×

A split-step method to include electron-electron collisions via Monte Carlo in multiple rate equation simulations. (English) Zbl 1351.82078

Summary: A split-step numerical method for calculating ultrafast free-electron dynamics in dielectrics is introduced. The two split steps, independently programmed in and 2003, are interfaced via the presented open source wrapper. The first step solves a deterministic extended multi-rate equation for the ionization, electron-phonon collisions, and single photon absorption by free-carriers. The second step is stochastic and models electron-electron collisions using Monte-Carlo techniques. This combination of deterministic and stochastic approaches is a unique and efficient method of calculating the nonlinear dynamics of 3D materials exposed to high intensity ultrashort pulses. Results from simulations solving the proposed model demonstrate how electron-electron scattering relaxes the non-equilibrium electron distribution on the femtosecond time scale.

MSC:

82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)
65C05 Monte Carlo methods

Software:

MersenneTwister
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Balling, P.; Schou, J., Femtosecond-laser ablation dynamics of dielectrics: basics and applications for thin films, Rep. Prog. Phys., 76, Article 036502 pp. (2013)
[2] Vogel, A.; Noack, J.; Huttman, G.; Paltauf, G., Mechanisms of femtosecond laser nanosurgery of cells and tissues, Appl. Phys. B, 81, 1015-1047 (2005)
[3] (Hannaford, P., Femtosecond Laser Spectroscopy (2005), Springer Science Business Media, Inc.)
[4] Boyd, R. W., Nonlinear Optics (2002), Academic Press
[5] Sutherland, R. L., Handbook of Nonlinear Optics (2003), Dekker: Dekker New York
[6] Bergé, L.; Skupin, S.; Nuter, R.; Kasparian, J.; Wolf, J.-P., Ultrashort filaments of light in weakly ionized, optically transparent media, Rep. Prog. Phys., 70, 1633 (2007)
[7] Couairon, A.; Brambilla, E.; Corti, T.; Majus, D.; de J. Ramírez-Góngora, O.; Kolesik, M., Practitioner’s guide to laser pulse propagation models and simulation, Eur. Phys. J., 199, 5-76 (2011)
[8] Lorin, E.; Chelkowski, S.; Bandrauk, A., A numerical Maxwell-Schrödinger model for intense laser-matter interaction and propagation, Comput. Phys. Commun., 177, 908-932 (2007) · Zbl 1196.78021
[9] Karle, C.; Schweitzer, J.; Hochbruck, M.; Spatschek, K., A parallel implementation of a two-dimensional fluid laser-plasma integrator for stratified plasma-vacuum systems, J. Comput. Phys., 227, 7701-7719 (2008) · Zbl 1270.76090
[10] Mauger, S.; de Verdière, G. C.; Bergé, L.; Skupin, S., Gpu accelerated fully space and time resolved numerical simulations of self-focusing laser beams in sbs-active media, J. Comput. Phys., 235, 606-625 (2013)
[11] Fischer, R.; Staudt, A.; Keitel, C., Simulation of atomic quantum dynamics in combined intense laser and weak electric fields, Comput. Phys. Commun., 157, 139-146 (2004)
[12] Rethfeld, B., Unified model for the free-electron avalanche in laser-irradiated dielectrics, Phys. Rev. Lett., 92, Article 187401 pp. (2004)
[13] Medvedev, N.; Rethfeld, B., A comprehensive model for the ultrashort visible light irradiation of semiconductors, J. Appl. Phys., 108, Article 103112 pp. (2010)
[14] Gulley, J. R.; Lanier, T. E., Model for ultrashort laser pulse-induced ionization dynamics in transparent solids, Phys. Rev. B, 90, Article 155119 pp. (2014)
[15] Wang, C.; Lin, T.; Caflisch, R.; Cohen, B. I.; Dimits, A. M., Particle simulation of Coulomb collisions: comparing the methods of Takizuka & Abe and Nanbu, J. Comput. Phys., 227, 4308-4329 (2008) · Zbl 1388.82032
[16] Kaiser, A.; Rethfeld, B.; Vicanek, M.; Simon, G., Microscopic processes in dielectrics under irradiation by subpicosecond laser pulses, Phys. Rev. B, 61, Article 11437 pp. (2000)
[17] Matsumoto, M.; Nishimura, T., Mersenne Twister: a 623-dimensionally equidistributed uniform pseudo-random number generator, ACM Trans. Model. Comput. Simul., 8, 3-30 (1998) · Zbl 0917.65005
[18] Rethfeld, B., Free-electron generation in laser-irradiated dielectrics, Phys. Rev. B, 73, Article 035101 pp. (2006)
[19] Keldysh, L. V., Ionization in the field of a strong electromagnetic wave, Sov. Phys. JETP, 20, 1307-1314 (1965)
[20] Christensen, B.; Balling, P., Modeling ultrashort-pulse laser ablation of dielectric materials, Phys. Rev. B, 79, Article 155424 pp. (2009)
[21] Nicholson, D. R., Introduction to Plasma Theory (Plasma Physics) (1983), Wiley
[22] Mitchner, M.; Kruger, C. H., Partially Ionized Gases (1973), Wiley: Wiley New York
[23] Binder, R.; Köhler, H. S.; Bonitz, M.; Kwong, N., Green’s function description of momentum-orientation relaxation of photoexcited electron plasmas in semiconductors, Phys. Rev. B, 55, 5110-5116 (1997)
[24] Ashcroft, N. W.; Mermin, N. D., Solid State Physics (1976), Cengage Learning · Zbl 1118.82001
[25] Reif, F., Fundamentals of Statistical and Thermal Physics (2008), Waveland Pr Inc
[26] Müller-Gronbach, T.; Novak, E.; Ritter, K., Monte Carlo-Algorithmen (2012), Springer: Springer Berlin · Zbl 1254.65012
[27] Graham, C.; Talay, D., Stochastic Simulation and Monte Carlo Methods. Mathematical Foundations of Stochastic Simulation (2013), Springer: Springer Berlin · Zbl 1281.65003
[28] Lieberman, M. A.; Lichtenberg, A. J., Principles of Plasma Discharges and Materials Processing (2005), Wiley-Interscience
[29] Arnold, D.; Cartier, E.; DiMaria, D. J., Acoustic-phonon runaway and impact ionization by hot electrons in silicon dioxide, Phys. Rev. B, 45, 1477-1480 (1992)
[30] Stuart, B. C.; Feit, M. D.; Herman, S.; Rubenchik, A. M.; Shore, B. W.; Perry, M. D., Nanosecond-to-femtosecond laser-induced breakdown in dielectrics, Phys. Rev. B, 53, 1749-1761 (1996)
[31] Colombier, J. P.; Combis, P.; Audouard, E.; Stoian, R., Transient optical response of ultrafast nonequilibrium excited metals: effects of electron-electron contribution to collisional absorption, Phys. Rev. E, 77, Article 036409 pp. (2008)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.