In a previous work, the transmission spectrum of long-period fiber gratings (LPFGs) was simulated and analyzed based on traditional coupled mode theory. However, for a strongly modulated few-mode LPFG, traditional coupled mode theory cannot be used to accurately analyze the coupling process between the core guide modes in the strong modulation region. This is because of its strong angular refractive index modulation and the obvious correction of the mode field distribution. In addition, the problem of change in the angular refractive index in the fiber core was not considered in the previous strongly modulated model, which is inconsistent with the change in actual gratings. This can easily result in the simulation spectrum not matching the actual spectrum. Therefore, based on local coupled mode theory, this study analyzed the coupling process between the fiber core fundamental mode and the high-order angular mode in an LPFG grating. This study also established a model for a strongly modulated few-mode LPFG, introduced asymmetric and angular modulation parameters into the model, realized a transmission spectrum simulation of the grating, and matched the existing experimental results. A method was thus realized for analyzing the coupling process between the guide modes of the fiber core in a strongly modulated few-mode LPFG, which provides a reference for preparing gratings with different experimental requirements.

Based on local coupling mode theory, a model of a strongly modulated LPFG written by a CO₂ laser was constructed to analyze the coupling process between the core guided modes in the modulated region of a few-mode grating. With asymmetric and angular refractive index modulations introduced into the model, the strong angular refractive index variation in grating modulation was characterized, and a more accurate mode coupling coefficient and propagation constant were derived. These were substituted into the coupling equation between the fundamental and third-order azimuthal modes to solve, and a simulation of the grating transmission spectrum was realized. The simulation and experimental results were then matched. In addition, based on changes to the grating model parameters (grating period, the number of periods, and modulation depth), the change in the corresponding transmission spectrum was studied, thereby providing a reference for designing and fabricating higher-order-mode strongly modulated LPFGs.

We first established a model for a strongly modulated few-mode LPFG by adding asymmetric and angular refractive index modulations. Figure 4 shows a comparison of the unmodulated and modulated mode fields, which reflects the necessity of angular modulation and enhancement of coupling between modes. Figure 5 shows a comparison between the simulation and experimental data. The simulation parameters of the grating were consistent with the experimental parameters. It can be seen that the shape, depth, and resonant wavelength of the experimental resonant peak are basically consistent with those of the simulation. Based on changes to the parameters of the established model (grating period, the number of periods, and modulation depth), the change rule of the grating transmission spectrum characteristics was analyzed, as shown in Figs. 6, 8, and 9. Thus, the simulation model can be applied to different optical fibers to guide the design and preparation of gratings with different requirements.

In this study, a simulation model of an LPFG is established, with emphasis given to analysis of the LPFG. Based on local coupled mode theory, the refractive index and coupling coefficient changes in the modulation region of the grating are calculated, and asymmetric and angular refractive index modulations are introduced. The spectral characteristics of a strongly modulated few-mode LPFG are obtained by numerically solving the local coupled-mode equations. The spectra of strongly modulated LPFG fabricated by using CO₂ laser in the experiment and the simulation results are in agreement. These results and the effects of grating period, the number of periods, and modulation depth on the transmission spectrum of the grating were analyzed. This simulation method is more suitable for analyzing LPFGs prepared by high-power local laser (such as CO₂ laser) irradiation methods and more accurately characterizes the coupling process between the fundamental and high-order angular modes in the fiber core area of a few-mode grating. This method has a reference value for realizing higher-order angular mode conversion and preparing LPFGs with different requirements. Compared with other methods, this method can more accurately analyze a series of LPFGs based on local high-intensity laser irradiation and heat treatment.