Anamorphic fractional Fourier transforms graded index lens designed using transformation optics.

An anamorphic fractional Fourier transform (AFrFT) lens based on graded index (GRIN) materials and designed with the help of transformation optics is proposed. Cross sections of the new lens are mapped from those of a standard quadratic GRIN lens via gradually varied conformal transformations. This lens can afford complicated anamorphic patterns in the fractional Fourier domain for any fractional order, possibly leading to many new applications. Three samples are shown, which offer higher distinguishability in the fractional Fourier domain, a more precisely recognized matched filter, and stronger security of the AFrFT-based optical encryption. With metamaterials development, including three-dimensional printing technologies, GRIN media fabrication has become more convenient; thus, the proposed lens may have vast application prospects in signal processing. The design also demonstrates the ability and flexibility of the transformation optics in exploring new Fourier optics devices.