â † k and âk are the creation and annihilation operators of the photon, respectively, δ k,k ′ is the Kronecker delta, and the frequency of mode k is ω j = c|k|. Here k = |k| k aligns in the direction of the unit vector k and êk ⊥ k is the polarization unit vector for Ê⊥ (r) and Â⊥ (r).