Theoretical description of filamentation in transparent media widely relies on nonlinear propagation equations like UPPE, NLSE, etc [1]. The nonlinear response of the medium is usually considered as independent additive responses of bound electrons (3rd and higher order polarization) and self-induced plasma calculated according to rate equations. Such a method provides only limited possibilities to account for the dispersion of nonlinearity, i.e. the dependence of nonlinear coefficients on the frequency of the optical pulse, which is important for the multi-harmonic pulses or ultraviolet pulse propagation. To provide the description of this dispersion, a quantum approach is desirable.
However, full-scale 3D-Shrӧdinger simulations of laser-atom interaction would be impossible to couple with 3D propagation simulations. For the reason of computational costs, the quantum model that can be introduced to propagation simulations must be one-dimensional at most [2]. A fair question here is how good can be 1D-Shrӧdinger equation to describe the response of the realistic medium to the high-intense femtosecond laser field [3].
In this work, we develop a one-dimensional quantum model of an atom that can be introduced into propagation equations. We select potential pit which reproduces the energy levels of xenon atom. The linear dispersion of the potential pit simulated by us is in reasonable agreement with the experimental data. Our model reproduces the multiphoton and tunnel regimes of Xe atom ionization. At the central wavelength of 214 nm (1400 THz) we have shown the resonance enhanced multiphoton ionization of Xe, observed in Ref. [4]. We accelerated our program code by a factor of 10 using GPU instead of CPU.

Nonlinear response of 1D multi-level system calculated
from nonstationary Shr ödinger equation

Abstract

Linear dispersion

1Faculty of Physics, Lomonosov Moscow State University, 1/62 Leninskie Gory, Moscow 119991, Russia;
2P. N. Lebedev Physical Institute of the Russian Academy of Sciences, 53 Leninskiy prospect, Moscow 119991, Russia;

N. R. Vrublevskaya1, D. E. Shipilo1,2, M. I. Kolychev1, I. A. Nikolaeva1,2, N. A. Panov1,2, O. G. Kosareva1,2

Model parameters and equations

Lorentz pit with a super-gaussian cut-off:

Tunnel and multiphoton ionization

The tunneling ionization mechanism is used to describe the interaction of femtosecond infrared radiation with matter, and the ionization rate in this case is equal to

With electric field

Nonlinear polarization

The linear dispersion evaluated for the intensities of 0.01–1 TW/cm2 reproduced the Sellmeier-type dependence with the resonances corresponding to the ionization potential and excited levels.

Tunnel ionization

Multiphoton ionization

Resonance enhanced multiphoton ionization

GPU versus CPU

[1] M. Kolesik, J. V. Moloney, Rep. Prog. Phys., 77(1), 016401 (2013)
[2] M. Kolesik et al., Optica, 1(5), 323 (2014)
[3] E. A. Volkova, A. M. Popov, Zh. Eksp. Teor. Fiz., 106, 735 (1994)
[4] V. D. Zvorykin et al., Laser Phys. Lett., 13 125404 (2016)

References

I = 0.01 TW/cm2

poster2021

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