We study the properties of nonlinear Bloch waves in a diamond chain waveguide lattice in the presence of a synthetic magnetic flux. In the linear limit, the lattice exhibits a completely flat (wavevector k-independent) band structure, resulting in perfect wave localization, known as Aharonov–Bohm caging. We find that in the presence of nonlinearity, the Bloch waves become sensitive to k, exhibiting bifurcations and instabilities. Performing numerical beam propagation simulations using the tight-binding model, we show how the instabilities can result in either the spontaneous or controlled formation of localized modes, which are immobile and remain pinned in place due to the synthetic magnetic flux.

中文翻译：

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光子Aharonov–Bohm笼中的非线性Bloch波动力学

我们研究了在存在合成磁通量的情况下钻石链波导晶格中非线性Bloch波的特性。在线性极限中，晶格展现出完全平坦的（与波矢k无关）的能带结构，从而实现了完美的波定位，称为Aharonov-Bohm笼式。我们发现，在存在非线性的情况下，Bloch波对k敏感，表现出分叉和不稳定性。使用紧束缚模型执行数字束传播模拟，我们展示了不稳定性如何导致自发或受控形成的局部模态，该模态由于合成磁通而无法移动并保持固定在适当的位置。