Fractional Fourier transform based on a temporal gradient-index lens

Abstract

In this paper, an approach to realize all optical fractional Fourier transform through a high-nonlinear fiber and an optical pump is discussed. Based on a gradient index (GRIN) time lens which is realized through cross-phase modulation by a temporal quadratic pump pulse, it is possible to achieve all optical fractional Fourier transform. The order of the fractional Fourier transform varies along the fiber propagation distance. In a fixed fiber, it can be adjusted by simply changing the peak power of the pump pulse.