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Obtaining a varying refractive index distribution has always been attracting a high interest in the optics community to produce gradient-index (GRIN) optics. The conventional way to store and process data by GRIN media is through volume holograms, where the recording is done by optical means, which prevents independently accessing each point in the volume. Additive manufacturing, specifically 2-photon polymerization, inherits this ability. Considering the scalability advantage of the 3D implementation of computation architectures and the power-speed advantage of optics, there lie many opportunities for additively manufactured GRIN optics performing complex tasks. Independent access to each voxel in fabrication volume opens the way for digital optimization techniques to design GRIN optics since each calculated voxel can be translated into fabrication. In this work, Learning Tomography (LT), which is a nonlinear optimization algorithm originally developed for optical diffraction tomography, is used as the optimization framework to calculate necessary refractive index distribution to perform computation tasks such as matrix multiplication. Here, instead of imaging an object in optical diffraction tomography, we calculate the 3D GRIN element that performs the desired task as defined by its input-output relation. This input-output relation can be chosen such that a computational functionality is satisfied. We report functional robust GRIN elements where the refractive index dynamic range (<0.005) is comparable to the dynamic range of conventional holography materials. We present the digital optimization methodology with details on the beam propagation method as the forward model and the corresponding error reduction scheme for the desired input-output mapping along with the experimental verification of the approach along with the details of the fabrication process by additive manufacturing.
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