If unit vectors are defined such that | R ⟩ ⟩ = d e f 1 2 ( 1 i ) and | L ⟩ ⟩ = d e f 1 2 ( 1 − − i ) then an arbitrary polarization state can be written in the "R–L basis" as | ψ ψ ⟩ ⟩ = ψ ψ R | R ⟩ ⟩ + ψ ψ L | L ⟩ ⟩ where ψ ψ R = ⟨ ⟨ R | ψ ψ ⟩ ⟩ = 1 2 ( cos ⁡ ⁡ θ θ exp ⁡ ⁡ ( i α α x ) − − i sin ⁡ ⁡ θ θ exp ⁡ ⁡ ( i α α y ) ) and ψ ψ L = ⟨ ⟨ L | ψ ψ ⟩ ⟩ = 1 2 ( cos ⁡ ⁡ θ θ exp ⁡ ⁡ ( i α α x ) + i sin ⁡ ⁡ θ θ exp ⁡ ⁡ ( i α α y ) ) .