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Manuscript Title: ClassSTRONG: Classical simulations of Strong Field processes
Authors: M.F. Ciappina, J.A. Pérez-Hernández, M. Lewenstein
Program title: ClassSTRONG
Catalogue identifier: AEQV_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 185(2014)398
Programming language: Mathematica.
Computer: Single machines using Linux or Windows (with cores with any clock speed, cache memory and bits in a word).
Operating system: Any OS that supports Mathematica. The notebooks have been tested under Windows and Linux and with versions 6.x, 7.x, 8.x and 9.x.
Keywords: Strong Field Physics, High-order harmonics generation, Above threshold ionization, classical simulations, Mathematica.
PACS: 34.10.+x, 34.50.-s, 34.50.Fa, 34.90.+q.
Classification: 2.5.

External routines: RootSearch.m (Included in the distribution file).

Nature of problem:
The Mathematica functions model high-order harmonic generation (HHG) and above-threshold ionization (ATI) using the classical equations of motion of an electron moving in an oscillating electric field. In Strong Field Physics HHG and ATI represent two of the most prominent examples of the nonperturbative interaction between strong laser sources and matter. In HHG an atomic or molecular bound electron is put into the continuum by the external laser electric field. Due to the oscillatory nature of the electromagnetic radiation, the electron is steered back and recombines with the parent ion converting its kinetic energy as high energy photons. For ATI the electron is laser-ionized in the same way as in HHG, but in its return it is elastically rescattered by the parent ion gaining even more kinetic energy. We incorporate functions for different laser pulse envelopes, namely sine-squared, gaussian, trapezoidal and numerically defined by the user. In addition we relax the assumption of spatial homogeneity of the laser electric field, allowing weak spatial variations with dierent functional forms. Finally we combine spatial and temporal synthesized laser fields to produce HHG and ATI. For all the cases the functions allow the extraction of pre-formatted graphs as well as raw data which can be used to generate plots with other graphical programs.

Solution method:
The functions employ the numerical solution of the Newton- Lorentz equation for an electron moving in a spatial and temporal varying electric field to calculate the energy and harmonic spectra features of HHG and ATI. Our approach neglects any magnetic effect.

Additional comments:
The set consists of the following 16 notebooks.
  • HHGSin2.nb - This notebook includes functions to calculate the high-order harmonic spectra features, both in terms of harmonic order and energy in eV, for atoms interacting with laser pulses with sine-squared envelopes.
  • HHGGauss.nb - This notebook includes functions to calculate the high-order harmonic spectra features, both in terms of harmonic order and energy in eV, for atoms interacting with laser pulses with gaussian envelopes.
  • HHGTrap.nb - This notebook includes functions to calculate the high-order harmonic spectra features, both in terms of harmonic order and energy in eV, for atoms interacting with laser pulses with trapezoidal envelopes.
  • HHGUser.nb - This notebook includes functions to calculate the high-order harmonic spectra features, both in terms of harmonic order and energy in eV, for atoms interacting with laser pulses defined by the user.
  • ATISin2.nb - This notebook includes functions to calculate the above-threshold ionization spectra features, both in terms of electron energy in eV and Up units, for atoms interacting with laser pulses with sine-squared envelopes.
  • ATIGauss.nb - This notebook includes functions to calculate the above-threshold ionization spectra features, both in terms of electron energy in eV and Up units, for atoms interacting with laser pulses with gaussian envelopes.
  • ATITrap.nb - This notebook includes functions to calculate the above-threshold ionization spectra features, both in terms of electron energy in eV and Up units, for atoms interacting with laser pulses with trapezoidal envelopes.
  • ATIUser.nb - This notebook includes functions to calculate the high-order harmonic spectra features, both in terms of harmonic order and energy in eV, for atoms interacting with laser pulses defined by the user.
  • HHGTemporal.nb - This notebook includes functions to calculate the high-order harmonic spectra features, both in terms of harmonic order and energy in eV, for atoms interacting with temporal synthesized laser pulses.
  • ATITemporal.nb - This notebook includes functions to calculate the above-threshold ionization spectra features, both in terms of electron energy in eV and Up units, for atoms interacting with temporal synthesized laser pulses.
  • HHGLinear.nb - This notebook includes functions to calculate the high-order harmonic spectra features, both in terms of harmonic order and energy in eV, for atoms interacting with spatial inhomogeneous laser pulses (linear case).
  • ATILinear.nb - This notebook includes functions to calculate the above-threshold ionization spectra features, both in terms of electron energy in eV and Up units, for atoms interacting with spatial inhomogeneous laser pulses (linear case).
  • HHGExp.nb - This notebook includes functions to calculate the high-order harmonic spectra features, both in terms of harmonic order and energy in eV, for atoms interacting with spatial inhomogeneous laser pulses (exponential case).
  • ATIExp.nb - This notebook includes functions to calculate the above-threshold ionization spectra features, both in terms of electron energy in eV and Up units, for atoms interacting with spatial inhomogeneous laser pulses (exponential case).
  • HHGTemporal&Spatial.nb - This notebook includes functions to calculate the high-order harmonic spectra features, both in terms of harmonic order and energy in eV, for atoms interacting with temporal and spatial synthesized laser pulses.
  • ATITemporal&Spatial.nb - This notebook includes functions to calculate the above-threshold ionization spectra features, both in terms of electron energy in eV and Up units, for atoms interacting with temporal and spatial synthesized laser pulses.
  • All the notebooks use the Mathematica package RootSearch.m developed by Ted Ersek (see e.g. [1] for more details).

Running time:
Computational times vary according to the number of points required for the numerical solution of the Newton-Lorentz equation and of the complexity of the spatial and temporal driving laser electric field. The typical running time is several minutes, but it can be larger for large number of optical cycles and spatially and temporal complex laser electric fields.

References:
[1] http://library.wolfram.com/infocenter/Demos/4482/