Abstract
In this paper, we rigorously deduce the coupled-mode equations of a long-period fiber grating and fiber Bragg grating in their cascaded structure (CLBG), based on coupled-mode theory. Next, through the difference iterative method, the total transfer matrix of CLBG is obtained. Mistakes in previous literature involving coupled-mode equations and the transfer matrix of CLBG are corrected, including the neglect of coupling behaviors and the application of incorrect methods of solving coupled-mode equations. Then, both reflection and transmission spectrum characteristics are simulated numerically. The simulation results indicate that the position and intensity of the transmission and reflection peaks coincide with existing experimental results, and the transmission spectrum is highly consistent with the reflection spectrum. However, a large deviation exists in the previous literature: the transmittance exceeds one in the simulation results. Finally, the temperature and surrounding refractive index characteristics of the reflection spectrum are theoretically simulated, and further verified by experiments. The experimental results coincide well with our simulation results, indicating the correctness of our proposed method. The method provided in the paper could provide effective and reliable theoretical guidance for CLBG characteristic analysis, structure optimization, and sensing applications.
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