Notice that ∇ ∇ ⋅ ⋅ π π e , p = 0 because P has no z dependence and is always perpendicular to z ^ ^ . Also, notice that the second and third terms are equivalent to the inhomogeneous wave equation, therefore, E p = − − 1 c 2 ∂ ∂ 2 π π e , p ∂ ∂ t 2 = − − 1 c 2 ( − − i ω ω ) 2 π π e , p = k 0 2 π π e , p