Introducing a Cartesian-based zone plate so called amplitude spiral orthogonal zone plate (ASOZP), an orthogonal zone plate which has spiral structure for the controlled generation of optical vortices.

Generating different kinds of focused vortices in the shape and structure. So, the number of the vortices and their vorticities up to second order are easily controllable.

Easily manipulating the vortices by using two topological charges P_x and P_y in the two orthogonal directions of Cartesian coordinates x and y.

Rotation of the focused vortices in the vicinity of the focal plane is the other interesting feature of the proposed model in generating vortices.

Experimental results are in a good agreement with the numerical computations.

The proposed method may be of interest for a large number of users in different areas as in optical trapping of particles and image processing or in focusing systems.