In this work, we demonstrate that the spectral self-imaging phenomenon is not restricted to phase-only sampled and
linearly chirped fiber Bragg gratings(LCFBGs), rather they can be implemented in phase-only sampled fiber Bragg
gratings (FBGs) with an arbitrarily chirped grating period. We derive the general conditions at which spectral Talbot
phenomenon, namely, integer and fractional spectral self-imaging occurs. The multiplication of spectral channels,
respectively in the linear, square and cubic chirp coefficient conditions, and/or together, are implemented and observed
in phase-only sampled FBGs with both integer and fractional types using the transfer matrix method.
The spectral self-imaging phenomenon is observed in binary phase-only sampled fiber Bragg gratings (SFBGs) using
numerical simulations. Integer and fractional Talbot effects are obtained under conditions of Talbot effect. The
characteristics of the Talbot spectrum in terms of channel spacing and the group delay from the phase-only sampled
FBGs are discussed.
We present an analytical expression for sampled fiber Bragg gratings (SFBGs) with arbitrary chirps in sampling function
or grating period or combination of both. The relationship among the wavelength of each channel, the chirp coefficient
of the sampling and the grating period, and the total length of the grating is explicitly given. Specifically, the chirped
sampling function is first expanded into a new function using Fourier theory; the equivalent local Bragg period is then
obtained to derive the expression of the reflection peak wavelength. The overall wavelength position is obtained by
summation of both contributions from sampling chirp and the grating chirp. The calculated results based on the analytical
expression are examined with the conventional numerical results, which are found to be in excellent agreement.