Hyperbolic deflecting lens

Deflecting lenses are distinguished tools for precisely manipulating light fields and generating virtual images. In this paper, we extend the concept of the deflecting lens into the hyperbolic domain and introduce general profiles for hyperbolic deflecting lenses (HDLs). By leveraging the correspondence between the phase space and the momentum space, we investigate the geometric optical properties of HDLs and provide a detailed analysis of the deflection mechanism. Besides, we demonstrate that the inside-out versions of HDLs correspond to the hyperbolic absolute instruments for the homogeneous region. Our work provides a valuable platform for the future development of the deflecting lenses in radially hyperbolic optical systems.