Tight-binding model in optical waveguides: Design principle and transferability for simulation of complex photonics networks

Integrated optical waveguides have been widely explored in the context of quantum simulation for various physical models based on paraxial diffraction of light, which are described by an equivalent Schr\"odinger equation. The physics in these systems can be formulated using the tight-binding models, in which the coupling between the waveguides can be tuned independently in a wide range, providing an excellent platform for simulation of various phenomena. In this work, we build a tight-binding model with parameters transported directly from two coupled waveguides, which are controlled by dielectric constant change, site distance, and geometries. This design principle can greatly save the simulation and experimental cost in real implementation. As compared with results from the exact simulation based on Maxwell equations, our numerical results demonstrate that the physics of the one- or two-dimensional large lattice systems could be well described by our tight-binding model, exhibiting the excellent transferability of the parameters in two coupled waveguides. In addition, some applications are further discussed: we show how to realize the topological Su-Schrieffer-Heeger (SSH) model, kinked SSH model, and study their associated topological phases and edge modes. Some two-dimensional models based on our tight-binding models are also discussed. Lastly, more intriguing applications, such as nonlinearity or disorder-induced effect and generation of the gauge potential are also briefly discussed. Our work intuitively provides an effective reference route for designing models for experiments and demonstrates the practicality of using the tight-binding approximation to solve complicated models. The design principle demonstrated in this work paves the foundation for the application of optical waveguides based on more complicated models, and will be readily verified experimentally in the near future.