For the complete solution, we add to the particular solution the general solution of the homogeneous equation which is a superposition of plane waves traveling in arbitrary directions ( E r a d c ) i = ∫ ∫ g i ( θ θ , ϕ ϕ ) exp ⁡ ⁡ ( i k ′ ⋅ ⋅ r ) d Ω Ω where k ′ is found from the homogeneous equation to be k ′ ′ 2 = μ μ 0 ϵ ϵ 0 ω ω 2 ( 1 + i σ σ ϵ ϵ 0 ω ω )