Absorbing boundaries in numerical solutions of the timedependent Schroedinger equation on a grid using exterior complex scaling
Abstract
We study the suppression of reflections in the numerical simulation of the timedependent Schroedinger equation for strongfield problems on a grid using exterior complex scaling (ECS) as an absorbing boundary condition. It is shown that the ECS method can be applied in both the length and the velocity gauge as long as appropriate approximations are applied in the ECS transformation of the electronfield coupling. It is found that the ECS method improves the suppression of reflection as compared to the conventional masking function technique in typical simulations of atoms exposed to an intense laser pulse. Finally, we demonstrate the advantage of the ECS technique to avoid unphysical artifacts in the evaluation of high harmonic spectra.
 Authors:
 MaxPlanckInstitut fuer Physik of komplexer Systeme, Noethnitzer Str.38, D01187 Dresden (Germany)
 Publication Date:
 OSTI Identifier:
 20982549
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.75.053407; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 74 ATOMIC AND MOLECULAR PHYSICS; APPROXIMATIONS; ATOMS; BOUNDARY CONDITIONS; COUPLING; ELECTRONS; GRIDS; INHIBITION; LASER RADIATION; NUMERICAL SOLUTION; PULSES; REFLECTION; SCALING; SCHROEDINGER EQUATION; SIMULATION; SPECTRA; TIME DEPENDENCE; TRANSFORMATIONS
Citation Formats
He, F., Ruiz, C., and Becker, A.. Absorbing boundaries in numerical solutions of the timedependent Schroedinger equation on a grid using exterior complex scaling. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.053407.
He, F., Ruiz, C., & Becker, A.. Absorbing boundaries in numerical solutions of the timedependent Schroedinger equation on a grid using exterior complex scaling. United States. doi:10.1103/PHYSREVA.75.053407.
He, F., Ruiz, C., and Becker, A.. Tue .
"Absorbing boundaries in numerical solutions of the timedependent Schroedinger equation on a grid using exterior complex scaling". United States.
doi:10.1103/PHYSREVA.75.053407.
@article{osti_20982549,
title = {Absorbing boundaries in numerical solutions of the timedependent Schroedinger equation on a grid using exterior complex scaling},
author = {He, F. and Ruiz, C. and Becker, A.},
abstractNote = {We study the suppression of reflections in the numerical simulation of the timedependent Schroedinger equation for strongfield problems on a grid using exterior complex scaling (ECS) as an absorbing boundary condition. It is shown that the ECS method can be applied in both the length and the velocity gauge as long as appropriate approximations are applied in the ECS transformation of the electronfield coupling. It is found that the ECS method improves the suppression of reflection as compared to the conventional masking function technique in typical simulations of atoms exposed to an intense laser pulse. Finally, we demonstrate the advantage of the ECS technique to avoid unphysical artifacts in the evaluation of high harmonic spectra.},
doi = {10.1103/PHYSREVA.75.053407},
journal = {Physical Review. A},
number = 5,
volume = 75,
place = {United States},
year = {Tue May 15 00:00:00 EDT 2007},
month = {Tue May 15 00:00:00 EDT 2007}
}

No abstract prepared.

Longtime solution of the timedependent Schroedinger equation for an atom in an electromagnetic field using complex coordinate contours
We demonstrate that exterior complex scaling (ECS) can be used to impose outgoing wave boundary conditions exactly on solutions of the timedependent Schrodinger equation for atoms in intense electromagnetic pulses using finite grid methods. The procedure is formally exact when applied in the appropriate gauge and is demonstrated in a calculation of high harmonic generation in which multiphoton resonances are seen for long pulse durations. However, we also demonstrate that while the application of ECS in this way is formally exact, numerical error can appear for long time propagations that can only be controlled by extending the finite grid. Amore » 
Longtime solution of the timedependent Schroedinger equation for an atom in an electromagnetic field using complex coordinate contours
We demonstrate that exterior complex scaling (ECS) can be used to impose outgoing wave boundary conditions exactly on solutions of the timedependent Schroedinger equation for atoms in intense electromagnetic pulses using finite grid methods. The procedure is formally exact when applied in the appropriate gauge and is demonstrated in a calculation of highharmonic generation in which multiphoton resonances are seen for long pulse durations. However, we also demonstrate that while the application of ECS in this way is formally exact, numerical error can appear for longtime propagations that can only be controlled by extending the finite grid. A mathematical analysismore » 
Symmetrized complex amplitudes for He double photoionization from the timedependent close coupling and exterior complex scaling methods
Symmetrized complex amplitudes for the double photoionization of helium are computed by the timedependent closecoupling and exterior complex scaling methods, and it is demonstrated that both methods are capable of the direct calculation of these amplitudes. The results are found to be in excellent agreement with each other and in very good agreement with results of other ab initio methods and experiment.