liu_2005 ======== Y\. Liu, H\. Jiang, Q\. Sun, Z\. Wu, H\. Yang, and Q\. Gong, "Different tendencies of breakdown threshold on pulse duration in the subpicosecond regime in fused silica", J\. Opt\. A\: Pure Appl\. Opt\. 7, 198\-203 \(2005\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1088/1464\-4258/7/4/008 `__ **Source kind:** measurement **Recorded technique:** Single\-shot laser\-induced breakdown inside bulk fused silica \(polished, 10 x 5 x 3 mm^3; grade not stated\) at 800 nm, pulse durations 240 fs to 2\.5 ps \(compressor grating\), each site irradiated once\. The spatially filtered beam underfills \(by ~3\) a 0\.4 or 0\.85 NA objective; the beam radius omega after the objective and its distance d to the focus measured by knife edge give the effective NA = omega/\(omega^2 \+ d^2\)^0\.5 = 0\.126 and 0\.255 \(focal radii ~2\.0 and 0\.95 um for a Gaussian beam\)\. Breakdown detected by imaging the plasma luminescence from the side onto a cooled CCD \(Princeton Instruments TE/CCD\-512/SB, a filter blocking 800 nm\), the threshold being the lowest input energy giving a plasma image \(p\. 199\)\. Depths 6, 170 and 300 um \(\+\-5 um\); the detailed data at 300 um\. Simulated with a 3\-D nonlinear envelope equation \(Eq\. 1\: diffraction, GVD, Kerr, plasma absorption and defocusing, multiphoton absorption\) coupled to an electron\-density rate equation \(Eq\. 2\: avalanche and multiphoton ionization, no recombination\) solved by an ADI method\. **Materials in structured entries:** SiO2 **Dataset quantities:** atom\_density, band\_gap, damage\_threshold\_energy, electron\_collision\_time, multiphoton\_ionization\_cross\_section, nonlinear\_index **Contents:** 6 datasets; 1 formula. Curation notes -------------- Journal pages 198\-203 = pdf pages 2\-7 \(journal page = 196 \+ pdf page; pdf page 1 is the IOP download cover\)\. Identity checked against the first page\. WHAT WAS MEASURED\. Fig\. 2 \(p\. 200\)\: the threshold energy against pulse duration \(240 fs \- 2\.5 ps\) at 300 um depth for effective NA 0\.126 \(squares\) and 0\.255 \(triangles\)\: with NA 0\.126 the threshold rises for pulses shorter than 700 fs; with NA 0\.255 it keeps decreasing from 2\.5 ps to 240 fs \(figure only, not digitised\)\. The depth changed the threshold by at most 10 % without changing the trend \(p\. 200\)\. The one threshold printed in the text\: Fig\. 1's example, NA 0\.255, 400 fs, 'For E\_in = 0\.17 uJ, an image of pure noise is obtained while for E\_in = 0\.18 uJ a clear image of the plasma can be seen\. Therefore the threshold in this case can be defined as 0\.18 uJ with an error of 0\.01 uJ' \(p\. 199\)\: dataset threshold\_energy\_400fs \(the depth of this example is not stated\)\. The energies are the input pulse energies \(E\_in\)\. THE MODEL AND ITS INPUTS \(p\. 200; assumed, datasets check\)\: Eq\. \(1\), \(i 2k d/dz \+ nabla\_perp^2\) eps = k k'' d^2 eps/d xi^2 \- 2 k k0 n2 \|eps\|^2 eps \- i k sigma \(1 \+ i omega0 tau\_c\) rho eps \- i k beta^\(K\) \|eps\|^\(2K\-2\) eps, with n2 = 3\.54 x 10^\-16 cm^2/W \(Ref\. 17, Sudrie et al\., Phys\. Rev\. Lett\. 89, 186601 \(2002\)\), beta^\(K\) = K hbar omega0 sigma\_K rho\_at; 'A band gap potential E\_g = 9 eV of the material yields the K = 6 required for the ionization and the multiphoton ionization \(MPI\) coefficient sigma\_K = 9\.8 x 10^\-70 s^\-1 cm^12 W^\-6' \(Ref\. 17\); the inverse\-bremsstrahlung cross section sigma = k e^2 tau\_c / omega0 m\_e eps0 \(1 \+ \(omega0 tau\_c\)^2\) = 1\.55 x 10^\-18 cm^2 with tau\_c = 2\.33 x 10^\-14 s \(Ref\. 17\); 'The critical plasma density rho\_c, and the background atom density, rho\_at = 2\.1 x 10^21 cm^\-3, are in the ratio rho\_at/rho\_c ~ 12' \(Ref\. 18, Ward and Berge 2003\)\. Eq\. \(2\)\: d rho/d xi = sigma/\(n0^2 E\_g\) rho \|eps\|^2 \+ sigma\_K rho\_at \|eps\|^\(2K\) \(\|eps\|^2 the intensity\); rho\_0 = 1\.0 x 10^8 cm^\-3 initial electrons \(Ref\. 8, Tien et al\. 1999\); recombination omitted \(a test with it changed little\)\. The MPI term is used 'not expressed by Keldysh's formula \.\.\. because the adiabaticity parameter gamma \>\> 1 in our experiments'\. k'' and n0 are not given\. CHECKS \(computed 2026\-09\-27\)\. rho\_c = eps0 m\_e omega0^2/e^2 = 1\.742e21 cm^\-3 at 800 nm, so rho\_at/rho\_c ~ 12 requires rho\_at = 2\.1e22 cm^\-3 \(12\.06\), not the printed 2\.1e21 \(1\.21\)\: erratum \(couairon\_2005, the same group's model inputs, prints rho\_at = 2\.1e22\)\. The printed sigma = 1\.55e\-18 cm^2 is not reproduced by its own formula with tau\_c = 2\.33e\-14 s\: with k = n0 omega0/c and n0 = 1\.45 it gives 1\.19e\-18 cm^2 \(1\.55e\-18 needs tau\_c ~ 1\.8e\-14 s\); not decidable, no erratum\. sigma\_K = 9\.8e\-70 against couairon\_2005's 9\.6e\-70 s^\-1 cm^12/W^6 for the same Keldysh limit\. THRESHOLD DENSITIES \(model results, notes only\)\. The simulated plasma density saturates below 1e19 cm^\-3 \(p\. 200\); with rho\_th = 1\.8e19 and 1\.45e19 cm^\-3 the NA 0\.126 thresholds rise below 1000 and 550 fs, with 1\.3e19 they are flat after 500 fs, with 1\.0e19 they keep decreasing \(Fig\. 3a\); the experiment matches rho\_th = 1\.45e19 cm^\-3 \(NA 0\.126\) and 6\.11e19 cm^\-3 \(NA 0\.255\), the integrated densities agreeing to 6 % \(p\. 201\); for NA 0\.126 the 300 and 700 fs density curves cross at 1\.4e19 cm^\-3; for NA 0\.255 slight saturation above 5\.6e19 cm^\-3 at 300 fs \(p\. 202\)\. The rise at loose focusing is attributed to plasma defocusing \(Figs\. 4\-6\)\. Figs\. 3\-6 are figures only\. FINDING \(the NA\)\. The paper prints 'effective NA = 0\.225' once \(p\. 202, in the discussion of Fig\. 6\) and 0\.255 everywhere else \(abstract, p\. 199, Figs\. 1\-4 captions\)\: a misprint in this paper, which hamam\_2018 carries into its tables\. REPRODUCTIONS OF THIS PAPER\. hamam\_2018 Table 2 attributes its threshold intensities and powers against pulse width to this paper, but this paper prints no intensities and no table \(Fig\. 2 gives input energies only\)\: hamam\_2018's values are its own conversion of Fig\. 2 \(listed for review; hamam\_2018 is another extraction's record\)\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- liu\_2005/threshold\_energy\_400fs ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "threshold_energy_400fs", "material": "SiO2", "table": "text", "quantity": "damage_threshold_energy", "unit": "uJ", "abscissa": "duration", "abscissa_unit": "fs", "use": "primary", "uncertainty": { "column": true, "level": "bound" }, "parameters": { "site": "bulk", "criterion": "plasma luminescence imaged from the side by a cooled CCD (first input energy giving a plasma image)", "shots": 1, "wavelength_nm": 800, "numerical_aperture": 0.255, "form": "bulk" } } 1 inline points in the source record. p\. 199 \(Fig\. 1\)\: the breakdown threshold for effective NA = 0\.255 and 400\-fs pulses, 0\.18 uJ 'with an error of 0\.01 uJ' \(the energy step between no plasma image at 0\.17 uJ and a clear one at 0\.18 uJ\)\. Input pulse energy, single shot, bulk; the focus depth of this example is not stated \(the Fig\. 2 series is at 300 um\)\. liu\_2005/model\_n2 ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_n2", "material": "SiO2", "table": "text", "quantity": "nonlinear_index", "unit": "cm2/W", "scale": 1e-16, "abscissa_unit": "nm", "use": "check", "reproduced_from": [ "L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis and A. Mysyrowicz, Phys. Rev. Lett. 89, 186601 (2002)" ], "parameters": { "part": "unknown", "coefficient": "self", "assumed": true } } 1 inline points in the source record. p\. 200\: 'the Kerr effect of the material with n2 = 3\.54 x 10^\-16 cm^2 W^\-1 \[17\]', a model input of Eq\. \(1\) \(couairon\_2005 derives the same number from a measured critical power at 800 nm, 160 fs\)\. Part not stated\. liu\_2005/model\_band\_gap ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_band_gap", "material": "SiO2", "table": "text", "quantity": "band_gap", "unit": "eV", "abscissa": "none", "use": "check", "parameters": { "kind": "assumed", "assumed": true } } 1 inline points in the source record. p\. 200\: 'A band gap potential E\_g = 9 eV of the material yields the K = 6 required for the ionization', a model input \(with Ref\. 17's sigma\_K\)\. liu\_2005/model\_sigma6 ~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_sigma6", "material": "SiO2", "table": "text", "quantity": "multiphoton_ionization_cross_section", "unit": "s-1 cm12/W6", "abscissa_unit": "nm", "use": "check", "reproduced_from": [ "L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis and A. Mysyrowicz, Phys. Rev. Lett. 89, 186601 (2002)" ], "parameters": { "photons": 6, "assumed": true } } 1 inline points in the source record. p\. 200\: 'the multiphoton ionization \(MPI\) coefficient sigma\_K = 9\.8 x 10^\-70 s^\-1 cm^12 W^\-6 \[17\]', per atom\: the MPI rate is sigma\_K rho\_at \|eps\|^\(2K\) \(Eq\. 2\) and the MPA coefficient beta^\(K\) = K hbar omega0 sigma\_K rho\_at\. couairon\_2005 prints 9\.6e\-70 for its Keldysh limit\. liu\_2005/model\_collision\_time ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_collision_time", "material": "SiO2", "table": "text", "quantity": "electron_collision_time", "unit": "s", "abscissa": "none", "use": "check", "reproduced_from": [ "L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis and A. Mysyrowicz, Phys. Rev. Lett. 89, 186601 (2002)" ], "parameters": { "assumed": true } } 1 inline points in the source record. p\. 200\: 'the electron collision time tau\_c = 2\.33 x 10^\-14 s \[17\]', the Drude input of sigma\. With it the printed sigma = 1\.55e\-18 cm^2 is not reproduced \(1\.19e\-18 with n0 = 1\.45; source notes\)\. couairon\_2005 uses 1e\-14 s\. liu\_2005/model\_atom\_density ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_atom_density", "material": "SiO2", "table": "text", "quantity": "atom_density", "unit": "cm-3", "abscissa": "none", "use": "check", "reproduced_from": [ "H. Ward and L. Berge, Phys. Rev. Lett. 90, 053901 (2003)" ], "parameters": { "counts": "atoms", "assumed": true } } 1 inline points in the source record. p\. 200\: 'The critical plasma density rho\_c, and the background atom density, rho\_at = 2\.1 x 10^21 cm^\-3, are in the ratio rho\_at/rho\_c ~ 12 \[18\]'\. Printed 2\.1e21; corrected to 2\.1e22 by the erratum \(the stated ratio 12\)\. Formulas -------- liu\_2005/rate\_equation ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "rate_equation", "material": "SiO2", "equation": "Eq. (2), p. 200, with the inputs of p. 200", "printed": "\\frac{\\partial \\rho}{\\partial \\xi} = \\frac{\\sigma}{n_0^2 E_g} \\rho |\\varepsilon|^2 + \\sigma_K \\rho_{at} |\\varepsilon|^{2K}, \\quad \\sigma = \\frac{k e^2 \\tau_c}{\\omega_0 m_e \\epsilon_0 (1 + (\\omega_0 \\tau_c)^2)}", "variable": "rho: conduction-electron density (cm^-3); |eps|^2: intensity (W/cm^2); xi = t - z/v_g; K = 6; k = n0 omega0/c", "range": "800 nm, 240 fs - 2.5 ps; no recombination", "coefficients": { "sigma": "1.55e-18 cm^2", "E_g": "9 eV", "K": "6", "sigma_K": "9.8e-70 s^-1 cm^12 W^-6", "tau_c": "2.33e-14 s", "rho_at": "2.1e21 cm^-3", "rho_0": "1.0e8 cm^-3" }, "check": "rho_at/rho_c ~ 12 as stated requires rho_at = 2.1e22 cm^-3 (rho_c = 1.742e21 cm^-3 at 800 nm; the printed 2.1e21 gives 1.2; erratum on the dataset). sigma from its formula with tau_c = 2.33e-14 s and n0 = 1.45 is 1.19e-18 cm^2, not the printed 1.55e-18 (computed 2026-09-27).", "corrections": [ { "term": "rho_at", "printed": "2.1e21 cm^-3", "corrected": "2.1e22 cm^-3", "reason": "The paper states rho_at/rho_c ~ 12 (p. 200); the printed 2.1 x 10^21 cm^-3 gives 1.2.", "evidence": "rho_c = 1.742e21 cm^-3 at 800 nm (computed 2026-09-27), 2.1e22/rho_c = 12.06; couairon_2005 prints rho_at = 2.1 x 10^22 cm^-3 for the same model inputs." } ] } The avalanche term 'comes from Drude model'; the threshold criterion is a density rho\_th chosen per focusing \(1\.45e19 and 6\.11e19 cm^\-3; source notes\)\. rho\_at is corrected as on the dataset model\_atom\_density\. Corrections ----------- .. code-block:: text [ { "dataset": "model_atom_density", "row": "1", "column": "value", "printed": "2.1e21", "corrected": "2.1e22", "reason": "The paper states that rho_at and the critical plasma density are 'in the ratio rho_at/rho_c ~ 12' (p. 200); with the printed 2.1 x 10^21 cm^-3 the ratio is 1.2. The power of ten is misprinted.", "evidence": "rho_c = eps0 m_e omega0^2/e^2 = 1.742e21 cm^-3 at 800 nm (computed 2026-09-27), so the stated ratio of 12 gives rho_at = 2.1e22 cm^-3 (2.1e22/1.742e21 = 12.06); couairon_2005, the model of the reference the paper takes its inputs from (Sudrie, Couairon et al.), prints 'rho_at = 2.1 x 10^22 cm^-3, the background atom density' (p. 125435-3); fused silica's molecular density is 2.2e22 cm^-3 (2.2 g/cm^3, 60.08 g/mol)." } ] 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.