Diffractive Optical Element Realizing A Logarithmic – Polar Transformation

It is shown that a diffractive optical element with four discreet levels can perform a logarithmic - polar transformation upon optical vortex beams. This fact is due to the fact a component with a four level discretized optical surface presents a phase function which up to a series of higher order Fourier terms is a good approximation of the one presented by an optical element with a continuous surface. The validity of this assumption was tested by diffracting optical vortices with by logarithmic - polar components with discrete and continuous surfaces and comparing the configuration of the diffracted field in the image plane, finding a quantitative agreement. This indicates that the four level components can be used in multiplexing/demultiplexing for free space optical communications with optical vortices.