# Absorbing boundaries in numerical solutions of the time-dependent Schroedinger equation on a grid using exterior complex scaling

## Abstract

We study the suppression of reflections in the numerical simulation of the time-dependent Schroedinger equation for strong-field 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 electron-field 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:

- Max-Planck-Institut fuer Physik of komplexer Systeme, Noethnitzer Str.38, D-01187 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 time-dependent 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 time-dependent 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 time-dependent 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 time-dependent 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 time-dependent Schroedinger equation for strong-field 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 electron-field 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}

}