The single-cavity bunch length monitor uses two eigenmodes in the resonant cavity to measure the bunch length in the order of picoseconds. The key is how to couple and extract two modes of different frequencies without interfering with each other. To solve this problem, based on the theory of low-pass and band-pass filters, a coaxial filter coupling structure and a diaphragm-loaded waveguide filter structure are proposed. The filters are modeled and simulated in CST Microwave Studio to obtain S parameters. In order to test the effect of the coupler, a bunch length monitor with the coupling structure is designed. According to the beam characteristics of the National Synchrotron Radiation Laboratory based on the tunable infrared laser energy chemistry research large-scale experimental device (FELiChEM), a beam simulation is performed on the designed monitor in CST. The simulation results show that the coupler can realize the coupling of specific modes and effectively reduce the interference of other modes. The resonant cavity monitor adopting the coaxial filter and the diaphragm-loaded waveguide filter can achieve high-precision measurement of the bunch length of the FELiChEM, and the measurement error is less than 2%.