A numerical analysis on the refractive index modulation in first and second order of type I fiber Bragg gratings (FBGs) written by prism interferometer fringes is presented. The analysis of FBG written by biprism interferometers has been carried out to optimize the writing position and by Lloyd prism interferometer to optimize FBG length with respect to ultraviolet (UV) beam parameter. It is analytically shown that in the biprism fringe depth, the fiber positions of maximum reflectivity in first and second orders are different and both are less than the distance of maximum beam overlap. The refractive index modulation of FBGs written by Lloyd prism varies along the FBG length. The evolution and saturation of the FBGs written by biprism and Llyod prism are different due to difference in magnitude and/or profile of the UV fringes contrast in the FBG writing plane.
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