Fig. 2: Cross-polarized two-photon photoemission in the density matrix formalism.

a Two-photon photoemission in a three-level system via real or virtual intermediate states for non-vanishing dot product \(\overrightarrow{E}\cdot \overrightarrow{\mu }\). b Illustration of the two-photon photoemission process in the density matrix for real (ρ₂₂, inner pathways) and virtual (ρ₁₃, ρ₃₁, outer pathways) intermediate states. Electrons are excited into the final state along every possible pathway of the matrix under all permutations of the electric fields. c Direction of the in-plane electric fields with regard to a fixed orientation of the optical transition dipoles yielding the angles φ₁₂ and φ₂₃, which have to be applied accordingly along the different pathways.