We present a detailed study of spectral self-imaging phenomena, namely, integer and fractional Talbot effects, observed in the reflection response of chirped sampled fiber Bragg gratings (C-SFBGs). The basic condition for observing spectral self-imaging effects is first derived heuristically, and an intuitive interpretation of the problem based on the notion of multislit interference is also provided. We then present a rigorous analysis of the spectral self-imaging problem in C-SFBGs, including the formal derivation of the conditions for observing the different spectral Talbot effects. This analysis reveals the existence of new effects, in particular, inverse integer and fractional self-images, which are described here for the first time, to our knowledge. Moreover, we also show that the grating physical parameters need to satisfy additional conditions in order for one to be able to observe spectral self-imaging phenomena in C-SFBGs. We also evaluate the impact of deviations from these ideal conditions on the reflection spectrum of a real device. We confirm our theoretical predictions by using numerical simulations, and we report the first experimental observation of fractional spectral Talbot effects in C-SFBGs. Besides their intrinsic physical interest, the results presented constitute the basis for exploiting the spectral self-imaging effect for practical applications, e.g., to optimize the design of SFBGs for applications requiring periodic comb filters with low in-band dispersion.
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