We demonstrate that it is possible to perform a fractional Fourier transform of an incident pulse with a continuously variable degree of fractionality, using a dispersive and nonlinear Kerr medium. This medium acts as a linear waveguide for the optical pulse if its intensity is small and if the refractive index is nonlinearly time-dependently modified by a simultaneously launched bright soliton. For optical pulses the dispersive and nonlinear medium is perfectly equivalent to a graded-index refractive medium for optical beams.
© 1999 Optical Society of America
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(190.4360) Nonlinear optics : Nonlinear optics, devices
(230.7370) Optical devices : Waveguides
(320.5550) Ultrafast optics : Pulses
D. Dragoman, M. Dragoman, and K.-H. Brenner, "Variant fractional Fourier transformer for optical pulses," Opt. Lett. 24, 933-935 (1999)