Theory of the partially coherent temporal Talbot effect

The behaviour of the temporal Talbot effect under carrier partial coherence is analysed. This effect finds application as a passive method for multiplying the repetition rate of the intensity of pulse trains in first-order dispersive media. The study is based on the representation of the average intensity of partially coherent modulated light after first order dispersion as a coherence-dependent low pass filter acting on the intensity distribution obtained with a monochromatic carrier. The resulting coherence limitations are more restrictive in Talbot devices with high indices, due to the necessity of highly coherent carriers to produce a faithful reconstruction of trains by multiple pulse-to-pulse interference. Coherence limitations for architectures composed of externally modulated cw sources are analysed. Generalizations of the theory to several spectral lines, and its relation with the Collett-Wolf theorem are also reported.