Numerical simulations of multiphoton ionization and above-threshold electron spectra

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Abstract
We study above-threshold ionization (ATI) of a one-dimensional model atom in a time-varying external laser field. The time-dependent Schrödinger equation is integrated in space and time using the Crank-Nicholson method, and the photoelectron energy spectrum is then computed by projecting the wave function onto the energy eigenstates of the time-independent zero-field Hamiltonian. We demonstrate an intensity-dependent ponderomotive shift of the ionization threshold, find a free-electron scaling of the number of ATI peaks with intensity and frequency of the field, and contrast the numerical simulations with two simple Keldysh-type models. For certain field parameters we encounter turn-on transients in the form of ‘‘energy-nonconserving’’ substructure within each ATI peak. Effects on the results of the physical parameters such as length and shape of the laser pulse on one hand, and of the iteration parameters on the other, are discussed in detail.