Analog photonic fractional signal processing

Abstract In this work, we provide an up to date overview on the subject of photonic fractional signal processing, including both, in-fiber and waveguide on-chip technology. Thus, we discuss in detail fractional differentiation, fractional integration, fractional Hilbert transforms, and finally, fractional Fourier transforms. In each case, the underlying mathematical principles are explained for each operation, together with a short historical discussion in the context of classical optics. After that, the different proposals to perform these operations photonically on the complex field envelope of a given light pulse are presented, divided according to its working principle. Finally, current applications for these operators are also discussed, as well as some of its future possibilities are envisaged.

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