Diffractive optical elements are ultra-thin optical components required for constructing very compact optical 3D sensors. However, the required wide-angle diffractive 2D fan-out gratings have been elusive due to design challenges. Here, we introduce a new strategy for optimizing such high-performance and wide-angle diffractive optical elements, offering unprecedented control over the power distribution among the desired diffraction orders with only low requirements with respect to computational power. The microstructure surfaces were designed by an iterative gradient optimization procedure based on an adjoint-state method, capable to account for application-dependent target functions while ensuring compatibility with existing fabrication processes. The results of the experimental characterization confirm the simulated tailored power distributions and optical efficiencies of the fabricated elements.

Diffractive optical elements with a large diffraction angle require feature sizes down to sub-wavelength dimensions, which require a rigorous electromagnetic computational model for calculation. However, the computational optimization of these diffractive elements is often limited by the large number of design parameters, making parametric optimization practically impossible due to large computation times. The adjoint method allows calculating the gradient of the target function with respect to all design variables with only two electromagnetic simulations, thus enabling gradient optimization. Here, we present the adjoint method for modeling wide-angle diffractive optical elements like 7x7 beam splitters with a maximum 53 • diffraction angle and a non-square 5x7 array generating beam splitter. After optimization we obtained beam splitter designs with a uniformity error of 16.35% (7x7) and 6.98% (5x7), respectively. After reviewing the experimental results obtained from fabricated elements based on our designs, we found that the adjoint optimization method is an excellent and fast method to design wide-angle diffractive fan-out beam-splitters.

Diffractive optical elements are ultra-thin optical components required for a variety of applications because of their high design flexibility. We introduce a gradient-based optimization method based on a step-transition perturbation approach which is an efficient approximation method using local field perturbations due to sharp surface profile transitions. Step-transition perturbation approach be available to calculate the gradient of figure of merit straightforwardly, we implemented optimization method based on this gradient. This fast and accurate inverse design creates binary (2-level) diffractive elements with small features generating the wide angle beam arrays. The results of the experimental characterization confirm that the optimization based on the perturbation method is valid for 1-to-117 fan-out grating generating beam pattern of linear array.

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Computational optimization of diffractive elements is often limited by a large number of design parameters. Adjoint method allows the gradient of target function respect to all design variables to be calculated with only two electromagnetic simulations. We show that detail results for optimized two-dimensional fan-out gratings.