Binary multi-order diffraction optical elements with variable fill factor for the formation and detection of optical vortices of arbitrary order.

In this paper we consider the calculation of binary diffraction optical elements (DOEs) for the formation and detection of optical vortices of arbitrary order. The synthesis of binary DOEs is based on a combination of the method of carrier spatial frequencies and binary coding with a variable fill factor. Unlike various methods of multiplication, the method of carrier spatial frequencies is characterized by great flexibility and versatility. It allows us to not only form the given field distributions in arbitrary diffraction orders, but also to give them arbitrary weight ratio (energy distribution in orders). As a rule, such universality leads to the need to form a complex amplitude-phase distribution in the input plane. To avoid this, in this paper it is proposed to use binary coding with a variable level. The effect of such coding is studied in detail both theoretically and numerically. It is shown that the level variation makes it possible to change the set of the observed diffraction orders. The positions and orders of the optical vortices formed are uniquely determined by the values of the carrying spatial frequencies and the topological charges of the vortices in the basic order. The results can be useful in optical communications.