Unconventional imaging and focusing properties are obtained when odd p
owers of the radial coordinate are present in a radial gradient-index
profile. We calculate the transmittance function for this kind of medi
um under a paraxial approximation by a quasi-geometrical approach. Lik
ewise, we analyze the pupil effect; that is, we evaluate the intensity
distribution diffracted by a gradient-index axicon at the image plane
.