Analysis of reflection-peak wavelengths of sampled fiber Bragg gratings with large chirp

The reflection-peak wavelengths (RPWs) in the spectra of sampled fiber Bragg gratings with large chirp (SFBGs-LC) are theoretically investigated. Such RPWs are divided into two parts, the RPWs of equivalent uniform SFBGs (U-SFBGs) and the wavelength shift caused by the large chirp in the grating period (CGP). We propose a quasi-equivalent transform to deal with the CGP. That is, the CGP is transferred into quasi-equivalent phase shifts to directly derive the Fourier transform of the refractive index modulation. Then, in the case of both the direct and the inverse Talbot effect, the wavelength shift is obtained from the Fourier transform. Finally, the RPWs of SFBGs-LC can be achieved by combining the wavelength shift and the RPWs of equivalent U-SFBGs. Several simulations are shown to numerically confirm these predicted RPWs of SFBGs-LC.