He assumes that the solutions are monochromatic and uses the phasor expressions E = E ( r ) e − − i ω ω t , H = H ( r ) e − − i ω ω t . The time average of the Poynting vector momentum density is then given by ⟨ ⟨ P ⟩ ⟩ = 1 4 c 2 [ E ∗ ∗ × × H + E × × H ∗ ∗ ] = ϵ ϵ 0 4 i ω ω [ E ∗ ∗ ⋅ ⋅ ( ∇ ∇ E ) − − ( ∇ ∇ E ∗ ∗ ) ⋅ ⋅ E + ∇ ∇ × × ( E ∗ ∗ × × E ) ] = μ μ 0 4 i ω ω [ H ∗ ∗ ⋅ ⋅ ( ∇ ∇ H ) − − ( ∇ ∇ H ∗ ∗ ) ⋅ ⋅ H + ∇ ∇ × × ( H ∗ ∗ × × H ) ] . We have used Maxwell's equations in passing from the first to the second and third lines, and in expression such as H ∗ ∗ ⋅ ⋅ ( ∇ ∇ H ) the scalar product is between the fields so that the vector character is determined by the ∇ ∇ .