Dammann Gratings Fifty Years On: Their Historical Evolution and New Opportunities

Significance Dammann gratings (DGs) are a type of diffractive optical elements used in beam splitting and are capable of generating tens to thousands of sub-beams in parallel with only a single integrated element. The efficiencies of DGs are typically in the range of approximately 70%-80% for binary gratings, and this efficiency can be further improved. Due to these unique properties, DGs are applicable in a variety of fields ranging from optical interconnections to integrated grating magneto-optical traps. Currently, the computing power required to process large amounts of data doubles approximately every 3.5 months, far exceeding the computing power supplied by electronic integrated circuits (EICs) that follow Moore's law. Compared with traditional electrons, photons are expected to accelerate computing, particularly customized computing, with high computing power, high energy efficiency, and low latency. DGs provide a powerful method for matching the demands of large-scale fan-in and fan-out in optical computing. Thus, this critical element plays a major role in this revived topic, particularly when fused with new technologies such as liquid crystal-based planar optics, metasurfaces, and planar integrated photonic circuits. With the continual development of the theory, design, and manufacturing technologies of DGs, their application scope has widened considerably in modern optics. Progress This review analyzes and discusses the principles, developments, and applications of various types of DGs and Dammann encoding gratings in terms of their historical evolution. First, the principles and theories of various DGs, including classical DGs,circular DGs (CDGs), and Dammann encoding gratings, are introduced. For a classical DG, splitting a single incident beam into multiple sub-beams using a single grating is easy, where the efficiency is typically greater than 70% for a binary pure-phase structure.The splitting ratio can be changed by reoptimizing the transitional points for these binary gratings, and the efficiency can be further improved by choosing a multilevel structure or reducing the period required to transform the gratings into the resonant region. In 2003, Zhou et al. proposed the concept of a CDG, and its rigorous theory was completed. This new diffractive optical element has been applied in many fields, including remote sensing, image coding, and circular pumping vortex lasers. Subsequently, the Dammann encoding method was generalized to various encoding gratings for generating numerous complex beam arrays. A major scenario involves the generation of vortex arrays when a spiral phase is encoded. Second, landmark progress and representative achievements are retrieved in historical order during the 50 years of evolution of DGs. In this review, the evolutionary history of DGs is divided into three main stages: start-up (1971-1995), developing (1996-2014), and recently advanced (2015-present). At every stage, the milestones and representative works are summarized in historical order. In addition to the classical Dammann beam splitters, other types of elements, including CDGs, Dammann vortex gratings (DVGs), distorted Dammann gratings, and Dammann zone plates, are introduced as part of the historical evolution of Dammann beam splitters. Some representative applications are also discussed and the challenges are analyzed. We also consider typical applications of DGs and the challenges under each scenario. In the early stages, DGs were used for star coupling into fiber arrays, optical computing and interconnection, and laser coherent beam combination. In addition, DGs have been used for splitting and measuring ultrashort laser pulses, parallel laser processing, direct writing lithography, three-dimensional measurements based on structured light, structured pumping lasers, multi-shearing for imaging and measurement, complex beam array generation, pattern detection, and grating magneto-optical traps. DGs have also been widely used in many fields of modern optics. Finally, we discuss future trends, directions, and challenges in the further development of DGs. Conclusions and Prospects As one of the most important fundamental components of modern optics, DGs have developed into a branch of diffraction optics. Over the past 50 years, the theoretical principles, design methods, and manufacturing technologies of DGs have constantly improved, and a variety of new diffractive optical elements based on the Dammann encoding method continue to emerge. In the future, the fusion of DGs with liquid crystal optics, metasurfaces, and planar integrated optics will accelerate, and the functions of various DGs will be continually enriched. DGs have evolved from single-wavelength to broadband operation, passive fixed functions to active adjustable control, simple beam splitting to complex array control, and traditional bulk devices to integrated miniaturization. With the rise of optical computing, DGs will usher in new opportunities and challenges when combined with new technologies such as liquid crystal-based planar optics, metasurfaces, and planar integrated photonic circuits.