Significance   Beam shaping plays an important role in many fields including laser material processing, medical treatment and laser fusion. The goal of beam shaping is to transform an incoming laser beam into a desired output irradiance (or intensity) distribution. Diffractive optical elements (DOEs) are one of the most promising ways for beam shaping. The design of DOEs plays a crucial role in high-quality beam shaping applications. To further promote the development of more advanced methods for designing DOEs which can better meet the requirements of different beam shaping applications, it is necessary to summarize the research progress of existing DOE design methods, discuss their advantages and disadvantages, and provide a necessary outlook.

  Progress  This review summarizes the design methods of phase-only DOEs for beam shaping. Since the DOE microrelief height function is lineally proportional to the phase function of the optical field generated by the DOE, the DOE design problem can be directly transferred into the calculation of the DOE phase distribution. There are two design methods of geometrical optics methods and physical optics methods to realize this goal. Geometrical optics methods usually generate continuous freeform optical surfaces. However, in many cases, the beam shaping quality can be degraded due to the diffraction effects. Physical optics methods, which describe the light propagation in a more accurate way, are commonly used to design phase-only DOEs for beam shaping. However, the iterative Fourier transform algorithms (IFTAs), which are the most commonly-used approach for designing DOEs, often generate complex and irregular shapes in DOE profiles. Such DOE profiles are difficult to fabricate and could generate speckles, which significantly impair the quality of the generated irradiance distribution. In addition, traditional IFTAs often surfers from slow convergence and iteration stagnation. Composite methods that combine the geometrical and physical optics methods have been proposed to address these issues. The freeform surfaces generated from the geometrical optics methods could provide good initial values for the following IFTAs, significantly improving the convergence. The resulting optical surface profiles are more regular than those of the traditional IFTAs, which are easier to fabricate and could achieve high-quality beam shaping.

  Conclusions and Prospects  We have summarized (some of) the design methods of DOEs for beam shaping. After a brief recall of the traditional physical optics methods and their limitations, we have paid more attention to the review of the composite methods which can generate freeform DOEs that are easier to fabricate and could achieve high-quality beam shaping. Future directions of the DOE design methods include developments of fast geometrical optics solvers and wide-angle light propagation algorithms, more considerations of different fabrication techniques, and other promising methods based on auto-differentiation.