Second-order topological photonic crystals support localized corner modes that deviate from the conventional bulk-edge correspondence. However, the frequency shift of corner modes spanning the photonic band gap has not been experimentally reported. Here, we observe the gapless corner modes of photonic crystal slabs within a parameter space by considering translation as an additional synthetic dimension. These corner modes, protected by topological pumping in synthetic translation dimensions, are found to exist independently of the specific corner configuration. The gapless corner modes are experimentally imaged via the near-field scanning measurement and validated numerically by full-wave simulations. We propose a topological rainbow with gradient translation, demonstrating the ability to extract and separate specific frequency components of light into different spatial locations. Our work contributes to the advancement of topological photonics and provides valuable insights into the exploration of gapless corner modes in synthetic dimensions.

中文翻译：

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合成平移维度中光子晶体板无间隙角模式的观察

二阶拓扑光子晶体支持偏离传统体边缘对应的局部角模式。然而，跨越光子带隙的角模的频移尚未有实验报道。在这里，我们通过将平移视为附加的合成维度来观察参数空间内光子晶体板的无间隙角模式。这些角模式受到合成平移维度中的拓扑泵浦的保护，被发现独立于特定的角配置而存在。通过近场扫描测量对无间隙角模式进行实验成像，并通过全波模拟进行数值验证。我们提出了一种具有梯度平移的拓扑彩虹，展示了提取光的特定频率分量并将其分离到不同空间位置的能力。我们的工作有助于拓扑光子学的进步，并为探索合成维度中的无间隙角模式提供了宝贵的见解。