Second, the initial solutions will be optimized by genetic algorithm based on the RCWA model. Although the scalar theory is no longer accurate at this situation, it is fast for the initial population of genetic algorithm. First, multiple scalar solutions are used as initial solutions based on the non-paraxial scalar Fourier iterative algorithm. In this work, A two-step optimization schematic is proposed based on RCWA. Thus, efficient DOE design algorithm enabling 2D beam splitter with wide diffraction angle is highly requirement. However, they did not give a design method to overcome this problem. Later, they presented another work about the diffraction symmetry in 2017, they found that the Hermitian symmetry is broken when the feature size is smaller than the designed wavelength . But they did not consider the vectorial effect, so the zero order is big. Giang-Nam Nguyen and his colleagues proposed an iterative scalar nonparaxial method to design wide diffraction angle DOE . Besides, all the above methods are only developed in 1D domain. Although time-consuming, a global resolution can still hardly be found. In addition, the time per iteration is approximately 5 min, and the design process requires approximately 1 h. However, the optimization is not a global search algorithm, which implies that it is lack of global comparison.
employ an iterative optimization algorithm combined with a rigorous electromagnetic computational method to design an aperiodic 1D 1-to-2 beam splitter, and its experiment results verified that the algorithm is effective and reliable. Similar to the simulated quenching method, the former is time-consuming because of its searching character the latter is a highly efficient optimization algorithm, but its design results are related to the particular choice of paraxial design algorithm. Combining the FDTD method with optimization algorithms were developed to design DOEs, such as the micro-genetic algorithm FDTD method and the Gerchberg–Saxton-algorithm FDTD method . Up to now, a small amount of literature has been reported on designing DOEs with sub-wavelength feature size. Consequently, rigorous electromagnetic computational methods are needed to obtain the diffraction performance of DOE so that accurate profile structures can be designed However, when the wavelength of the light beam is larger than the characteristic size of DOE , the vectorial effect become pronounced that makes the scalar diffraction theory invalid. In recent decades, with the rapid development on photo-lithography technology, fabricating subwavelength DOEs has became feasible and economical, thereby leading to a wide utilization DOEs in application, such as wave-front correction , beam shaping, , beam splitter, laser material processing , three-dimensional reconstruction , facial recognition, optical network and so on. Diffractive optical element (DOE) has attracted extensive attention in the community of optics owing to their versatility in function, light weight and compactness.
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