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30 January 2024
Imaging with an Ultrathin Reciprocal Lens
A groundbreaking study spearheaded by a team from The Hong Kong University of Science and Technology (HKUST) led by Prof. C. T. Chan, in collaboration with a team from Fudan University led by Prof. Jian Zi, has been published in Physical Review X. This study, titled "Imaging with an Ultrathin Reciprocal Lens", introduces a paradigm-shifting imaging mechanism—the "reciprocal lens." This novel lens performs imaging by shifting light rays rather than bending them like conventional lenses. It can directly produce upright real images. This research has potential for wide-ranging applications.

Lenses are indispensable in imaging systems. Lenses like those used in optical systems including cameras and microscopes form images by bending light rays entering the lens structure. The rays originating from the object are altered in direction as they pass through the lens. The bent rays converge on a single point on the image plane to reconstruct the object's image. This relies on the lens having varying optical properties and thickness to properly deviate the rays' paths. In recent years, "metalenses" fabricated using micro- and nano- techniques utilize flat nanostructures to control phases and bend rays by imposing phase gradients. However, both conventional and metamaterial lenses share the fundamental mechanism of bending rays (Fig. 1).

The reciprocal lens designed and implemented by the research team enables imaging through a different mechanism than bending rays. It controls the lateral shifts of rays based on their incidence angle (Fig. 1). The lens imposes an angle-dependent phase distribution that causes rays entering at different angles to shift laterally by varying amounts after passing through. This engineered angle-dependent ray shifting makes rays originating from a point source converge after exiting the lens, achieving the imaging functionality. The team utilized geometric optics theory to derive the conditions and phase modulation requirements for reciprocal lens imaging.

Figure 1: Schematics comparing the mechanisms of the reciprocal lens and conventional/metalenses.

For this study, research team members constructed an ultra-thin reciprocal lens operating in the microwave frequency range (28.5 GHz) using standard printed circuit boards (PCB) as shown in Fig. 2a. The lens consists of a core layer featuring a hexagonal lattice of holes and patches, sandwiched by two cladding layers. This structure supports multiple guided resonances that provide the necessary phase modulation effect. The researchers tested the propagation phase through the lens and confirmed it satisfies the phase distribution relationship needed for reciprocal lens imaging.  Experiments showed the 1 mm-thick core layer could produce focal lengths on the order of centimeters, enabling imaging (Fig. 2b). The team also tested imaging using objects of various shapes, demonstrating the reciprocal lens's imaging ability without shape constraints.

Figure 2: Imaging of an "F" slit using the PCB-based reciprocal lens shown in (a). The upright real image obtained with the lens shows sharper edges and improved resolution compared to the reference image captured without any lens.

The reciprocal lens realized in this study enables imaging without bending light rays, completely subverting the conventional imaging mechanism and providing a new choice for lens and imaging technologies. The reciprocal lens is ultra-thin and alignment-free, uniquely suited for constrained applications. This research outcome has expanded the theoretical foundations of imaging technology and has also opened up new directions for wavefront modulation.

Research supported by the Research Grants Council of Hong Kong, Croucher Foundation, National Natural Science Foundation of China, and other agencies.