Nanoscale surface optical constants of copper determined by angle-resolved photoemission

We study angle-resolved photoemission peak intensities I(ψ) on Cu(1 1 0) and Cu(1 1 1) surfaces varying the light incidence angle ψ of p-polarized light with photon energies between ℏω=8.44 eV and ℏω=21.22 eV. Transitions out of several initial states are probed, including the well-known surface states at the Γ- and Y-point, bulk bands of sp- and d-like orbital character, as well as an oxygen-derived adsorbate state on Cu(1 1 0)(2×1)O. All data can well be explained within the dipole approximation I(ψ)=|A→(ψ,ε)·P→fi|2, where A→ is the vector potential of the photon field and P→fi the momentum matrix element. Especially it is not necessary to include “surface photoemission” via a 〈f|divA→|i〉 term in the photoemission matrix elements. However, quantitative agreement with experimental data is obtained if and only if A→ is calculated using Fresnelʹs equations with a modified surface optical constant εs, which differs drastically from the bulk parameters εb. Surprisingly independent of ℏω all results can be explained using εs=(1.0±0.1)+i(0.1±0.1), which is much closer to the vacuum value than to εb.