Agile photonic fractional Fourier transformation of optical and RF signals

Abstract

The last 20 years have seen the spectacular emergence of optically assisted solutions for the analog generation and processing of radio-frequency (RF) signals [J. Lightwave Technol.27, 314 (2009)JLTEDG0733-872410.1109/JLT.2008.2009551]. Among these, real-time Fourier transformation (FT) is of particular importance for signal processing and filtering, but is of limited use for analyzing signals with time-dependent spectrum, especially chirped RF waveforms. On the contrary, fractional Fourier transformation (FrFT), which decomposes a waveform onto a continuous basis of linearly chirped functions, provides a generalization of FT and constitutes a valuable tool for analyzing signals with time-dependent spectrum [Signal Process.91, 1351 (2011)10.1016/j.sigpro.2010.10.008]. Here we prove a new and simple concept, enabling agile computation of the FrFT of both optical and RF signals in real time, with minimum latency time and a frequency resolution in the tens of kHz range. We demonstrate two practical applications of the technique: the absolute measurement of RF/optical chirp rates and the detection of weak chirped RF signals buried under noise. The introduced concept should be of practical interest for RF signal filtering and radar signal processing.