This paper deals with a group velocity dispersion issue and a peak reflectivity issue in a non-uniform fiber Bragg gratings (FBG) due to an arbitrary refractive index profile along the length of grating. The paper shows that by using more complicated refractive index profile one can significantly reduce the group velocity dispersion and side lobes intensity and that in main lobe the bandwidth of reflectivity would also increase substantially due to a complicated refractive index profile. To the authors' knowledge, there has not been any work reported in this direction. Generally, coupled mode theory is used to analyze the uniform fiber Bragg grating (UFBG). The analysis results in two coupled first order ordinary differential equations with constant coefficients for which closed form solutions can be found for appropriate boundary conditions. Most fiber gratings designed for practical applications, however, are non uniform. The main reason for using non uniform grating is that it reduces the side lobes in the reflectivity spectrum. Due to the complexity of analysis, no particular method for an analysis of the non-uniform fiber Bragg grating would be found. The two standard approaches for calculating the reflection and transmission spectra of a non uniform FBG are direct numerical integration of coupled mode equations and piecewise uniform approximation approach. The former is more accurate but computationally intensive. In this paper, piecewise uniform approximation approach is used to study a dispersion characteristic due to an arbitrary refractive index profile. The usefulness in FBG based sensors has been demonstrated.
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