Figure 1. Passive waveform amplification concept.

Coherent addition of repetitive pulse waveforms is achieved by tailoring the temporal phase of the input waveform train and subsequent propagation through a dispersive medium such that the individual waveform intensity (energy) is amplified by an amount the repetition rate is reduced. A portion of the temporal Talbot carpet, top, provides the map of the temporal phase modulation and spectral phase-only filtering from dispersion required for passive amplification. In this representation, z_T is the Talbot distance at which an exact (integer) ‘self-image’ of a flat-phase incoming pulse train (signal at z=0), with original repetition period T′, is obtained by simple propagation through the dispersive medium. In the amplification example illustrated here, bottom, by applying the temporal phase variation corresponding to the multiplied Talbot self-image at distance 2z_T/3 on an input waveform train with repetition period T(=T′/3), subsequent propagation through z_T/3 of dispersive delay coherently shifts energy such that the output repetition rate is reduced by a factor of three and the waveform intensity is correspondingly enhanced by a factor of three.