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Diffractive optical elements (DOEs) which consist of microstructure surface relief permit the generation of the spatial distribution of light beams by using a single element. Due to their compact size, design flexibility, and mass productivity, they are used for a variety of applications, from optical metrology to biotechnology. However, the required wide angle DOEs have been elusive due to design challenges. Conventional design approaches such as iterative Fourier transform algorithm (ITFA) fail when applied to DOEs containing very small features or nano-structures. But it is exactly the small features that are required to create high performance wide diffraction angle diffractive optics. This thesis aims to extend the range of DOEs applications by developing designing and optimization algorithms for wide angle DOEs which is far beyond the limits of scalar paraxial diffraction model such as thin element approximation (TEA). The development of inverse design, where computational optimization techniques are used to find the geometry needed for the desired functionality, has led to the discovery of superior and non-intuitive design. Among various approaches, gradient-based optimization methods have been one of the most important techniques to obtain the optimal structure described by a huge number of design variables. These methodologies are made possible when the gradient of a merit function with respect to all design parameters efficiently enables to be calculated. Here, two approaches are considered: optimization based on the step transition perturbation approach and the adjoint-state method. The step transition perturbation approach (STPA) is based on the evaluation of local field perturbations due to sharp surface profile transitions. When we used the positions of transition points as design parameters in DOEs, it facilitates describing an analytical solution of the gradient of diffraction efficiency with respect to the positions of transition points. The gradient-based optimization with STPA creates various one-dimensional diffractive beam splitters generating wide angle spot arrays. The results of the experimental characterization confirm that this optimization tool is valid for wide angle DOEs. We discuss the adjoint method with rigorous electromagnetic theory, for example, rigorous coupled-wave analysis (RCWA), to optimize the DOEs with small features for generating even wider angles. Due to the adjoint method, we can compute the gradient of the objective function with respect to all design parameters efficiently even using a rigorous electromagnetic calculation. Hence, the permittivity distribution in the geometry of DOEs is used as the design variable during the optimization. This method also is able to account for application-dependent target functions while ensuring compatibility with existing fabrication processes. Thus we design the various wide angle DOEs including two-dimensional diffractive beam splitters by adjoint method. The results of the experimental characterization confirm that this optimization tool is valid in wide angle beam splitters creating a square spot array with maximal diffraction angle up to 53° from the center to diagonal edges, which is far beyond the limit of any scalar paraxial diffraction regime.