Mode Field And The Coupling Of The Long Period Fiber Grating

In this paper ,based on the analysis of the current situation of development on long-period fiber grating and theory of mode of weakly guiding fiber, we focus on the problem of coupling from guided core mode to radiation mode about a long-period fiber grating written by CO2 laser when its ambient refractive index is equal or higher than the cladding refractive index. Firstly, we use the method of scalar quantity to deduce the eigenvalue equation of weakly guiding fiber and dichotomy to compute the effective index of guided core mode, then get the core mode equation. Secondly, we employ a three-layer model to present the deduction and analysis of cladding mode . Thirdly, we deduce the radiation mode and the normalization of this mode in detail . Moreover , we study the difference of coupling equations between long-period fiber gratings and fiber Bragg gratings. Subsequently, we simplify and modify the coupling equations ,and make them suitable for long-period fiber gratings written by CO2 laser.