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 Schrödinger 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.

中文翻译：

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光波导中的紧束缚模型：复杂光子网络仿真的设计原理和可转移性

在基于光的近轴衍射的各种物理模型的量子模拟背景下，集成光波导已被广泛探索，这些模型由等效的薛定谔方程描述。这些系统中的物理场可以使用紧束缚模型来表述，其中波导之间的耦合可以在很宽的范围内独立调整，为各种现象的模拟提供了一个极好的平台。在这项工作中，我们建立了一个紧束缚模型，其参数直接从两个耦合波导传输，这些波导受介电常数变化、位置距离和几何形状的控制。这种设计原理在实际实现中可以大大节省仿真和实验成本。与基于麦克斯韦方程的精确模拟结果相比，我们的数值结果表明，我们的紧束缚模型可以很好地描述一维或二维大晶格系统的物理特性，表现出两个耦合波导中参数的出色转移性。此外，还进一步讨论了一些应用：我们展示了如何实现拓扑 Su-Schrieffer-Heeger (SSH) 模型、扭结 SSH 模型，并研究它们相关的拓扑相和边缘模式。还讨论了一些基于我们的紧束缚模型的二维模型。最后，还简要讨论了更有趣的应用，例如非线性或无序引起的效应和规范电位的产生。我们的工作直观地为设计实验模型提供了有效的参考途径，并证明了使用紧束缚近似解决复杂模型的实用性。这项工作中展示的设计原理为基于更复杂模型的光波导的应用奠定了基础，并将在不久的将来通过实验轻松验证。