where S 0f αβ = ⟨0|μ α |f ⟩⟨f |μ β |0⟩. In the equations above, ω is the frequency of the external electric field (the incident light beam), ε αβγ is the Levi-Civita tensor, and implicit summation over repeated indices is implied, where indices α, β, and γ run over the three Cartesian coordinates x, y, and z.