mareev_2018 =========== E\. Mareev, V\. Aleshkevich, F\. Potemkin, V\. Bagratashvili, N\. Minaev and V\. Gordienko, Opt\. Express 26, 13229 \(2018\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1364/oe\.26\.013229 `__ **Source kind:** measurement **Recorded technique:** Spectral broadening by self\-phase modulation of 1240 nm Cr\:forsterite pulses \(200 fs in the set\-up description, '150\-fs laser pulse' in the Fig\. 5 caption; up to 2 mJ, 10 Hz, energy kept below filamentation\) through an 11\.6 cm stainless\-steel supercritical\-fluid cell with two 5 mm sapphire windows, at pressures up to 200 bar along isotherms \(CO2 33\.5 and 50 C; Xe 24 and 34 C\); RMS spectral widths averaged over 20 pulses; n2 from the RMS broadening formula \(Eq\. 14\) and the nonlinear phase \(Eq\. 9\); the accuracy was 'verified' on a 5 mm fused\-silica window with n2 = 2\.8 \+\- 0\.3 x 10^\-20 m^2/W \(their ref\. 32\)\. **Materials in structured entries:** CO2, Xe **Dataset quantities:** nonlinear\_index **Contents:** 2 datasets; 0 formulas. Curation notes -------------- Defining equations\. Theory \(p\. 4\-5\)\: n = 1 \+ N beta/3 \+ \(4 pi N beta^2 / \(45 k T\)\) E^2 = n0 \+ n2 E^2 \(Eq\. 1\), n2 = 4 pi N beta^2/\(45 k\_B T\) ~ N beta^2 \(Eq\. 2\)\: a Langevin orientational model with the mean polarizability beta, used to motivate the cluster\-driven rise of n2 near the Widom line; it is not a model of the electronic n2 \(an isotropic atom has no orientational Kerr effect\)\. Measurement \(p\. 6\-7\)\: phi\_max = \-L \(w0/c\) \(n2/n0\) I0 \(Eq\. 9; plus a fluctuating part\) and Delta w\_out/Delta w\_in = \(1 \+ \(4/\(3 sqrt 3\)\) phi\_max^2\)^2 \(Eq\. 14, as printed, for a transform\-limited Gaussian pulse, from their ref\. 31\)\. The values are in m^2/W, so n2 multiplies the intensity \(coefficient = self, SPM of one beam\)\. No beam size or intensity is reported\. Values \(Fig\. 5 caption, p\. 9, checked in the PDF text layer\)\: 'First bar corresponds to the n2 = 3\.4 \+\- 0\.6\*10^\-22 m2/W in CO2 and n2 = 6\.2 \+\- 1\.6\*10^\-22 m2/W in Xe at atmospheric pressure' \(the library's markdown reads 'm/W' for CO2; the PDF has m2/W\); 'First bar' is the 1 bar point of the pressure scans\. The temperature is that of the isotherm, not stated for the 1 bar points\: the lower isotherm is assumed \(CO2 306\.65 K, Xe 297\.15 K\)\. Maxima near the ridge \(Widom line\), supercritical states, not gas\-phase values \(abstract\)\: 4\.8 x 10^\-20 m^2/W \(CO2\), 3\.5 x 10^\-20 m^2/W \(Xe\)\. Density slopes \(p\. 9\)\: n2 ~ \(0\.9 \+\- 0\.2\) rho \(CO2, 1\-60 bar\), \(0\.8 \+\- 0\.2\) rho \(90\-150 bar\), \(0\.7 \+\- 0\.2\) rho \(Xe, 0\-45 bar\), \(0\.4 \+\- 0\.1\) rho \(70\-90 bar\), in 'm5/\(W\*kg\)' with rho in kg/m^3\: a factor of about 1e\-22 is evidently missing \(the 1 bar values over the densities, about 1\.7 and 5\.3 kg/m^3 with molar masses 44\.01 and 131\.29 g/mol and optmat's densities, give 2\.0e\-22 and 1\.2e\-22 m^5/\(W kg\)\)\. Not extracted\. Both 1 bar values are excluded\: they are about ten times the established values\. Xe\: 6\.2e\-22 m^2/W against 5\.8e\-23 m^2/W at 800 nm \(Wahlstrand et al\. 2012b, quoted by pigeon\_2018; the dispersion to 1240 nm lowers it by a few per cent\), a factor 11; CO2\: 3\.4e\-22 against Geints et al\.'s 1\.0e\-23 \(50 fs\) and 5\.4e\-23 m^2/W \(500 fs\) at 800 nm \(geints\_2025\), a factor 6 to 34 \(rotation explains at most the long\-pulse part\)\. Why \(an assessment; the paper gives no error budget beyond the silica check\)\: \(1\) the two 5 mm sapphire windows\. With the paper's own fused\-silica value as a stand\-in for sapphire, the windows' n2 L \(2\.8e\-22 m\) is about 40 times that of 11\.6 cm of Xe at 1 bar \(6\.6e\-24 m for n2 = 5\.7e\-23 m^2/W\); the paper does not say how the window SPM was separated from the gas SPM, and an incomplete subtraction at 1 bar, where the gas adds about 2 % to the phase, inflates the gas value by a large factor\. \(2\) The intensity I0 of Eq\. \(9\) is not reported; an error in it scales n2 directly\. \(3\) Eq\. \(14\) as printed \(an outer square\) gives broadening 1 \+ \(8/\(3 sqrt 3\)\) phi^2 for small phi; any misprint in that exponent changes n2 by a factor of about 2, not 10\. An earlier reading's 'about 10 times too high' is confirmed for Xe; the cause cannot be settled from the paper\. Wavelength 1240 nm \(medium not stated\)\. Parts\: Xe electronic; CO2 at 200 fs includes part of the rotational response \(instantaneous\)\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- mareev\_2018/spm\_1bar\_CO2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "spm_1bar_CO2", "material": "CO2", "table": "text", "quantity": "nonlinear_index", "unit": "m2/W", "scale": 1e-22, "abscissa_unit": "nm", "state": { "pressure_pa": 100000.0, "temperature_k": 306.65 }, "use": "excluded", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "part": "instantaneous", "coefficient": "self", "pulse_fs": 200 } } 1 inline points in the source record. Fig\. 5 caption \(p\. 9\)\: n2 = 3\.4 \+\- 0\.6 x 10^\-22 m^2/W 'at atmospheric pressure' \(1 bar point of the 33\.5 C isotherm assumed\)\. Excluded\: 6 to 34 times Geints et al\.'s 800 nm values; see the record's notes for the likely causes\. mareev\_2018/spm\_1bar\_Xe ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "spm_1bar_Xe", "material": "Xe", "table": "text", "quantity": "nonlinear_index", "unit": "m2/W", "scale": 1e-22, "abscissa_unit": "nm", "state": { "pressure_pa": 100000.0, "temperature_k": 297.15 }, "use": "excluded", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "part": "electronic", "coefficient": "self", "pulse_fs": 200 } } 1 inline points in the source record. Fig\. 5 caption \(p\. 9\)\: n2 = 6\.2 \+\- 1\.6 x 10^\-22 m^2/W 'at atmospheric pressure' \(1 bar point of the 24 C isotherm assumed\)\. Excluded\: about 11 times the established Xe value; see the record's notes\. 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 ` for the checks and decisions.