ClassSTRONG: Classical simulations of strong field processes

A set of Mathematica functions is presented to model classically two of the most important processes in strong field physics, namely high-order harmonic generation (HHG) and above-threshold ionization (ATI). Our approach is based on the numerical solution of the Newton–Lorentz equation of an electron moving on an electric field and takes advantage of the symbolic languages features and graphical power of Mathematica. Like in the Strong Field Approximation (SFA), the effects of atomic potential on the motion of electron in the laser field are neglected. The SFA was proven to be an essential tool in strong field physics in the sense that it is able to predict with great precision the harmonic (in the HHG) and energy (in the ATI) limits. We have extended substantially the conventional classical simulations, where the electric field is only dependent on time, including spatial nonhomogeneous fields and spatial and temporal synthesized fields. Spatial nonhomogeneous fields appear when metal nanosystems interact with strong and short laser pulses and temporal synthesized fields are routinely generated in attosecond laboratories around the world. Temporal and spatial synthesized fields have received special attention nowadays because they would allow to exceed considerably the conventional harmonic and electron energy frontiers. Classical simulations are an invaluable tool to explore exhaustively the parameters domain at a cheap computational cost, before massive quantum mechanical calculations, absolutely indispensable for the detailed analysis, are performed.Program summaryProgram title: ClassSTRONGCatalogue identifier: AEQV_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEQV_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 60 847No. of bytes in distributed program, including test data, etc.: 2 018 279Distribution format: tar.gzProgramming 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.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 implement different functions corresponding to a variety of 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 different 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/