Properties of vortex light fields generated by generalized spiral phase plates

Abstract

We present a theoretical and experimental investigation of a diffractive optical element---a generalized spiral phase plate (GSPP) with a transmission function of $\mathrm{exp}[ig(\ensuremath{\varphi})]$, where $g(\ensuremath{\varphi})$ is an unambiguous function. In contrast to the conventional spiral phase plate that is widely used for the generation of ring-shaped vortex beams with an orbital angular momentum (OAM), the GSPP can be used for the generation of nonring (including spiral-shaped) laser beams with a helical wave front. Some examples of the function $g(\ensuremath{\varphi})$ were investigated in detail, showing the features arising in these cases. The proposed GSPP demonstrates angle-dependent distortion resistance properties, whereby for different angular positions of an opaque obstacle on the surface of the element, different values of root-mean-square error are obtained. The angular harmonics spectra of the generated vortex light fields strongly depend on the growth rate of the function $g(\ensuremath{\varphi})$. In addition, the OAM density of the generated nonring light fields is nonuniform and the total OAM also depends on the angular coordinate of the obstacle. The experimentally and numerically obtained results are in good qualitative and quantitative agreement.