  Coronagraphy is a very efficient technique for identifying and characterizing
extra-solar planets orbiting in the habitable zone of their parent star,
especially when used in a space environment. An important family of
coronagraphs is based on phase plates located at an intermediate image plane of
the optical system, that spread the starlight outside the "Lyot" exit pupil
plane of the instrument. In this communication 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. Numerical
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.
