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A flexible vortex beam generator (VBG) is proposed based on transformation optics (TO) to convert input plane waves to various output vortex beams. The methodology is a geometrical one that is based on the topological equivalence between the vortex beam cross section disc and a belt, turning the in-plane curvilinear distributed phase or polarization structures in the disc to be redistributed around the belt. Consequently, abundant vortex beams can be exported by simply configuring the incidence angles and polarization directions of the plane waves. The topology and wave propagation characteristics behind the system are investigated, and TO is used to obtain the desired materials by adopting a specific space mapping. Some sample numerical simulations are described to verify the feasibility of the proposed design, including several complex orbital angular momentum and cylindrical vector beams. Due to its flexibility and simplicity, the proposed VBG likely has extensive application prospects.

Gradient refractive index (GRIN) lens-based chirp signal chirpiness detection usually relies on the fractional Fourier transform (FRFT) functionality of a quadratic GRIN lens and is limited by paraxial conditions. In this paper, a non-FRFT mechanism-based chirpiness detection GRIN lens is proposed that converts the Luneburg lens’ focus capacity of input plane waves to the designed lens’ focusing of input chirp waves using transformation optics, and the source chirpiness can be obtained by sweeping the illumination wavelength rather than locating the focusing pulse, consequently greatly increasing the upper limit of the chirpiness detection range. The feasibility and robustness of the method are verified through numerical simulations.