All diffractive optical element setup for creating and characterizing optical vortices with high topological charges: Analytical models and numerical results

Abstract

We introduce the concept of an all-diffractive optical element (DOE) setup for generating and characterizing optical vortices (OVs), and present analytical models and numerical results by using two-dimensional chirp z-transform (2-D CZT) algorithm. Such an all-DOE setup consists of a spiral zone plate (SZP) to generate focused OVs with topological charge (TC) up to 50, and a gradually changing-period grating (GCPG) to sensitively measure orbital angular momentum. Especially, 2-D CZT based Fresnel diffraction integral algorithm is derived for scalar wave propagation with different sampling rates on DOE and observation planes, respectively. Due to the broad applicability, flexible aperture matching can be easily realized in the all-DOE setup. The numerical comparisons show that 2-D CZT based FDI, direct integration and fast Fourier transform based methods are equivalent expressions. The computation speed of 2-D CZT based FDI is 3 orders faster than fast Fourier transform based method and 5 orders faster than direct integration method, respectively. Both the SZP and the GCPG are fabricated by standard lithography technology. The characteristic intensity distribution of the focused OVs passing through the GCPG is observed, agreeing well with the numerical simulation results. Our results provide an easy and convenient way to create all-DOE setup in the production and measurement of OVs with high TC.