After the plane-wave expansion, the photon spin can be re-expressed in a simple and intuitive form in the wave-vector space S = ℏ ℏ ∫ ∫ d 3 k ϕ ϕ ^ ^ k † † s ^ ^ ϕ ϕ ^ ^ k where the column-vector ϕ ϕ ^ ^ k = [ a ^ ^ k , 1 , a ^ ^ k , 2 , a ^ ^ k , 3 ] T is the field operator of the photon in wave-vector space and the 3 × × 3 matrix s ^ ^ = ∑ ∑ λ λ = 1 3 s ^ ^ λ λ ϵ ϵ ( k , λ λ ) is the spin-1 operator of the photon with the SO(3) rotation generators s ^ ^ 1 = [ 0 0 0 0 0 − − i 0 i 0 ] , s ^ ^ 2 = [ 0 0 i 0 0 0 − − i 0 0 ] , s ^ ^ 3 = [ 0 − − i 0 i 0 0 0 0 0 ] , and the two unit vectors ϵ ϵ ( k , 1 ) ⋅ ⋅ k = ϵ ϵ ( k , 2 ) ⋅ ⋅ k = 0 denote the two transverse polarizations of light in free space and unit vector ϵ ϵ ( k , 3 ) = k / | k | denotes the longitudinal polarization.