Study on the Numerical Simulation of LPFG

The researches on the theory and numerical simulation of LPFG are important to the fabrication, spectrum characteristics and sensing characteristics. Based on the mode coupling theory of three-layer fiber model, the paper shows implicit characteristic equations of the core mode and cladding modes of LPFG using the boundary conditions at the interfaces. Avoiding the tedious derivation process of explicit characteristic expression, Maple software and the algorithm combined with fast research and successive approximation are adopted to solve implicit characteristic equations directly in the paper. Ten effective refractive indices with the accuracy of 11 digits after the decimal point, which is in accordance with the results of graphic method using explicit characteristic expression, are calculated within six minutes, which proves that the numerical simulation method has advantages of fast speed and high precision.