The demand for high optical resolution has brought researchers to explore the use of beam shaping diffractive optical elements (DOEs) for improving performance of high numerical aperture (NA) optical systems. DOEs can be designed to modulate the amplitude, phase and/or polarization of a laser beam such that it focuses into a targeted irradiance distribution, or point spread function (PSF). The focused PSF can be reshaped in both the transverse focal plane and along the optical axis. Optical lithography, microscopy and direct laser writing are but a few of the many applications in which a properly designed DOE can significantly improve optical performance of the system. Designing DOEs for use in high-NA applications is complicated by electric field depolarization that occurs with tight focusing. The linear polarization of off-axis rays is tilted upon refraction towards the focal point, generating additional transverse and longitudinal polarization components. These additional field components contribute significantly to the shape of the PSF under tight focusing and cannot be neglected as in scalar diffraction theory. The PSF can be modeled more rigorously using the electromagnetic diffraction integrals derived by Wolf, which account for the full vector character of the field. In this work, optimization algorithms based on vector diffraction theory were developed for designing DOEs that reshape the PSF of a 1.4-NA objective lens. The optimization techniques include simple exhaustive search, iterative optimization (Method of Generalized Projections), and evolutionary computation (Particle Swarm Optimization). DOE designs were obtained that can reshape either the transverse PSF or the irradiance distribution along the optical axis. In one example of transverse beam shaping, all polarization components were simultaneously reshaped so their vector addition generates a focused flat-top square irradiance pattern. Other designs were obtained that can be used to narrow the axial irradiance distribution, giving a focused beam that is superresolved relative to the diffraction limit. In addition to theory, experimental studies were undertaken that include (1) fabricating an axially superresolving DOE, (2) incorporating the DOE into the optical setup, (3) imaging the focused PSF, and (4) measuring aberrations in the objective lens to study how these affect performance of the DOE
