一维三格点光格子中拓扑振荡及拓扑非对称边缘态

Topological Oscillations and Asymmetric Edge States in One-dimensional Trimer Lattices

为了全面认识奇数格点原胞中拓扑保护对于光束稳定传输的重要性,系统研究了一维三格点光格子模型中的光传输特性。利用能带理论和耦合模方程,对模型进行了模拟和仿真,发现两种在经典的两格点模型中不存在的具有拓扑保护的光传输行为,即具有拓扑保护的类拉比振荡光传输和具有拓扑保护的非对称传输,揭示了这两类光传输现象的物理机制,深入解析了光束振荡的本质,并验证了这两类光传输行为的鲁棒性,强调了光学系统在不同条件下的稳定性和可靠性。该研究可为利用奇数格点原胞中拓扑性质操纵光传输的潜在应用提供启示,并为新型拓扑光学器件的设计提供新的思路。

In the Su-Schrieffer-Heeger model,the topological properties and optical evolution dynamics of two-site lattice chains have been extensively studied,providing a theoretical basis for investigating the topological properties of even-length unit cell lattice chains.However,research on the topological properties of odd-site unit cell lattice systems with three or more energy bands is relatively limited.This is because symmetry breaking exists in three-site systems,making it challenging to directly apply theoretical methods developed for even-band systems.Therefore,this study aims to explore topologically protected optical transmission behaviors missing in the classical two-site model using a one-dimensional trimer lattice model,establishing a framework for topological photonics theory applicable to odd-band systems.This model will employ theoretical methods such as coupled mode equations and band theory for investigation.By integrating the one-dimensional trimer lattice model with a waveguide array using coupled mode theory,the model will simulate the evolution process of light beams in the waveguide array.This will involve substituting plane waves into coupled mode equations,adjusting coupling coefficients,and observing localized optical phenomena and intensity distribution during beam transmission.Eigenenergies and wave functions of the model will be computed using band theory,facilitating the generation of real-space band diagrams and probability distribution maps of wave functions.Through analysis of these data and images,a deeper understanding of the mechanisms behind topological oscillating light beams and asymmetric edge states observed in the one-dimensional trimer lattice model can be obtained.Furthermore,by computing topological invariants and statistically analyzing the distribution of edge states,phase diagrams of the system can be plotted,comprehensively displaying the distribution of topological edge states across the entire parameter range.Introducing defects midway through the long-distance evolution of light beams will be conducted to validate the robustness of topological edge states in the model.Based on a one-dimensional trimer lattice model,the evolution of light beams in the waveguide array and the intrinsic band structure are analyzed,thereby discovering topologically protected Rabi-like oscillatory light transmission and asymmetric edge states.The research simulates the evolution of light beams in the one-dimensional trimer lattice model under both spatial inversion symmetry and symmetry-breaking conditions.The results indicate that under symmetric distribution,Rabi-like oscillatory transmission occurs,with this topological oscillation state localized at the left and right edges of the waveguide array,exhibiting symmetric distribution and stable transmission under short-term evolution.However,upon introducing symmetry breaking,the system exhibits asymmetric topologically protected light transmission phenomena.Further analysis of the energy spectrum and eigenstate distributions reveals the physical mechanisms behind the generation of Rabi-like oscillation edge states and asymmetric edge states,showing a close correlation between the oscillation and the incident position and phase of the light beam.Phase diagrams plotted clarify the regions where topological edge states exist under different parameter conditions.By introducing defects,the robustness of topological localized oscillatory light beams against perturbations is verified,demonstrating the system's stable topological properties even under symmetry breaking.The conclusions drawn from the above analysis are as follows in the optical evolution of the one-dimensional trimer lattice model,Rabi-like oscillation phenomena,not previously observed in two-band systems,are present.By adjusting the incident position and phase of the light beam,the oscillation of light beam transmission can be controlled.This study also demonstrates that even under symmetry breaking,the trimer waveguide array retains stable topological properties,with asymmetric edge states robustly transmitting.This finding not only provides a theoretical reference for odd-site unit cell systems but also offers new insights into the design and optimization of optical devices,opening up possibilities for potential applications in optical transmission,information processing,and sensing.