gulley_2012 =========== J\. R\. Gulley, S\. W\. Winkler, W\. M\. Dennis, C\. M\. Liebig and R\. Stoian, "Interaction of ultrashort\-laser pulses with induced undercritical plasmas in fused silica", Phys\. Rev\. A 85, 013808 \(2012\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1103/physreva\.85\.013808 `__ **Source kind:** measurement **Recorded technique:** 800\-nm Ti\:sapphire amplifiers \(120\-150 fs, 1 kHz; the text's pulse is 140 fs FWHM\) focused by a 25\-cm lens onto the front surface of a 200\-um fused\-silica plate in air; beam profiles before and after the sample, multi\-SHG\-FROG of the transmitted pulse; the sample was not translated \(~1e7 pulses per site\)\. Simulated with a 3\+1D nonlinear Schrodinger equation \(Eq\. 1\) with Drude dispersion corrections, coupled to Rethfeld's multiple rate equation with Keldysh photoionization, from the measured beam profile and FROG field\. **Materials in structured entries:** SiO2 **Dataset quantities:** band\_gap, damage\_threshold\_energy, damage\_threshold\_fluence, effective\_mass, electron\_collision\_time, electron\_trapping\_time, group\_delay\_dispersion, nonlinear\_index, raman\_fraction, raman\_response\_time, refractive\_index **Contents:** 13 datasets; 1 formula. Curation notes -------------- Journal pages 013808\-1 to \-10 = PDF pages 1\-10\. Identity validated\. MEASURED DAMAGE \(text, p\. 013808\-3\)\: 'These damage thresholds are summarized as follows\: 60 uJ \(5\.1 J/cm2\) for Secs\. IV A and IV B, 45 uJ \(3\.8 J/cm2\) for Sec\. IV C 2, and 55 uJ \(4\.7 J/cm2\) for Sec\. IV C 3\.' 'The multishot damage threshold was determined in the experiment, by visual inspection, to be 60 uJ \(5\.1 J/cm2\)\. Since the sample was not translated in the experiment the surface was exposed to multiple \(~10^7\) pulses of the same energy \.\.\. lowering the damage threshold by approximately 25%\. \[35\] The single\-shot optical damage threshold is therefore expected to be around 80 uJ \(6\.8 J/cm2\)\.' The fluences are 'peak single\-shot fluence on the front sample surface' \(p\. 013808\-3\); all five pairs share the ratio E/F = 1\.18e\-5 cm2 \(checked 2026\-09\-26\), one spot size\. The Sec\. IV C 2 and IV C 3 values are 'destruction thresholds' in the FROG series, the second with the laser of the Laboratoire Hubert Curien \(p\. 013808\-9\); 'some of the subsections have different damage threshold measurements, as some were measured under different experimental conditions' \(p\. 013808\-3\), which are not detailed further\. Site\: the front surface \(the beam focused onto it; the simulations put the single\-shot damage there too\)\. No uncertainty stated\. Grade not stated\. SIMULATION INPUTS\: 'All other numerical parameters for the computer simulation \(summarized in Table I\) were taken from Ref\. \[19\]' \(Winkler et al\., Appl\. Phys\. A 84, 413 \(2006\); p\. 013808\-3\), so Table I's values are reproduced from ref\. 19 and assumed\. Table I \(p\. 013808\-3, tbl\_763380c3ceb4, image checked\)\: lambda 800 nm; R\(tau\) = \[\(tau\_1^2 \+ tau\_2^2\)/\(tau\_1 tau\_2^2\)\] exp\(\-tau/tau\_2\) sin\(tau/tau\_1\) with tau\_1 = 32 fs, tau\_2 = 12\.2 fs; f\_r = 0\.18; n0 = 1\.45; k\_2 = '361 fs^2 W^\-1'; n2 = 2\.48 x 10^\-16 cm2 W^\-1; U = 9 eV; m\_e = 9\.1 x 10^\-31 kg; tau\_c 'Multiple values used'\. Text \(p\. 013808\-2\)\: the Keldysh rate 'with a reduced electron\-hole mass of half the electron rest mass'; 'a recombination time of 150 fs \[19,34\]' \(Winkler 2006; Wu, Chowdhury and Xu, Phys\. Rev\. B 72, 085128 \(2005\)\); the damage criterion of the simulation, a free\-electron density above 1e21 cm^\-3 anywhere \(p\. 013808\-3\)\. FINDINGS\. \(1\) k\_2's unit is printed 'fs^2 W^\-1' in the image\: impossible for a GVD coefficient \(fs^2 per length\); the same number, 361, is couairon\_2005's k'' at 800 nm in fs2/cm, and it is recorded as fs2/cm \(an interpretation\)\. \(2\) R\(tau\)\: as printed, tau\_2 = 12\.2 fs is the decay time and tau\_1 = 32 fs the oscillation period parameter, the reverse of couairon\_2005 \(sin\(t/12 fs\) exp\(\-t/32 fs\)\) and berge\_2010 \(tau\_R 32 fs decay at 1550 nm\); either the definition or the values are swapped relative to the others\: not resolvable from this paper, recorded as printed\. \(3\) The critical power is written P\_cr = lambda^2/\(8 pi n0 n2\) \(p\. 013808\-4\), a quarter of the usual lambda^2/\(2 pi n0 n2\) \(0\.71 against 2\.83 MW with Table I's values; computed 2026\-09\-26\); no value is printed\. \(4\) The absorption cross section sigma = e^2 tau\_c/\[m\_e n0 eps0 c \(1 \+ omega0^2 tau\_c^2\)\] peaks at tau\_c = 1/omega0 = 0\.425 fs \(printed 'approximately tau\_c = 0\.42 fs', p\. 013808\-4; checked\)\. THE COLLISION TIME\: Fig\. 2 gives the simulated single\-shot threshold against tau\_c; 'Since the single\-shot threshold is estimated from experiment to be 80 uJ \(6\.8 J/cm2\) Fig\. 2 suggests an approximate collision time of the order of 10 fs \.\.\. Therefore a 10\-fs collision time is assumed hereafter' \(p\. 013808\-4\); these simulations then predict a single\-shot threshold of 80\-85 uJ \(6\.8\-7\.2 J/cm2\) \(p\. 013808\-6\)\. With G = 1 the simulated threshold 'never exceeds 30 uJ \(2\.5 J/cm2\)'\. TABLE II \(p\. 013808\-9, tbl\_f6dc38765622\) is scrambled in the library; transcribed from the image in the script \(checked against the scrambled characters\)\. FROG retrieval diagnostics, not material data\: pulse energy \(uJ\), trace dimensions, G\_error, OC\: 1, 256 x 128, 0\.00319, 0\.0115; 10, 0\.00417, 0\.0135; 17, 0\.0036, 0\.0105; 25, 0\.0041, 0\.008; 35, 0\.00623, 0\.01; 46, 0\.0051, 0\.011; 50, 0\.00536, 0\.0095; 55, 0\.0062, 0\.01 \(all 256 x 128\)\. FIGURES ONLY\: Fig\. 2 \(simulated thresholds against tau\_c, three curves\), Figs\. 3\-11 \(plasma densities, beam profiles, FROG traces and fields\)\. **Recorded bibliographic identity status:** VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- gulley\_2012/damage\_fluence ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "damage_fluence", "material": "SiO2", "table": "text", "quantity": "damage_threshold_fluence", "unit": "J/cm2", "abscissa": "duration", "abscissa_unit": "fs", "use": "primary", "parameters": { "site": "surface", "criterion": "visible damage (visual inspection) of the front surface", "shots": "~1e7 (sample not translated, 1 kHz)", "wavelength_nm": 800 } } 3 inline points in the source record. p\. 013808\-3, the three measured thresholds as peak fluence on the front surface \(rows\: the sections they belong to\)\. IV A\: multishot \(~1e7 pulses, sample not translated\), 'by visual inspection'\. IV C 2 and IV C 3\: 'destruction threshold' of the FROG series \(IV C 3 with the Saint\-Etienne laser\); conditions otherwise not detailed\. The duration is the text's 140 fs FWHM \(the lasers give 120\-150 fs\)\. gulley\_2012/damage\_energy ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "damage_energy", "material": "SiO2", "table": "text", "quantity": "damage_threshold_energy", "unit": "uJ", "abscissa": "duration", "abscissa_unit": "fs", "use": "primary", "parameters": { "site": "surface", "criterion": "visible damage (visual inspection) of the front surface", "shots": "~1e7 (sample not translated, 1 kHz)", "wavelength_nm": 800 } } 3 inline points in the source record. p\. 013808\-3, the same thresholds as pulse energies \(see damage\_fluence\); focusing by a 25\-cm lens onto the front surface, NA not stated\. gulley\_2012/single\_shot\_estimate ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "single_shot_estimate", "material": "SiO2", "table": "text", "quantity": "damage_threshold_fluence", "unit": "J/cm2", "abscissa": "duration", "abscissa_unit": "fs", "use": "check", "parameters": { "site": "surface", "criterion": "estimated single-shot threshold", "shots": 1, "wavelength_nm": 800 } } 1 inline points in the source record. p\. 013808\-3\: 'The single\-shot optical damage threshold is therefore expected to be around 80 uJ \(6\.8 J/cm2\)', the multishot 60 uJ raised by the ~25 % incubation lowering of Schaffer et al\. \(ref\. 35, Proc\. SPIE 3451, 2 \(1998\)\)\: an estimate, not a measurement\. gulley\_2012/model\_band\_gap ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_band_gap", "material": "SiO2", "file": "SiO2/gulley_2012__band_gap.csv", "table": "tbl_763380c3ceb4", "quantity": "band_gap", "unit": "eV", "abscissa": "none", "use": "check", "reproduced_from": [ "S. W. Winkler, I. M. Burakov, R. Stoian, N. M. Bulgakova, A. Husakou, A. Mermillod-Blondin, A. Rosenfeld, D. Ashkenasi and I. V. Hertel, Appl. Phys. A 84, 413 (2006)" ], "parameters": { "kind": "assumed", "assumed": true } } Table I, U 'Band gap energy' 9 eV; taken from ref\. 19 \(source notes\)\. gulley\_2012/model\_refractive\_index ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_refractive_index", "material": "SiO2", "file": "SiO2/gulley_2012__refractive_index.csv", "table": "tbl_763380c3ceb4", "quantity": "refractive_index", "abscissa_unit": "nm", "use": "check", "reproduced_from": [ "S. W. Winkler, I. M. Burakov, R. Stoian, N. M. Bulgakova, A. Husakou, A. Mermillod-Blondin, A. Rosenfeld, D. Ashkenasi and I. V. Hertel, Appl. Phys. A 84, 413 (2006)" ], "parameters": { "assumed": true } } Table I n0 = 1\.45 at the 800\-nm peak wavelength\. gulley\_2012/model\_gvd ~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_gvd", "material": "SiO2", "file": "SiO2/gulley_2012__gvd.csv", "table": "tbl_763380c3ceb4", "quantity": "group_delay_dispersion", "unit": "fs2/m", "scale": 100, "abscissa_unit": "nm", "use": "check", "reproduced_from": [ "S. W. Winkler, I. M. Burakov, R. Stoian, N. M. Bulgakova, A. Husakou, A. Mermillod-Blondin, A. Rosenfeld, D. Ashkenasi and I. V. Hertel, Appl. Phys. A 84, 413 (2006)" ], "parameters": { "assumed": true } } Table I k\_2 = 361, unit printed 'fs^2 W^\-1' \(image confirmed\), impossible for a GVD\: read as fs2/cm \(scale 100 to fs2/m\), the unit of the same value in couairon\_2005 at 800 nm\. An interpretation of a misprinted unit\. gulley\_2012/model\_n2 ~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_n2", "material": "SiO2", "file": "SiO2/gulley_2012__n2.csv", "table": "tbl_763380c3ceb4", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-16, "abscissa_unit": "nm", "use": "check", "reproduced_from": [ "S. W. Winkler, I. M. Burakov, R. Stoian, N. M. Bulgakova, A. Husakou, A. Mermillod-Blondin, A. Rosenfeld, D. Ashkenasi and I. V. Hertel, Appl. Phys. A 84, 413 (2006)" ], "parameters": { "part": "total", "coefficient": "self", "assumed": true } } Table I n2 = 2\.48 x 10^\-16 cm2 W^\-1, the total Kerr coefficient of Eq\. \(1\), split into \(1 \- f\_r\) instantaneous and f\_r Raman parts\. gulley\_2012/model\_raman\_fraction ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_raman_fraction", "material": "SiO2", "file": "SiO2/gulley_2012__raman_fraction.csv", "table": "tbl_763380c3ceb4", "quantity": "raman_fraction", "abscissa": "none", "use": "check", "reproduced_from": [ "S. W. Winkler, I. M. Burakov, R. Stoian, N. M. Bulgakova, A. Husakou, A. Mermillod-Blondin, A. Rosenfeld, D. Ashkenasi and I. V. Hertel, Appl. Phys. A 84, 413 (2006)" ], "parameters": { "definition": "f_r in Eq. (1): i(k0 n2/n0)(1 - f_r) T I A + i(k0 n2/n0) f_r T [int R(tau - tau') I(tau') dtau'] A", "assumed": true } } Table I f\_r, 'Raman fraction of nonlinear polarization'\. gulley\_2012/model\_raman\_tau\_1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_raman_tau_1", "material": "SiO2", "file": "SiO2/gulley_2012__raman_tau_1.csv", "table": "tbl_763380c3ceb4", "quantity": "raman_response_time", "unit": "fs", "abscissa": "none", "use": "check", "reproduced_from": [ "S. W. Winkler, I. M. Burakov, R. Stoian, N. M. Bulgakova, A. Husakou, A. Mermillod-Blondin, A. Rosenfeld, D. Ashkenasi and I. V. Hertel, Appl. Phys. A 84, 413 (2006)" ], "parameters": { "constant": "tau_1 (in sin(tau/tau_1), as printed)", "model": "R(tau) = [(tau_1^2 + tau_2^2)/(tau_1 tau_2^2)] exp(-tau/tau_2) sin(tau/tau_1)", "assumed": true } } Table I tau\_1 = 32 fs; in the printed R\(tau\) it is the oscillation parameter, sin\(tau/tau\_1\), the reverse of couairon\_2005's assignment \(source notes, finding 2\)\. gulley\_2012/model\_raman\_tau\_2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_raman_tau_2", "material": "SiO2", "file": "SiO2/gulley_2012__raman_tau_2.csv", "table": "tbl_763380c3ceb4", "quantity": "raman_response_time", "unit": "fs", "abscissa": "none", "use": "check", "reproduced_from": [ "S. W. Winkler, I. M. Burakov, R. Stoian, N. M. Bulgakova, A. Husakou, A. Mermillod-Blondin, A. Rosenfeld, D. Ashkenasi and I. V. Hertel, Appl. Phys. A 84, 413 (2006)" ], "parameters": { "constant": "tau_2 (in exp(-tau/tau_2), as printed)", "model": "R(tau) = [(tau_1^2 + tau_2^2)/(tau_1 tau_2^2)] exp(-tau/tau_2) sin(tau/tau_1)", "assumed": true } } Table I tau\_2 = 12\.2 fs; in the printed R\(tau\) it is the decay time, exp\(\-tau/tau\_2\) \(source notes, finding 2\)\. gulley\_2012/model\_reduced\_mass ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_reduced_mass", "material": "SiO2", "table": "text", "quantity": "effective_mass", "unit": "m_e", "abscissa": "none", "use": "check", "parameters": { "carrier": "reduced", "assumed": true } } 1 inline points in the source record. p\. 013808\-2\: the Keldysh rate 'with a reduced electron\-hole mass of half the electron rest mass'\. The Drude cross section of Table I uses the free\-electron mass m\_e\. gulley\_2012/model\_recombination\_time ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_recombination_time", "material": "SiO2", "table": "text", "quantity": "electron_trapping_time", "unit": "fs", "abscissa": "none", "use": "check", "reproduced_from": [ "S. W. Winkler, I. M. Burakov, R. Stoian, N. M. Bulgakova, A. Husakou, A. Mermillod-Blondin, A. Rosenfeld, D. Ashkenasi and I. V. Hertel, Appl. Phys. A 84, 413 (2006)", "A. Q. Wu, I. H. Chowdhury and X. Xu, Phys. Rev. B 72, 085128 (2005)" ], "parameters": { "assumed": true } } 1 inline points in the source record. p\. 013808\-2\: 'we also assume an exponential loss of free carriers from the conduction band with a recombination time of 150 fs \[19,34\]'\. gulley\_2012/model\_collision\_time ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_collision_time", "material": "SiO2", "table": "text", "quantity": "electron_collision_time", "unit": "fs", "abscissa": "none", "use": "check", "parameters": { "assumed": true } } 1 inline points in the source record. p\. 013808\-4\: chosen by matching the simulated single\-shot threshold \(Fig\. 2\) to the estimated 80 uJ\: 'Fig\. 2 suggests an approximate collision time of the order of 10 fs \.\.\. Therefore a 10\-fs collision time is assumed hereafter'\. An order\-of\-magnitude, model\-dependent choice\. Formulas -------- gulley\_2012/propagation\_model ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "propagation_model", "material": "SiO2", "equation": "Eq. (1), p. 013808-2, and Table I", "printed": "dA/dz = (i/(2k0)) T^-1 nabla_perp^2 A + i D_b A + i (k0 n2/n0)(1 - f_r) T I A + i (k0 n2/n0) f_r T [int_-inf^tau dtau' R(tau - tau') I(tau')] A - (W_PI U/(2I)) A - (sigma/2)(1 + i omega0 tau_c) G^-1 [rho A]; I = (1/2) n0 c eps0 |A|^2; D_b = sum_{m>=2} (k_m/m!)(i d_tau)^m; T = 1 + (i/omega0) d_tau; G = 1 + (i/omega0) g d_tau; g = (-i omega0 tau_c)/(1 - i omega0 tau_c); sigma = e^2 tau_c/(m_e n0 eps0 c (1 + omega0^2 tau_c^2)); R(tau) = [(tau_1^2 + tau_2^2)/(tau_1 tau_2^2)] exp(-tau/tau_2) sin(tau/tau_1)", "variable": "A: complex field envelope, E = (1/2) A exp[i(k0 z - omega0 t)] + c.c.; tau = t - z k_1; rho the free-carrier density from Rethfeld's multiple rate equation (rethfeld_2004)", "coefficients": { "tau_1": "32 fs", "tau_2": "12.2 fs", "f_r": "0.18", "n0": "1.45", "k_2": "361 (unit printed fs^2 W^-1)", "n2": "2.48e-16 cm^2/W", "U": "9 eV", "tau_c": "10 fs (chosen)", "tau_rec": "150 fs" }, "reproduced_from": [ "J. R. Gulley and W. M. Dennis, Phys. Rev. A 81, 033818 (2010)" ], "check": "sigma peaks at tau_c = 1/omega0 = 0.425 fs at 800 nm (printed 'approximately tau_c = 0.42 fs'); at tau_c = 10 fs, sigma = 1.32e-18 cm2 (computed, not printed) (2026-09-26)." } The Drude dispersion operator G is the paper's subject \(ref\. 30\); only the GVD term of D\_b is kept\. P\_cr is written lambda^2/\(8 pi n0 n2\) in the self\-focusing length z\_sf = pi w\_xy^2/\(lambda sqrt\(P/P\_cr \- 1\)\) \(p\. 013808\-4; source notes, finding 3\)\. 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.