If unit vectors are defined such that | x ⟩ ⟩ = d e f ( 1 0 ) and | y ⟩ ⟩ = d e f ( 0 1 ) then the linearly polarized polarization state can be written in the "x–y basis" as | ψ ψ ⟩ ⟩ = cos ⁡ ⁡ θ θ exp ⁡ ⁡ ( i α α ) | x ⟩ ⟩ + sin ⁡ ⁡ θ θ exp ⁡ ⁡ ( i α α ) | y ⟩ ⟩ = ψ ψ x | x ⟩ ⟩ + ψ ψ y | y ⟩ ⟩ .