Gouy's Phase Anomaly in Electron Waves Produced by Strong-Field Ionization

Ionization of atoms by strong laser fields produces photoelectron momentum distributions that exhibit modulations due to the interference of outgoing electron trajectories. For a faithful modeling, it is essential to include previously overlooked phase shifts occurring when trajectories pass through focal points. Such phase shifts are known as Gouy's phase anomaly in optics or as Maslov phases in semiclassical theory. Because of Coulomb focusing in three dimensions, one out of two trajectories in photoelectron holography goes through a focal point as it crosses the symmetry axis in momentum space. In addition, there exist observable Maslov phases already in two dimensions. Clustering algorithms enable us to implement a semiclassical model with the correct preexponential factor that affects both the weight and the phase of each trajectory. We also derive a simple rule to relate two-dimensional and three-dimensional models for linear polarization. It explains the shifted interference fringes and weaker high-energy yield in three dimensions. The results are in excellent agreement with solutions of the time-dependent Schrödinger equation.