Unconventional imaging and focusing properties are obtained when odd powers of the radial coordinate are present in a radial gradient-index profile. We calculate the transmittance function for this kind of medium under a paraxial approximation by a quasi-geometrical approach. Likewise, we analyze the pupil effect; that is, we evaluate the intensity distribution diffracted by a gradient-index axicon at the image plane.
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Gonzalez et al. (1994) studied this question.
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