Ultrafast all-optical first- and higher-order differentiators based on interferometers

We demonstrate that a conventional two-arm interferometer can implement first-order temporal differentiation of ultrafast arbitrary optical waveforms. Straightforward extension of this technique to $n\text{th}$-order optical differentiation is also suggested. This approach is experimentally demonstrated by an efficient and accurate first- and second-order temporal differentiation of (sub-)picosecond Gaussian optical pulses.