wahlstrand_2013#
J. K. Wahlstrand, J. H. Odhner, E. T. McCole, Y.-H. Cheng, J. P. Palastro, R. J. Levis and H. M. Milchberg, “Effect of two-beam coupling in strong-field optical pump-probe experiments”, Phys. Rev. A 87, 053801 (2013)
Source record · Catalogue · Review register
DOI: 10.1103/PhysRevA.87.053801
Source kind: theory
Recorded technique: Theory and numerical calculation of the probe phase shift in pump-probe experiments with bound-electronic (instantaneous chi(3)), plasma (PPT/Popruzhenko ionization) and rotational (first-order density matrix) nonlinearities, including the pump-probe interference (‘grating’) terms, for degenerate and nondegenerate probes; simulations of the Loriot et al. transient-birefringence experiment (90 fs, 800 nm, Gaussian beams crossing at 4 degrees) and of SSSI; new degenerate experiments in Ar and air (spectrally resolved transient birefringence, 42 fs; degenerate chirped-pulse spectral interferometry in 0.5 atm Ar, 40 fs, crossing 3 degrees) supporting the plasma grating as the origin of the negative birefringence (secs. II-IV).
Materials in structured entries: Ar, N2, O2
Dataset quantities: nonlinear_index
Contents: 8 datasets; 0 formulas.
Curation notes#
Journal pages 053801-1 to -12 = PDF pages 1-12 (p. 13 references). Identity checked against the first page. No new absolute n2 is measured here; the paper establishes the self/probe factor 2 and corrects Loriot’s degenerate-probe values.
DEFINING EQUATIONS (Gaussian units). Fields (p. 2): pump E_e = (1/2) A_e exp(i k_e.r - i omega_e t) + c.c., probe likewise, so A is the full complex amplitude and the field is Re[A exp(...)]. Eq. (3), p. 2: (P_el)_i = chi(3)_ijkl E_j E_k E_l with the total real field (instantaneous response). p. 3: ‘defining the Kerr coefficient n2 = 12 pi^2 chi(3)_xxxx / (n0^2 c)’, with I_e = n0 c / (8 pi) |A_e|^2 the pump intensity. Eq. (6), p. 3: dPhi_x/dz - (n0/c) dPhi_x/dt = k_p (2 n2 I_e): ‘the effective Kerr nonlinear refractive index for the probe is found to be Delta n_K^cross = 2 n2 I_e, twice as large as the change in nonlinear index calculated for the pump beam on itself, Delta n_K = n2 I_e. The phase shift of the probe is enhanced by a factor of 2 regardless of whether the probe is degenerate or nondegenerate with the pump’ (p. 3). Perpendicular probe: Eq. (5), the same with n2/3 (chi_yyxx = chi_yxyx = chi_yxxy = chi_xxxx/3, Appendix A). Birefringence at low intensity: Delta n_par - Delta n_perp = 2 n2 - 2 n2/3 = 4 n2/3 (p. 8). For a nondegenerate probe the plasma and rotational grating terms vanish, so ‘the only difference between the experimentally measured Delta n and the true nonlinear index Delta n is the factor of 2 enhancement in the bound electronic contribution’ (p. 7); ‘These calculations provide theoretical justification for the analysis performed in recent absolute measurements of the nonlinearity in the noble gases, N2, O2, and N2O [17,18]’ (= wahlstrand_2012, wahlstrand_2012b). With a degenerate probe the rotational grating adds an effectively instantaneous positive signal that would make n2 appear larger (p. 6), and the plasma grating a negative one (p. 6-8). Rotational response: B = 2.0 (N2), 1.44 cm^-1 (O2), T = 293 K, n2 and Delta alpha from [17] (p. 5); the vibrational response is neglected (‘less than 10 % of the electronic nonlinearity [43]’, p. 5).
TABLE I (p. 8; image checked; the cells file matches). n2 in 1e-20 cm2/W: Ref. [17] = wahlstrand_2012 (reproduced); Ref. [10] = Loriot et al.’s erratum (Opt. Express 18, 3011 (2010)), which ‘corrected’ the Kerr coefficients ‘for the effect of a pulse on itself’ (p. 1): self coefficients, reproduced; ‘Ref. [10] corrected for rot. grating’: this paper’s subtraction of the calculated rotational-grating contribution (90 fs transform-limited Gaussian pulses) from Loriot’s N2 and O2 values, after which Loriot and Wahlstrand agree within error (p. 8). Loriot’s normalized intensity is the peak intensity divided by 1.7 (p. 8).
HIGHER-ORDER KERR (notes only): the negative birefringence Loriot et al. attributed to negative n4, n6, ... is explained by the plasma grating of a degenerate probe; the spectrally resolved birefringence in Ar and air (Fig. 5) matches the plasma-grating model better than the higher-order Kerr model, and in the degenerate interferometry the negative t = 0 signal appears together with the long-lived plasma signal (Fig. 6; pp. 9-10). Note [41]: a second-order rotational response (proportional to I^2) at high pulse energy would give an effective n4 through its grating.
STATE. Table I prints no state; the reproduced values keep their sources’ states (wahlstrand_2012: 1 atm; Loriot: 1 bar, room temperature), recorded as there.
Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
wahlstrand_2013/ref17_Ar#
{
"id": "ref17_Ar",
"material": "Ar",
"file": "Ar/wahlstrand_2013__ref17_Ar.csv",
"table": "tbl_2cd9818d136f",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-20,
"abscissa_unit": "nm",
"state": {
"pressure_pa": 101325.0,
"temperature_k": 293.15
},
"use": "reproduced",
"reproduced_from": [
"wahlstrand_2012"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"part": "electronic",
"coefficient": "self",
"pulse_fs": 40
}
}
Table I, ‘Ref. [17]’ column: wahlstrand_2012 Table I, state and parameters as there.
wahlstrand_2013/ref17_N2#
{
"id": "ref17_N2",
"material": "N2",
"file": "N2/wahlstrand_2013__ref17_N2.csv",
"table": "tbl_2cd9818d136f",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-20,
"abscissa_unit": "nm",
"state": {
"pressure_pa": 101325.0,
"temperature_k": 293.15
},
"use": "reproduced",
"reproduced_from": [
"wahlstrand_2012"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"part": "electronic_vibrational",
"coefficient": "self",
"pulse_fs": 40
}
}
Table I, ‘Ref. [17]’ column: wahlstrand_2012 Table I.
wahlstrand_2013/ref17_O2#
{
"id": "ref17_O2",
"material": "O2",
"file": "O2/wahlstrand_2013__ref17_O2.csv",
"table": "tbl_2cd9818d136f",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-20,
"abscissa_unit": "nm",
"state": {
"pressure_pa": 101325.0,
"temperature_k": 293.15
},
"use": "reproduced",
"reproduced_from": [
"wahlstrand_2012"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"part": "electronic_vibrational",
"coefficient": "self",
"pulse_fs": 40
}
}
Table I, ‘Ref. [17]’ column: wahlstrand_2012 Table I.
wahlstrand_2013/ref10_Ar#
{
"id": "ref10_Ar",
"material": "Ar",
"file": "Ar/wahlstrand_2013__ref10_Ar.csv",
"table": "tbl_2cd9818d136f",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-20,
"abscissa_unit": "nm",
"state": {
"pressure_pa": 100000.0,
"temperature_k": 293.15
},
"use": "reproduced",
"reproduced_from": [
"loriot_2010"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"part": "instantaneous",
"coefficient": "self",
"pulse_fs": 90
}
}
Table I, ‘Ref. [10]’ column: Loriot et al.’s erratum value (self coefficient); degenerate transient birefringence, 90 fs, 800 nm, 1 bar, room temperature (293.15 K assumed).
wahlstrand_2013/ref10_N2#
{
"id": "ref10_N2",
"material": "N2",
"file": "N2/wahlstrand_2013__ref10_N2.csv",
"table": "tbl_2cd9818d136f",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-20,
"abscissa_unit": "nm",
"state": {
"pressure_pa": 100000.0,
"temperature_k": 293.15
},
"use": "reproduced",
"reproduced_from": [
"loriot_2010"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"part": "instantaneous",
"coefficient": "self",
"pulse_fs": 90
}
}
Table I, ‘Ref. [10]’ column: Loriot et al.’s erratum value, including the degenerate probe’s rotational-grating signal.
wahlstrand_2013/ref10_O2#
{
"id": "ref10_O2",
"material": "O2",
"file": "O2/wahlstrand_2013__ref10_O2.csv",
"table": "tbl_2cd9818d136f",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-20,
"abscissa_unit": "nm",
"state": {
"pressure_pa": 100000.0,
"temperature_k": 293.15
},
"use": "reproduced",
"reproduced_from": [
"loriot_2010"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"part": "instantaneous",
"coefficient": "self",
"pulse_fs": 90
}
}
Table I, ‘Ref. [10]’ column: Loriot et al.’s erratum value, including the rotational-grating signal.
wahlstrand_2013/corrected_N2#
{
"id": "corrected_N2",
"material": "N2",
"file": "N2/wahlstrand_2013__corrected_N2.csv",
"table": "tbl_2cd9818d136f",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-20,
"abscissa_unit": "nm",
"state": {
"pressure_pa": 100000.0,
"temperature_k": 293.15
},
"use": "check",
"reproduced_from": [
"loriot_2010"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"part": "electronic_vibrational",
"coefficient": "self",
"pulse_fs": 90
}
}
Table I, ‘Ref. [10] corrected for rot. grating’: Loriot’s value minus this paper’s calculated rotational-grating contribution (90 fs transform-limited Gaussian pulses, T = 293 K). A re-analysis of Loriot’s measurement, not an independent one: ‘check’. The error bar is Loriot’s, unchanged. Part: rotation removed, the adiabatic vibrational part kept.
wahlstrand_2013/corrected_O2#
{
"id": "corrected_O2",
"material": "O2",
"file": "O2/wahlstrand_2013__corrected_O2.csv",
"table": "tbl_2cd9818d136f",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-20,
"abscissa_unit": "nm",
"state": {
"pressure_pa": 100000.0,
"temperature_k": 293.15
},
"use": "check",
"reproduced_from": [
"loriot_2010"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"part": "electronic_vibrational",
"coefficient": "self",
"pulse_fs": 90
}
}
Table I, ‘Ref. [10] corrected for rot. grating’: as corrected_N2.
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 review register for the checks and decisions.