\<4\.0 × 10\-6', i\.e\. \< 4\.0e\-6 cm/MW\); 'In materials with band gaps larger than 2 hbar omega, the nonlinear absorption is below the detection limit' \(abstract\)\. Not a measured beta\. Sanders Associates crystal; 'The newly developed window material LiYF4 has no detectable nonlinear loss at 266 nm' \(abstract\); orientation not stated\.

liu\_1979/band\_gap\_MgF2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "band_gap_MgF2",
     "material": "MgF2",
     "file": "MgF2/liu_1979__band_gap_MgF2.csv",
     "table": "tbl_14fb6f23a7e6",
     "quantity": "band_gap",
     "unit": "eV",
     "abscissa": "none",
     "use": "check",
     "parameters": {
       "kind": "not stated"
     }
   }

Table I \(p\. 1017\), column 'Band gap \(eV\)' \(footnote a\: 'Band gaps are listed when available'\)\. Printed without a source \('listed when available'\)\.

liu\_1979/band\_gap\_BaF2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "band_gap_BaF2",
     "material": "BaF2",
     "file": "BaF2/liu_1979__band_gap_BaF2.csv",
     "table": "tbl_14fb6f23a7e6",
     "quantity": "band_gap",
     "unit": "eV",
     "abscissa": "none",
     "use": "reproduced",
     "reproduced_from": [
       "W. H. Strehlow and E. L. Cook, J. Phys. Chem. Ref. Data 2, 163 (1973)"
     ],
     "parameters": {
       "kind": "not stated"
     }
   }

Table I \(p\. 1017\), column 'Band gap \(eV\)' \(footnote a\: 'Band gaps are listed when available'\)\. Printed without a source in the table; the text calls it 'a published band gap of 9\.06 eV' \(Ref\. 13, Strelow \[Strehlow\] and Cook 1973\) and doubts it\: BaF2 shows no two\-photon absorption at 266 nm \(2 hbar omega = 9\.32 eV\)\.

liu\_1979/band\_gap\_CdF2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "band_gap_CdF2",
     "material": "CdF2",
     "file": "CdF2/liu_1979__band_gap_CdF2.csv",
     "table": "tbl_14fb6f23a7e6",
     "quantity": "band_gap",
     "unit": "eV",
     "abscissa": "none",
     "use": "check",
     "parameters": {
       "kind": "not stated"
     }
   }

Table I \(p\. 1017\), column 'Band gap \(eV\)' \(footnote a\: 'Band gaps are listed when available'\)\. Printed '~6' \(approximate; the tilde is in the printed cell\)\. The sample's transmission was 'much higher than the published data' \(p\. 1017\)\.

liu\_1979/band\_gap\_LiYF4
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "band_gap_LiYF4",
     "material": "LiYF4",
     "file": "LiYF4/liu_1979__band_gap_LiYF4.csv",
     "table": "tbl_14fb6f23a7e6",
     "quantity": "band_gap",
     "unit": "eV",
     "abscissa": "none",
     "use": "check",
     "parameters": {
       "kind": "not stated"
     }
   }

Table I \(p\. 1017\), column 'Band gap \(eV\)' \(footnote a\: 'Band gaps are listed when available'\)\. Printed '~11' \(approximate; the tilde is in the printed cell\)\.

liu\_1979/band\_gap\_SiO2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "band_gap_SiO2",
     "material": "SiO2",
     "file": "SiO2/liu_1979__band_gap_SiO2.csv",
     "table": "tbl_14fb6f23a7e6",
     "quantity": "band_gap",
     "unit": "eV",
     "abscissa": "none",
     "use": "check",
     "parameters": {
       "kind": "not stated"
     }
   }

Table I \(p\. 1017\), column 'Band gap \(eV\)' \(footnote a\: 'Band gaps are listed when available'\)\. Fused silica; printed without a source \(liu\_1978 prints the same 7\.8 eV\)\.

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.