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We apply a fundamental definition of time delay, as the difference betweenthe time a particle spends within a finite region of a potential and the time afree particle spends in the same region, to determine results forphotoionization of an electron by an extreme ultraviolet (XUV) laser fieldusing numerical simulations on a grid. Our numerical results are in goodagreement with those of the Wigner-Smith time delay, obtained as the derivativeof the phase shift of the scattering wave packet with respect to its energy,for the short-range Yukawa potential. In case of the Coulomb potential weobtain time delays for any finite region, while - as expected - the results donot converge as the size of the region increases towards infinity. The impactof an ultrashort near-infrared probe pulse on the time delay is analyzed forboth the Yukawa as well as the Coulomb potential and is found to be small forintensities below $10^{13}$ W/cm$^2$.

Numerical simulation of time delays in light induced ionization