patwardhan_2021
===============

G\. N\. Patwardhan, J\. S\. Ginsberg, C\. Y\. Chen, M\. M\. Jadidi and A\. L\. Gaeta, "Nonlinear refractive index of solids in mid\-infrared", Opt\. Lett\. 46, 1824 \(2021\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/patwardhan_2021.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1364/ol\.421469 <https://doi.org/10.1364/ol.421469>`__

**Source kind:** measurement

**Recorded technique:** Spectrally resolved two\-beam coupling \(SRTBC\)\: a weak probe and a strong pump of the same centre frequency, split from one OPA / nonlinear difference\-frequency output \(1\-10 um, \< 150 fs; pumped by a Coherent Legend Ti\:sapphire amplifier, 800 nm, 35 fs, 1 kHz\), crossed at 4 degrees in the sample \(15 cm parabolic mirror; spot 190\-220 um\); the spectrally resolved probe transmission change Delta T/T against delay and detuning \(Horiba iHR320 monochromator, HgCdTe detector\) is fitted with Kang et al\.'s formula \(Eq\. 1, chirp\-free, at 2\.3 um\) or its chirped form \(Eq\. 2, Wang et al\., at 3\.5\-8\.3 um, chirp b = \(1\.7\-2\.7\) x 10^26 s^\-2\)\. Samples 500 um thick \(CaF2, MgF2, sapphire, fused silica\) and 1 mm \(ZnSe, ZnS\); interaction length 795 um \(2\.3, 3\.5 um\) or about 1 mm \(4\.5, 8\.3 um\), the smaller of it and the thickness used \(pp\. 1824\-1826\)\.

**Materials in structured entries:** Al2O3, CaF2, MgF2, SiO2, ZnS, ZnSe

**Dataset quantities:** band\_gap, nonlinear\_index

**Contents:** 18 datasets; 1 formula.

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

Journal pages 1824\-1827 = PDF pages 1\-4\. Identity checked against the first page\.

DEFINING RELATIONS \(p\. 1824\)\: the method measures chi\(3\)\(omega; omega, omega, \-omega\), with n2 = 3 Re\[chi\(3\)\] / \(4 n0^2 eps0 c\) and beta = 3 omega Im\[chi\(3\)\] / \(2 n0^2 eps0 c^2\) \(SI\)\. In Eq\. \(1\), Delta T/T = \(2/sqrt\(6\)\) exp\(\-\(delta t0\)^2/3 \- 2 tau^2/\(3 t0^2\)\) \[2 Delta Phi sin\(2 delta tau/3\) \- q cos\(2 delta tau/3\)\], with Delta Phi = k n2 I\_pu L the nonlinear phase and q = beta I\_pu L\. The factor 2 of cross\-phase modulation is explicit in the formula, so the n2 of Table 1 is the self coefficient n = n0 \+ n2 I\. Polarization not stated\.

ABSOLUTE AND RELATIVE \(p\. 1826\)\: 'Absolute measurement of n2 was performed at each wavelength for one material \(FS at 2\.3 um, Saph at 3\.5 and 4\.5 um, and ZnSe at all four wavelengths\), and the n2 for other materials \(CaF2, MgF2, and ZnS\) was obtained by a relative measurement\.' 'Most of the error in n2 arises from the uncertainty in determining the pump intensity'; the level of the \+\- is not stated\. Maximum intensities a few 10^11 W/cm^2, typical a few 10^9 W/cm^2\. beta was negligible in all measurements\. Fused silica only to 3\.5 um \(linear absorption beyond 4 um\); no 8\.3 um value except for ZnSe and ZnS \(too little pump power\)\.

PULSES AND PART\. OPA/NDFG pulses \< 150 fs; 75 fs FWHM \(with chirp\) fitted at 3\.5 um, 100 fs FWHM at 4\.5 um \(Fig\. 1\(c\), Fig\. 2\); the duration at 2\.3 um is not stated\. 'Our minimum pulse durations were \>65 fs, which prevented us from distinguishing the electronic contribution from the nuclear response' \(p\. 1827\)\: part = 'unknown'\. No pulse\_fs is recorded \(it differs by wavelength and is not given for every one\)\.

THEORY COLUMN\: the two\-band model of Sheik\-Bahae et al\. \[1\] 'with K' = 0\.86 x 10^\-8, E\_P = 21 eV' and the band gaps of the table \('includes contributions from TPA, Raman, linear, and quadratic Stark effects and the divergent term', p\. 1827\)\: use = 'check'\. See the formula entry\: not reproduced here \(the paper gives neither G2 nor the n0 used\)\.

BAND GAPS\: 'Obtained from \[1,15,16\]' \(Table 1 footnote b\)\: the inputs of the theory column, taken from the literature, not measured\: kind 'assumed', assumed = true, use = 'check'\. \[1\] Sheik\-Bahae, Hutchings, Hagan & Van Stryland, IEEE J\. Quantum Electron\. 27, 1296 \(1991\); \[15\] N\. M\. Saeed, Al\-Nahrain J\. Sci\. 14, 86 \(2011\); \[16\] P\. D'Amico, A\. Calzolari, A\. Ruini and A\. Catellani, Sci\. Rep\. 7, 1 \(2017\); which gap comes from which reference is not said\.

MATERIALS\: ZnS '\(polycrystalline\)'; ZnSe crystallinity not stated; 'Sapphire' = Al2O3, axis not stated; fused silica grade not stated\. Text comparisons \(p\. 1827\)\: ZnS \(50 \+\- 12\.5\) and ZnSe \(120 \+\- 30\) x 10^\-20 m^2/W at 3\.9 um by Z\-scan \[2\] \(Ensley & Bambha 2019\) and \[3\] \(Werner et al\. 2019\)\: reproductions of ensley\_2019's Table 1 \(and Werner\), not extracted here\.

refractiveindex\.info \(Patwardhan n2 pages, checked 2026\-09\-26\)\: Al2O3 2\.44, 2\.62, 2\.66; CaF2 1\.09, 1\.19, 1\.12; MgF2 0\.66, 0\.74, 0\.82 \(x 10^\-20 m^2/W at 2\.3, 3\.5, 4\.5 um\); SiO2 1\.94, 2\.0 \(2\.3, 3\.5 um\)\: the measured values, identical\. The pages label the pulse '100 fs' for every wavelength \(the paper\: 75 fs at 3\.5 um, 100 fs at 4\.5 um, not stated at 2\.3 um\)\. There are no pages for ZnSe and ZnS \(all four wavelengths including 8\.3 um\), and no theory values\.

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

Datasets
--------

patwardhan\_2021/exp\_ZnSe
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "exp_ZnSe",
     "material": "ZnSe",
     "file": "ZnSe/patwardhan_2021__exp_ZnSe.csv",
     "table": "tbl_2daca1ccb18c",
     "quantity": "nonlinear_index",
     "unit": "m2/W",
     "scale": 1e-20,
     "abscissa_unit": "um",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "part": "unknown",
       "coefficient": "self",
       "technique": "spectrally resolved two-beam coupling",
       "form": "bulk"
     }
   }

Table 1, Exp\., row 'ZnSe'\. Absolute at all four wavelengths\. Samples 1 mm thick\.

patwardhan\_2021/theory\_ZnSe
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "theory_ZnSe",
     "material": "ZnSe",
     "file": "ZnSe/patwardhan_2021__theory_ZnSe.csv",
     "table": "tbl_2daca1ccb18c",
     "quantity": "nonlinear_index",
     "unit": "m2/W",
     "scale": 1e-20,
     "abscissa_unit": "um",
     "use": "check",
     "parameters": {
       "part": "electronic",
       "coefficient": "self"
     }
   }

Table 1, Theory, row 'ZnSe'\: the two\-band model \(formula two\_band\_theory\) with the band gap of band\_gap\_ZnSe\.

patwardhan\_2021/band\_gap\_ZnSe
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "band_gap_ZnSe",
     "material": "ZnSe",
     "file": "ZnSe/patwardhan_2021__band_gap_ZnSe.csv",
     "table": "tbl_2daca1ccb18c",
     "quantity": "band_gap",
     "unit": "eV",
     "abscissa": "none",
     "use": "check",
     "reproduced_from": [
       "sheik_bahae_1991",
       "N. M. Saeed, Al-Nahrain J. Sci. 14, 86 (2011)",
       "P. D'Amico, A. Calzolari, A. Ruini, and A. Catellani, Sci. Rep. 7, 1 (2017)"
     ],
     "parameters": {
       "kind": "assumed",
       "assumed": true
     }
   }

Table 1, 'Bandgap E\_g \(eV\)', row 'ZnSe'\: 'Obtained from \[1,15,16\]', the input of the theory column \(source notes\)\.

patwardhan\_2021/exp\_ZnS
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "exp_ZnS",
     "material": "ZnS",
     "file": "ZnS/patwardhan_2021__exp_ZnS.csv",
     "table": "tbl_2daca1ccb18c",
     "quantity": "nonlinear_index",
     "unit": "m2/W",
     "scale": 1e-20,
     "abscissa_unit": "um",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "part": "unknown",
       "coefficient": "self",
       "technique": "spectrally resolved two-beam coupling",
       "form": "bulk"
     }
   }

Table 1, Exp\., row 'ZnS \(polycrystalline\)'\. Relative to the absolutely measured material at each wavelength \(source notes\)\. Polycrystalline\. Samples 1 mm thick\.

patwardhan\_2021/theory\_ZnS
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "theory_ZnS",
     "material": "ZnS",
     "file": "ZnS/patwardhan_2021__theory_ZnS.csv",
     "table": "tbl_2daca1ccb18c",
     "quantity": "nonlinear_index",
     "unit": "m2/W",
     "scale": 1e-20,
     "abscissa_unit": "um",
     "use": "check",
     "parameters": {
       "part": "electronic",
       "coefficient": "self"
     }
   }

Table 1, Theory, row 'ZnS \(polycrystalline\)'\: the two\-band model \(formula two\_band\_theory\) with the band gap of band\_gap\_ZnS\.

patwardhan\_2021/band\_gap\_ZnS
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "band_gap_ZnS",
     "material": "ZnS",
     "file": "ZnS/patwardhan_2021__band_gap_ZnS.csv",
     "table": "tbl_2daca1ccb18c",
     "quantity": "band_gap",
     "unit": "eV",
     "abscissa": "none",
     "use": "check",
     "reproduced_from": [
       "sheik_bahae_1991",
       "N. M. Saeed, Al-Nahrain J. Sci. 14, 86 (2011)",
       "P. D'Amico, A. Calzolari, A. Ruini, and A. Catellani, Sci. Rep. 7, 1 (2017)"
     ],
     "parameters": {
       "kind": "assumed",
       "assumed": true
     }
   }

Table 1, 'Bandgap E\_g \(eV\)', row 'ZnS \(polycrystalline\)'\: 'Obtained from \[1,15,16\]', the input of the theory column \(source notes\)\.

patwardhan\_2021/exp\_Al2O3
~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "exp_Al2O3",
     "material": "Al2O3",
     "file": "Al2O3/patwardhan_2021__exp_Al2O3.csv",
     "table": "tbl_2daca1ccb18c",
     "quantity": "nonlinear_index",
     "unit": "m2/W",
     "scale": 1e-20,
     "abscissa_unit": "um",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "part": "unknown",
       "coefficient": "self",
       "technique": "spectrally resolved two-beam coupling",
       "form": "bulk"
     }
   }

Table 1, Exp\., row 'Sapphire'\. Absolute at 3\.5 and 4\.5 um; relative at 2\.3 um \(source notes\)\. Axis not stated\. Samples 500 um thick\.

patwardhan\_2021/theory\_Al2O3
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "theory_Al2O3",
     "material": "Al2O3",
     "file": "Al2O3/patwardhan_2021__theory_Al2O3.csv",
     "table": "tbl_2daca1ccb18c",
     "quantity": "nonlinear_index",
     "unit": "m2/W",
     "scale": 1e-20,
     "abscissa_unit": "um",
     "use": "check",
     "parameters": {
       "part": "electronic",
       "coefficient": "self"
     }
   }

Table 1, Theory, row 'Sapphire'\: the two\-band model \(formula two\_band\_theory\) with the band gap of band\_gap\_Al2O3\.

patwardhan\_2021/band\_gap\_Al2O3
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "band_gap_Al2O3",
     "material": "Al2O3",
     "file": "Al2O3/patwardhan_2021__band_gap_Al2O3.csv",
     "table": "tbl_2daca1ccb18c",
     "quantity": "band_gap",
     "unit": "eV",
     "abscissa": "none",
     "use": "check",
     "reproduced_from": [
       "sheik_bahae_1991",
       "N. M. Saeed, Al-Nahrain J. Sci. 14, 86 (2011)",
       "P. D'Amico, A. Calzolari, A. Ruini, and A. Catellani, Sci. Rep. 7, 1 (2017)"
     ],
     "parameters": {
       "kind": "assumed",
       "assumed": true
     }
   }

Table 1, 'Bandgap E\_g \(eV\)', row 'Sapphire'\: 'Obtained from \[1,15,16\]', the input of the theory column \(source notes\)\.

patwardhan\_2021/exp\_CaF2
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "exp_CaF2",
     "material": "CaF2",
     "file": "CaF2/patwardhan_2021__exp_CaF2.csv",
     "table": "tbl_2daca1ccb18c",
     "quantity": "nonlinear_index",
     "unit": "m2/W",
     "scale": 1e-20,
     "abscissa_unit": "um",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "part": "unknown",
       "coefficient": "self",
       "technique": "spectrally resolved two-beam coupling",
       "form": "bulk"
     }
   }

Table 1, Exp\., row 'CaF2'\. Relative to the absolutely measured material at each wavelength \(source notes\)\. Samples 500 um thick\.

patwardhan\_2021/theory\_CaF2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "theory_CaF2",
     "material": "CaF2",
     "file": "CaF2/patwardhan_2021__theory_CaF2.csv",
     "table": "tbl_2daca1ccb18c",
     "quantity": "nonlinear_index",
     "unit": "m2/W",
     "scale": 1e-20,
     "abscissa_unit": "um",
     "use": "check",
     "parameters": {
       "part": "electronic",
       "coefficient": "self"
     }
   }

Table 1, Theory, row 'CaF2'\: the two\-band model \(formula two\_band\_theory\) with the band gap of band\_gap\_CaF2\.

patwardhan\_2021/band\_gap\_CaF2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "band_gap_CaF2",
     "material": "CaF2",
     "file": "CaF2/patwardhan_2021__band_gap_CaF2.csv",
     "table": "tbl_2daca1ccb18c",
     "quantity": "band_gap",
     "unit": "eV",
     "abscissa": "none",
     "use": "check",
     "reproduced_from": [
       "sheik_bahae_1991",
       "N. M. Saeed, Al-Nahrain J. Sci. 14, 86 (2011)",
       "P. D'Amico, A. Calzolari, A. Ruini, and A. Catellani, Sci. Rep. 7, 1 (2017)"
     ],
     "parameters": {
       "kind": "assumed",
       "assumed": true
     }
   }

Table 1, 'Bandgap E\_g \(eV\)', row 'CaF2'\: 'Obtained from \[1,15,16\]', the input of the theory column \(source notes\)\.

patwardhan\_2021/exp\_MgF2
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "exp_MgF2",
     "material": "MgF2",
     "file": "MgF2/patwardhan_2021__exp_MgF2.csv",
     "table": "tbl_2daca1ccb18c",
     "quantity": "nonlinear_index",
     "unit": "m2/W",
     "scale": 1e-20,
     "abscissa_unit": "um",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "part": "unknown",
       "coefficient": "self",
       "technique": "spectrally resolved two-beam coupling",
       "form": "bulk"
     }
   }

Table 1, Exp\., row 'MgF2'\. Relative to the absolutely measured material at each wavelength \(source notes\)\. Samples 500 um thick\.

patwardhan\_2021/theory\_MgF2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "theory_MgF2",
     "material": "MgF2",
     "file": "MgF2/patwardhan_2021__theory_MgF2.csv",
     "table": "tbl_2daca1ccb18c",
     "quantity": "nonlinear_index",
     "unit": "m2/W",
     "scale": 1e-20,
     "abscissa_unit": "um",
     "use": "check",
     "parameters": {
       "part": "electronic",
       "coefficient": "self"
     }
   }

Table 1, Theory, row 'MgF2'\: the two\-band model \(formula two\_band\_theory\) with the band gap of band\_gap\_MgF2\.

patwardhan\_2021/band\_gap\_MgF2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "band_gap_MgF2",
     "material": "MgF2",
     "file": "MgF2/patwardhan_2021__band_gap_MgF2.csv",
     "table": "tbl_2daca1ccb18c",
     "quantity": "band_gap",
     "unit": "eV",
     "abscissa": "none",
     "use": "check",
     "reproduced_from": [
       "sheik_bahae_1991",
       "N. M. Saeed, Al-Nahrain J. Sci. 14, 86 (2011)",
       "P. D'Amico, A. Calzolari, A. Ruini, and A. Catellani, Sci. Rep. 7, 1 (2017)"
     ],
     "parameters": {
       "kind": "assumed",
       "assumed": true
     }
   }

Table 1, 'Bandgap E\_g \(eV\)', row 'MgF2'\: 'Obtained from \[1,15,16\]', the input of the theory column \(source notes\)\.

patwardhan\_2021/exp\_SiO2
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "exp_SiO2",
     "material": "SiO2",
     "file": "SiO2/patwardhan_2021__exp_SiO2.csv",
     "table": "tbl_2daca1ccb18c",
     "quantity": "nonlinear_index",
     "unit": "m2/W",
     "scale": 1e-20,
     "abscissa_unit": "um",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "part": "unknown",
       "coefficient": "self",
       "technique": "spectrally resolved two-beam coupling",
       "form": "bulk"
     }
   }

Table 1, Exp\., row 'Fused silica'\. Absolute measurement at 2\.3 um; the other wavelengths relative \(source notes\)\. Samples 500 um thick\.

patwardhan\_2021/theory\_SiO2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "theory_SiO2",
     "material": "SiO2",
     "file": "SiO2/patwardhan_2021__theory_SiO2.csv",
     "table": "tbl_2daca1ccb18c",
     "quantity": "nonlinear_index",
     "unit": "m2/W",
     "scale": 1e-20,
     "abscissa_unit": "um",
     "use": "check",
     "parameters": {
       "part": "electronic",
       "coefficient": "self"
     }
   }

Table 1, Theory, row 'Fused silica'\: the two\-band model \(formula two\_band\_theory\) with the band gap of band\_gap\_SiO2\.

patwardhan\_2021/band\_gap\_SiO2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "band_gap_SiO2",
     "material": "SiO2",
     "file": "SiO2/patwardhan_2021__band_gap_SiO2.csv",
     "table": "tbl_2daca1ccb18c",
     "quantity": "band_gap",
     "unit": "eV",
     "abscissa": "none",
     "use": "check",
     "reproduced_from": [
       "sheik_bahae_1991",
       "N. M. Saeed, Al-Nahrain J. Sci. 14, 86 (2011)",
       "P. D'Amico, A. Calzolari, A. Ruini, and A. Catellani, Sci. Rep. 7, 1 (2017)"
     ],
     "parameters": {
       "kind": "assumed",
       "assumed": true
     }
   }

Table 1, 'Bandgap E\_g \(eV\)', row 'Fused silica'\: 'Obtained from \[1,15,16\]', the input of the theory column \(source notes\)\.

Formulas
--------

patwardhan\_2021/two\_band\_theory
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "two_band_theory",
     "equation": "Table 1 note a and p. 1827",
     "printed": "Theoretical value is calculated using two-band model theory in [1] ... (with K' = 0.86 x 10^-8, E_P = 21 eV [1])",
     "variable": "photon energy over the band gap, hbar omega / E_g (the model of Sheik-Bahae et al. 1991)",
     "coefficients": {
       "K_prime": "0.86 x 10^-8",
       "E_P": "21 eV"
     },
     "check": "Not reproduced: the paper names the model and its two constants but prints neither the dispersion function G2 nor the linear indices n0 it used (checked 2026-09-26). K' = 0.86e-8 differs from DeSalvo et al.'s 7.33e-9 and from the 1.5e-8 of Sheik-Bahae et al. 1991 (desalvo_1996, p. 1328). Added 2026-09-27, from the original (sheik_bahae_1991, p. 1304): 0.86e-8 is Sheik-Bahae et al.'s own fit to the wide-gap solids (its Table III '*' column), and its G2 (formula sheik_bahae_1991/g2_degenerate, which reproduces that table) makes this column computable once n0 is chosen; ZnSe, sapphire, CaF2, MgF2 and fused-silica gaps here equal that table's, the ZnS gap (3.2 eV) does not (3.54 eV there)."
   }

The Theory columns of Table 1 are this model's values; recorded as use = 'check' datasets\.

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.