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The combination of higher-order topological insulators and valley photonic crystals has recently aroused extensive attentions due to the great potential in flexible and efficient optical field manipulations. Here, we computationally propose a photonic device for the 1550 nm communication band, in which the topologically protected electromagnetic modes with high quality can be selectively triggered and modulated on demand. Through introducing two valley photonic crystal units without any structural alteration, we successfully achieve multi-dimensional coupled topological states thanks to the diverse electromagnetic characteristics of two valley edge states. According to the simulations, the constructed topological photonic devices can realize Fano lines on the spectrum and show high-quality localized modes by tuning the coupling strength between the zero-dimensional valley corner states and the one-dimensional valley edge states. Furthermore, we extend the valley-locked properties of edge states to higher-order valley topological insulators, where the selected corner states can be directionally excited by chiral source. More interestingly, we find that the modulation of multi-dimensional coupled photonic topological states with pseudospin dependence become more efficient compared with those uncoupled modes. This work presents a valuable approach for multi-dimensional optical field manipulation, which may support potential applications in on-chip integrated nanophotonic devices. [ABSTRACT FROM AUTHOR]

In the quest to connect bulk topological quantum numbers to measurable parameters in real materials, current established approaches often necessitate specific conditions, limiting their applicability. Here we propose and demonstrate an approach to link the non-trivial hierarchical bulk topology to the multidimensional partition of local density of states (LDOS), denoted as the bulk-LDOS correspondence. In finite-size topologically nontrivial photonic crystals, we observe the LDOS partitioned into three distinct regions: a two-dimensional interior bulk area, a one-dimensional edge region, and zero-dimensional corner sites. Contrarily, topologically trivial cases exhibit uniform LDOS distribution across the entire two-dimensional bulk area. Our findings provide a general framework for distinguishing topological insulators and uncovering novel aspects of topological directional band-gap materials, even in the absence of in-gap states. Current approaches to distinguish topological phases from topologically-trivial phases have limited general applicability. Here, in a photonic-crystal context, the authors demonstrate that in trivial structures the bulk local density of states (LDOS) extends all the way to the edges and corners, while in topological structures the bulk LDOS actually avoids the edges and corners. [ABSTRACT FROM AUTHOR]

Higher-order topological insulators have drawn great research attention in nanophotonics due to their ability to both support robust edge states and lower dimensional corner states. In this work, we present a theoretical proposal for achieving topologically switchable and valley-selective corner states based on two-dimensional C3-symmetric photonic crystals (PCs), with breaking of inversion symmetry. Through the concatenation of two valley PCs with contrasting topological indices, we demonstrate the emergence of two types of valley-locked chiral topological edge states resulting from the valley–valley interaction. More importantly, we find that the system exhibits two distinct types of corner states, characterized by strong robustness and high localization, when the PCs are spliced at a 60° angle. However, the corner states are absent when the splicing angle is set as 120°. According to the theoretical analysis, the selective activation of topological valley corner states is related to the sign flip of valley Chern number at the corner. Based on this feature, we further propose a topological photonic switching device, in which the corner can be lighted up or off selectively. By combining the benefits of higher-order topology and valley degree of freedom, our work provides an efficient and flexible method for light manipulation. [ABSTRACT FROM AUTHOR]

Higher‐order topological (HOT) insulators have been extensively studied for their unique multidimensional boundary states such as hinge states and corner states. However, most of the recent studies are limited to static excitation of topological boundary states, restricting the development of their practical devices that possess the capability of diverse and programmable dynamic control of states. Here, a facile approach to achieve flexible control of light‐steering based on the symmetrized wave profiles of topological corner states is introduced. Specifically, multiple coherent sources are imported at symmetrical positions in higher‐order topological photonic crystals. By engineering phase differences among the sources, a controllable spatial‐resolved excitation of topological corner states is realized and a coding technique via controllable excitation of topological corner states is raised conceptually. Furthermore, an effective way to achieve direction‐selective excitation of topological edge states without the requirement of circularly polarized sources is proposed. The result provides a reliable active technique to modulate HOT boundary states while keeping the photonic structure invariable, which might be a practical alternative to manipulate light flexibly in integrated topological photonic devices with fixed configuration. [ABSTRACT FROM AUTHOR]