“…For the first type, namely the generation of linearly-polarized OAM (LP-OAM) modes, the LP-OAM modes in the x and y polarized directions can be obtained by eliminating other component in the OAM mode bases except one, such as (x −l , y −l , x +l , y +l ) T = (1, 0, 0, 0) T , which corresponds tô xOAM −l , an x-linear polarized OAM beam with TC = +l. The expression in other mode bases can be obtained by substituting this vector into Equation (2) or Equation (4). (x −l , y −l , x +l , y +l ) T = (1, 0, 0, 0) T is equivalent as (A, B, C, D) T = 0.5, 0.5i, 0.5, −0.5i T and (x e , y e , x o , y o ) T = (1, 0, −i, 0) T .…”