Corner States in 2D Square Lattice Second‐Order Photonic Topological Insulators Composed of L‐Shaped Sublattices

Abstract

Higher‐order photonic topological states have recently attracted great attention due to the realizability of photonic nanocavities with high robustness against structural disorder. Herein, it is revealed that square‐lattice photonic crystals with L‐shaped sublattices exhibit second‐order photonic topological phases. In the approximation considering only the nearest‐neighbor interactions, the photonic system with an expanded sublattice exhibits topologically nontrivial phase represented by the nonzero polarization, approaching P = ( 1 4 , 1 4 ) in the extreme case, whereas it is trivial for the cases of the shrunken one. Unlike the conventional square lattices with four dielectric rods, the proposed photonic systems have a single corner state for squared topological boundaries, while they exhibit three corner states when they have triangular boundaries. Although the weakly anisotropic systems with the expanded L‐shaped sublattices exhibit different corner states, they disappear for a substantial increase of anisotropy. The results obtained in this work enrich the diversity and understanding of higher‐order photonic topological systems and pave the way for wide applications of higher‐order topological phases in photonics, including coherent nanosources based on nanolasing and nonlinear frequency conversion.

Simultaneous Appearance of Different Topological Phases in a Single Photonic System: Coexisting Phases Characterized by Bulk Polarization and Valley‐Chern Number Enabling Dual‐Band Second‐Order Topological States

“…The nonzero Berry curvatures are not the necessarily required for topologically nontrivial phases, [ 36 ] and higher‐order topological phases [ 37,38 ] have recently been discovered in the systems even with vanishing Berry curvatures. In these new phases, the conventional bulk–boundary correspondence [ 39 ] is generalized such that n ‐order N‐ dimensional topological systems exhibit ( N –2), …, ( N – n ) dimensional edge states as well as ( N − 1) dimensional ones, [ 34,40,41 ] enabling the realization of 0D corner states with 2D photonic systems. Second‐order photonic topological phases in 2D photonic systems have been first predicted in the square lattice photonic crystals composed of four equal dielectric rods [ 34 ] and have been experimentally verified.…”

Multiple Second‐Order Topological Photonic Systems for Multichannel Beam Splitting and Wavelength Demultiplexing

“…The concepts of recently discovered higherorder topological phases [16,17] have shortly been transferred into photonics [18] and second-order photonic topological corner states have been observed in square lattice photonic crystals composed of four dielectric rods. [19] The extensive studies have shortly been followed for extending these fundamental concepts [20][21][22][23][24][25] and applying to various systems such as asymmetric, [26][27][28] nonlinear, [29,30] and non-Hermitian ones, [31][32][33] leading to novel photonic applications [34,35] such as topological beam splitting, [36][37][38] nonlinear frequency conversion, [39][40][41][42] topological lasing, [43,44] and topological slow light effect. [45] The previous studies of topological systems, however, have been focused mainly on single topological phases in single photonic systems.…”

Second‐Harmonic Generation Based on the Dual‐Band Second‐Order Topological Corner States

“…Unlike the conventional (first-order) topological phase whose N dimensional bulk has only (N À 1) dimensional edge states according to the bulk edge correspondence, [27] n-order topological systems exhibit (N À 2), …, (N À n) dimensional edge states as well as (N À 1) dimensional one. These new phases can be characterized by various topological invariants such as bulk polarization [28][29][30] and quadrupole moment. [31][32][33] The earlier described higher-order topological phases have already been experimentally verified.…”