wahlstrand_2012b ================ J\. K\. Wahlstrand, Y\.\-H\. Cheng and H\. M\. Milchberg, "High Field Optical Nonlinearity and the Kramers\-Kronig Relations", Phys\. Rev\. Lett\. 109, 113904 \(2012\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1103/PhysRevLett\.109\.113904 `__ **Source kind:** measurement **Recorded technique:** Single\-shot supercontinuum spectral interferometry \(as wahlstrand\_2012\)\: 40\-fs, 3\.5\-mJ, 800\-nm Ti\:sapphire pump; supercontinuum probe \(120 nm bandwidth, generated in SF6\) and reference 2 ps apart; thin gas flow \(L\_eff ~ 200\-400 um depending on gas\) in a vacuum chamber; 1000 interferograms averaged \(phase shifts down to 5e\-3 rad\)\. 'An auxiliary spatial interferometry beam \[7\] allowed extraction of the absolute linear phase shift of the Ar stationary gas flow; all other gases were referenced to Ar'; the absolute index shift is 'calibrated by a measurement in a backfilled vacuum chamber at low pressure, as in \[7\]' \(p\. 1\)\. Delta n measured against peak intensity up to the ionization threshold of each gas, and compared with a Kramers\-Kronig calculation from the PPT\-type ionization rate of Popruzhenko et al\. \(pp\. 2\-4\)\. **Materials in structured entries:** Ar, He, Kr, Ne, Xe **Dataset quantities:** nonlinear\_index **Contents:** 5 datasets; 0 formulas. Curation notes -------------- Journal pages 113904\-1 to \-5 = PDF pages 1\-5\. Identity checked against the first page\. He, Ne, Ar, Kr, Xe\. DEFINING EQUATIONS \(p\. 1, quoted\)\: 'The nonlinear refractive index shift is Delta n\(x, t\) = \(k0 L\_eff\)^\-1 Delta Phi\(x, t\)' \.\.\. 'Below the ionization threshold, we write Delta n\(x, t\) = 2 n2 I\(x, t\), where I\(x, t\) is determined directly from the pump pulse energy and from I\(x, t\) proportional to Delta Phi\(x, t\) at low intensity in Ar\. The factor of 2 recognizes that Delta n describes cross\-phase modulation and n2 is the nonlinear self\-refractive index\.' p\. 4\: 'The experimentally measured values of n2 = Delta n / 2I are in good agreement with previous estimates using harmonic generation \[25 = Shelton and Rice\]'\. So the tabulated n2 is the SELF coefficient\. Kramers\-Kronig, Eq\. \(1\)\: Delta n\(omega, E\) = \(c/pi\) P int Delta alpha\(Omega, E\) / \(Omega^2 \- omega^2\) dOmega \(Delta alpha here an absorption coefficient\); average\-frequency approximation, Eq\. \(2\)\. No chi\(3\) or gamma is defined\. Gaussian conventions\. VALUES\. The n2 values exist only as labels printed in the panels of Fig\. 3 \(p\. 4; the figure is a raster image, its text is not in the pdf text layer\), read from the figure image\: He \(3\.1 \+\- 0\.4\) x 1e\-21, Ne \(8\.7 \+\- 1\.1\) x 1e\-21, Ar \(9\.7 \+\- 1\.2\) x 1e\-20, Kr \(2\.2 \+\- 0\.4\) x 1e\-19, Xe \(5\.8 \+\- 1\.1\) x 1e\-19 cm2/W\. Each is the slope of a linear fit of Delta n to 2 n2 I over the measured points below the ionization threshold \(Fig\. 3 caption\)\. Horizontal error bars are the intensity calibration, vertical the phase extraction; the meaning of the \+\- on n2 is not stated\. The Ar value equals wahlstrand\_2012's Ar value \(same calibration\)\. REFERENCE STATE\. Not stated in this Letter; the calibration is 'as in \[7\]' \(wahlstrand\_2012, 1 atm\)\. Recorded as 101325 Pa, 290\.9 K\: the density of that N2 flow calibration \(wahlstrand\_2012 notes; TC\-316\)\. Pump 800 nm \(1\.55 eV, p\. 2\), vacuum assumed; probe wavelength not stated here \(the supercontinuum of wahlstrand\_2012, ~550\-635 nm\)\. PART\. Noble gases\: electronic\. The response is linear in intensity up to the measured ionization threshold of each gas \(Fig\. 3, dotted lines; not tabulated; note \[24\]\: the Ar threshold here is ~20 % lower than in Wahlstrand et al\. PRL 107, 103901 \(2011\), because that experiment overestimated the peak intensity\)\. This contradicts the saturating and inverting higher\-order Kerr series of Bree et al\. \(and Loriot et al\.\)\: Fig\. 3 overlays Bree et al\.'s self index and the probe index obtained by multiplying their n\_2k by k \+ 1 \(Supplemental Material \[18\], not in the library\)\. **Recorded bibliographic identity status:** VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- wahlstrand\_2012b/n2\_He ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "n2_He", "material": "He", "table": "text", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-21, "abscissa_unit": "nm", "state": { "pressure_pa": 101325.0, "temperature_k": 290.9 }, "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "part": "electronic", "coefficient": "self", "pulse_fs": 40 } } 1 inline points in the source record. Fig\. 3, top panel label 'n2 = \(3\.1 \+\- 0\.4\) x 10^\-21 cm2/W' \(read from the figure image, p\. 4\)\. Fit up to ~360 TW/cm2 \(ionization threshold ~390 TW/cm2 from the figure\)\. State assumed \(source notes\)\. wahlstrand\_2012b/n2\_Ne ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "n2_Ne", "material": "Ne", "table": "text", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-21, "abscissa_unit": "nm", "state": { "pressure_pa": 101325.0, "temperature_k": 290.9 }, "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "part": "electronic", "coefficient": "self", "pulse_fs": 40 } } 1 inline points in the source record. Fig\. 3, second panel label 'n2 = \(8\.7 \+\- 1\.1\) x 10^\-21 cm2/W' \(figure image, p\. 4\)\. State assumed\. wahlstrand\_2012b/n2\_Ar ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "n2_Ar", "material": "Ar", "table": "text", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-20, "abscissa_unit": "nm", "state": { "pressure_pa": 101325.0, "temperature_k": 290.9 }, "use": "check", "reproduced_from": [ "wahlstrand_2012" ], "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "part": "electronic", "coefficient": "self", "pulse_fs": 40 } } 1 inline points in the source record. Fig\. 3, third panel label 'n2 = \(9\.7 \+\- 1\.2\) x 10^\-20 cm2/W' \(figure image, p\. 4\)\. Identical to wahlstrand\_2012/n2\_Ar, which this Letter's calibration rests on \(Ar is the absolute reference here\); whether it is a new fit to the Fig\. 3 points or the earlier value is not stated\. Kept as 'check' so the Ar value is not counted twice; wahlstrand\_2018 uses it as its intensity calibration\. wahlstrand\_2012b/n2\_Kr ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "n2_Kr", "material": "Kr", "table": "text", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-19, "abscissa_unit": "nm", "state": { "pressure_pa": 101325.0, "temperature_k": 290.9 }, "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "part": "electronic", "coefficient": "self", "pulse_fs": 40 } } 1 inline points in the source record. Fig\. 3, fourth panel label 'n2 = \(2\.2 \+\- 0\.4\) x 10^\-19 cm2/W' \(figure image, p\. 4\)\. State assumed\. wahlstrand\_2012b/n2\_Xe ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "n2_Xe", "material": "Xe", "table": "text", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-19, "abscissa_unit": "nm", "state": { "pressure_pa": 101325.0, "temperature_k": 290.9 }, "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "part": "electronic", "coefficient": "self", "pulse_fs": 40 } } 1 inline points in the source record. Fig\. 3, bottom panel label 'n2 = \(5\.8 \+\- 1\.1\) x 10^\-19 cm2/W' \(figure image, p\. 4\)\. State assumed\. 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.