jukna_2018 ========== V\. Jukna, N\. Garejev, G\. Tamosauskas and A\. Dubietis, "Role of external focusing geometry in supercontinuum generation in bulk solid\-state media", J\. Opt\. Soc\. Am\. B 36, A54 \(2019\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1364/josab\.36\.000a54 `__ **Source kind:** measurement **Recorded technique:** Supercontinuum generation in a 4\-mm sapphire plate by 210\-fs, 1\.3\-um pulses \(OPA signal stretched by a 9\-nm interference filter, up to 6 uJ\), focused by an f = \+100 mm lens \(23 um FWHM spot\) on the input face or 1 mm inside; spectra 0\.2\-1\.8 um with Si and Ge detectors; filament\-induced luminescence photographed from the side\. Simulated with a unidirectional nonparaxial propagation equation \(Eqs\. 1\-3\) and a photoionization\-avalanche\-recombination rate equation \(Eq\. 4\)\. **Materials in structured entries:** Al2O3 **Dataset quantities:** atom\_density, avalanche\_coefficient, band\_gap, electron\_collision\_time, electron\_trapping\_time, nonlinear\_index, refractive\_index **Contents:** 7 datasets; 1 formula. Curation notes -------------- Journal pages A54\-A60 = PDF pages 1\-7; 'published 20 December 2018' in the February 2019 issue \(vol\. 36, no\. 2\)\: the source id keeps the library's 2018, the citation the volume year 2019\. Identity validated\. MEASURED \(no curated quantity\)\: supercontinuum threshold 2 uJ with the focus on the input face and 1\.48 uJ with the focus 1 mm inside, where the continuum is suppressed between 2\.0 and 2\.5 uJ and recovers above 2\.5 uJ \(pp\. A55\-A56\); the continuum spans 470 nm \- 1\.8 um at the 1e\-5 level; the luminescence band of sapphire peaks at 325 nm, attributed to 11\-photon absorption 'assuming its bandgap of 9\.9 eV and photon energy of 0\.95 eV' \(p\. A55; 9\.9/0\.954 = 10\.4, so 11 photons\: checked 2026\-09\-26\)\. Polarization and crystal orientation \(c\-axis\) not stated\. SIMULATION INPUTS \(pp\. A56\-A57, datasets assumed\)\: 'n0 = 1\.75 and n2 = 3\.1 x 10^\-16 cm2/W \[29\] are the linear and nonlinear refractive indices of sapphire, respectively; sigma = 1\.9 x 10^\-21 m2 is the cross section for inverse Bremsstrahlung; tau\_c = 1 fs is the effective electron collision time; rho\_nt = 2\.35 x 10^22 cm^\-3 is the density of neutral molecules'; 'The intensity\-dependent photoionization rate W was calculated from Keldysh's theory with electron\-hole mass ratio m\* = 1 and assuming bandgap of sapphire U\_g = 9\.9 eV \[28\]'; 'tau\_rec = 100 ps \[30\] is the free electron recombination time'; n\(omega\) 'from a Sellmeier equation \[28\]' \(Weber, Handbook of Optical Materials, CRC 2002; the formula is not printed\)\. Ref\. 29 is Major et al\., Opt\. Lett\. 29, 602 \(2004\); ref\. 30 Guizard et al\., Europhys\. Lett\. 29, 401 \(1995\)\. The 'electron\-hole mass ratio m\* = 1' is ambiguous \(a mass in electron masses, or a ratio of the electron and hole masses\)\: not recorded as a dataset\. The Kerr response of Eq\. \(2\) is instantaneous \(no Raman term\)\. Simulated input\: 210 fs, 30\-um FWHM Gaussian beam, flat phase at the focus\. CHECK \(2026\-09\-26\)\: the Drude cross section e^2 tau\_c/\(m\_e n0 eps0 c \(1 \+ omega0^2 tau\_c^2\)\) at 1\.3 um with tau\_c = 1 fs and n0 = 1\.75 is 1\.957e\-21 m2; printed 1\.9e\-21 m2 \(truncated rather than rounded, or a slightly different n0 or mass\)\. REPRODUCES\: silva\_2012 \(ref\. 13\) and dubietis\_2019's review \(ref\. 1, Lith\. J\. Phys\. 2017 version\) are cited for context only\. **Recorded bibliographic identity status:** VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- jukna\_2018/model\_refractive\_index ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_refractive_index", "material": "Al2O3", "table": "text", "quantity": "refractive_index", "abscissa_unit": "nm", "use": "check", "parameters": { "assumed": true } } 1 inline points in the source record. p\. A56\: 'n0 = 1\.75 \.\.\. the linear \.\.\. refractive index of sapphire' at the 1\.3\-um carrier \(the dispersion itself from a Sellmeier equation of ref\. 28\)\. Axis not stated\. jukna\_2018/model\_n2 ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_n2", "material": "Al2O3", "table": "text", "quantity": "nonlinear_index", "unit": "cm2/W", "abscissa_unit": "nm", "use": "check", "reproduced_from": [ "A. Major, F. Yoshino, I. Nikolakakos, J. S. Aitchison and P. W. E. Smith, Opt. Lett. 29, 602 (2004)" ], "parameters": { "part": "unknown", "coefficient": "self", "assumed": true } } 1 inline points in the source record. p\. A56\: 'n2 = 3\.1 x 10^\-16 cm2/W \[29\]', used as the instantaneous Kerr coefficient of Eq\. \(2\) at 1\.3 um\. Axis and polarization not stated\. jukna\_2018/model\_avalanche\_cross\_section ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_avalanche_cross_section", "material": "Al2O3", "table": "text", "quantity": "avalanche_coefficient", "unit": "m2", "abscissa_unit": "nm", "use": "check", "parameters": { "definition": "sigma in eps0^-1 J = n0 c [sigma (1 + i omega0 tau_c) rho + ...] E (Eq. 3) and the avalanche term (sigma/U_g)|E|^2 rho (1 - rho/rho_nt) of Eq. (4)", "assumed": true } } 1 inline points in the source record. p\. A56\: 'sigma = 1\.9 x 10^\-21 m2 is the cross section for inverse Bremsstrahlung'; the Drude value for tau\_c = 1 fs, n0 = 1\.75 is 1\.957e\-21 m2 \(source notes\)\. jukna\_2018/model\_collision\_time ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_collision_time", "material": "Al2O3", "table": "text", "quantity": "electron_collision_time", "unit": "fs", "abscissa": "none", "use": "check", "parameters": { "assumed": true } } 1 inline points in the source record. p\. A56\: 'tau\_c = 1 fs is the effective electron collision time'; no source\. jukna\_2018/model\_molecule\_density ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_molecule_density", "material": "Al2O3", "table": "text", "quantity": "atom_density", "unit": "cm-3", "abscissa": "none", "use": "check", "parameters": { "counts": "molecules", "assumed": true } } 1 inline points in the source record. p\. A56\: 'rho\_nt = 2\.35 x 10^22 cm^\-3 is the density of neutral molecules'; no source\. jukna\_2018/model\_band\_gap ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_band_gap", "material": "Al2O3", "table": "text", "quantity": "band_gap", "unit": "eV", "abscissa": "none", "use": "check", "reproduced_from": [ "M. J. Weber, Handbook of Optical Materials (CRC Press, 2002)" ], "parameters": { "kind": "assumed", "assumed": true } } 1 inline points in the source record. p\. A57\: 'assuming bandgap of sapphire U\_g = 9\.9 eV \[28\]', the gap of the Keldysh rate; also used for the 11\-photon count of the luminescence \(p\. A55\)\. jukna\_2018/model\_recombination\_time ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_recombination_time", "material": "Al2O3", "table": "text", "quantity": "electron_trapping_time", "unit": "ps", "abscissa": "none", "use": "check", "reproduced_from": [ "S. Guizard, P. Martin, P. Daguzan, G. Petite, P. Audebert, J. P. Geindre, A. Dos Santos and A. Antonnetti, Europhys. Lett. 29, 401 (1995)" ], "parameters": { "assumed": true } } 1 inline points in the source record. p\. A57\: 'tau\_rec = 100 ps \[30\] is the free electron recombination time'\. Formulas -------- jukna\_2018/propagation\_model ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "propagation_model", "material": "Al2O3", "equation": "Eqs. (1)-(4), pp. A56-A57", "printed": "dE^/dz = i (sqrt(k^2(omega) - k_perp^2) - k0 - k0' omega) E^ + i (omega/(2 n(omega) c)) eps0^-1 (P^ + i J^/omega) (1); eps0^-1 P = 2 n0 n2 |E|^2 E (2); eps0^-1 J = n0 c [sigma (1 + i omega0 tau_c) rho + (W U_g/|E|^2)(1 - rho/rho_nt)] E (3); d rho/dt = W (1 - rho/rho_nt) + (sigma/U_g) |E|^2 rho (1 - rho/rho_nt) - rho/tau_rec (4)", "variable": "E^(omega, k_perp, z): the envelope's spectrum; W the Keldysh photoionization rate", "coefficients": { "n0": "1.75", "n2": "3.1e-16 cm^2/W", "sigma": "1.9e-21 m^2", "tau_c": "1 fs", "rho_nt": "2.35e22 cm^-3", "U_g": "9.9 eV", "m_star": "1 ('electron-hole mass ratio')", "tau_rec": "100 ps" }, "reproduced_from": [ "A. Couairon, E. Brambilla, T. Corti, D. Majus, O. de J. Ramirez-Gongora and M. Kolesik, Eur. Phys. J. Spec. Top. 199, 5 (2011)" ], "check": "sigma: 1.957e-21 m2 from the Drude formula with tau_c = 1 fs, n0 = 1.75 at 1.3 um (printed 1.9e-21) (2026-09-26)." } The photoionization term of Eq\. \(4\) is W \(1 \- rho/rho\_nt\), a rate per volume already \(as printed\)\. 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.