Realizing that all the fields have the same time dependence exp ⁡ ⁡ ( − − i ω ω t ) , the time derivatives are straightforward and we obtain the following inhomogeneous wave equation ∇ ∇ 2 E r a d + μ μ 0 ω ω 2 ( ϵ ϵ 0 + i σ σ / ω ω ) E r a d = − − i μ μ 0 ω ω σ σ E v a c ( z ) with particular solution E r a d P = − − E v a c ( z )