Dependence of fringe spacing on the grating separation in a long-period fiber grating pair

The spectral spacing of the interference fringes formed by a pair of long-period fiber gratings was investigated. The variation of the fringe spacing was measured while the separation between the gratings was changed from 22 to 500 mm. When the grating separation was much longer than the length of the individual grating, the inverse of the fringe spacing became linearly proportional to the grating separation and to the differential effective group index of the fiber. In the third stop band of the grating pair, made along a dispersion-shifted fiber centered at 1.55 microm, the differential effective group index was calculated to be approximately 6.4 x 10(-3), which is approximately twice the differential effective index of the fiber. The discrepancy between the two indices was observed to decrease with the band order, a phenomenon that is explained by the first-order dispersion of the fiber. The measured interference fringes were not regularly spaced in the frequency domain, but regular spacing is required in wavelength-division multiplexing communication systems. Analysis of the second-order dispersion of the fiber and the grating-induced nonlinear phase shift within grating regions as the factors that induce chirping on the fringe spacing is presented.