The fraction of energy in the x component of the plane wave is f x = | E | 2 cos 2 ⁡ ⁡ θ θ | E | 2 = ψ ψ x ∗ ∗ ψ ψ x = cos 2 ⁡ ⁡ θ θ with a similar expression for the y component resulting in f y = sin 2 ⁡ ⁡ θ θ .