## 1 Introduction  
Diffraction gratings are diffractive optical elements with periodic structures that divide light comprised of different wavelengths into spectra. These spectra may be used to investigate the structure or composition of experimental materials. With the rapid advancement of science, there is an exceptionally high demand in the optical industry for highly integrated micro-nano optoelectronic devices. Micro-nano-structured diffraction grating devices with periodic variation and diffraction capabilities simultaneously offer superior integration, accuracy, and efficiency. Diffraction gratings are widely used in many fields, including laser beam combining [1; 2; 3], chirped pulse compression [4; 5; 6], spectroscopy [7; 8; 9], and liquid crystal displays and photonic devices [10]. Gratings can be classified as transmission or reflection gratings based on the material used; however, the principles of functioning can vary widely among gratings of the same type. A thin grating, for example, is defined as a grating that generates Raman-Nas state diffraction and may alternatively be defined as a grating with a narrow angle and wavelength selectivity. Thick gratings (or volume gratings) are gratings that cause Bragg zone diffraction. In contrast to the diffraction state formulation, there is a straightforward boundary (d/\(\Lambda\) = 10) between thin and thick grating diffraction. This term has been thoroughly researched in several papers [11]. Diffraction gratings come in a variety of shapes and sizes, such as thin gratings, with new design methodologies introduced to achieve extremely high efficiency and volume gratings with new structures and materials, inter alia [12; 13; 14]. In this paper, our study focuses on metal-film and multilayer-dielectric-film gratings to achieve extremely high diffraction efficiency and high laser-induced damage thresholds.  
As early as the 1780s [15], the American astronomer [PERSON] fabricated a transmission grating with a width of 12.7 mm using thin wires and saw a blurred color image through a shutter in a dark room, which was the first chromatic dispersion experiment using a grating. [PERSON] fabricated a 315 lines/mm reflection grating in 1823 by carving grooves on a glass surface covered with gold film. He established grating theory by first measuring the wavelengths of light and explaining the phenomena of diffraction and then deriving the grating equation. In 1870, [PERSON] produced a diffraction grating with a line density of 860 lines/mm, the resolution of which surpassed that of a prism for the first time, which made a great stride in spectral analysis technology into a new century. [PERSON], regarded as the inventor of modern diffraction gratings, used the mechanical scribing method. However, the production cycle of this method is extensive, and requires high experimental condition standards, which present substantial challenges in grating manufacture. After the passage of time and the continuous in-depth research of scientists, [PERSON] in the United Kingdom fabricated gratings through holography for the first time in the 1950s. [PERSON] et al. in Germany demonstrated the feasibility of producing gratings through holography in the late 1960s. Since then, grating manufacturing has advanced to a new level, with the development of key novel methods, such as holographic lithography, electron-beam lithography, and nanoimprinting.  
The production of diffractive optical elements and their use in spectroscopy contribute significantly to scientific, economic, and social development. This review outlines the current state of diffraction grating development. Metal gratings, dielectric-film gratings, and significant technical indicators are examined in the first part. The second part describes grating preparation techniques, including mechanical scribing, holographic exposure, electron-beam lithography, and nanoimprinting. The third part provides a summary and considers future prospects for diffraction gratings.