光子Lieb-kagome晶格中的倾斜Dirac锥和非对称锥形衍射
Tilted Dirac cones and asymmetric conical diffraction in photonic Lieb-kagome lattices
摘要：
Lieb晶格和kagome晶格，这两个都是众所周知的狄拉克锥和平带，可以连续转换成彼此的剪切变换。在这个转变过程中，平带被破坏，但狄拉克锥保持不变，并变得倾斜，在不同的参数下出现I、II和III型。在这项工作中，我们首先使用紧束缚模型研究这些倾斜的狄拉克锥，揭示它们如何被设计成不同的类型。然后，我们证明锥形衍射的光子晶格实现的Lieb-kagome晶格使用分步光束传播模拟，获得的狄拉克锥在不同方向倾斜的存在的证据。最后，我们进行了实验与光子晶格激光写在熔融石英（SiO $_2$），以验证模拟的结果。这些研究推进了对Lieb-kagome晶格和倾斜狄拉克锥的理解，并为进一步研究这个有趣的可调晶格系统提供了基础。
英文摘要：
The Lieb lattice and the kagome lattice, which are both well known for their Dirac cones and flat bands, can be continuously converted into each other by a shearing transformation. During this transformation, the flat band is destroyed, but the Dirac cones remain and become tilted, with types I, II, and III occurring for different parameters. In this work, we first study these tilted Dirac cones using a tight-binding model, revealing how they can be engineered into the different types. We then demonstrate conical diffraction in a photonic lattice realization of the Lieb-kagome lattice using split-step beam propagation simulations, obtaining evidence of the presence of Dirac cones tilted in different directions. Finally, we performed experiments with photonic lattices laser-written in fused silica (SiO$_2$) to validate the results of the simulations. These studies advance the understanding of the Lieb-kagome lattice and tilted Dirac cones in general and provide a basis for further research into this interesting tunable lattice system.
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