×

Nonlinear nonperturbative optics model enriched by evolution equation for polarization. (English) Zbl 1400.78022

Summary: In this work, we extend and analyze the nonperturbative Maxwell-Schrödinger-plasma (MASP) model. This model was proposed to describe the high order optical nonlinearities, and the low density free electron plasma generated by a laser pulse propagating in a gas. The MASP model is based on nonasymptotic, ab initio equations, and accurately uses self-consistent description of micro (quantum)- and macro (field)-variables. However, its major drawback is a high computational cost, which in practice means that only short propagation lengths can be calculated. In order to reduce this cost, we study the MASP models enriched by a macroscopic evolution equation for polarization, from its simplest version in the form of a transport equation, to more complex nonlinear variants. We show that the homogeneous transport equation is a more universal tool to simulate the high harmonic spectra at shorter times and/or at a lower computational cost, while the nonlinear equation could be useful for modeling the pulse profiles when the ionization level is moderate. The gain associated with the considered modifications of the MASP model, being expressed in reduction of computational time and the number of processors involved, is of 2–3 orders of magnitude.

MSC:

78A60 Lasers, masers, optical bistability, nonlinear optics
78M20 Finite difference methods applied to problems in optics and electromagnetic theory
81V80 Quantum optics
35Q60 PDEs in connection with optics and electromagnetic theory
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] M. V. Ammosov, N. V. Delone, and V. P. Krainov, Tunnel ionization of complex atoms and atomic ions in electromagnetic field, Sov. Phys. JETP, 91 (1986), pp. 2008–2013.
[2] I. Babushkin and L. Bergé, The fundamental solution of the unidirectional pulse propagation equation, J. Math. Phys., 55 (2014), 032903. · Zbl 1290.78014
[3] A. D. Bandrauk, E. Lorin, and J. V. Moloney, eds., Laser Filamentation. Mathematical Methods and Models, CRM Ser. Math. Phys., Springer, 2016. · Zbl 1336.78001
[4] L. Baudouin, O. Kavan, and J.-P. Puel, Regularity for a Schrödinger equation with singular potential and application to bilinear optimal control, J. Differential Equations, 216 (2005), pp. 188–222.
[5] P. Béjot, E. Cormier, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, and O. Faucher, High-field quantum calculation reveals time-dependent negative Kerr contribution, Phys. Rev. Lett., 110 (2013), 043902.
[6] P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Higher-order Kerr terms allow ionization-free filamentation in gases, Phys. Rev. Lett., 104 (2010), 103903.
[7] M. Bennett and A. Aceves, Numerical integration of Maxwell’s full-vector equations in nonlinear focusing media, Phys. D, 184 (2003), pp. 352–375. · Zbl 1030.78013
[8] L. Bergé, C. Gouédard, J. Schjodt-Eriksen, and H. Ward, Filamentation patterns in Kerr media vs. beam shape robustness, nonlinear saturation and polarization states, Phys. D, 176 (2003), pp. 181–211. · Zbl 1011.78009
[9] L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, Ultrashort filaments of light in weakly ionized, optically transparent media, Rep. Progr. Phys., 70 (2007), pp. 1633–1713.
[10] R. W. Boyd, Nonlinear Optics, 3rd ed., Academic Press, Amsterdam, 2008.
[11] T. Brabec and F. Krausz, Nonlinear optical pulse propagation in the single-cycle regime, Phys. Rev. Lett., 78 (1997), pp. 3282–3285.
[12] T. Brabec and F. Krausz, Intense few-cycle laser fields: Frontiers of nonlinear optics, Rev. Mod. Phys., 72 (2000), pp. 545–591.
[13] A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, Self-channeling of high-peak-power femtosecond laser pulses in air, Opt. Lett., 20 (1995), pp. 73–75.
[14] S. Champeaux, L. Bergé, D. Gordon, A. Ting, J. Peano, and P. Sprangle, (3+1)\em-dimensional numerical simulations of femtosecond laser filaments in air: Toward a quantitative agreement with experiments, Phys. Rev. E, 77 (2008), 036406.
[15] S. Chelkowski, C. Foisy, and A. Bandrauk, Electron-nuclear dynamics of multiphoton H\(_2^{+}\) dissociative ionization in intense laser field, Phys. Rev. A, 57 (1998), pp. 1176–1185.
[16] F. F. Chen, Introduction to Plasma Physics and Controlled Fusion. V.1: Plasma Physics, 2nd ed., Plenum Press. New York, 1984.
[17] A. Couairon and A. Mysyrowicz, Organizing multiple femtosecond filaments in air, Phys. Rep., 41 (2007), pp. 47–189.
[18] A. Ferrando, M. Zacarés, P. Fernándes de Córdoba, D. Binosi, and A. Montero, Forward-backward equations for nonlinear propagation in axially invariant optical systems, Phys. Rev. E, 71 (2005), 016601.
[19] M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, Multiple-harmonic conversion of 1064 nm radiation in rare gases, J. Phys. B, 21 (1988), pp. L31–L35.
[20] J.-Y. Ge and Z. H. Zhang, Use of negative complex potential as absorbing potential, J. Chem. Phys., 108 (1998), pp. 1429–1432.
[21] G. Genty, P. Kinsler, B. Kibler, and J. M. Dudley, Nonlinear envelope equation modeling of sub-cycle dynamics and harmonic generation in nonlinear waveguides, Opt. Express, 15 (2007), pp. 5382–5387.
[22] A. V. Husakou and J. Herrmann, Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers, Phys. Rev. Lett., 87 (2001), 203901.
[23] R. Iório, Jr., and D. Marchesin, On the Schrödinger equation with time-dependent electric fields, Proc. Roy. Soc. Edinburgh Sect. A, 96 (1984), pp. 117–134. · Zbl 0573.47005
[24] V. P. Kalosha and J. Herrmann, Self-phase modulation and compression of few-optical-cycle pulses, Phys. Rev. A, 62 (2000), 011804(R).
[25] L. V. Keldysh, Ionization in field of a strong electromagnetic wave, Sov. Phys. JETP, 20 (1965), pp. 1307–1314.
[26] P. Kinsler, Limits of the unidirectional pulse propagation approximation, J. Opt. Soc. Am. B, 24 (2007), pp. 2363–2368.
[27] P. Kinsler and G. H. C. New, Few-cycle pulse propagation, Phys. Rev. A, 67 (2003), 023813.
[28] C. Köhler, R. Guichard, E. Lorin, S. Chelkowski, A. D. Bandrauk, L. Bergé, and S. Skupin, Saturation of the nonlinear refractive index in atomic gases, Phys. Rev. A, 87 (2013), 043811.
[29] M. Kolesik and J. V. Moloney, Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations, Phys. Rev. E, 70 (2004), 036604.
[30] M. Kolesik and J. V. Moloney, Modeling and simulation techniques in extreme nonlinear optics of gaseous and condensed media, Rep. Progr. Phys., 77 (2014), 016401.
[31] M. Kolesik, E. M. Wright, and J. V. Moloney, Femtosecond filamentation in air and higher-order nonlinearities, Opt. Lett., 35 (2010), pp. 2550–2552.
[32] E. Lorin, S. Chelkowski, and A. D. Bandrauk, A numerical Maxwell-Schrödinger model for laser-matter interaction and propagation, Comput. Phys. Commun., 177 (2007), pp. 908–932. · Zbl 1196.78021
[33] E. Lorin, S. Chelkowski, and A. D. Bandrauk, The WASP model: A micro-macro system of wave-Schrödinger-plasma equations for filamentation, Commun. Comput. Phys., 9 (2011), pp. 406–440. · Zbl 1364.35302
[34] E. Lorin, S. Chelkowski, E. Zaoui, and A. D. Bandrauk, Maxwell-Schroedinger-Plasma (MASP) model for laser-molecule interactions: Towards quantum filamentation with intense ultrashort pulses, Phys. D, 241 (2012), pp. 1059–1071.
[35] E. Lorin, M. Lytova, and A. D. Bandrauk, Nonperturbative nonlinear Maxwell-Schrödinger models for intense laser pulse propagation, in Laser Filamentation: Mathematical Methods and Models, A. Bandrauk, E. Lorin, and J. Moloney, eds., Springer, Cham, 2016, pp. 167–183.
[36] E. Lorin, M. Lytova, A. Memarian, and A. D. Bandrauk, Development of nonperturbative nonlinear optics models including effects of high order nonlinearities and of free electron plasma: Maxwell-Schrödinger equations coupled with evolution equations for polarization effects, and the SFA-like nonlinear optics model, J. Phys. A, 48 (2015), 105201. · Zbl 1318.78009
[37] M. Lytova, E. Lorin, and A. D. Bandrauk, Propagation of intense and short circularly polarized pulses in a molecular gas: From multiphoton ionization to nonlinear macroscopic effects, Phys. Rev. A, 94, 013421.
[38] R. C. McOwen, Partial Differential Equations: Methods and Applications, Pearson Education, Upper Saddle River, NJ, 2003.
[39] A. McPherson, G. Gibson, H. Jara, U. Johann, T. S. Luk, I. A. McIntyre, K. Boyer, and C. K. Rhodes, Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases, J. Opt. Soc. Am. B, 4 (1987), pp. 595–601.
[40] T. Morishita, A.-T. Le, Z. Chen, and C. D. Lin, Accurate retrieval of structural information from laser-induced photoelectron and high-order harmonic spectra by few-cycle laser pulses, Phys. Rev. Lett., 100 (2008), 013903.
[41] A. C. Newell, Short pulse evolution equation, in Laser Filamentation. Mathematical Methods and Models, A. Bandrauk, E. Lorin, and J. Moloney, eds., Springer, Cham, 2016, pp. 1–17.
[42] A. C. Newell and J. V. Moloney, Nonlinear Optics, Advanced Topics in the Interdisciplinary Mathematical Sciences, Addison-Wesley, Redwood City, CA, 1992.
[43] P. Panagiotopoulos, P. T. Whalen, M. Kolesik, and J. V. Moloney, Numerical simulation of ultra-short laser pulses, in Laser Filamentation. Mathematical Methods and Models, A. Bandrauk, E. Lorin, and J. Moloney, eds., Springer, Cham, 2016, pp. 185–213.
[44] P. Polynkin, M. Kolesik, E. M. Wright, and J. V. Moloney, Experimental tests of the new paradigm for laser filamentation in gases, Phys. Rev. Lett., 106 (2011), 153902.
[45] M. Richter, S. Patchkovskii, F. Morales, O. Smirnova, and M. Ivanov, The role of the Kramers-Henneberger atom in the higher-order Kerr effect, New J. Phys., 15 (2013), 083012.
[46] E. Sali, P. Kinsler, G. H. C. New, K. J. Mendham, T. Halfmann, J. W. G. Tisch, and J. P. Marangos, Behavior of high-order stimulated Raman scattering in a highly transient regime, Phys. Rev. A, 72 (2005), 013813.
[47] K. J. Schafer, B. Yang, L. F. Dimauro, and K. C. Kulander, Above threshold ionization beyond the high harmonic cutoff, Phys. Rev. Lett., 70 (1993), pp. 1599–1602.
[48] S. Skupin and L. Bergé, Self-guiding of femtosecond light pulses in condensed media: Plasma generation versus chromatic dispersion, Phys. D, 220 (2006), pp. 14–30. · Zbl 1109.78016
[49] A. Spott, A. Jaro-Becker, and A. Becker, Ab initio and perturbative calculations of the electric susceptibility of atomic hydrogen, Phys. Rev. A, 90 (2014), 013426.
[50] G. Strang, On the construction and comparison of difference schemes, SIAM J. Numer. Anal., 5 (1968), pp. 506–517, . · Zbl 0184.38503
[51] V. V. Strelkov, High-Order Optical Processes: Towards Nonperturbative Nonlinear Optics, preprint, , 2015.
[52] J. C. Strikwerda, Finite Difference Schemes and Partial Differential Equations, 2nd ed., SIAM, Philadelphia, 2004, . · Zbl 1071.65118
[53] M. E. Taylor, Partial Differential Equations I. Basic Theory, 2nd ed., Appl. Math. Sci. 115, Springer, New York, 2011. · Zbl 1206.35002
[54] A. Vinçotte and L. Bergé, Atmospheric propagation of gradient-shaped and spinning femtosecond light pulses, Phys. D, 223 (2006), pp. 163–173. · Zbl 1255.78032
[55] H.-M. Yin, Existence and regularity of a weak solution to Maxwell’s equations with a thermal effect, Math. Methods Appl. Sci., 29 (2006), pp. 1199–1213. · Zbl 1109.35110
[56] K.-J. Yuan, S. Chelkowski, and A. D. Bandrauk, Molecular photoelectron angular distribution rotation in multi-photon resonant ionization of H\(_2^{+}\) by circularly polarized ultraviolet laser pulses, J. Chem. Phys., 142 (2015), 144303.
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.