le_2016 ======= A\.\-T\. Le, H\. Wei, C\. Jin and C\. D\. Lin, "Strong\-field approximation and its extension for high\-order harmonic generation with mid\-infrared lasers", J\. Phys\. B\: At\. Mol\. Opt\. Phys\. 49, 053001 \(2016\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1088/0953\-4075/49/5/053001 `__ **Source kind:** theory **Recorded technique:** Numerical solution of the time\-dependent Schrodinger equation \(TDSE\) for atomic hydrogen \(section 2\.5\.3, Fig\. 12\), compared with the ADK, the PPT cycle\-averaged rate \(Eq\. 91\) and the strong\-field approximation without \(SFA, Eqs\. 87\-90, length gauge\) and with a Coulomb correction factor \(SFA\-CC\)\. The TDSE's method \(grid, gauge, absorber, propagator\), its reference and its measure of the ionisation probability are not stated, nor is it cited\: the section says only 'we compare them with the TDSE calculations in two illustrative examples' \(p\. 17\), Fig\. 13's H2 TDSE being Saenz et al\.'s \(ref\. 117\)\. Pulses\: 'The laser pulse duration \(full duration with the sine\-square envelope\) is 12\-cycle for 400 nm, and 6\-cycle for the other cases' \(pp\. 18\-19\)\. **Materials in structured entries:** H **Dataset quantities:** ionization\_yield **Contents:** 3 datasets; 0 formulas. Curation notes -------------- PDF pages 2\-38 = journal pages 1\-37 \(PDF page 1 is IOPscience's download cover\); Fig\. 12 is on PDF page 19, printed p\. 18, its text in section 2\.5\.3 \(pp\. 18\-19\)\. Identity checked on the first page \(2026\-10\-02\)\: 'Tutorial\. Strong\-field approximation and its extension for high\-order harmonic generation with mid\-infrared lasers', Anh\-Thu Le, Hui Wei, Cheng Jin and C D Lin \(Kansas State University; Nanjing University of Science and Technology\), 'Received 30 June 2014, revised 1 August 2015, Accepted for publication 15 September 2015, Published 15 February 2016', J\. Phys\. B\: At\. Mol\. Opt\. Phys\. 49 \(2016\) 053001\. WHAT IS PRINTED\. No table\: the TDSE probabilities of hydrogen are in Fig\. 12 only \(a vector drawing; no supplement\)\. Caption\: 'Comparison of different methods for ionization probability for hydrogen atom vs laser intensity for the wavelength of 400 nm \(a\), 800 nm \(b\), and 1600 nm \(c\)\. Note that for each wavelength the PPT and SFA results have been multiplied by a factor given in the labels\. The vertical dotted lines indicate the position with gamma = 1\.' The legends \(glyphs, read on the page\)\: 'TDSE', 'ADK', 'PPT \(x0\.33\)', 'SFA \(x12\)', 'SFA\-CC \(x0\.051\)' \(400 nm\); x0\.33, x15, x0\.064 \(800 nm\); x0\.5, x20, x0\.073 \(1600 nm\)\. Axes\: 'Laser intensity \(10^14 W/cm^2\)', 0\.1\-1\.5 in \(a\) and \(b\), 0\.2\-1\.5 in \(c\); 'Ionization probability', log, 10^\-14 to 1 \(a\), 10^\-14 to about 10^\-1 \(b\), 10^\-10 to 1 \(c\)\. Text \(p\. 18\)\: 'Comparison for the TDSE, ADK, PPT, and SFA for the wavelength of 400 nm, 800 nm, and 1600 nm is shown in figure 12 for a range of intensity from 1 x 10^13 to 1\.5 x 10^14 W cm^\-2' \(\(c\)'s axis begins at 2 x 10^13\); 'These parameters were chosen so that the Keldysh parameter gamma ~ 1 is well within the intensity range for 800 nm and the ionization probability is still far from saturation'; at 800 nm 'the SFA result \(rescaled by a factor of 15\) agrees fairly well with the TDSE', 'The SFA\-CC \(rescaled by 0\.064\) agrees much better', 'The ADK result only agrees at high intensities above about 1 x 10^14 W cm^\-2 \.\.\. no scaling factor is used for the ADK', 'at 4 x 10^13 W cm^\-2 the ADK underestimates by almost two orders of magnitude', 'The PPT result \(rescaled by a factor of 1/3\) nicely reproduces the TDSE result for the whole range of laser intensity'; at 1600 nm 'relatively good agreement among all the methods'; 'in all these cases, the SFA underestimates, whereas the SFA\-CC overestimates, and the PPT slightly overestimates the ionization probability for hydrogen' \(p\. 19\)\. THE PPT \(Eq\. 91, p\. 18, not data\: a model\)\. The cycle\-averaged rate for a linear molecule along the field, for atoms PPT's\: W\(0\) = \(3 E\_0/\(pi kappa^3\)\)^\(1/2\) B^2\(m\)/\(2^\|m\| \|m\|\!\) A\_m\(omega, gamma\)/kappa^\(2 Z\_c/kappa \- 1\) \(2 kappa^3/E\_0\)^\(2 Z\_c/kappa \- \|m\| \- 1\) \(1 \+ gamma^2\)^\(\|m\|/2 \+ 3/4\) exp\(\-2 kappa^3 g\(gamma\)/\(3 E\_0\)\), with A\_m and g 'found in \[104, 113\]' \(Perelomov, Popov and Terent'ev 1966; Ilkov, Decker and Chin 1992\), B\(m\) = sum\_l C\_l Q\(l, m\), Q\(l, m\) = \(\-1\)^\(\(m \+ \|m\|\)/2\) sqrt\(\(2l \+ 1\)\(l \+ \|m\|\)\!/\(2\(l \- \|m\|\)\!\)\), kappa = sqrt\(2 I\_p\)\: the static Coulomb factor \(2 kappa^3/E\_0\)^\(2 Z\_c/kappa\), not Popruzhenko et al\.'s 'improved' one \(ref\. 115, mentioned\)\. The structure coefficient used for hydrogen \(Tong et al\.'s C\_l, 2 for the 1s\) and how the rate was integrated over the pulse are not stated\. Its multipliers in Fig\. 12\: 0\.33, 0\.33 and 0\.5 \(the legends; the text's '1/3' at 800 nm\)\. The drawn PPT curves \(the green dash\-dotted lines, the factor taken out\) over the TDSE at the TDSE's vertices \(le\_2016\.py's report\)\: 400 nm 7\.2 at 1\.0e13 W/cm^2, 3\.0 at 8\.0e13, 6\.2 at 1\.5e14; 800 nm 2\.5\-3\.0 over 1\.0e13\-1\.5e14; 1600 nm 1\.34 at 2\.0e13, 1\.57\-1\.88 at 2\.1\-9\.9e13, 1\.89\-2\.03 at 1\.0\-1\.5e14\. So with its factor the PPT is 0\.82\-1\.01 times the TDSE at 800 nm, 0\.67\-1\.02 at 1600 nm and 0\.98\-2\.4 at 400 nm\. Reproduced \(2026\-10\-02, a calculation outside the record\: optmat\.gas\.ionisation\_rates with the static Coulomb factor, no static correction, C\_0 = 2, l = m = 0, the cycle\-averaged rate on a sin^2 envelope of the field over the stated cycles, P = 1 \- exp\(\-int W dt\)\)\: the 1600 nm curve within 4 % \(0\.90\-0\.98 of it\), the 800 nm curve 0\.83 times \(0\.6\-0\.9\), the 400 nm curve 0\.9\-1\.85 times; with the sin^2 on the intensity 1\.33, 1\.15 and 1\.1\-2\.6 times\. The PPT is therefore Eq\. \(91\) as described, and the sin^2 is more likely of the field, but the reproduction is not exact below 1600 nm \(A\_m and the averaging may differ\) and does not settle it\. EXTRACTED \(2026\-10\-02\) by tools/extract/le\_2016\.py from the vector drawing of Fig\. 12, whose docstring describes the reading\: the axes calibrated from the frames' own ticks \(x 150\.97 pt per 10^14 W/cm^2 in \(a\) and \(b\), 162\.58 in \(c\), every tick within 0\.009 pt of its fitted scale; y 10\.568, 11\.381 and 14\.795 pt per decade, within 0\.001 pt\), the y labels' glyphs one at each tick, the x labels' spanning the long ticks \(checked\)\. The TDSE is each panel's one black solid curve \(the legend's first sample, black, as wide as the curve; checked\)\. It is drawn differently from the other curves\: they are polylines with a vertex at every multiple of 10^12 W/cm^2 \(the SFA, 141 vertices in \(a\) and \(b\), 132 in \(c\); the SFA\-CC likewise, a few skipped in \(a\)\) or on a geometric grid \(ADK and PPT, 53 and 40\), whereas the TDSE paths mix straight segments with cubic Bezier segments\: \(a\) 8 vertices, two cubics spanning 1\.2\-7\.9e13 and 8\.1\-14\.8e13 W/cm^2; \(b\) 38 vertices, 8 cubics of 13 or 14 steps of 10^12; \(c\) 106 vertices, 3 cubics of 9 steps above 1\.13e14 and one straight segment from 4\.3 to 4\.5e13\. Every vertex the curve passes through lies on a multiple of 10^12 W/cm^2 within 0\.008e12 \(the drawing's quantum\)\: they are the calculation's \(or its plot's\) points, kept where the drawing was simplified, and only they are read; the cubics' control points are not data, nor is the curve between them\. Read\: \(a\) 1\.0, 1\.1, 1\.2, 7\.9, 8\.0, 8\.1, 14\.8 and 15\.0 x 10^13 W/cm^2, 7\.08e\-6 to 0\.0728; \(b\) 1\.0e13 to 1\.5e14, 1\.43e\-8 to 0\.0525; \(c\) every 10^12 from 2\.0e13 to 1\.13e14 \(but 4\.4e13\) and 1\.22\-1\.26, 1\.35\-1\.37, 1\.46\-1\.50 x 10^14, 4\.96e\-8 to 0\.0769\. The \(c\) points scatter about a smooth trend by up to 10 % from one 10^12 step to the next \(the drawn PPT, a smooth curve, over them varies so\)\: structure in the TDSE, not the reading\. The ends are drawn twice at the frame's edge \(0\.02 pt apart\); the vertex nearer the grid is kept\. CHECKS \(the script's checks\(\), 2026\-10\-02\)\. \(1\) The gamma = 1 dotted lines lie at 1\.1413e14 W/cm^2 \(800 nm\) and 2\.8541e13 \(1600 nm\), hydrogen's gamma = omega sqrt\(2 I\_p\)/F0 = 1 with I\_p = 0\.5 hartree and I = c eps0 F0^2/2 at 1\.1384e14 and 2\.8460e13 \(0\.25 % and 0\.28 % above\)\: an independent check of the x axes, and the intensity is the peak of the cycle\-averaged intensity of a linearly polarised field \(circular polarisation's I = c eps0 F0^2 would put them at half\)\. \(a\) has none\: gamma = 1 is at 4\.55e14 W/cm^2, beyond its axis\. \(2\) The TDSE curves span 1\.0e13\-1\.5e14 W/cm^2 in \(a\) and \(b\), the text's range, and 2\.0e13\-1\.5e14 in \(c\)\. \(3\) Every read vertex on the 10^12 W/cm^2 grid \(above\)\. \(4\) The extracted points drawn on the rendered page and inspected \(2026\-10\-02\)\: every vertex on the black curve, none elsewhere; the legend and the other curves excluded\. Reported, not checked\: the text's 'at 4 x 10^13 W cm^\-2 the ADK underestimates by almost two orders of magnitude' at 800 nm\: the drawn ADK over the drawn TDSE is 1/17 there \(1\.2 orders\), 1/78 at 3e13 and 1/900 at 2e13 \(at 400 nm, 1/1100 at 4e13\)\: the text's 'almost two' holds near 3 x 10^13\. ADK/TDSE at 800 nm is 0\.67 at 1e14, 0\.87 at 1\.2e14 and 1\.20 at 1\.5e14 \('agrees at high intensities above about 1 x 10^14'\)\. NOT STATED\. The TDSE's method and accuracy; its measure of ionisation \(1 \- the bound populations, the norm lost to an absorber, or the outgoing flux\); the polarisation \(linear\: Eq\. 91 is the linear\-polarisation average, and the gamma = 1 lines fit linear polarisation's intensity, above\); whether the intensity is the peak \(the gamma = 1 lines fit the peak\); whether the sin^2 envelope is of the field \(or vector potential\) or of the intensity; the carrier\-envelope phase; the pulse's FWHM \(from the full duration\: 0\.364 times it in intensity for a sin^2 field, 0\.5 for a sin^2 intensity\)\. The datasets' pulse\_fs is the full duration, derived\: the stated cycles times lambda/c\. WHAT THE TDSE YIELD IS\. The probability that atomic hydrogen's one electron has been ionised by the pulse, presumably at its end, from the 1s state \(exact one\-electron problem, infinite nuclear mass assumed\)\. The datasets' uncertainty is the digitising \(1 %\: the drawing's 0\.02 pt quantum is 0\.3\-0\.45 % of the value\); whether the drawing's simplification moved the kept vertices cannot be checked, and the TDSE's own accuracy is not stated\. Use \(a\) with care\: 8 points in three clusters\. REGISTER\. Curated in TC\-835; the comparison with optmat's hydrogen model is optmat\.gas\.ionisation\_validation\.hydrogen\_yields \(TC\-833\)\. **Recorded bibliographic identity status:** VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- le\_2016/fig12a\_tdse\_H\_400nm ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "fig12a_tdse_H_400nm", "material": "H", "file": "H/le_2016__fig12a_tdse_H_400nm.csv", "table": "fig_d7530dc1bd66", "digitised": "vector", "quantity": "ionization_yield", "unit": "1", "abscissa": "intensity", "abscissa_unit": "W/cm2", "use": "check", "uncertainty": { "relative": 0.01, "level": "not stated" }, "parameters": { "wavelength_nm": 400, "pulse_fs": 16.01, "pulse_fs_definition": "the full duration of the sin^2 envelope, derived, not printed: 'The laser pulse duration (full duration with the sine-square envelope) is 12-cycle for 400 nm' (pp. 18-19), 12 x 1.3343 fs; of the field or of the intensity not stated (its FWHM in intensity 5.8 or 8.0 fs)", "pulse_cycles": 12, "polarization": "linear", "polarization_definition": "not stated for Fig. 12; Eq. (91) is the linear-polarisation cycle average, and the gamma = 1 lines of (b) and (c) fit linear polarisation's intensity (the record's notes)", "pulse_envelope": "sin^2", "pulse_envelope_of": "not stated (field or intensity)", "cep": "not stated", "intensity": "'Laser intensity': the peak of the cycle-averaged intensity, c eps0 F0^2/2, implied by (b)'s and (c)'s gamma = 1 lines (checked), not stated", "measure": "not stated", "electrons": "one electron (atomic hydrogen)", "orbital": "1s", "model_ionization_energy_au": 0.5, "method": "TDSE, not described or cited" } } Fig\. 12\(a\), p\. 18, 'TDSE' \(black solid line\)\: the TDSE ionisation probability of atomic hydrogen at 400 nm against the laser intensity, 12\-cycle sin^2 pulse\. Only 8 points\: the drawn curve's vertices at 1\.0, 1\.1, 1\.2, 7\.9, 8\.0, 8\.1, 14\.8 and 15\.0 x 10^13 W/cm^2 \(7\.08e\-6 to 0\.0728\), each on the calculation's 10^12 W/cm^2 grid; between 1\.2 and 7\.9e13 \(four decades\) and between 8\.1 and 14\.8e13 the drawing is one cubic Bezier each, not data \(the record's notes\)\. The PPT \(Eq\. 91, static Coulomb factor\) is 7\.2, 3\.0 and 6\.2 times it at 1\.0e13, 8\.0e13 and 1\.5e14 \(the legend's x0\.33 taken out\)\. 1 %\: the digitising \(the y scale's 0\.02 pt quantum is 0\.44 %\); the intensity to 0\.01e12 W/cm^2\. The TDSE's own accuracy, method and measure are not stated\. le\_2016/fig12b\_tdse\_H\_800nm ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "fig12b_tdse_H_800nm", "material": "H", "file": "H/le_2016__fig12b_tdse_H_800nm.csv", "table": "fig_d7530dc1bd66", "digitised": "vector", "quantity": "ionization_yield", "unit": "1", "abscissa": "intensity", "abscissa_unit": "W/cm2", "use": "check", "uncertainty": { "relative": 0.01, "level": "not stated" }, "parameters": { "wavelength_nm": 800, "pulse_fs": 16.01, "pulse_fs_definition": "the full duration of the sin^2 envelope, derived, not printed: '6-cycle for the other cases' (pp. 18-19), 6 x 2.6685 fs; of the field or of the intensity not stated (its FWHM in intensity 5.8 or 8.0 fs)", "pulse_cycles": 6, "polarization": "linear", "polarization_definition": "not stated for Fig. 12; Eq. (91) is the linear-polarisation cycle average, and the gamma = 1 line fits linear polarisation's intensity (the record's notes)", "pulse_envelope": "sin^2", "pulse_envelope_of": "not stated (field or intensity)", "cep": "not stated", "intensity": "'Laser intensity': the peak of the cycle-averaged intensity, c eps0 F0^2/2, implied by the gamma = 1 line at 1.1413e14 W/cm^2 (1.1384e14 computed; checked), not stated", "measure": "not stated", "electrons": "one electron (atomic hydrogen)", "orbital": "1s", "model_ionization_energy_au": 0.5, "method": "TDSE, not described or cited" } } Fig\. 12\(b\), p\. 18, 'TDSE' \(black solid line\)\: the TDSE ionisation probability of atomic hydrogen at 800 nm against the laser intensity, 6\-cycle sin^2 pulse, 38 points, 1\.0e13\-1\.5e14 W/cm^2, 1\.43e\-8 to 0\.0525\: the drawn curve's vertices, each on the calculation's 10^12 W/cm^2 grid; 8 stretches of 13\-14 steps are drawn as cubic Bezier segments, not data \(the record's notes\)\. The PPT \(Eq\. 91, static Coulomb factor\) is 2\.5\-3\.0 times it \(the legend's x0\.33, the text's '1/3', taken out\)\. 1 %\: the digitising \(the y scale's 0\.02 pt quantum is 0\.4 %\); the intensity to 0\.01e12 W/cm^2\. The TDSE's own accuracy, method and measure are not stated\. le\_2016/fig12c\_tdse\_H\_1600nm ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "fig12c_tdse_H_1600nm", "material": "H", "file": "H/le_2016__fig12c_tdse_H_1600nm.csv", "table": "fig_d7530dc1bd66", "digitised": "vector", "quantity": "ionization_yield", "unit": "1", "abscissa": "intensity", "abscissa_unit": "W/cm2", "use": "check", "uncertainty": { "relative": 0.01, "level": "not stated" }, "parameters": { "wavelength_nm": 1600, "pulse_fs": 32.02, "pulse_fs_definition": "the full duration of the sin^2 envelope, derived, not printed: '6-cycle for the other cases' (pp. 18-19), 6 x 5.3370 fs; of the field or of the intensity not stated (its FWHM in intensity 11.6 or 16.0 fs)", "pulse_cycles": 6, "polarization": "linear", "polarization_definition": "not stated for Fig. 12; Eq. (91) is the linear-polarisation cycle average, and the gamma = 1 line fits linear polarisation's intensity (the record's notes)", "pulse_envelope": "sin^2", "pulse_envelope_of": "not stated (field or intensity)", "cep": "not stated", "intensity": "'Laser intensity': the peak of the cycle-averaged intensity, c eps0 F0^2/2, implied by the gamma = 1 line at 2.8541e13 W/cm^2 (2.8460e13 computed; checked), not stated", "measure": "not stated", "electrons": "one electron (atomic hydrogen)", "orbital": "1s", "model_ionization_energy_au": 0.5, "method": "TDSE, not described or cited" } } Fig\. 12\(c\), p\. 18, 'TDSE' \(black solid line\)\: the TDSE ionisation probability of atomic hydrogen at 1600 nm against the laser intensity, 6\-cycle sin^2 pulse, 106 points, 2\.0e13\-1\.5e14 W/cm^2, 4\.96e\-8 to 0\.0769\: the drawn curve's vertices, every 10^12 W/cm^2 to 1\.13e14 \(but 4\.4e13\), then 1\.22\-1\.26, 1\.35\-1\.37 and 1\.46\-1\.50e14, the stretches between drawn as cubic Bezier segments, not data \(the record's notes\)\. The points scatter about the trend by up to 10 % from step to step \(structure in the TDSE\)\. The PPT \(Eq\. 91, static Coulomb factor\) is 1\.34 times it at 2e13, 1\.57\-1\.88 at 2\.1\-9\.9e13 and 1\.89\-2\.03 at 1\.0\-1\.5e14 \(the legend's x0\.5 taken out\)\. 1 %\: the digitising \(the y scale's 0\.02 pt quantum is 0\.3 %\); the intensity to 0\.01e12 W/cm^2\. The TDSE's own accuracy, method and measure are not stated\. 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.