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.