All-optical differentiator in frequency domain

Signal processing is a focused topic with communication technologies developing rapidly nowadays. However, optical signal processing methods are not so mature compared to the digital signal processors. Here, we propose an all-optical differentiator in frequency domain designed with fundamental optical elements, which is able to give the first order differentiation of the input signal. A fully theoretical description of the differentiator and its transfer function are demonstrated and discussed. According to experiments, the differentiator is proved reliable and the results match well with simulations. Moreover, an application of the frequency domain differentiator for measuring small time delay changes is also demonstrated and discussed. We believe that this work can give different perspectives of optical signal processing in frequency domain.