Inspired by the concept of topological insulators from condensed matter physics, the field of photonic crystal research has advanced rapidly in recent years, particularly in the exploration of topologically nontrivial states. Topological characteristics, as global features, are inherently insensitive to local perturbations, which endows topologically protected edge states with remarkable robustness. This robustness implies that light fields or electrons within such states are not susceptible to defects and impurities introduced by manufacturing errors and are resistant to decay due to backscattering during transmission. As a result, photonic crystals exhibit numerous exceptional properties and hold great promise for a wide range of applications, including optical waveguides, optical beam splitters, optical isolators, and resonant cavities. Notably, research into topological lasers based on photonic crystals has attracted considerable attention.This paper first investigates the parameter combinations necessary to achieve topologically nontrivial states in an infinitely large Su-Schrieffer-Heeger model using tight-binding and transfer matrix methods. The study identifies that the coupling strengths between different lattice sites, the gain and loss, and the presence of an imaginary gauge field are key factors contributing to the system's topologically nontrivial characteristics. After determining the parameters capable of inducing topologically nontrivial states, stable edge states and topological supermode protected by topology are observed in a finite-sized microring resonator array. By solving the rate equations for a semiconductor laser with multiple coupled cavities, the study examines the laser output characteristics under topological supermode conditions. It is found that, within a reasonable range of parameters, lasers composed of coupled-resonator optical waveguide arrays can operate under topological supermode, successfully demonstrating stable laser output characterized by supermode.In theoretical research, the tight-binding method is commonly employed to investigate the energy bands of photonic crystals and calculate their topological invariants in order to reveal the topological properties of these materials. However, the photonic crystals that constitute topological lasers are generally finite-sized systems, and the variations in coupling between laser light fields are significant, which limits the applicability of the tight-binding method. It has been shown that the transfer matrix method offers distinct advantages over the traditional tight-binding method when addressing such challenges. This paper utilizes both the tight-binding and transfer matrix methods based on coupled-resonator optical waveguides to examine the band structure and topological characteristics of both infinitely large and finite-sized Su-Schrieffer-Heeger models. The results indicate that in an infinitely large SSH model, topologically nontrivial states can be effectively realized by adjusting the coupling strengths between lattice sites and introducing an imaginary gauge field, while topological changes solely caused by gain and loss are distinctly observed only in a four-site Su-Schrieffer-Heeger model.In the finite-length Su-Schrieffer-Heeger model composed of coupled-resonator optical waveguides, a system containing 33 microrings was constructed, and the transfer matrix method was employed to verify the conditions for the existence and stability of edge states in finite-length coupled-resonator optical waveguides arrays under various parameter combinations. The study found that when specific conditions are met, the imaginary gauge field gives rise to a new zero-energy mode, referred to as the topological supermode, which is globally distributed throughout the system. Although this supermode does not manifest as localized at the edges, it remains topologically protected and exhibits unique stability as a laser output mode.Finally, the laser output behavior under topological supermode conditions was simulated using laser rate equations. These equations describe the variations in light field intensity and carrier density in microrings over time. A set of reasonable parameters was selected for the study, and dimensionless processing was conducted to facilitate the simulation calculations. The simulation results demonstrate that when the imaginary gauge field satisfies specific conditions,lasers in coupled-resonator optical waveguide arrays can operate under topological supermode. Specifically, the laser output intensity stabilizes rapidly at a fixed value after initial relaxation oscillations, forming globally stable laser output throughout the system. Topological supermode not only exhibit stability within individual microrings but also maintain a consistent light field distribution across the entire array. This global stability is crucial for the continuity and consistency of laser output.To further verify the advantages of topological supermode, the study compared laser output under non-topological supermode conditions. The results indicate that when the conditions for topological supermode are not met, the laser output intensity of individual microrings exhibits oscillatory characteristics, however, the intensity fluctuations are significant and challenging to stabilize. This suggests that laser output under non-topological supermode conditions lacks consistency and stability, demonstrating the superiority of topological supermode in stabilizing laser output. Additionally, the study analyzed the trend of instantaneous amplitude changes in laser output, finding that lasers require a longer time to accumulate energy to achieve the first output during the initial stage. Once stable operation is attained, lasers can continuously output stable laser pulses at shorter intervals. Overall, the introduction of topological supermode significantly enhances the operational stability and output consistency of lasers, providing new insights and methods for the research and application of topological lasers. Moreover, we explored the transition of laser output from a globally distributed topological supermode to a localized topological edge state by adjusting the coupling strength and pump current, offering a novel strategy for controlling the output mode of lasers. The performance of topological supermode lasers and topological edge lasers was compared in terms of threshold and linewidth, laying the foundation for future experimental research.