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Analog photonic fractional Fourier transformation

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Fractional Fourier transformation (FrFT) can be seen as the generalization of the Fourier transform (FT) along any direction intermediate between the direct and the Fourier-dual domain. We have demonstrated a photonic platform, enabling the analog generation of the FrFT of optical and microwave signals with full reconfigurability.

To process a microwave signal (frequency in the MHz to 100 GHz range), a widespread technique is digital processing, that combines signal acquisition (sampling, quantizing, coding), processing, and digital-to-analog conversion (ADC). However this approach is limited in practice by the speed of analog-to-digital and digital-to-analog converters. Therefore analog signal processing is an alternative solution for the processing of broadband microwave signals (> 10 GHz). For this aim, photonic-based solutions are especially interesting, due to the intrinsic huge bandwidth of optical systems.
We have demonstrated a platform based on a photonic frequency-shifting loop, that enables to generate in real-time, the fractional Fourier transform of arbitrary optical and microwave input signals. The frequency shifting loop realizes the coherent addition of replicas of the input signal, shifted along both the temporal and the frequency domain. The resulting signal (at the output of the loop) maps repeatedly in time, the FrFT of the input signal. The order of the FrFT is set by the relation between the time and the frequency shift : it is readily reconfigurable by changing the parameters of the loop. We have reported two practical applications of the system : the measurement of the chirp rate of an input waveform with linear frequency modulation, and the extraction of a linearly chirped signal buried in the noise. The results have been published in Optica.

These results have been published in Optica : .