# Integrated Deep Ultraviolet Doublet Metalens for Projection Imaging
## 1 Introduction  
In recent years, the study of metasurfaces has become a major topic due to the unique electromagnetic modulation properties of the sub-wavelength micro-nano structure in micro-nano optics [1; 2; 3; 4; 5; 6]. There are many research directions regarding metasurfaces, including holograms [7; 8; 9], beam shaping [10; 11; 12], sensing [13; 14], polarization control [15; 16; 17], absorbers [18; 19; 20; 21; 22], biosensing [23; 24], and metalenses [25; 26; 27; 28; 29; 30; 31; 32; 33]. Lenses are crucial optical components in various applications, including security, automotives, lasers, digital cameras, and optical instruments. Metalenses represent a popular research direction as they can control light waves through arrays of micro-nano structures. They have the advantages of being ultra-light, ultra-thin, easy to integrate, etc., and are expected to open up a new path for micro and micro-nano optical imaging and optoelectronic equipment. The study of metalenses in the visible [26] and near-infrared [27] regions has developed well, and single-wavelength [28; 29], multi-wavelength [30], and achromatic metalenses [31; 32; 33] in visible wavelengths have been realized. However, studies on metalenses [34; 35; 36] in the deep UV band are still scarce. Recently, high-bandgap materials such as HfO\({}_{2}\)[37] and TiO\({}_{2}\)[38] have been introduced as compelling material platforms for UV-range applications. There are also many excellent research results on multilayer metasurfaces [39; 40]. There are many application scenarios for deep ultraviolet systems [41; 42; 43], such as large-relative-aperture deep ultraviolet detection [44; 45; 43], deep ultraviolet microscope systems [41; 46; 47], laser beam combining systems [48; 49], deep ultraviolet lithography systems [50], etc. Among them, the deep ultraviolet large-relative-aperture warning opticalsystem [43; 44; 45] requires the optical system to have a large field of view, large relative aperture, simple structure, and small light energy loss. This requires a combination of spherical mirrors, diffractive elements, and aspheric mirrors, and the system is difficult and costly to handle. The laser beam combining system [48; 49] achieves laser output with high power and power density while maintaining high beam quality. By spatially rearranging the output beam of each light-emitting unit or refracting and reflecting the optical path, the output beam of each light-emitting unit can be combined into a beam close to a single light-emitting unit, improving the beam quality and output density. The projection lithography objective lens [50] is also an essential deep ultraviolet system; it is the core component of the projection lithography machine. Its performance determines the image transfer capability of the deep ultraviolet lithography machine. The projection objective lens group often requires a complex lens combination of nearly 30 lenses and more than a dozen movable lenses with sub-nanometer machining accuracy. The deep ultraviolet metalens based on the metasurface has a powerful wavefront control capability. It can use as few lens combinations as possible to achieve the functions of a traditional lens group. In this paper, we propose an integrated deep ultraviolet all-dielectric doublet metalens to solve the problem of the complex structure of the existing traditional deep ultraviolet system. This can be used in a projection deep ultraviolet lithography machine system, laser beam combining systems, and deep ultraviolet detection. Two metalenses are designed on two parallel surfaces on the SiO\({}_{2}\) substrate, respectively, with the same numerical aperture and focal length ratio of 4:1. The centers of the two metalenses are aligned and spaced at the sum of the two focal lengths. The beam reduction of the parallel deep ultraviolet light is realized through the design optimization of each metalens.