Absorbing boundaries in numerical solutions of the time-dependent Schr\"odinger equation on a grid using exterior complex scaling

We study the suppression of reflections in the numerical simulation of the time-dependent Schr\odinger equation for strong-field problems on a grid using exterior complex scaling (ECS) as 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 restrictions 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 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.