tzortzakis_2001 =============== S\. Tzortzakis, L\. Sudrie, M\. Franco, B\. Prade, A\. Mysyrowicz, A\. Couairon and L\. Berge, "Self\-Guided Propagation of Ultrashort IR Laser Pulses in Fused Silica", Phys\. Rev\. Lett\. 87, 213902 \(2001\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1103/physrevlett\.87\.213902 `__ **Source kind:** measurement **Recorded technique:** 160\-fs, 800\-nm pulses \(200 kHz\) focused by an f = 80 mm lens near the entrance face of moving fused\-silica plates \(2, 5, 10 mm\); filament diameter imaged along z with a 20x objective and CCD, autocorrelation \(BBO\) and spectrum of the output\. Simulated with an extended nonlinear Schrodinger equation for the envelope coupled to a multiphoton\-plus\-avalanche rate equation \(Eqs\. 1\-2\)\. **Materials in structured entries:** SiO2 **Dataset quantities:** atom\_density, avalanche\_coefficient, band\_gap, critical\_power, electron\_trapping\_time, group\_delay\_dispersion, multiphoton\_ionization\_cross\_section, nonlinear\_index, refractive\_index **Contents:** 9 datasets; 1 formula. Curation notes -------------- Journal pages 213902\-1 to \-4 = PDF pages 1\-4\. Identity validated\. The library text's 'mJ' for the input energy is 'uJ' in the pdf \(a Symbol\-font mu\)\: 'E\_in = 2 uJ' \(Fig\. 1 caption, p\. 213902\-2\); 2 uJ in 160 fs is 12\.5 MW, about 5 P\_cr as stated\. MEASURED \(no curated quantity\)\: filamentation requires P \> ~3 P\_cr; filament diameter 10\-40 um over several mm \(Fig\. 1c\); peak intensity 'of the order of 10^13 W/cm2' inferred from the size; the 160\-fs pulse splits into two ~60\-fs subpulses 120 fs apart \(autocorrelation, Fig\. 2a; spectral fringes 16 nm apart, Fig\. 2b\); less than 1 % of the energy in the visible continuum \(p\. 213902\-2\)\. SIMULATION INPUTS \(p\. 213902\-1 and \-3; datasets assumed\)\: P\_cr = lambda0^2/\(2 pi n0 n2\) ~ 2\.3 MW 'with n0 = 1\.453 being the linear refraction index and n2 = 3\.2 x 10^\-16 cm2/W the nonlinear refraction index for fused silica' \(no source\); k'' = 361 fs2/cm; the inverse\-bremsstrahlung cross section sigma = 2\.78 x 10^\-18 cm2 \[5\] \(Mlejnek, Wright and Moloney, Opt\. Lett\. 23, 382 \(1998\), which the paper's introduction lists among the atmospheric\-filamentation references \[1\-7\]\); rho\_at = 2\.1 x 10^22 atoms/cm3, rho\_at/rho\_c ~ 12; U\_i = 7\.6 eV \[24\] \(Tohmon et al\., Phys\. Rev\. B 39, 1337 \(1989\)\), so K = 5; sigma\_K = 1\.3 x 10^\-55 s^\-1 cm^2K/W^K \(no source\); alpha = sigma/\(n0^2 U\_i\); tau\_r ~ 150 fs \[23\] \(Audebert et al\. 1994\); input waist 30 um \(measured\), FWHM 160 fs\. The Kerr term is instantaneous \(no Raman response in Eq\. 1\)\. CHECKS \(2026\-09\-26\)\: lambda0^2/\(2 pi n0 n2\) = 2\.19 MW with the printed n0 and n2, not '~2\.3 MW' \(5 % high; hamam\_2018 gets 2\.19 MW from the same n2\); rho\_at/rho\_c = 12\.06 with rho\_c = omega0^2 eps0 m\_e/e^2 \(printed ~12\); 7\.6 eV/1\.55 eV = 4\.90, K = 5; the Drude cross section e^2 tau\_c/\(m\_e n0 eps0 c \(1 \+ omega0^2 tau\_c^2\)\) equals 2\.78e\-18 cm2 for tau\_c = 4\.69 fs \(or 0\.038 fs\) with n0 = 1\.453, the paper states no tau\_c\. MODEL RESULTS\: I\_max = 1\.5e13 W/cm2 computed; filament length Delta z ~ 1 cm from Delta z ~ ln\[P\_in/P\(z\)\]/\(beta^\(K\) I\_max^\(K\-1\)\) \(p\. 213902\-3\); figures only otherwise\. REPRODUCED BY\: hamam\_2018 \(tau\_rec = 1\.5e\-13 s, ref\. 23 there\); couairon\_2005 and berge\_2010 cite it for the loose\-focusing filament\. **Recorded bibliographic identity status:** VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- tzortzakis\_2001/model\_n2 ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_n2", "material": "SiO2", "table": "text", "quantity": "nonlinear_index", "unit": "cm2/W", "abscissa_unit": "nm", "use": "check", "parameters": { "part": "unknown", "coefficient": "self", "assumed": true } } 1 inline points in the source record. p\. 213902\-1\: 'n2 = 3\.2 x 10^\-16 cm2/W the nonlinear refraction index for fused silica'; no source, no pulse duration; the model's Kerr response is instantaneous\. tzortzakis\_2001/model\_refractive\_index ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_refractive_index", "material": "SiO2", "table": "text", "quantity": "refractive_index", "abscissa_unit": "nm", "use": "check", "parameters": { "assumed": true } } 1 inline points in the source record. p\. 213902\-1\: 'n0 = 1\.453 being the linear refraction index'; no source\. tzortzakis\_2001/model\_critical\_power ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_critical_power", "material": "SiO2", "table": "text", "quantity": "critical_power", "unit": "MW", "abscissa_unit": "nm", "use": "check", "parameters": { "definition": "P_cr = lambda0^2/(2 pi n0 n2), n0 = 1.453, n2 = 3.2e-16 cm2/W" } } 1 inline points in the source record. p\. 213902\-1\: 'P\_cr = lambda0^2/2 pi n0 n2 ~ 2\.3 MW'\. The printed n0 and n2 give 2\.19 MW \(source notes\)\. tzortzakis\_2001/model\_gvd ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_gvd", "material": "SiO2", "table": "text", "quantity": "group_delay_dispersion", "unit": "fs2/m", "scale": 100, "abscissa_unit": "nm", "use": "check", "parameters": { "assumed": true } } 1 inline points in the source record. p\. 213902\-3\: 'normal GVD with coefficient k'' = 361 fs2/cm' \(scale 100 to fs2/m\); no source \(couairon\_2005 computes the same from Malitson's formula\)\. tzortzakis\_2001/model\_avalanche\_cross\_section ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_avalanche_cross_section", "material": "SiO2", "table": "text", "quantity": "avalanche_coefficient", "unit": "cm2", "abscissa_unit": "nm", "use": "check", "reproduced_from": [ "M. Mlejnek, E. M. Wright and J. V. Moloney, Opt. Lett. 23, 382 (1998)" ], "parameters": { "definition": "sigma, the inverse-bremsstrahlung cross section of Eq. (1); Eq. (2) avalanche term alpha rho |E|^2 with alpha = sigma/(n0^2 U_i)", "assumed": true } } 1 inline points in the source record. p\. 213902\-3\: 'plasma absorption with inverse Bremsstrahlung cross section sigma = 2\.78 x 10^\-18 cm2 \[5\]'; ref\. 5 is among the paper's atmospheric\-filamentation references\. The avalanche coefficient of Eq\. \(2\) is alpha = sigma/\(n0^2 U\_i\)\. Equal to the Drude value with tau\_c = 4\.69 fs \(source notes\)\. tzortzakis\_2001/model\_band\_gap ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_band_gap", "material": "SiO2", "table": "text", "quantity": "band_gap", "unit": "eV", "abscissa": "none", "use": "check", "reproduced_from": [ "R. Tohmon, H. Mizuno, Y. Ohki, K. Sasagane, K. Nagasawa and Y. Hama, Phys. Rev. B 39, 1337 (1989)" ], "parameters": { "kind": "assumed", "assumed": true } } 1 inline points in the source record. p\. 213902\-3\: 'Band\-to\-band transitions are induced in silica through the gap potential U\_i = 7\.6 eV \[24\], yielding the number of photons K = 5 required for ionization\.' tzortzakis\_2001/model\_sigma5 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_sigma5", "material": "SiO2", "table": "text", "quantity": "multiphoton_ionization_cross_section", "unit": "s-1 cm10/W5", "abscissa_unit": "nm", "use": "check", "parameters": { "photons": 5, "assumed": true } } 1 inline points in the source record. p\. 213902\-3\: 'The MPI coefficient then reads as sigma\_K = 1\.3 x 10^\-55 s^\-1 cm^2K/W^K' with K = 5 \(printed cm^2K/W^K\); per atom, the rate being sigma\_K \|E\|^2K \(rho\_at \- rho\) \(Eq\. 2\)\. No source; the multiphoton absorption coefficient is beta^\(K\) = K hbar omega0 sigma\_K rho\_at\. tzortzakis\_2001/model\_atom\_density ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "model_atom_density", "material": "SiO2", "table": "text", "quantity": "atom_density", "unit": "cm-3", "abscissa": "none", "use": "check", "parameters": { "counts": "atoms", "assumed": true } } 1 inline points in the source record. p\. 213902\-3\: 'rho\_at is the background atom density \(rho\_at/rho\_c ~ 12 where rho\_at = 2\.1 x 10^22 atoms/cm3\)'\. tzortzakis\_2001/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": [ "P. Audebert et al., Phys. Rev. Lett. 73, 1990 (1994)" ], "parameters": { "assumed": true } } 1 inline points in the source record. p\. 213902\-3\: 'electron recombination with a characteristic time tau\_r ~ 150 fs in fused silica \[23\]'\. Formulas -------- tzortzakis\_2001/propagation\_model ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "propagation_model", "material": "SiO2", "equation": "Eqs. (1)-(2), p. 213902-3", "printed": "dE/dz = (i/(2k)) T^-1 (d^2/dr^2 + (1/r) d/dr) E - (i k''/2) d^2E/dtau^2 + i k0 n2 T(|E|^2 E) - (sigma/2 + i k0/(2 rho_c)) T^-1 (rho E) - (beta^(K)/2) |E|^(2K-2) E (1); d rho/dtau = sigma_K |E|^2K (rho_at - rho) + alpha rho |E|^2 - rho/tau_r (2); beta^(K) = K hbar omega0 sigma_K rho_at; alpha = sigma/(n0^2 U_i); T = 1 + (i/omega0) d/dtau", "variable": "E: envelope (|E|^2 an intensity); tau = t - z/v_g; k = n0 k0", "coefficients": { "n0": "1.453", "n2": "3.2e-16 cm^2/W", "k2": "361 fs^2/cm", "sigma": "2.78e-18 cm^2", "rho_at": "2.1e22 atoms/cm^3", "U_i": "7.6 eV", "K": "5", "sigma_K": "1.3e-55 s^-1 cm^10/W^5", "tau_r": "150 fs" }, "check": "rho_at/rho_c = 12.06 (printed ~12); K = 5 (7.6/1.55 = 4.90) (checked 2026-09-26). The filament-length estimate Delta z ~ ln[P_in/P(z)]/(beta^(K) I_max^(K-1)) ~ 1 cm with I_max = 1.5e13 W/cm2 is not recomputed (P(z) not given)." } Solved with a Fourier decomposition in time and Crank\-Nicholson in space; Gaussian input, waist 30 um, 160 fs FWHM, E\_in = 2 uJ \(P\_in ~ 5 P\_cr\)\. 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.