Abstract
This paper is devoted to the derivation of nonperturbative nonlinear models for intense and short laser pulses propagating in a gas. Starting from a computationally complex micro-macro Maxwell–Schrödinger–Plasma model (Lorin et al., Comput Phys Commun 177(12):908, 2007; Lorin et al., Commun Comput Phys 9(2):406, 2011) we derive an optics model, where the nonlinear response is nonperturbatively computed using a nonlinear evolution evolution equation of polarization. Only initial data of the polarization equation are computed at the microscopic level via TDSEs, thus providing for an efficient algorithm in Maxwell–Schrödinger’s problems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
E. Lorin, M. Lytova, A. Memarian, A.D. Bandrauk, J. Phys. A 48(10), 105201 (2015)
T. Brabec, F. Krausz, Rev. Mod. Phys. 72(2), 545 (2000)
A.V. Husakou, J. Herrmann, Phys. Rev. Lett. 87(20), 203901 (2001)
A. Couairon, A. Mysyrowicz, Phys. Rep. 441(2–4), 47 (2007)
L. Bergé, S. Skupin, R. Nuter, J. Kasparian, J.P. Wolf, Rep. Prog. Phys. 70(10), 1633 (2007)
M. Kolesik, J.V. Moloney, Rep. Prog. Phys. 77(1), 016401 (2014)
I. Babushkin, L. Bergé, J. Math. Phys. 55(3), 032903 (2014)
M. Kolesik, J.V. Moloney, Phys. Rev. E 70(3), 036604 (2004)
S. Skupin, L. Bergé, Physica D 220(1), 14 (2006)
S. Champeaux, L. Bergé, D. Gordon, A. Ting, J. Peñano, P. Sprangle, Phys. Rev. E 77(3), 036406 (2008)
A. Vinçotte, L. Bergé, Physica D 223(2), 163 (2006)
M. Kolesik, E.M. Wright, J.V. Moloney, Opt. Lett. 35(15), 2550 (2010)
L. Bergé, C. Gouédard, J. Schjodt-Eriksen, H. Ward, Physica D 176(3–4), 181 (2003)
P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, J.P. Wolf, Phys. Rev. Lett. 104(10), 103903 (2010)
A. Spott, A. Jaroń-Becker, A. Becker, Phys. Rev. A 90(1), 013426 (2014)
M. Richter, S. Patchkovskii, F. Morales, O. Smirnova, M. Ivanov, New J. Phys. 15(8), 083012 (2013)
C. Köhler, R. Guichard, E. Lorin, S. Chelkowski, A.D. Bandrauk, L. Bergé, L., S. Skupin, Phys. Rev. A 87(4), 043811 (2013)
P. Béjot, E. Cormier, E. Hertz, B. Lavorel, J. Kasparian, J.P. Wolf, O. Faucher, Phys. Rev. Lett. 110(4), 043902 (2013)
P. Polynkin, M. Kolesik, E.M. Wright, J.V. Moloney, Phys. Rev. Lett. 106(15), 153902 (2011)
T. Morishita, A.T. Le, Z. Chen, C.D. Lin, Phys. Rev. Lett. 100(1), 013903 (2008)
E. Lorin, S. Chelkowski, A. Bandrauk, Comput. Phys. Commun. 177(12), 908 (2007)
E. Lorin, S. Chelkowski, A. Bandrauk, Commun. Comput. Phys. 9(2), 406 (2011)
E. Lorin, S. Chelkowski, A. Bandrauk, in High-Dimensional Partial Differential Equations in Science and Engineering, vol. 41, ed. by A. Bandrauk, M.C. Delfour, C. Le Bris. CRM Proc. Lecture Notes (American Mathematical Society, Providence, 2007), pp. 161–182
E. Lorin, S. Chelkowski, E. Zaoui, A. Bandrauk, Physica D 241(12), 1059 (2012)
P.B. Corkum, Phys. Rev. Lett. 71(13), 1994 (1993)
A.D. Bandrauk, S. Chelkowski, S. Goudreau, J. Mod. Opt. 52(2–3), 411 (2005)
R.W. Boyd, Nonlinear Optics, 2nd edn. (Academic, San Diego, 2003)
A.D. Bandrauk, F. Fillion-Gourdeau, E. Lorin, J. Phys. B 46(15), 153001 (2013)
E. Lorin, A.D. Bandrauk, J. Comput. Sci. 3(3), 159 (2012)
H.S. Nguyen, A. Suda, K. Midorikawa, Phys. Rev. A 60(3), 2587 (1999)
J. Crank, P. Nicolson, Adv. Comput. Math. 6, 207 (1996)
K.J. Yuan, A.D. Bandrauk, J. Phys. B 45(7), 074001 (2012)
B. Bidégaray-Fesquet, Hiérarchie de modèles en optique quantique. De Maxwell-Bloch à Schrödinger non-linéaire. Mathématiques and Applications, vol. 49 (Springer, Berlin, 2006)
Acknowledgements
The authors thank the CRM (Centre de recherches mathématiques, Montréal), the KITP (Kavli Institute of Theoretical Physics, University of California, Santa Barbara) for supporting this research via workshops and Compute Canada for access to high performance parallel computers.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Lorin, E., Lytova, M., Bandrauk, A.D. (2016). Nonperturbative Nonlinear Maxwell–Schrödinger Models for Intense Laser Pulse Propagation. In: Bandrauk, A., Lorin, E., Moloney, J. (eds) Laser Filamentation. CRM Series in Mathematical Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-23084-9_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-23084-9_7
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-23083-2
Online ISBN: 978-3-319-23084-9
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)