Asymmetrical Three-Dimensional Conformal Imaging Lens

Abstract

Absolute instrument refers to a media that can make light rays to propagate in a closed orbit and perform imaging and self-imaging. In the past few decades, traditional investigations into absolute instrument have been centered on the two-dimensional plane and rotational symmetry situations, and have paid less attention to three-dimensional counterparts. In this article, we design two types of three-dimensional non-spherically symmetric absolute instruments based on conformal inverse transformation, which originated from the three-dimensional Luneburg lens and Lissajous lens. We carry out ray tracing on the optical performance of these new lenses and analyze the imaging laws. Our work enlarges the family of absolute instruments from two dimensions to three dimensions and symmetry to asymmetry, which may allow for imaging applications in optical waves.

Keywords

• three-dimensional conformal transformation
• absolute instruments
• inverse mapping
• non-spherical symmetry