Characterization of single-mode fiber with fiber Bragg gratings for the design of long-period gratings

We propose a simple method to determine the dispersion characteristics of the core mode and the cladding modes of a single-mode fiber for the design of long-period gratings (LPGs). The method is based on measuring the effective indexes of the core mode and the cladding modes from the transmission spectra of a number of slightly tilted fiber Bragg gratings (FBGs) that are composed of properly separated Bragg wavelengths. By using four FBGs written in a photosensitive fiber, we obtained 19 phase-matching curves for the design of LPGs over the (S + C + L)-band, which correspond, respectively, to the couplings between the core mode and the first 19 symmetric cladding modes of the fiber. The accuracy of the phase-matching curves is verified with a number of LPGs fabricated in the same fiber using various grating pitches.