wahlstrand_2015 =============== J\. K\. Wahlstrand, S\. Zahedpour, Y\.\-H\. Cheng, J\. P\. Palastro and H\. M\. Milchberg, "Absolute measurement of the ultrafast nonlinear electronic and rovibrational response in H2 and D2", Phys\. Rev\. A 92, 063828 \(2015\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1103/PhysRevA\.92\.063828 `__ **Source kind:** measurement **Recorded technique:** Single\-shot supercontinuum spectral interferometry\: 3\-mJ, 40\-fs pump near 800 nm; supercontinuum probe and reference \(500\-700 nm, from ~2\.5 atm SF6 or Xe; chirp beta2 = 1675 fs^2, beta3 = 396 fs^3, omega0 = 3\.05 fs^\-1\), collinear with the pump; thin laser\-drilled gas\-flow tube \(absolute, calibrated as in wahlstrand\_2012\) or backfilled chamber \(~0\.3 atm\)\. Rotational parameters \(B, D, Delta alpha\) from the delayed response \(pulse widths varied at fixed 34 uJ\); the vibrational part separated from the electronic one through the resonant two\-beam\-coupling phase shift as a function of the pump\-probe beat frequency Delta omega \(chirped probe\), fitted with a one\-mode rovibrational density\-matrix model \(pp\. 2\-5\)\. **Materials in structured entries:** D2, H2 **Dataset quantities:** nonlinear\_index, polarizability\_anisotropy **Contents:** 14 datasets; 0 formulas. Curation notes -------------- Journal pages 063828\-1 to \-10 = PDF pages 1\-10\. Identity checked against the first page\. H2 and D2\. DEFINING EQUATIONS \(Gaussian\)\. p\. 1\: Delta n\(x, t\) = \(k0 L\_eff\)^\-1 Delta Phi\(x, t\), k0 the probe central wavenumber\. p\. 4\: the probe's instantaneous polarization P\_p^inst = chi\_eff A\_p exp\[i\(k\_p\.r \- omega\_p t\)\] with '2 pi chi\_eff = Delta n = n2 I\_e', n2 = n2,elec \+ n2,vib, n2,vib = n2,vib^s \+ n2,vib^g; 'for a nonresonant electronic response, the smooth and grating terms are the same, so n2,elec = n2,elec^s \+ n2,elec^g = 2 n2,elec^s\. The nonlinear refractive index for a weak probe pulse is a factor of 2 larger than for a pulse acting on itself \[19\]' \(p\. 4\)\. So the tabulated n2,elec^s is the SELF coefficient\. Eqs\. \(8\)\-\(9\), p\. 4 \(cw limit\)\: n2,vib^s = 4 pi^2 N \(d alpha/dQ\)^2 / \(n0 c mu Omega\_v^2\), n2,vib^g = 4 pi^2 N \(d alpha/dQ\)^2 / \[n0 c mu \(Omega\_v^2 \- Delta omega^2\)\], alpha = alpha\_par/3 \+ 2 alpha\_perp/3, mu the reduced mass; Eq\. \(10\) the finite\-pulse grating term \(Dawson function\)\. Probe prompt index n2,prompt = 2 n2,elec^s \+ n2,vib^s \+ n2,vib^g \(p\. 5\)\. Effective n2 of a pulse I\(t\) = I0 g\(t\), Eq\. \(11\), p\. 6\. Long\-pulse total \(p\. 6\)\: n2,tot = n2,elec^s \+ n2,rot \+ n2,vib; the rotational adiabatic n2,rot as in \[22\] = wahlstrand\_2012\. No chi\(3\) or gamma is defined\. TABLE I \(p\. 5; image checked, the cells file matches; extracted by tools/extract/wahlstrand\_2015\.py\)\. Caption\: 'Measured electronic Kerr coefficient n2,elec^s at 1 atm \(at probe wavelength of 600 nm and pump wavelength of 800 nm\), polarizability anisotropy Delta alpha, and polarizability derivative d alpha/dQ \.\.\. The rightmost column shows n2 estimates at 1 atm based on our experimental results for a long pulse at 800 nm\.' d alpha/dQ \(1e\-16 cm2\), not extracted \(no quantity\)\: this experiment H2 1\.3 \+\- 0\.2, D2 1\.4 \+\- 0\.3; Ref\. \[31\] \(Bishop and Pipin 1993\) H2 1\.24; Ref\. \[39\] \(Raman scattering\) H2 1\.30 \+\- 0\.10, D2 1\.22 \+\- 0\.10\. Check\: n2,elec^s \+ n2,rot \+ n2,vib = n2,tot \(H2 6\.5 \+ 2\.7 \+ 1\.0 = 10\.2; D2 5\.8 \+ 3\.9 \+ 1\.2 = 10\.9\)\. Which vibrational coefficient \(smooth or smooth \+ grating\) the long\-pulse n2,vib is, is not stated; for a pulse acting on itself it should be the smooth one \(TC\-279\)\. PART\. n2,elec^s is electronic\: the vibrational part is separated through the resonant two\-beam coupling \(not by pulse duration\), the rotational part by its delay\. The vibrational response is effectively instantaneous for pulses longer than ~8 fs \(H2\) and ~12 fs \(D2\); the rotational one adiabatic above ~100 fs \(H2\) and ~200 fs \(D2\) \(p\. 6\)\. REFERENCE STATE\. 1 atm \(Table I caption\), no temperature\. The measurements are 'calibrated as in wahlstrand\_2012', whose N2 flow calibration corresponds to 290\.9 K at 1 atm \(TC\-316\)\: this paper's own values are recorded at 101325 Pa, 290\.9 K; the Shelton and Rice column, the authors' computation, at 293\.15 K \(assumed\)\. Normal \(thermal ortho/para\) H2 and D2 at room temperature assumed\. TEXT \(not extracted\)\. Fits \(p\. 2\)\: B = 58\.9 \(\+\- 3\.0\) cm^\-1, D = 0\.05 \(\+\- 0\.02\) cm^\-1 for H2; B = 29\.3 \(\+\- 1\.5\), D = 0\.021 \(\+\- 0\.008\) cm^\-1 for D2 \('in good agreement with the literature values'\)\. Vibrational constants used \(p\. 5\)\: H2 omega\_e = 0\.829 fs^\-1, omega\_e x\_e = 0\.023 fs^\-1; D2 0\.567, 0\.012 fs^\-1 \(Huber and Herzberg\); Omega\_v = 0\.783 \(H2\), 0\.543 fs^\-1 \(D2\)\. The prompt response of H2 and D2 is linear in intensity up to the ionization threshold \(~80 TW/cm2 used; ~1e14 W/cm2\)\. Uncertainty\: 'The most important source of error is the determination of the pump laser intensity' \(p\. 5\)\. **Recorded bibliographic identity status:** VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- wahlstrand\_2015/n2\_elec\_H2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "n2_elec_H2", "material": "H2", "file": "H2/wahlstrand_2015__n2_elec_H2.csv", "table": "tbl_64c4c34f908d", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-20, "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, "probe_nm": 600 } } Table I, n2,elec^s 'This expt\.'\: the electronic self coefficient at 1 atm \(290\.9 K, the density of the N2 flow calibration, as wahlstrand\_2012; TC\-316\), pump 800 nm, probe 600 nm; vibrational part separated by resonant two\-beam coupling, rotational part by its delay\. wahlstrand\_2015/n2\_shelton\_rice\_H2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "n2_shelton_rice_H2", "material": "H2", "file": "H2/wahlstrand_2015__n2_shelton_rice_H2.csv", "table": "tbl_64c4c34f908d", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-20, "abscissa_unit": "nm", "state": { "pressure_pa": 101325.0, "temperature_k": 293.15 }, "use": "check", "reproduced_from": [ "shelton_1994" ], "parameters": { "part": "electronic", "coefficient": "self" } } Table I, n2,elec^s 'Ref\. \[35\]' \(Shelton and Rice, Chem\. Rev\. 94, 3 \(1994\)\)\: an n2 the authors derived from Shelton and Rice's electronic hyperpolarizability; the computation \(dispersion, density\) is not stated\. Comparison value\. wahlstrand\_2015/dalpha\_H2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "dalpha_H2", "material": "H2", "file": "H2/wahlstrand_2015__dalpha_H2.csv", "table": "tbl_64c4c34f908d", "quantity": "polarizability_anisotropy", "unit": "cm3", "scale": 1e-25, "abscissa_unit": "nm", "use": "primary", "uncertainty": { "column": true, "level": "not stated" } } Table I, Delta alpha 'This expt\.' \(1e\-25 cm3\)\: fitted to the absolute rotational response \(t \> 200 fs\) with density\-matrix simulations using the measured B and D\. The rotational signal scales as Delta alpha\(pump\) x Delta alpha\(probe\)\: wavelength recorded as the pump's \(800 nm\), probe 600 nm\. wahlstrand\_2015/dalpha\_bridge\_buckingham\_H2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "dalpha_bridge_buckingham_H2", "material": "H2", "file": "H2/wahlstrand_2015__dalpha_bridge_buckingham_H2.csv", "table": "tbl_64c4c34f908d", "quantity": "polarizability_anisotropy", "unit": "cm3", "scale": 1e-25, "abscissa_unit": "nm", "use": "reproduced", "reproduced_from": [ "N. J. Bridge and A. D. Buckingham, Proc. R. Soc. London, Ser. A 295, 334 (1966)" ] } Table I, Delta alpha 'Ref\. \[30\]'\: N\. J\. Bridge and A\. D\. Buckingham, Proc\. R\. Soc\. London, Ser\. A 295, 334 \(1966\) \(light\-scattering depolarization; not in the library\)\. Its wavelength is not stated here\. wahlstrand\_2015/n2\_rot\_H2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "n2_rot_H2", "material": "H2", "file": "H2/wahlstrand_2015__n2_rot_H2.csv", "table": "tbl_64c4c34f908d", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-20, "abscissa_unit": "nm", "state": { "pressure_pa": 101325.0, "temperature_k": 290.9 }, "use": "check", "parameters": { "part": "rotational", "coefficient": "self" } } Table I, rightmost columns \('n2 at 800 nm \.\.\. for a long pulse'\)\: n2,rot\: the adiabatic \(long\-pulse\) rotational coefficient computed from the measured Delta alpha \(expression as in wahlstrand\_2012\); 1 atm \(290\.9 K, as the measured values\)\. Derived from this paper's measured parameters, not measured directly\: 'check'\. Applies to pulses longer than ~100 fs \(H2\) or ~200 fs \(D2\) for the rotational part\. wahlstrand\_2015/n2\_vib\_H2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "n2_vib_H2", "material": "H2", "file": "H2/wahlstrand_2015__n2_vib_H2.csv", "table": "tbl_64c4c34f908d", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-20, "abscissa_unit": "nm", "state": { "pressure_pa": 101325.0, "temperature_k": 290.9 }, "use": "check", "parameters": { "part": "vibrational", "coefficient": "self" } } Table I, rightmost columns \('n2 at 800 nm \.\.\. for a long pulse'\)\: n2,vib\: the adiabatic vibrational coefficient computed from the measured d alpha/dQ \(Eq\. \(8\)\); 1 atm \(290\.9 K, as the measured values\)\. Derived from this paper's measured parameters, not measured directly\: 'check'\. Applies to pulses longer than ~100 fs \(H2\) or ~200 fs \(D2\) for the rotational part\. wahlstrand\_2015/n2\_tot\_H2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "n2_tot_H2", "material": "H2", "file": "H2/wahlstrand_2015__n2_tot_H2.csv", "table": "tbl_64c4c34f908d", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-20, "abscissa_unit": "nm", "state": { "pressure_pa": 101325.0, "temperature_k": 290.9 }, "use": "check", "parameters": { "part": "total", "coefficient": "self" } } Table I, rightmost columns \('n2 at 800 nm \.\.\. for a long pulse'\)\: n2,tot = n2,elec^s \+ n2,rot \+ n2,vib, the long\-pulse total; 1 atm \(290\.9 K, as the measured values\)\. Derived from this paper's measured parameters, not measured directly\: 'check'\. Applies to pulses longer than ~100 fs \(H2\) or ~200 fs \(D2\) for the rotational part\. wahlstrand\_2015/n2\_elec\_D2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "n2_elec_D2", "material": "D2", "file": "D2/wahlstrand_2015__n2_elec_D2.csv", "table": "tbl_64c4c34f908d", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-20, "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, "probe_nm": 600 } } Table I, n2,elec^s 'This expt\.'\: the electronic self coefficient at 1 atm \(290\.9 K, the density of the N2 flow calibration, as wahlstrand\_2012; TC\-316\), pump 800 nm, probe 600 nm; vibrational part separated by resonant two\-beam coupling, rotational part by its delay\. wahlstrand\_2015/n2\_shelton\_rice\_D2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "n2_shelton_rice_D2", "material": "D2", "file": "D2/wahlstrand_2015__n2_shelton_rice_D2.csv", "table": "tbl_64c4c34f908d", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-20, "abscissa_unit": "nm", "state": { "pressure_pa": 101325.0, "temperature_k": 293.15 }, "use": "check", "reproduced_from": [ "shelton_1994" ], "parameters": { "part": "electronic", "coefficient": "self" } } Table I, n2,elec^s 'Ref\. \[35\]' \(Shelton and Rice, Chem\. Rev\. 94, 3 \(1994\)\)\: an n2 the authors derived from Shelton and Rice's electronic hyperpolarizability; the computation \(dispersion, density\) is not stated\. Comparison value\. wahlstrand\_2015/dalpha\_D2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "dalpha_D2", "material": "D2", "file": "D2/wahlstrand_2015__dalpha_D2.csv", "table": "tbl_64c4c34f908d", "quantity": "polarizability_anisotropy", "unit": "cm3", "scale": 1e-25, "abscissa_unit": "nm", "use": "primary", "uncertainty": { "column": true, "level": "not stated" } } Table I, Delta alpha 'This expt\.' \(1e\-25 cm3\)\: fitted to the absolute rotational response \(t \> 200 fs\) with density\-matrix simulations using the measured B and D\. The rotational signal scales as Delta alpha\(pump\) x Delta alpha\(probe\)\: wavelength recorded as the pump's \(800 nm\), probe 600 nm\. wahlstrand\_2015/dalpha\_bridge\_buckingham\_D2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "dalpha_bridge_buckingham_D2", "material": "D2", "file": "D2/wahlstrand_2015__dalpha_bridge_buckingham_D2.csv", "table": "tbl_64c4c34f908d", "quantity": "polarizability_anisotropy", "unit": "cm3", "scale": 1e-25, "abscissa_unit": "nm", "use": "reproduced", "reproduced_from": [ "N. J. Bridge and A. D. Buckingham, Proc. R. Soc. London, Ser. A 295, 334 (1966)" ] } Table I, Delta alpha 'Ref\. \[30\]'\: N\. J\. Bridge and A\. D\. Buckingham, Proc\. R\. Soc\. London, Ser\. A 295, 334 \(1966\) \(light\-scattering depolarization; not in the library\)\. Its wavelength is not stated here\. wahlstrand\_2015/n2\_rot\_D2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "n2_rot_D2", "material": "D2", "file": "D2/wahlstrand_2015__n2_rot_D2.csv", "table": "tbl_64c4c34f908d", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-20, "abscissa_unit": "nm", "state": { "pressure_pa": 101325.0, "temperature_k": 290.9 }, "use": "check", "parameters": { "part": "rotational", "coefficient": "self" } } Table I, rightmost columns \('n2 at 800 nm \.\.\. for a long pulse'\)\: n2,rot\: the adiabatic \(long\-pulse\) rotational coefficient computed from the measured Delta alpha \(expression as in wahlstrand\_2012\); 1 atm \(290\.9 K, as the measured values\)\. Derived from this paper's measured parameters, not measured directly\: 'check'\. Applies to pulses longer than ~100 fs \(H2\) or ~200 fs \(D2\) for the rotational part\. wahlstrand\_2015/n2\_vib\_D2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "n2_vib_D2", "material": "D2", "file": "D2/wahlstrand_2015__n2_vib_D2.csv", "table": "tbl_64c4c34f908d", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-20, "abscissa_unit": "nm", "state": { "pressure_pa": 101325.0, "temperature_k": 290.9 }, "use": "check", "parameters": { "part": "vibrational", "coefficient": "self" } } Table I, rightmost columns \('n2 at 800 nm \.\.\. for a long pulse'\)\: n2,vib\: the adiabatic vibrational coefficient computed from the measured d alpha/dQ \(Eq\. \(8\)\); 1 atm \(290\.9 K, as the measured values\)\. Derived from this paper's measured parameters, not measured directly\: 'check'\. Applies to pulses longer than ~100 fs \(H2\) or ~200 fs \(D2\) for the rotational part\. wahlstrand\_2015/n2\_tot\_D2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "n2_tot_D2", "material": "D2", "file": "D2/wahlstrand_2015__n2_tot_D2.csv", "table": "tbl_64c4c34f908d", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-20, "abscissa_unit": "nm", "state": { "pressure_pa": 101325.0, "temperature_k": 290.9 }, "use": "check", "parameters": { "part": "total", "coefficient": "self" } } Table I, rightmost columns \('n2 at 800 nm \.\.\. for a long pulse'\)\: n2,tot = n2,elec^s \+ n2,rot \+ n2,vib, the long\-pulse total; 1 atm \(290\.9 K, as the measured values\)\. Derived from this paper's measured parameters, not measured directly\: 'check'\. Applies to pulses longer than ~100 fs \(H2\) or ~200 fs \(D2\) for the rotational part\. 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.