Spectral interpretation of Talbot self-healing effect and application to optical arbitrary waveform generation

The Talbot effect has the intrinsic capability of mitigating the effects of grating imperfections. Here we investigate, in the frequency domain, the influence of an imperfect grating on the Talbot images. In particular, we show that for specific propagation distances, the spectra of the individual Talbot images are directly related to the envelope of the grating transmission function, mapped in the spectral domain. This novel space-to-frequency mapping property enables us to describe the capability of image restoration (or self-healing) of the Talbot effect, in terms of spectral filtering. The transposition of this effect from the spatial to the temporal domain offers promising possibilities for the spectral shaping of optical waveforms.