Modified phase synthesis for a tunable vortex phase plate working on the Alvarez-Lohmann concept

A tunable element based on the Alvarez-Lohmann concept is a combination of two elements whose combined transmittance corresponds to that of a plane parallel plate. This two-element combination assumes the desired transmittance upon shearing one element over the other. A vortex phase plate with tunable topological charge can be realized using this concept. In the design, normally, the separation distance between the elements is assumed to be zero, but in reality, it is not so. Due to the finite thickness of the two elements and that the second element needs some space to accommodate the shearing operation, the finite separation between the elements is inevitable. Therefore, the phase transmittance of the second element needs some correction for better performance. In this paper, we provide a method to realize a phase distribution for the second element that allows a finite separation between the two-element combinations. The additional space that is made available using this process can be used for the insertion of a third element in the future to manipulate the polarization degree of freedom.