Optical vortices generated by multi-level achromatic spiral phase plates for broadband beams

We analyze the characterizations of the optical vortices generated by a multi-level achromatic spiral phase plate. The effective topological charge of the multi-level fractional spiral phase plate is expanded into Fourier series and the analytical formula of the relative intensity of each component is obtained. It is shown that the fractional part of the topological charge sharply reduces the purity of vortices. Using the 36 levels achromatic spiral phase plate, we can obtain a vortex beam with purity larger than 95% across a bandwidth exceeding 140 nm in the visible region of the spectrum.