Gradient-index (GRIN) media offer advantages over thin optical elements for beam shaping of strongly diffracting fields. A numerical GRIN design method is presented, where diffraction effects are considered in solving for the refractive index profile. The index profile is found by specifying a desired beam transformation throughout the GRIN volume and solving a series of phase retrieval problems. A Gaussian to flat-top beam shaper and a coherent beam combiner are shown as examples. Reduced beam distortion is demonstrated in comparison to a purely geometric design method.
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