All-optical ultrafast fractional differentiator

Abstract

In this work we present a technique for the implementation of an ultrafast all-optical temporal differentiator. A photonic Mach-Zehnder interferometer can provide the required spectral response for fractional differentiation within certain fractional order extent. This device shows a good accuracy calculating the fractional time derivatives of the complex field of an arbitrary input optical waveform. Analytical expressions were found relating the photonic Mach-Zehnder parameters and the required spectral characteristics of the differentiator for integer and fractional operation. The introduced concept is supported by numerical simulations.