Manipulating and detecting the chirpiness of spatial chirp signals via fractional Fourier lenses designed by transformation optics

Estimating the chirpiness of a spatial chirp signal is important in many optical engineering applications. With the help of transformation optics, a new kind of fractional Fourier transform lens is designed by deforming the conventional graded index lens through conformal mapping, which can manipulate the chirpiness of the input chirp signal. The low-input chirpiness is magnified by the transformation material, and the error of the detection is kept approximately the same; thus, the designed lens has enhanced chirpiness detection precision and distinguishability for low chirpiness. The design is validated by numerical simulations.