Theoretical and experimental study of hybrid optical computing engine for arbitrary-order FRFT.

Fractional Fourier transform (FRFT) is the generalization of Fourier transform. It provides many significant advantages, such as fractional order as the new degree of freedom and high efficiency and great performance for non-stationary signal analysis/processing, that other operations including Fourier transform cannot. Here, we report a hybrid optical system for computation of arbitrary-order FRFT of temporal signals. In experiment, the fractional-domain information of input temporal signals could be directly acquired by detector. In addition, the optical computing results are in good agreement with numerical results. Then we apply the optical computing engine to demodulation of chirp spread spectrum signals. Using sub-Nyquist sampling, the proposed technology could greatly save the number of measurements in demodulation. The compression ratio could be as low as 0.4%, because of the high compression performance of chirp signals in FRFT domain. As a result, the proposed technology has unique advantages in analysis and information extraction for non-stationary signals, especially for chirp-like signals, and may become a powerful optical time-frequency analysis tool for temporal signals.