Comparing and analysis of calculation methods of long-period fiber gratings transmission spectra

Many methods are considered for calculating long-period fiber gratings (LPFGs) transmission spectra such as integral method, formula method and transfer matrix method. In this paper, these methods are analyzed based on the coupled-mode theory and their characteristics and the conditions of application are pointed out. Exact solution for multi-mode transmission spectrum can be obtained directly by integral method in a wide wavelength range, however, the computation process of this method is complicated. The formula method is convenient for calculating and expressing, but it can only solve single mode transmission spectrum directly in a narrow wavelength range. The transfer matrix method is suitable for calculating transmission spectra of non-uniform fiber gratings, it has higher calculation accuracy and faster speed. Through the analysis and comparing with the three methods, we will provide a best method with high precision and simple calculation for long-period fiber gratings transmission spectra in theory, which is important for the research and application of LPFGs.