Non-Hermitian skin effect (NHSE) has led to interesting physics and sophisticated applications beyond the conventional framework. However, NHSE studies have been limited to an individual dimension due to the difficulty of constructing nonreciprocal coupling in higher-dimensional systems. With the concept of synthetic dimension, we realize two-dimensional (2D) NHSE in a synthetic photonic lattice. The synthetic photonic lattice is composed of a spatial dimension and a synthetic frequency dimension, which is constructed by introducing gain and loss and dynamically modulating the complex refractive index in a one-dimensional ring-resonator array. In the synthetic 2D NHSE system, we can manipulate the spatial position and frequency mode of the light in real time, thus enabling programmable light propagation and frequency conversion. Specifically, the incident light can be localized in the spatial dimension and the frequency dimension simultaneously, leading to second-order corner modes in the synthetic 2D NHSE lattice. Besides, the 2D NHSE system exhibits an excellent robustness for the disorder and point defect in the lattice. This work generalizes the non-Hermitian skin effect in synthetic dimension to control the light in different dimensions, which shows great promise for potential applications in on-chip light manipulation, frequency synthesis, and information processing.

中文翻译：

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合成光子晶格中的二维非赫米特皮肤效应

非赫密特人的皮肤效应（NHSE）导致了超出常规框架的有趣的物理学和复杂的应用程序。但是，由于难以在高维系统中构建不可逆耦合，因此NHSE研究仅限于单个维。利用合成维数的概念，我们在合成光子晶格中实现了二维（2D）NHSE。合成光子晶格由空间维度和合成频率维度组成，其通过引入增益和损耗并动态调制一维环形谐振器阵列中的复折射率来构造。在合成2D NHSE系统中，我们可以实时控制光的空间位置和频率模式，从而实现可编程的光传播和频率转换。特别，入射光可以同时定位在空间维和频率维上，从而在合成2D NHSE晶格中产生二阶角模。此外，二维NHSE系统对晶格中的无序和点缺陷表现出出色的鲁棒性。这项工作在合成维度上推广了非赫密特集肤效应，以控制不同维度的光，这为片上光处理，频率合成和信息处理的潜在应用展示了广阔的前景。