We can write the circularly polarized states as | s ⟩ ⟩ where s = 1 for | R ⟩ ⟩ and s = −1 for | L ⟩ ⟩ . An arbitrary state can be written | ψ ψ ⟩ ⟩ = ∑ ∑ s = − − 1 , 1 a s exp ⁡ ⁡ ( i α α x − − i s θ θ ) | s ⟩ ⟩ where α α 1 and α α − − 1 are phase angles, θ is the angle by which the frame of reference is rotated, and ∑ ∑ s = − − 1 , 1 | a s | 2 = 1.