This paper introduces the working principle of the balanced heterodyne detection system, establishes the corresponding mathematical model, deduces the signal to noise ratio (SNR) formula of the balanced heterodyne detection. By comparing balance heterodyne detection with general coherent detection with MATlab numerical simulation, the superiority of balance heterodyne detection system is proved theoretically. Finally, the simulation models of ordinary heterodyne detection, balance detection and double balance detection system are built by OptiSystem. The simulation results are consistent with the conclusions derived from the mathematical analysis, which provides a new method for the research of weak laser detection technology.

Currently, coupled mode theory (CMT) is widely used for calculating the coupling coefficient of twin-core fibers (TCFs) that are used in a broad range of important applications. This approach is highly accurate for scenarios with weak coupling between the cores but shows significant errors in the strong coupling scenarios, necessitating the use of a more accurate method for coupling coefficient calculations. Therefore, in this work, we calculate the coupling coefficients of TCFs using the supermode theory with finite element method (FEM) that has higher accuracy than CMT, particularly for the strong coupling TCF. To investigate the origin of the differences between the results obtained by these two methods, the modal field distributions of the supermodes of TCF are simulated and analyzed in detail.