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 7×7 beam splitters with a maximum 53° diffraction angle and a non-square 5×7 array generating beam splitter. After optimization we obtained beam splitter designs with a uniformity error of 16:35% (7×7) and 6:98% (5×7), 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.
Nowadays, diffractive optical elements are used for a variety of applications because of their high design flexibility, compact size, and mass productivity. At the same time, they require having high and complex optical functionalities such as a large number of diffraction orders and a wide diffraction angle, which is beyond the limits of scalar paraxial diffraction domain. We propose a stable and fast gradient-based optimization algorithm based on step-transition perturbation approach applied to design binary diffractive elements with small and many features for being performed in a large number of diffraction orders and wide diffraction angles. Using our optimization, we obtained high-performance elements than using optimization based on purely scalar theory. In addition, it needs much less calculation time than parametric optimization based on rigorous diffraction theory. Upon verification with the experimental results, we observed that our gradient-based optimization method is valid for 1-by-117 fan-out grating with some small features (on the order of the illumination wavelength) and about 22° full pattern diffraction angle.
In this work we demonstrate the advantages of investigating diffractive optical elements in the phase domain. In this regime we can detect features that are not restrained by the diffraction limit and relate them to the geometrical and optical properties of the sample under test. To accomplish that, we use the custom made spectral high resolution interference microscope. Phase map recordings allow for easier and more precise localization of the positions, where phase changes happen. We show the localization capabilities by detecting phase singularities created by a trench. We also apply the concept to abrupt phase jumps of a phase diffractive component and determine the achievable resolution.
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