## 3 Results
### Multi-Objective Optimization Results  
In order to make the exit pupil of the diffractive waveguide expand uniformly and, at the same time, ensure a good utilization rate of light energy, we use Holo-RCWA combined with the evolutionary algorithm NSGA-II to carry out inverse design of the grating preparation process. The inverse design goal of the process parameters in Table 1 is to make the diffraction efficiency distribution of the outcoupling grating array as shown in Figure 12b.  
Figure 17a shows the single-objective optimization results of direct weighted summation of the evaluation function when the incident excitation of the 2D diffraction grating is set as TE wave, TM wave, and plane wave whose polarization direction is on the bisector of TE and TM polarization direction angles. The maximum number of evolution generations is 50, and the number of individuals in the population is 50. When the evolutionary generation reaches 15 generations, the individual that best meets the objective function has appeared, and the average performance of the population becomes better as the evolutionary generation increases. However, no method has been found to prove that the solution obtained by the weighted sum satisfies the three polarization states and is the closest to the inverse design goal. Therefore, it is necessary to establish evaluation functions for different polarization states at the same time and use a multi-objective optimization algorithm for inverse design. Figure 17b shows the multi-objective nondominated solution set when using NSGA-II. The maximum number of evolution generations is 100, and the number of individuals in the population is 50. The figure shows 32 Pareto solutions, and the co-ordinate value of each Pareto solution in the solution space represents the objective function value when different polarization states are incident, and each point represents a set of experimental parameters. Therefore, according to the optimization results of single-objective and multi-objective optimization, the corresponding experimental parameters can be further determined and a 2D grating conforming to the predetermined efficiency distribution can be prepared. Performing 19 inverse designs in parallel and adjusting the experimental parameters makes the holographic waveguide system with 19 sub-area out-coupling grating arrays meet the exit pupil illumination distribution as shown in Figure 12b.  
In this section, the single-objective optimization takes 1 to 2 h, while the multi-objective optimization takes about 8 h. Compared with the optimization time of the traditional method of 2 to 3 days, the method proposed in this paper can, indeed, greatly shorten the development cycle. At the same time, genetic algorithms can naturally further improve optimization efficiency through parallel computing [30]. CUDA is a parallel computing platform and programing model developed by NVIDIA that allows developers to utilize NVIDIA's GPUs for general-purpose parallel computing. The CUDA version of Holo-RCWA and NSGA-II predictably have the ability to further reduce the original optimization time from 8 h to shorter but, unfortunately, due to the lack of corresponding hardware conditions, this paper did not conduct specific comparative experiments.  
Figure 16: Three-dimensional structure of 2D holographic grating.