Continuous and discrete diffractive elements with polar symmetries

Diffractive elements are considered with polar symmetry, i.e., where the transmission function depends on the radial and/or the azimuthal coordinate. Well-known examples are the axicon, the Fresnel zone plate, and the Siemens star. Here, we are particularly interested in elements where both coordinates are coupled, as in the case of the spiral axicon. The spiral axicon is known for generating a wave field with an orbital angular momentum. We consider the variety of elements that can be generated. In particular, we analyze the performance of the element in the case where the continuous structure is broken up and discretized. This leads to the generation of off-axis intensity zeroes and vortices. For this conceptual study, the scalar diffraction theory is used for the analysis, and numerical simulations were used to calculate examples of generated light distributions. (C) 2016 Optical Society of America