Coronagraphy is a very efficient technique for identifying and characterizing extra-solar planets orbiting in the habitable zone of their parent star, especially in a space environment. An important family of coronagraphs is actually based on phase plates located at an intermediate image plane of the optical system, and spreading the starlight outside the "Lyot" exit pupil plane of the instrument. In this commutation we present a set of candidate phase functions generating a central null at the Lyot plane, and study how it propagates to the image plane of the coronagraph. These functions include linear azimuthal phase ramps (the well-known optical vortex), azimuthally cosine-modulated phase profiles, and circular phase gratings. Nnumerical simulations of the expected null depth, inner working angle, sensitivity to pointing errors, effect of central obscuration located at the pupil or image planes, and effective throughput including image mask and Lyot stop transmissions are presented and discussed. The preliminary conclusion is that azimuthal cosine functions appear as an interesting alternative to the classical optical vortex of integer topological charge.