Far-field Talbot waveforms generated by acousto-optic frequency shifting loops

We report on the description of the optical fields generated by acousto-optic Frequency-Shifting Loops (FSL) in the temporal Fraunhofer domain when the loop is operated in the vicinity of integer or fractional Talbot conditions. Using self-heterodyne detection, we experimentally demonstrate the equivalence of the Talbot phases generated at fractional conditions with the Gauss perfect phase sequences, and identify deviations from the standard frequency-to-time mapping description of the far field. In particular, we show the existence of ripples in the pulse intensity, of unavoidable pulse-to-pulse interference in the pulse train, of small oscillations, of the order of hundreds of MHz, in the expected linear pulse chirp, and the capture of the phase at the pulse's trailing edge by the adjacent pulse. Using asymptotic analysis, we construct a field model that accounts for these features, which are due to corrections to the frequency-to-time mapped field created by the sharp spectral edge of the FSL spectrum, in analogy to diffraction. Practical design consequences for signal generation and processing systems based on FSL are discussed.