ClassSTRONG: Classical simulations of strong field processes

Abstract

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. Similarly as in the Strong Field Approximation (SFA), the effects of atomic potential on the motion of electron in the laser field are neglected. The SFA has 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 detailed analysis, are performed. 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 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. PACSSolution method: The functions employ the numerical solution of the NewtonLorentz equat...

Comparison of high harmonic generation and attosecond pulse from 3D hydrogen atom in three kinds of inhomogeneous fields

“…The inhomogeneous field E ic (z, t) is a polynomial-type case [24,25,27,31], which is definitely more accurate than the inhomogeneous cases with E ia (z, t) and E ib (z, t), the linear functional forms. In the following discussion, we will compare HHG from 3D H atom in three kinds of inhomogeneous fields together.…”

“…After that, some alternative approaches to realize plasmonic field enhancement were explored by employing different kinds of metallic nanostructures [16,17]. Subsequently, there is a lot of theoretical work [18][19][20][21][22][23][24][25][26] on the characteristic of HHG and attosecond pulse generation of atoms in inhomogeneous field, such as the coherent extreme ultraviolet photons generation beyond the carbon K edge [27], the extension of plateau [28,29], quantum path control [30], wavelength and carrier-envelope phase dependence [31], above-threshold ionization process [32,33], and so on. Most of theoretical study is based on linear-form inhomogeneous electric field, and the comparation between linear-form and polynomial-form fields still needs further investigation.…”

Electron path control of high-order harmonic generation by a spatially inhomogeneous field

“…There has been considerable theoretical work looking at HHG [37][38][39][40][41][42][43][44][45][46][47][48][49][50] and ATI [51][52][53] driven by spatially nonhomogeneous fields. Also, classical approach (numerical) for studies of strong field phenomena driven by spatial non-homogeneous fields has been introduced in [54].…”

High-order-harmonic generation from Rydberg atoms driven by plasmon-enhanced laser fields

“…In this section, we perform semi-classical simulations extended to atoms in a plasmon-enhanced field [21][22][23]66]. In order to simulate Rydberg atoms we consider two cases; the electron is released either from a n = 1 state or a n = 2 state.…”