farrow_1985
===========

R\. L\. Farrow and L\. A\. Rahn, J\. Opt\. Soc\. Am\. B 2, 903 \(1985\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/farrow_1985.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1364/josab\.2\.000903 <https://doi.org/10.1364/josab.2.000903>`__

**Source kind:** measurement

**Recorded technique:** Crossed\-beam, polarization\-resolved CARS with a frequency\-doubled Nd\:YAG pump \(532 nm; single axial mode \<= 0\.01 cm^\-1, or multimode 0\.7 cm^\-1\) and a pulsed dye probe \(Stokes, \<= 0\.03 cm^\-1\); fully resolved N2 Q\-branch spectra in 1\.00 % N2 in Ar and the O\(18\) line of pure N2, 297 K, 200\-1000 Torr, fitted with theoretical spectra \(Schrotter and Klockner's Q\-branch cross section, argon\-broadened linewidths measured by inverse Raman spectroscopy, Table 1\) to find the nonresonant susceptibility relative to the N2 resonant one\.

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

**Dataset quantities:** nonlinear\_susceptibility, raman\_linewidth

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

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

Nonresonant CARS susceptibilities of Ar and N2 referenced to the N2 Raman resonance \(the paper's main subject is the convolution of CARS spectra with multimode pumps; Table 3's concentration errors are not extracted\)\. Table 1's N2\-Ar collisional\-broadening coefficients are the Raman dataset table1\_Ar \(added 2026\-09\-26, TC\-439; see its notes\)\.

Definition\: Table 2's caption\: 'chi\_nr measurements expressed using the definition of relation \(1\)', Yuratich's expression, relation \(1\), p\. 903\: I\_4 proportional to the integral of \|sum\_j K\_j L\_j\(w1 \- w3\) \+ chi\_nr\|^2 I\_1 I\_2 I\_3, with L\_j = gamma\_j/\(w\_j \- w \+ w\_3 \- i gamma\_j\) and K\_j = c^4 Delta N\_j \(d sigma/d Omega\)\_j / \(hbar w\_3^4 gamma\_j\), i\.e\. the CARS\-literature susceptibility per unit volume, chi^CARS \(Rosasco and Hurst's Eq\. \(A4\), whose P\(w\_as\) = \(1/4\) chi^CARS E\_L^2 E\_s\*, Eq\. \(A5\), with the E/2 amplitude convention\)\. The paper does not print the density; the values are per amagat \(2\.687e19 cm^\-3\)\: Table 2's Ref\. 13 column equals 3 x Lundeen et al\.'s per\-molecule chi x 2\.687e19 \(Ar 131e\-39 \-\> 10\.56, N2 105e\-39 \-\> 8\.46, N2 \+\-14 \-\> \+\-1\.13, printed 10\.6, 8\.5 \+\- 1\.1\) and its Ref\. 12 column equals 12 x Rosasco and Hurst's 3 sigma/24 at 1 amagat \(Ar 0\.788 \-\> 9\.46, printed 9\.5\), as Rosasco and Hurst's \(A6\)\-\(A7\) and \(A26\)\-\(A28\) require \(checked 2026\-09\-26\)\. Hence chi^CARS = 12 chi\_1111 = 3 sigma/2 = N0 gamma\_T/2 at 1 amagat\: gamma\_T = 2 chi^CARS/N0 \(1e\-18 cm^3/erg per amagat = 7\.443e\-38 esu = 147\.8 au\)\. These are nonlinear susceptibilities per amagat, without a state \(unit recorded as cm3/\(erg amagat\), as Farrow et al\. 1987 and Hahn and Lee 1995 print it; this paper prints only 'cm^3/erg'\)\.

Results \(p\. 904\)\: fitting the resolved spectra required reducing Hall and Eckbreth's chi\_nr \(Rado rescaled\: Ar 11\.6, N2 10\.1, Figs\. 1, 2\) by 17 % for Ar \(\+\-6 % from the fit\) and 16 \+\- 8 % for N2\: chi\_nr = 9\.6 \+\- 1\.0 \(Ar\) and 8\.5 \+\- 0\.9 \(N2\) x 10^\-18 cm^3/erg in the text, but Table 2 prints N2 8\.5 \+\- 1\.3 \(image checked\)\: the uncertainties disagree, unresolved; the table's is recorded\. The N2 value comes from the O\(18\) line \(linewidth 0\.05 \+\- 0\.007 cm^\-1 HWHM at 1000 Torr, inferred from the CARS spectrum\), the Ar value from the Q branch of 1 % N2 in Ar with IRS\-measured widths\. 'Our error bounds for the chi\_nr of nitrogen arise predominantly from uncertainties in linewidth, the dependence of chi\_r on the Raman depolarization ratio as well as the cross section, and the moderate temperature sensitivity of the J = 18 state' \(p\. 904\)\.

Part\: the CARS nonresonant background; for Ar electronic; for N2 the background near its Raman lines, i\.e\. electronic plus small off\-resonant Raman contributions not separated \(Lundeen et al\. compute \-3 and \+3 of 105 for the vibrational and rotational tails at 4155 cm^\-1\)\: recorded electronic, with that caveat\. The orientational term does not enter CARS at these detunings\.

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

Datasets
--------

farrow\_1985/this\_work\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "this_work_Ar",
     "material": "Ar",
     "file": "Ar/farrow_1985__this_work_Ar.csv",
     "table": "tbl_0abf9a86f7ed",
     "quantity": "nonlinear_susceptibility",
     "unit": "cm3/(erg amagat)",
     "scale": 1e-18,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "process": "cars",
       "convention": "chi_cars_per_amagat",
       "part": "electronic"
     }
   }

Table 2 \(p\. 904\), chi\_nr in 10^\-18 cm^3/erg per amagat \(the CARS chi^CARS of relation \(1\); gamma\_T = 2 chi^CARS/N0, about 148 au per unit; see the source notes\), column This Work\: 9\.6 \+\- 1\.0 \(Q branch of 1 % N2 in Ar, 532 nm pump\)\. CARS chi\(\-w\_as; w\_p, w\_p, \-w\_s\)\.

farrow\_1985/this\_work\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "this_work_N2",
     "material": "N2",
     "file": "N2/farrow_1985__this_work_N2.csv",
     "table": "tbl_0abf9a86f7ed",
     "quantity": "nonlinear_susceptibility",
     "unit": "cm3/(erg amagat)",
     "scale": 1e-18,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "process": "cars",
       "convention": "chi_cars_per_amagat",
       "part": "electronic"
     }
   }

Table 2 \(p\. 904\), chi\_nr in 10^\-18 cm^3/erg per amagat \(the CARS chi^CARS of relation \(1\); gamma\_T = 2 chi^CARS/N0, about 148 au per unit; see the source notes\), column This Work\: 8\.5 \+\- 1\.3 \(the text, p\. 904, says \+\- 0\.9; O\(18\) of pure N2, 532 nm pump\)\. CARS chi\(\-w\_as; w\_p, w\_p, \-w\_s\)\.

farrow\_1985/hall\_eckbreth\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "hall_eckbreth_Ar",
     "material": "Ar",
     "file": "Ar/farrow_1985__hall_eckbreth_Ar.csv",
     "table": "tbl_0abf9a86f7ed",
     "quantity": "nonlinear_susceptibility",
     "unit": "cm3/(erg amagat)",
     "scale": 1e-18,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "reproduced",
     "reproduced_from": [
       "R. J. Hall and A. C. Eckbreth, in Laser Applications, Vol. 5, edited by J. F. Ready and R. K. Erf (Academic, New York, 1984), p. 213"
     ],
     "parameters": {
       "process": "cars",
       "convention": "chi_cars_per_amagat",
       "part": "electronic"
     }
   }

Table 2 \(p\. 904\), chi\_nr in 10^\-18 cm^3/erg per amagat \(the CARS chi^CARS of relation \(1\); gamma\_T = 2 chi^CARS/N0, about 148 au per unit; see the source notes\), column Ref\. 1 \(Hall and Eckbreth\)\: 'scaled from the results of Rado and thus simply represent a correction factor different from that discussed in Ref\. 13', 'currently the most widely used values' \(note a\)\. Rado's ruby experiment \(694\.3 nm\); no uncertainty\. CARS chi\(\-w\_as; w\_p, w\_p, \-w\_s\)\.

farrow\_1985/hall\_eckbreth\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "hall_eckbreth_N2",
     "material": "N2",
     "file": "N2/farrow_1985__hall_eckbreth_N2.csv",
     "table": "tbl_0abf9a86f7ed",
     "quantity": "nonlinear_susceptibility",
     "unit": "cm3/(erg amagat)",
     "scale": 1e-18,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "reproduced",
     "reproduced_from": [
       "R. J. Hall and A. C. Eckbreth, in Laser Applications, Vol. 5, edited by J. F. Ready and R. K. Erf (Academic, New York, 1984), p. 213"
     ],
     "parameters": {
       "process": "cars",
       "convention": "chi_cars_per_amagat",
       "part": "electronic"
     }
   }

Table 2 \(p\. 904\), chi\_nr in 10^\-18 cm^3/erg per amagat \(the CARS chi^CARS of relation \(1\); gamma\_T = 2 chi^CARS/N0, about 148 au per unit; see the source notes\), column Ref\. 1 \(Hall and Eckbreth\), Rado rescaled \(note a\); 694\.3 nm; no uncertainty\. CARS chi\(\-w\_as; w\_p, w\_p, \-w\_s\)\.

farrow\_1985/rosasco\_hurst\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "rosasco_hurst_Ar",
     "material": "Ar",
     "file": "Ar/farrow_1985__rosasco_hurst_Ar.csv",
     "table": "tbl_0abf9a86f7ed",
     "quantity": "nonlinear_susceptibility",
     "unit": "cm3/(erg amagat)",
     "scale": 1e-18,
     "abscissa_unit": "nm",
     "wavelength_medium": "standard_air",
     "use": "reproduced",
     "reproduced_from": [
       "rosasco_1985"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "process": "cars",
       "convention": "chi_cars_per_amagat",
       "part": "electronic"
     }
   }

Table 2 \(p\. 904\), chi\_nr in 10^\-18 cm^3/erg per amagat \(the CARS chi^CARS of relation \(1\); gamma\_T = 2 chi^CARS/N0, about 148 au per unit; see the source notes\), column Ref\. 12 \(Rosasco and Hurst, 'to be published'; = rosasco\_1985, whose Table IV 3 sigma/24 = 0\.788 x 12 = 9\.46\)\: phase\-modulated cw coherent Raman, 676\.4 nm pump \(Kr\-ion line, standard air\)\. CARS chi\(\-w\_as; w\_p, w\_p, \-w\_s\)\.

farrow\_1985/lundeen\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "lundeen_Ar",
     "material": "Ar",
     "file": "Ar/farrow_1985__lundeen_Ar.csv",
     "table": "tbl_0abf9a86f7ed",
     "quantity": "nonlinear_susceptibility",
     "unit": "cm3/(erg amagat)",
     "scale": 1e-18,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "reproduced",
     "reproduced_from": [
       "lundeen_1983"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "process": "cars",
       "convention": "chi_cars_per_amagat",
       "part": "electronic"
     }
   }

Table 2 \(p\. 904\), chi\_nr in 10^\-18 cm^3/erg per amagat \(the CARS chi^CARS of relation \(1\); gamma\_T = 2 chi^CARS/N0, about 148 au per unit; see the source notes\), column Ref\. 13 \(Lundeen et al\.\)\: their 131e\-39 cm^6/\(erg molecule\) x 3 x 2\.687e19 = 10\.56; 532 nm pump\. CARS chi\(\-w\_as; w\_p, w\_p, \-w\_s\)\.

farrow\_1985/lundeen\_N2
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "lundeen_N2",
     "material": "N2",
     "file": "N2/farrow_1985__lundeen_N2.csv",
     "table": "tbl_0abf9a86f7ed",
     "quantity": "nonlinear_susceptibility",
     "unit": "cm3/(erg amagat)",
     "scale": 1e-18,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "reproduced",
     "reproduced_from": [
       "lundeen_1983"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "process": "cars",
       "convention": "chi_cars_per_amagat",
       "part": "electronic"
     }
   }

Table 2 \(p\. 904\), chi\_nr in 10^\-18 cm^3/erg per amagat \(the CARS chi^CARS of relation \(1\); gamma\_T = 2 chi^CARS/N0, about 148 au per unit; see the source notes\), column Ref\. 13 \(Lundeen et al\.\)\: their \(105 \+\- 14\)e\-39 x 3 x 2\.687e19 = 8\.46 \+\- 1\.13; 532 nm pump\. CARS chi\(\-w\_as; w\_p, w\_p, \-w\_s\)\.

farrow\_1985/rado\_lundeen\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "rado_lundeen_Ar",
     "material": "Ar",
     "file": "Ar/farrow_1985__rado_lundeen_Ar.csv",
     "table": "tbl_0abf9a86f7ed",
     "quantity": "nonlinear_susceptibility",
     "unit": "cm3/(erg amagat)",
     "scale": 1e-18,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "reproduced",
     "reproduced_from": [
       "lundeen_1983",
       "W. G. Rado, Appl. Phys. Lett. 11, 123 (1967)"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "process": "cars",
       "convention": "chi_cars_per_amagat",
       "part": "electronic"
     }
   }

Table 2 \(p\. 904\), chi\_nr in 10^\-18 cm^3/erg per amagat \(the CARS chi^CARS of relation \(1\); gamma\_T = 2 chi^CARS/N0, about 148 au per unit; see the source notes\), column Ref\. 11 \(Rado\) 'as scaled by' Lundeen et al\. \(p\. 905\)\: Lundeen's Rado column \(Ar 118\) x 3 x 2\.687e19 = 9\.51; ruby 694\.3 nm\. CARS chi\(\-w\_as; w\_p, w\_p, \-w\_s\)\.

farrow\_1985/rado\_lundeen\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "rado_lundeen_N2",
     "material": "N2",
     "file": "N2/farrow_1985__rado_lundeen_N2.csv",
     "table": "tbl_0abf9a86f7ed",
     "quantity": "nonlinear_susceptibility",
     "unit": "cm3/(erg amagat)",
     "scale": 1e-18,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "reproduced",
     "reproduced_from": [
       "lundeen_1983",
       "W. G. Rado, Appl. Phys. Lett. 11, 123 (1967)"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "process": "cars",
       "convention": "chi_cars_per_amagat",
       "part": "electronic"
     }
   }

Table 2 \(p\. 904\), chi\_nr in 10^\-18 cm^3/erg per amagat \(the CARS chi^CARS of relation \(1\); gamma\_T = 2 chi^CARS/N0, about 148 au per unit; see the source notes\), column Ref\. 11 \(Rado\) as scaled by Lundeen et al\.\: N2 is that scaling's reference \(105 \+\- 14 \-\> 8\.46\); the \+\- 0\.8 is not Lundeen's \+\- 1\.1\: unexplained; ruby 694\.3 nm\. CARS chi\(\-w\_as; w\_p, w\_p, \-w\_s\)\.

farrow\_1985/table1\_Ar
~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table1_Ar",
     "material": "N2",
     "file": "N2/farrow_1985__table1_Ar.csv",
     "table": "tbl_da579f77cd0b",
     "quantity": "raman_linewidth",
     "unit": "cm-1/atm",
     "scale": 0.001,
     "abscissa": "label",
     "use": "primary",
     "excluded_rows": {
       "Q(0)": "printed '55^a', note a 'Extrapolated' (the paper's extrapolation, not a measurement)",
       "Q(1)": "printed '46^a', note a 'Extrapolated' (the paper's extrapolation, not a measurement)"
     },
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "transition": "Q(J), v = 0 -> 1, per row",
       "width": "hwhm",
       "perturber": "Ar"
     }
   }

Table 1 \(p\. 904\), 'Argon Collisional\-Broadening Coefficients for Nitrogen Q\-Branch Transitions \(HWHM x 10^3 cm^\-1\)'\: the HALF width at half maximum of the N2 Q\(J\) lines \(v = 0 \-\> 1\) per unit pressure of Ar, 'pressure\-broadening coefficients' \(p\. 904\)\. The caption prints only 'cm^\-1'; per atm is inferred\: the text \(p\. 906\) gives HWHM 'of the order of 0\.015 cm^\-1' for 1\-5 % N2 in Ar at 300 Torr \(0\.395 atm\), i\.e\. about 0\.038 cm^\-1/atm, as the table's mid\-J values\. Measured by high\-resolution inverse Raman spectroscopy \(Ref\. 8\) in a 25 % N2\-in\-Ar mixture, 'correcting for the nitrogen\-nitrogen broadening using the nitrogen self\-broadening coefficients reported by Rosasco' \(Ref\. 9\: Rosasco, Lempert, Hurst and Fein, Chem\. Phys\. Lett\. 97, 435 \(1983\) = rosasco\_1983, whose Table 1 gives the N2 self\-broadening HWHM per atm at 298 K, J = 0\-18; curated 2026\-09\-27\), p\. 904\. The IRS temperature is not stated \(the CARS measurements are at 297 K\)\. The '\(n\)' is the error in the last digit, its level not stated\. J = 0, 1 are extrapolated \(excluded\)\. Added 2026\-09\-26 \(TC\-439\)\.

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.