Optical Darboux Transformer

Abstract: The Optical Darboux Transformer is introduced as a photonic device which performs the Darboux transformation directly in the optical domain. This enables two major advances for signal processing based on the nonlinear Fourier transform: (i) the multiplexing of different solitonic waveforms corresponding to arbitrary number of discrete eigenvalues of the Zakharov-Shabat system in the optical domain, and (ii) the selective filtering of an arbitrary number of individual solitons too. The Optical Darboux Transformer can be built using existing commercially available photonic technology components and constitutes a universal tool for signal processing, optical communications, optical rogue waves generation, and waveform shaping and control in the nonlinear Fourier domain.