All-Optical Discrete Fourier Transform Based on Multilevel Phase Modulation and a Dispersive Element

In this letter, we propose to realize the all-optical discrete Fourier transform (DFT) using a dispersive element, i.e., a piece of fiber, a fiber Bragg grating, or a tunable dispersion compensator. The theory of the proposed discrete transform is analogous to the self-image theory. By properly adjusting the phase of signals and the dispersion of the dispersive element, a highly precise DFT can be achieved.