Over the last 20 years, thin and lightweight optical elements have become very desirable, especially for the terahertz (THz) range. Reduction of the volume of optical elements alongside an increase in their effective efficiency has begun a new direction of research leading to many practical applications. On top of that, diffractive optical elements can not only focus the incident beam, but also can shape the incoming wavefront into a desirable distribution or can redirect the energy. Starting from theoretical calculations of Fourier optics, diffractive elements have been transformed and nowadays form complicated structures that do not resemble a typical Fresnel lens. The precise control over a phase shift introduced by the designed element creates an opportunity to almost freely transform an incident wavefront. Moreover, the vast diversity of computer-generated holograms (also called synthetic) contributes substantially to this topic. Diffractive elements have a great impact on THz optical systems because their manufacturing is very simple in comparison with any other range of radiation (infrared, visible, ultraviolet, etc.). This review paper underlines developments in evolution of diffractive optics and highlights main principles and technological approaches for fabrication of diffraction optics within the terahertz range, thus serving as a guide to design and production considerations.

A method of color image projection is experimentally validated. It assumes a simultaneous illumination of a spatial light modulator (SLM) with three laser beams converging in a common point on a projection screen. The beams are masked with amplitude filters so that each one illuminates one third of the area of the SLM. A Fourier hologram of a chosen color component of an input image is calculated, and its phase pattern is addressed on a corresponding part of the SLM area. A full-color flat image is formed on the screen as a result of color mixing. Additional techniques of image optimization are applied: time-integral speckle averaging and an off-axis shift of a zero-order peak. Static and animated experimental results of such a color holographic projection with a good image quality are presented.

Diffractive optical elements are well known for being not only flat but also lightweight, and are characterised by low attenuation. In different spectral ranges, they provide better efficiency than commonly used refractive lenses. An overview of the recently invented terahertz optical structures based on diffraction design is presented. The basic concepts of structure design together with various functioning of such elements are described. The methods for structure optimization are analysed and the new approach of using neural network is shown. The paper illustrates the variety of structures created by diffractive design and highlights optimization methods. Each structure has a particular complex transmittance that corresponds to the designed phase map. This precise control over the incident radiation phase changes is limited to the design wavelength. However, there are many ways to overcome this inconvenience allowing for broadband functioning.

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Passive terahertz (THz) setups require optical elements with large diameters for optimal harvesting of weak signals. High $f$-number implies sophisticated aspheric designs to ensure optimal resolution and good energetic efficiency. Trial and error testing of such optics is expensive and numerical modeling is time consuming; hence, we propose extremely cheap diffractive lenses for THz made of regular paper. They are easy to manufacture even with large diameters, and the optical function can be easily customized, which can be used for initial experimental testing of THz setups. Characterization of the proposed diffractive lenses with time-domain spectroscopy is presented and discussed.

THz beam shaping via a single diffractive optical element is used to convert a divergent beam into a focal line segment perpendicular to the optical axis. The novel structure was designed for narrowband applications as a kinoform element and we successfully applied it in active, high-speed, THz linear scanners. The theoretical approach and experimental results are presented.